LMFDB - Embedded newform 42.8.e.a.25.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [42,8,Mod(25,42)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(42, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

N = Newforms(chi, 8, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("42.25");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 42 = 2 \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	42.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$13.1201710703$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			25.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	42.25
Dual form			42.8.e.a.37.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.00000 + 6.92820i) q^{2} +(-13.5000 + 23.3827i) q^{3} +(-32.0000 + 55.4256i) q^{4} +(-82.5000 - 142.894i) q^{5} -216.000 q^{6} +(-171.500 - 891.140i) q^{7} -512.000 q^{8} +(-364.500 - 631.333i) q^{9} +O(q^{10})$	\(q+(4.00000 + 6.92820i) q^{2} +(-13.5000 + 23.3827i) q^{3} +(-32.0000 + 55.4256i) q^{4} +(-82.5000 - 142.894i) q^{5} -216.000 q^{6} +(-171.500 - 891.140i) q^{7} -512.000 q^{8} +(-364.500 - 631.333i) q^{9} +(660.000 - 1143.15i) q^{10} +(1027.50 - 1779.68i) q^{11} +(-864.000 - 1496.49i) q^{12} +2720.00 q^{13} +(5488.00 - 4752.75i) q^{14} +4455.00 q^{15} +(-2048.00 - 3547.24i) q^{16} +(7854.00 - 13603.5i) q^{17} +(2916.00 - 5050.66i) q^{18} +(-3376.00 - 5847.40i) q^{19} +10560.0 q^{20} +(23152.5 + 8020.26i) q^{21} +16440.0 q^{22} +(-15414.0 - 26697.8i) q^{23} +(6912.00 - 11971.9i) q^{24} +(25450.0 - 44080.7i) q^{25} +(10880.0 + 18844.7i) q^{26} +19683.0 q^{27} +(54880.0 + 19011.0i) q^{28} -118305. q^{29} +(17820.0 + 30865.1i) q^{30} +(73758.5 - 127753. i) q^{31} +(16384.0 - 28377.9i) q^{32} +(27742.5 + 48051.4i) q^{33} +125664. q^{34} +(-113190. + 98025.4i) q^{35} +46656.0 q^{36} +(-155866. - 269968. i) q^{37} +(27008.0 - 46779.2i) q^{38} +(-36720.0 + 63600.9i) q^{39} +(42240.0 + 73161.8i) q^{40} -491400. q^{41} +(37044.0 + 192486. i) q^{42} -577174. q^{43} +(65760.0 + 113900. i) q^{44} +(-60142.5 + 104170. i) q^{45} +(123312. - 213583. i) q^{46} +(427431. + 740332. i) q^{47} +110592. q^{48} +(-764718. + 305661. i) q^{49} +407200. q^{50} +(212058. + 367295. i) q^{51} +(-87040.0 + 150758. i) q^{52} +(-583442. + 1.01055e6i) q^{53} +(78732.0 + 136368. i) q^{54} -339075. q^{55} +(87808.0 + 456264. i) q^{56} +182304. q^{57} +(-473220. - 819641. i) q^{58} +(83539.5 - 144695. i) q^{59} +(-142560. + 246921. i) q^{60} +(-513637. - 889645. i) q^{61} +1.18014e6 q^{62} +(-500094. + 433094. i) q^{63} +262144. q^{64} +(-224400. - 388672. i) q^{65} +(-221940. + 384411. i) q^{66} +(1.63406e6 - 2.83027e6i) q^{67} +(502656. + 870626. i) q^{68} +832356. q^{69} +(-1.13190e6 - 392102. i) q^{70} +3.04684e6 q^{71} +(186624. + 323242. i) q^{72} +(1.60456e6 - 2.77917e6i) q^{73} +(1.24693e6 - 2.15974e6i) q^{74} +(687150. + 1.19018e6i) q^{75} +432128. q^{76} +(-1.76216e6 - 610431. i) q^{77} -587520. q^{78} +(-3.56399e6 - 6.17302e6i) q^{79} +(-337920. + 585295. i) q^{80} +(-265720. + 460241. i) q^{81} +(-1.96560e6 - 3.40452e6i) q^{82} +4.36591e6 q^{83} +(-1.18541e6 + 1.02659e6i) q^{84} -2.59182e6 q^{85} +(-2.30870e6 - 3.99878e6i) q^{86} +(1.59712e6 - 2.76629e6i) q^{87} +(-526080. + 911197. i) q^{88} +(5.99811e6 + 1.03890e7i) q^{89} -962280. q^{90} +(-466480. - 2.42390e6i) q^{91} +1.97299e6 q^{92} +(1.99148e6 + 3.44934e6i) q^{93} +(-3.41945e6 + 5.92266e6i) q^{94} +(-557040. + 964822. i) q^{95} +(442368. + 766204. i) q^{96} +1.33436e7 q^{97} +(-5.17656e6 - 4.07548e6i) q^{98} -1.49810e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 8 q^{2} - 27 q^{3} - 64 q^{4} - 165 q^{5} - 432 q^{6} - 343 q^{7} - 1024 q^{8} - 729 q^{9}+O(q^{10}) $ 2 * q + 8 * q^2 - 27 * q^3 - 64 * q^4 - 165 * q^5 - 432 * q^6 - 343 * q^7 - 1024 * q^8 - 729 * q^9	\( 2 q + 8 q^{2} - 27 q^{3} - 64 q^{4} - 165 q^{5} - 432 q^{6} - 343 q^{7} - 1024 q^{8} - 729 q^{9} + 1320 q^{10} + 2055 q^{11} - 1728 q^{12} + 5440 q^{13} + 10976 q^{14} + 8910 q^{15} - 4096 q^{16} + 15708 q^{17} + 5832 q^{18} - 6752 q^{19} + 21120 q^{20} + 46305 q^{21} + 32880 q^{22} - 30828 q^{23} + 13824 q^{24} + 50900 q^{25} + 21760 q^{26} + 39366 q^{27} + 109760 q^{28} - 236610 q^{29} + 35640 q^{30} + 147517 q^{31} + 32768 q^{32} + 55485 q^{33} + 251328 q^{34} - 226380 q^{35} + 93312 q^{36} - 311732 q^{37} + 54016 q^{38} - 73440 q^{39} + 84480 q^{40} - 982800 q^{41} + 74088 q^{42} - 1154348 q^{43} + 131520 q^{44} - 120285 q^{45} + 246624 q^{46} + 854862 q^{47} + 221184 q^{48} - 1529437 q^{49} + 814400 q^{50} + 424116 q^{51} - 174080 q^{52} - 1166883 q^{53} + 157464 q^{54} - 678150 q^{55} + 175616 q^{56} + 364608 q^{57} - 946440 q^{58} + 167079 q^{59} - 285120 q^{60} - 1027274 q^{61} + 2360272 q^{62} - 1000188 q^{63} + 524288 q^{64} - 448800 q^{65} - 443880 q^{66} + 3268114 q^{67} + 1005312 q^{68} + 1664712 q^{69} - 2263800 q^{70} + 6093684 q^{71} + 373248 q^{72} + 3209110 q^{73} + 2493856 q^{74} + 1374300 q^{75} + 864256 q^{76} - 3524325 q^{77} - 1175040 q^{78} - 7127987 q^{79} - 675840 q^{80} - 531441 q^{81} - 3931200 q^{82} + 8731818 q^{83} - 2370816 q^{84} - 5183640 q^{85} - 4617392 q^{86} + 3194235 q^{87} - 1052160 q^{88} + 11996214 q^{89} - 1924560 q^{90} - 932960 q^{91} + 3945984 q^{92} + 3982959 q^{93} - 6838896 q^{94} - 1114080 q^{95} + 884736 q^{96} + 26687278 q^{97} - 10353112 q^{98} - 2996190 q^{99}+O(q^{100}) \) 2 * q + 8 * q^2 - 27 * q^3 - 64 * q^4 - 165 * q^5 - 432 * q^6 - 343 * q^7 - 1024 * q^8 - 729 * q^9 + 1320 * q^10 + 2055 * q^11 - 1728 * q^12 + 5440 * q^13 + 10976 * q^14 + 8910 * q^15 - 4096 * q^16 + 15708 * q^17 + 5832 * q^18 - 6752 * q^19 + 21120 * q^20 + 46305 * q^21 + 32880 * q^22 - 30828 * q^23 + 13824 * q^24 + 50900 * q^25 + 21760 * q^26 + 39366 * q^27 + 109760 * q^28 - 236610 * q^29 + 35640 * q^30 + 147517 * q^31 + 32768 * q^32 + 55485 * q^33 + 251328 * q^34 - 226380 * q^35 + 93312 * q^36 - 311732 * q^37 + 54016 * q^38 - 73440 * q^39 + 84480 * q^40 - 982800 * q^41 + 74088 * q^42 - 1154348 * q^43 + 131520 * q^44 - 120285 * q^45 + 246624 * q^46 + 854862 * q^47 + 221184 * q^48 - 1529437 * q^49 + 814400 * q^50 + 424116 * q^51 - 174080 * q^52 - 1166883 * q^53 + 157464 * q^54 - 678150 * q^55 + 175616 * q^56 + 364608 * q^57 - 946440 * q^58 + 167079 * q^59 - 285120 * q^60 - 1027274 * q^61 + 2360272 * q^62 - 1000188 * q^63 + 524288 * q^64 - 448800 * q^65 - 443880 * q^66 + 3268114 * q^67 + 1005312 * q^68 + 1664712 * q^69 - 2263800 * q^70 + 6093684 * q^71 + 373248 * q^72 + 3209110 * q^73 + 2493856 * q^74 + 1374300 * q^75 + 864256 * q^76 - 3524325 * q^77 - 1175040 * q^78 - 7127987 * q^79 - 675840 * q^80 - 531441 * q^81 - 3931200 * q^82 + 8731818 * q^83 - 2370816 * q^84 - 5183640 * q^85 - 4617392 * q^86 + 3194235 * q^87 - 1052160 * q^88 + 11996214 * q^89 - 1924560 * q^90 - 932960 * q^91 + 3945984 * q^92 + 3982959 * q^93 - 6838896 * q^94 - 1114080 * q^95 + 884736 * q^96 + 26687278 * q^97 - 10353112 * q^98 - 2996190 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/42\mathbb{Z}\right)^\times$.

$n$	$29$	$31$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	4.00000	+	6.92820i	0.353553	+	0.612372i
$2$	4.00000	+	6.92820i	0.353553	+	0.612372i
$3$	−13.5000	+	23.3827i	−0.288675	+	0.500000i
$3$	−13.5000	+	23.3827i	−0.288675	+	0.500000i
$4$	−32.0000	+	55.4256i	−0.250000	+	0.433013i
$5$	−82.5000	−	142.894i	−0.295161	−	0.511234i	0.679861	−	0.733341i	$-0.262040\pi$
$5$	−82.5000	−	142.894i	−0.295161	−	0.511234i	−0.975022	+	0.222107i	$0.928707\pi$
$6$	−216.000			−0.408248
$7$	−171.500	−	891.140i	−0.188982	−	0.981981i
$7$	−171.500	−	891.140i	−0.188982	−	0.981981i
$8$	−512.000			−0.353553
$9$	−364.500	−	631.333i	−0.166667	−	0.288675i
$10$	660.000	−	1143.15i	0.208710	−	0.361497i
$11$	1027.50	−	1779.68i	0.232760	−	0.403151i	−0.725860	−	0.687843i	$-0.758558\pi$
$11$	1027.50	−	1779.68i	0.232760	−	0.403151i	0.958619	+	0.284692i	$0.0918912\pi$
$12$	−864.000	−	1496.49i	−0.144338	−	0.250000i
$13$	2720.00			0.343374			0.171687	−	0.985152i	$-0.445078\pi$
$13$	2720.00			0.343374			0.171687	+	0.985152i	$0.445078\pi$
$14$	5488.00	−	4752.75i	0.534522	−	0.462910i
$15$	4455.00			0.340823
$16$	−2048.00	−	3547.24i	−0.125000	−	0.216506i
$17$	7854.00	−	13603.5i	0.387721	−	0.671553i	−0.604421	−	0.796665i	$-0.706596\pi$
$17$	7854.00	−	13603.5i	0.387721	−	0.671553i	0.992143	+	0.125112i	$0.0399290\pi$
$18$	2916.00	−	5050.66i	0.117851	−	0.204124i
$19$	−3376.00	−	5847.40i	−0.112918	−	0.195580i	0.804027	−	0.594592i	$-0.202687\pi$
$19$	−3376.00	−	5847.40i	−0.112918	−	0.195580i	−0.916946	+	0.399012i	$0.869353\pi$
$20$	10560.0			0.295161
$21$	23152.5	+	8020.26i	0.545545	+	0.188982i
$22$	16440.0			0.329172
$23$	−15414.0	−	26697.8i	−0.264161	−	0.457539i	0.703183	−	0.711009i	$-0.251762\pi$
$23$	−15414.0	−	26697.8i	−0.264161	−	0.457539i	−0.967343	+	0.253470i	$0.918428\pi$
$24$	6912.00	−	11971.9i	0.102062	−	0.176777i
$25$	25450.0	−	44080.7i	0.325760	−	0.564233i
$26$	10880.0	+	18844.7i	0.121401	+	0.210273i
$27$	19683.0			0.192450
$28$	54880.0	+	19011.0i	0.472456	+	0.163663i
$29$	−118305.			−0.900762			−0.450381	−	0.892836i	$-0.648712\pi$
$29$	−118305.			−0.900762			−0.450381	+	0.892836i	$0.648712\pi$
$30$	17820.0	+	30865.1i	0.120499	+	0.208710i
$31$	73758.5	−	127753.i	0.444679	−	0.770206i	−0.553351	−	0.832948i	$-0.686651\pi$
$31$	73758.5	−	127753.i	0.444679	−	0.770206i	0.998030	+	0.0627422i	$0.0199846\pi$
$32$	16384.0	−	28377.9i	0.0883883	−	0.153093i
$33$	27742.5	+	48051.4i	0.134384	+	0.232760i
$34$	125664.			0.548321
$35$	−113190.	+	98025.4i	−0.446241	+	0.386456i
$36$	46656.0			0.166667
$37$	−155866.	−	269968.i	−0.505877	−	0.876206i	−0.999977	−	0.00680009i	$-0.997835\pi$
$37$	−155866.	−	269968.i	−0.505877	−	0.876206i	0.494099	−	0.869405i	$-0.335498\pi$
$38$	27008.0	−	46779.2i	0.0798454	−	0.138296i
$39$	−36720.0	+	63600.9i	−0.0991235	+	0.171687i
$40$	42240.0	+	73161.8i	0.104355	+	0.180748i
$41$	−491400.			−1.11350			−0.556752	−	0.830679i	$-0.687953\pi$
$41$	−491400.			−1.11350			−0.556752	+	0.830679i	$0.687953\pi$
$42$	37044.0	+	192486.i	0.0771517	+	0.400892i
$43$	−577174.			−1.10705			−0.553525	−	0.832833i	$-0.686718\pi$
$43$	−577174.			−1.10705			−0.553525	+	0.832833i	$0.686718\pi$
$44$	65760.0	+	113900.i	0.116380	+	0.201576i
$45$	−60142.5	+	104170.i	−0.0983870	+	0.170411i
$46$	123312.	−	213583.i	0.186790	−	0.323529i
$47$	427431.	+	740332.i	0.600515	+	1.04012i	0.992743	+	0.120254i	$0.0383709\pi$
$47$	427431.	+	740332.i	0.600515	+	1.04012i	−0.392229	+	0.919868i	$0.628296\pi$
$48$	110592.			0.144338
$49$	−764718.	+	305661.i	−0.928571	+	0.371154i
$50$	407200.			0.460694
$51$	212058.	+	367295.i	0.223851	+	0.387721i
$52$	−87040.0	+	150758.i	−0.0858435	+	0.148685i
$53$	−583442.	+	1.01055e6i	−0.538309	+	0.932379i	0.460686	+	0.887563i	$0.347603\pi$
$53$	−583442.	+	1.01055e6i	−0.538309	+	0.932379i	−0.998995	+	0.0448157i	$0.985730\pi$
$54$	78732.0	+	136368.i	0.0680414	+	0.117851i
$55$	−339075.			−0.274806
$56$	87808.0	+	456264.i	0.0668153	+	0.347183i
$57$	182304.			0.130387
$58$	−473220.	−	819641.i	−0.318467	−	0.551602i
$59$	83539.5	−	144695.i	0.0529553	−	0.0917214i	−0.838333	−	0.545159i	$-0.816469\pi$
$59$	83539.5	−	144695.i	0.0529553	−	0.0917214i	0.891288	+	0.453438i	$0.149803\pi$
$60$	−142560.	+	246921.i	−0.0852056	+	0.147580i
$61$	−513637.	−	889645.i	−0.289736	−	0.501837i	0.684011	−	0.729472i	$-0.260234\pi$
$61$	−513637.	−	889645.i	−0.289736	−	0.501837i	−0.973747	+	0.227635i	$0.926901\pi$
$62$	1.18014e6			0.628870
$63$	−500094.	+	433094.i	−0.251976	+	0.218218i
$64$	262144.			0.125000
$65$	−224400.	−	388672.i	−0.101351	−	0.175544i
$66$	−221940.	+	384411.i	−0.0950237	+	0.164586i
$67$	1.63406e6	−	2.83027e6i	0.663751	−	1.14965i	−0.315871	−	0.948802i	$-0.602297\pi$
$67$	1.63406e6	−	2.83027e6i	0.663751	−	1.14965i	0.979622	−	0.200849i	$-0.0643700\pi$
$68$	502656.	+	870626.i	0.193861	+	0.335777i
$69$	832356.			0.305026
$70$	−1.13190e6	−	392102.i	−0.394425	−	0.136633i
$71$	3.04684e6			1.01029			0.505145	−	0.863035i	$-0.331439\pi$
$71$	3.04684e6			1.01029			0.505145	+	0.863035i	$0.331439\pi$
$72$	186624.	+	323242.i	0.0589256	+	0.102062i
$73$	1.60456e6	−	2.77917e6i	0.482753	−	0.836152i	−0.517051	−	0.855954i	$-0.672970\pi$
$73$	1.60456e6	−	2.77917e6i	0.482753	−	0.836152i	0.999804	+	0.0198024i	$0.00630371\pi$
$74$	1.24693e6	−	2.15974e6i	0.357709	−	0.619571i
$75$	687150.	+	1.19018e6i	0.188078	+	0.325760i
$76$	432128.			0.112918
$77$	−1.76216e6	−	610431.i	−0.439874	−	0.152377i
$78$	−587520.			−0.140182
$79$	−3.56399e6	−	6.17302e6i	−0.813284	−	1.40865i	−0.910554	−	0.413391i	$-0.864344\pi$
$79$	−3.56399e6	−	6.17302e6i	−0.813284	−	1.40865i	0.0972700	−	0.995258i	$-0.468989\pi$
$80$	−337920.	+	585295.i	−0.0737902	+	0.127808i
$81$	−265720.	+	460241.i	−0.0555556	+	0.0962250i
$82$	−1.96560e6	−	3.40452e6i	−0.393683	−	0.681879i
$83$	4.36591e6			0.838111			0.419055	−	0.907961i	$-0.362361\pi$
$83$	4.36591e6			0.838111			0.419055	+	0.907961i	$0.362361\pi$
$84$	−1.18541e6	+	1.02659e6i	−0.218218	+	0.188982i
$85$	−2.59182e6			−0.457761
$86$	−2.30870e6	−	3.99878e6i	−0.391401	−	0.677927i
$87$	1.59712e6	−	2.76629e6i	0.260028	−	0.450381i
$88$	−526080.	+	911197.i	−0.0822929	+	0.142536i
$89$	5.99811e6	+	1.03890e7i	0.901881	+	1.56210i	0.825050	+	0.565059i	$0.191147\pi$
$89$	5.99811e6	+	1.03890e7i	0.901881	+	1.56210i	0.0768306	+	0.997044i	$0.475520\pi$
$90$	−962280.			−0.139140
$91$	−466480.	−	2.42390e6i	−0.0648916	−	0.337186i
$92$	1.97299e6			0.264161
$93$	1.99148e6	+	3.44934e6i	0.256735	+	0.444679i
$94$	−3.41945e6	+	5.92266e6i	−0.424628	+	0.735477i
$95$	−557040.	+	964822.i	−0.0666582	+	0.115455i
$96$	442368.	+	766204.i	0.0510310	+	0.0883883i
$97$	1.33436e7			1.48448			0.742238	−	0.670136i	$-0.233764\pi$
$97$	1.33436e7			1.48448			0.742238	+	0.670136i	$0.233764\pi$
$98$	−5.17656e6	−	4.07548e6i	−0.555584	−	0.437409i
$99$	−1.49810e6			−0.155173
$100$	1.62880e6	+	2.82116e6i	0.162880	+	0.282116i
$101$	−5.31755e6	+	9.21026e6i	−0.513554	+	0.889502i	0.486322	+	0.873780i	$0.338338\pi$
$101$	−5.31755e6	+	9.21026e6i	−0.513554	+	0.889502i	−0.999876	+	0.0157225i	$0.994995\pi$
$102$	−1.69646e6	+	2.93836e6i	−0.158287	+	0.274160i
$103$	5.67667e6	+	9.83228e6i	0.511874	+	0.886592i	0.999905	+	0.0137658i	$0.00438193\pi$
$103$	5.67667e6	+	9.83228e6i	0.511874	+	0.886592i	−0.488031	+	0.872826i	$0.662285\pi$
$104$	−1.39264e6			−0.121401
$105$	−764033.	−	3.97003e6i	−0.0644094	−	0.334681i
$106$	−9.33506e6			−0.761284
$107$	699784.	+	1.21206e6i	0.0552231	+	0.0956493i	0.892315	−	0.451412i	$-0.149080\pi$
$107$	699784.	+	1.21206e6i	0.0552231	+	0.0956493i	−0.837092	+	0.547062i	$0.815746\pi$
$108$	−629856.	+	1.09094e6i	−0.0481125	+	0.0833333i
$109$	−967351.	+	1.67550e6i	−0.0715470	+	0.123923i	−0.899579	−	0.436757i	$-0.856127\pi$
$109$	−967351.	+	1.67550e6i	−0.0715470	+	0.123923i	0.828032	+	0.560680i	$0.189460\pi$
$110$	−1.35630e6	−	2.34918e6i	−0.0971586	−	0.168284i
$111$	8.41676e6			0.584137
$112$	−2.80986e6	+	2.43341e6i	−0.188982	+	0.163663i
$113$	−2.63859e7			−1.72027			−0.860137	−	0.510063i	$-0.829622\pi$
$113$	−2.63859e7			−1.72027			−0.860137	+	0.510063i	$0.829622\pi$
$114$	729216.	+	1.26304e6i	0.0460988	+	0.0798454i
$115$	−2.54331e6	+	4.40514e6i	−0.155940	+	0.270096i
$116$	3.78576e6	−	6.55713e6i	0.225191	−	0.390041i
$117$	−991440.	−	1.71722e6i	−0.0572290	−	0.0991235i
$118$	1.33663e6			0.0748902
$119$	−1.34696e7	−	4.66601e6i	−0.732724	−	0.253823i
$120$	−2.28096e6			−0.120499
$121$	7.63207e6	+	1.32191e7i	0.391646	+	0.678351i
$122$	4.10910e6	−	7.11716e6i	0.204874	−	0.354852i
$123$	6.63390e6	−	1.14903e7i	0.321441	−	0.556752i
$124$	4.72054e6	+	8.17622e6i	0.222339	+	0.385103i
$125$	−2.12891e7			−0.974929
$126$	−5.00094e6	−	1.73238e6i	−0.222718	−	0.0771517i
$127$	−1.84987e7			−0.801362			−0.400681	−	0.916218i	$-0.631226\pi$
$127$	−1.84987e7			−0.801362			−0.400681	+	0.916218i	$0.631226\pi$
$128$	1.04858e6	+	1.81619e6i	0.0441942	+	0.0765466i
$129$	7.79185e6	−	1.34959e7i	0.319578	−	0.553525i
$130$	1.79520e6	−	3.10938e6i	0.0716657	−	0.124129i
$131$	1.86425e6	+	3.22897e6i	0.0724527	+	0.125492i	0.899976	−	0.435940i	$-0.143584\pi$
$131$	1.86425e6	+	3.22897e6i	0.0724527	+	0.125492i	−0.827523	+	0.561432i	$0.810251\pi$
$132$	−3.55104e6			−0.134384
$133$	−4.63187e6	+	4.01132e6i	−0.170717	+	0.147845i
$134$	2.61449e7			0.938686
$135$	−1.62385e6	−	2.81259e6i	−0.0568038	−	0.0983870i
$136$	−4.02125e6	+	6.96501e6i	−0.137080	+	0.237430i
$137$	1.82542e7	−	3.16171e7i	0.606513	−	1.05051i	−0.385298	−	0.922792i	$-0.625901\pi$
$137$	1.82542e7	−	3.16171e7i	0.606513	−	1.05051i	0.991810	−	0.127718i	$-0.0407654\pi$
$138$	3.32942e6	+	5.76673e6i	0.107843	+	0.186790i
$139$	4.51678e7			1.42652			0.713259	−	0.700900i	$-0.247218\pi$
$139$	4.51678e7			1.42652			0.713259	+	0.700900i	$0.247218\pi$
$140$	−1.81104e6	−	9.41044e6i	−0.0557802	−	0.289842i
$141$	−2.30813e7			−0.693414
$142$	1.21874e7	+	2.11091e7i	0.357191	+	0.618673i
$143$	2.79480e6	−	4.84074e6i	0.0799235	−	0.138432i
$144$	−1.49299e6	+	2.58594e6i	−0.0416667	+	0.0721688i
$145$	9.76016e6	+	1.69051e7i	0.265870	+	0.460500i
$146$	2.56729e7			0.682715
$147$	3.17652e6	−	2.20076e7i	0.0824786	−	0.571429i
$148$	1.99508e7			0.505877
$149$	1.11978e7	+	1.93952e7i	0.277320	+	0.480333i	0.970718	−	0.240222i	$-0.0772204\pi$
$149$	1.11978e7	+	1.93952e7i	0.277320	+	0.480333i	−0.693398	+	0.720555i	$0.743887\pi$
$150$	−5.49720e6	+	9.52143e6i	−0.132991	+	0.230347i
$151$	3.94970e7	−	6.84108e7i	0.933566	−	1.61698i	0.156394	−	0.987695i	$-0.450013\pi$
$151$	3.94970e7	−	6.84108e7i	0.933566	−	1.61698i	0.777172	−	0.629289i	$-0.216654\pi$
$152$	1.72851e6	+	2.99387e6i	0.0399227	+	0.0691481i
$153$	−1.14511e7			−0.258481
$154$	−2.81946e6	−	1.46503e7i	−0.0622076	−	0.323240i
$155$	−2.43403e7			−0.525007
$156$	−2.35008e6	−	4.07046e6i	−0.0495617	−	0.0858435i
$157$	−3.12108e7	+	5.40588e7i	−0.643660	+	1.11485i	0.340949	+	0.940082i	$0.389252\pi$
$157$	−3.12108e7	+	5.40588e7i	−0.643660	+	1.11485i	−0.984609	+	0.174771i	$0.944082\pi$
$158$	2.85119e7	−	4.93841e7i	0.575078	−	0.996065i
$159$	−1.57529e7	−	2.72849e7i	−0.310793	−	0.538309i
$160$	−5.40672e6			−0.104355
$161$	−2.11480e7	+	1.83147e7i	−0.399373	+	0.345867i
$162$	−4.25153e6			−0.0785674
$163$	9.20007e6	+	1.59350e7i	0.166393	+	0.288201i	0.937149	−	0.348929i	$-0.113455\pi$
$163$	9.20007e6	+	1.59350e7i	0.166393	+	0.288201i	−0.770756	+	0.637130i	$0.780121\pi$
$164$	1.57248e7	−	2.72362e7i	0.278376	−	0.482161i
$165$	4.57751e6	−	7.92848e6i	0.0793297	−	0.137403i
$166$	1.74636e7	+	3.02479e7i	0.296317	+	0.513236i
$167$	−4.31800e7			−0.717423			−0.358712	−	0.933448i	$-0.616784\pi$
$167$	−4.31800e7			−0.717423			−0.358712	+	0.933448i	$0.616784\pi$
$168$	−1.18541e7	−	4.10637e6i	−0.192879	−	0.0668153i
$169$	−5.53501e7			−0.882094
$170$	−1.03673e7	−	1.79567e7i	−0.161843	−	0.280320i
$171$	−2.46110e6	+	4.26276e6i	−0.0376395	+	0.0651935i
$172$	1.84696e7	−	3.19902e7i	0.276762	−	0.479367i
$173$	4.27411e7	+	7.40297e7i	0.627601	+	1.08704i	0.988032	+	0.154251i	$0.0492965\pi$
$173$	4.27411e7	+	7.40297e7i	0.627601	+	1.08704i	−0.360430	+	0.932786i	$0.617370\pi$
$174$	2.55539e7			0.367735
$175$	−4.36468e7	−	1.51197e7i	−0.615629	−	0.213260i
$176$	−8.41728e6			−0.116380
$177$	2.25557e6	+	3.90676e6i	0.0305738	+	0.0529553i
$178$	−4.79849e7	+	8.31122e7i	−0.637726	+	1.10457i
$179$	6.43783e7	−	1.11506e8i	0.838984	−	1.45316i	−0.0517610	−	0.998659i	$-0.516483\pi$
$179$	6.43783e7	−	1.11506e8i	0.838984	−	1.45316i	0.890745	−	0.454503i	$-0.150183\pi$
$180$	−3.84912e6	−	6.66687e6i	−0.0491935	−	0.0852056i
$181$	−1.08221e7			−0.135655			−0.0678277	−	0.997697i	$-0.521607\pi$
$181$	−1.08221e7			−0.135655			−0.0678277	+	0.997697i	$0.521607\pi$
$182$	1.49274e7	−	1.29275e7i	0.183541	−	0.158951i
$183$	2.77364e7			0.334558
$184$	7.89197e6	+	1.36693e7i	0.0933949	+	0.161765i
$185$	−2.57179e7	+	4.45447e7i	−0.298631	+	0.517243i
$186$	−1.59318e7	+	2.75947e7i	−0.181539	+	0.314435i
$187$	−1.61400e7	−	2.79552e7i	−0.180492	−	0.312621i
$188$	−5.47112e7			−0.600515
$189$	−3.37563e6	−	1.75403e7i	−0.0363696	−	0.188982i
$190$	−8.91264e6			−0.0942690
$191$	2.31039e7	+	4.00172e7i	0.239922	+	0.415556i	0.960692	−	0.277618i	$-0.0895449\pi$
$191$	2.31039e7	+	4.00172e7i	0.239922	+	0.415556i	−0.720770	+	0.693174i	$0.756212\pi$
$192$	−3.53894e6	+	6.12963e6i	−0.0360844	+	0.0625000i
$193$	−1.67473e7	+	2.90072e7i	−0.167685	+	0.290439i	−0.937606	−	0.347701i	$-0.886963\pi$
$193$	−1.67473e7	+	2.90072e7i	−0.167685	+	0.290439i	0.769920	+	0.638140i	$0.220296\pi$
$194$	5.33746e7	+	9.24474e7i	0.524842	+	0.909052i
$195$	1.21176e7			0.117030
$196$	7.52954e6	−	5.21662e7i	0.0714286	−	0.494872i
$197$	−1.34731e8			−1.25556			−0.627778	−	0.778392i	$-0.716036\pi$
$197$	−1.34731e8			−1.25556			−0.627778	+	0.778392i	$0.716036\pi$
$198$	−5.99238e6	−	1.03791e7i	−0.0548619	−	0.0950237i
$199$	3.93267e7	−	6.81159e7i	0.353755	−	0.612721i	−0.633149	−	0.774030i	$-0.718238\pi$
$199$	3.93267e7	−	6.81159e7i	0.353755	−	0.612721i	0.986904	+	0.161309i	$0.0515714\pi$
$200$	−1.30304e7	+	2.25693e7i	−0.115174	+	0.199486i
$201$	4.41195e7	+	7.64173e7i	0.383217	+	0.663751i
$202$	−8.50807e7			−0.726275
$203$	2.02893e7	+	1.05426e8i	0.170228	+	0.884531i
$204$	−2.71434e7			−0.223851
$205$	4.05405e7	+	7.02182e7i	0.328663	+	0.569261i
$206$	−4.54133e7	+	7.86582e7i	−0.361950	+	0.626915i
$207$	−1.12368e7	+	1.94627e7i	−0.0880535	+	0.152513i
$208$	−5.57056e6	−	9.64849e6i	−0.0429217	−	0.0743426i
$209$	−1.38754e7			−0.105131
$210$	2.44490e7	−	2.11735e7i	0.182177	−	0.157770i
$211$	8.94413e7			0.655465			0.327732	−	0.944771i	$-0.393716\pi$
$211$	8.94413e7			0.655465			0.327732	+	0.944771i	$0.393716\pi$
$212$	−3.73403e7	−	6.46752e7i	−0.269155	−	0.466189i
$213$	−4.11324e7	+	7.12433e7i	−0.291645	+	0.505145i
$214$	−5.59828e6	+	9.69650e6i	−0.0390487	+	0.0676343i
$215$	4.76169e7	+	8.24748e7i	0.326758	+	0.565961i
$216$	−1.00777e7			−0.0680414
$217$	−1.26496e8	−	4.38194e7i	−0.840363	−	0.291110i
$218$	−1.54776e7			−0.101183
$219$	4.33230e7	+	7.50376e7i	0.278717	+	0.482753i
$220$	1.08504e7	−	1.87934e7i	0.0687015	−	0.118995i
$221$	2.13629e7	−	3.70016e7i	0.133133	−	0.230594i
$222$	3.36671e7	+	5.83131e7i	0.206524	+	0.357709i
$223$	1.60136e8			0.966990			0.483495	−	0.875347i	$-0.339367\pi$
$223$	1.60136e8			0.966990			0.483495	+	0.875347i	$0.339367\pi$
$224$	−2.80986e7	−	9.73363e6i	−0.167038	−	0.0578638i
$225$	−3.71061e7			−0.217173
$226$	−1.05544e8	−	1.82807e8i	−0.608209	−	1.05345i
$227$	1.08874e8	−	1.88575e8i	0.617778	−	1.07002i	−0.372113	−	0.928187i	$-0.621367\pi$
$227$	1.08874e8	−	1.88575e8i	0.617778	−	1.07002i	0.989890	−	0.141835i	$-0.0453001\pi$
$228$	−5.83373e6	+	1.01043e7i	−0.0325967	+	0.0564592i
$229$	−7.95294e7	−	1.37749e8i	−0.437626	−	0.757991i	0.559879	−	0.828574i	$-0.310847\pi$
$229$	−7.95294e7	−	1.37749e8i	−0.437626	−	0.757991i	−0.997506	+	0.0705828i	$0.977514\pi$
$230$	−4.06930e7			−0.220532
$231$	3.80627e7	−	3.29633e7i	0.203169	−	0.175950i
$232$	6.05722e7			0.318467
$233$	−4.73771e6	−	8.20596e6i	−0.0245371	−	0.0424995i	0.853496	−	0.521099i	$-0.174478\pi$
$233$	−4.73771e6	−	8.20596e6i	−0.0245371	−	0.0424995i	−0.878033	+	0.478600i	$0.841145\pi$
$234$	7.93152e6	−	1.37378e7i	0.0404670	−	0.0700909i
$235$	7.05261e7	−	1.22155e8i	0.354497	−	0.614007i
$236$	5.34653e6	+	9.26046e6i	0.0264777	+	0.0458607i
$237$	1.92456e8			0.939099
$238$	−2.15514e7	−	1.11984e8i	−0.103623	−	0.538440i
$239$	7.63912e7			0.361952			0.180976	−	0.983488i	$-0.442074\pi$
$239$	7.63912e7			0.361952			0.180976	+	0.983488i	$0.442074\pi$
$240$	−9.12384e6	−	1.58030e7i	−0.0426028	−	0.0737902i
$241$	1.14307e8	−	1.97986e8i	0.526035	−	0.911119i	−0.473505	−	0.880791i	$-0.657012\pi$
$241$	1.14307e8	−	1.97986e8i	0.526035	−	0.911119i	0.999540	−	0.0303279i	$-0.00965516\pi$
$242$	−6.10566e7	+	1.05753e8i	−0.276936	+	0.479666i
$243$	−7.17445e6	−	1.24265e7i	−0.0320750	−	0.0555556i
$244$	6.57455e7			0.289736
$245$	1.06766e8	+	8.40568e7i	0.463824	+	0.365167i
$246$	1.06142e8			0.454586
$247$	−9.18272e6	−	1.59049e7i	−0.0387732	−	0.0671572i
$248$	−3.77644e7	+	6.54098e7i	−0.157218	+	0.272309i
$249$	−5.89398e7	+	1.02087e8i	−0.241942	+	0.419055i
$250$	−8.51565e7	−	1.47495e8i	−0.344689	−	0.597019i
$251$	1.13193e8			0.451816			0.225908	−	0.974149i	$-0.427465\pi$
$251$	1.13193e8			0.451816			0.225908	+	0.974149i	$0.427465\pi$
$252$	−8.00150e6	−	4.15770e7i	−0.0314970	−	0.163663i
$253$	−6.33515e7			−0.245944
$254$	−7.39949e7	−	1.28163e8i	−0.283324	−	0.490732i
$255$	3.49896e7	−	6.06037e7i	0.132144	−	0.228880i
$256$	−8.38861e6	+	1.45295e7i	−0.0312500	+	0.0541266i
$257$	−7.77032e7	−	1.34586e8i	−0.285544	−	0.494577i	0.687197	−	0.726471i	$-0.258841\pi$
$257$	−7.77032e7	−	1.34586e8i	−0.285544	−	0.494577i	−0.972741	+	0.231895i	$0.925508\pi$
$258$	1.24670e8			0.451951
$259$	−2.13848e8	+	1.85198e8i	−0.764815	+	0.662349i
$260$	2.87232e7			0.101351
$261$	4.31222e7	+	7.46898e7i	0.150127	+	0.260028i
$262$	−1.49140e7	+	2.58318e7i	−0.0512318	+	0.0887361i
$263$	4.03791e7	−	6.99386e7i	0.136871	−	0.237067i	−0.789440	−	0.613828i	$-0.789629\pi$
$263$	4.03791e7	−	6.99386e7i	0.136871	−	0.237067i	0.926311	+	0.376761i	$0.122962\pi$
$264$	−1.42042e7	−	2.46023e7i	−0.0475118	−	0.0822929i
$265$	1.92536e8			0.635551
$266$	−4.63187e7	−	1.60453e7i	−0.150894	−	0.0522711i
$267$	−3.23898e8			−1.04140
$268$	1.04580e8	+	1.81137e8i	0.331876	+	0.574825i
$269$	1.36505e8	−	2.36433e8i	0.427577	−	0.740585i	−0.569080	−	0.822282i	$-0.692701\pi$
$269$	1.36505e8	−	2.36433e8i	0.427577	−	0.740585i	0.996657	+	0.0816968i	$0.0260339\pi$
$270$	1.29908e7	−	2.25007e7i	0.0401663	−	0.0695701i
$271$	−2.91049e8	−	5.04112e8i	−0.888330	−	1.53863i	−0.841849	−	0.539714i	$-0.818533\pi$
$271$	−2.91049e8	−	5.04112e8i	−0.888330	−	1.53863i	−0.0464812	−	0.998919i	$-0.514801\pi$
$272$	−6.43400e7			−0.193861
$273$	6.29748e7	+	2.18151e7i	0.187326	+	0.0648916i
$274$	2.92067e8			0.857738
$275$	−5.22998e7	−	9.05858e7i	−0.151647	−	0.262661i
$276$	−2.66354e7	+	4.61339e7i	−0.0762566	+	0.132080i
$277$	−2.92118e8	+	5.05963e8i	−0.825808	+	1.43034i	0.0754922	+	0.997146i	$0.475947\pi$
$277$	−2.92118e8	+	5.05963e8i	−0.825808	+	1.43034i	−0.901300	+	0.433195i	$0.857386\pi$
$278$	1.80671e8	+	3.12932e8i	0.504351	+	0.873561i
$279$	−1.07540e8			−0.296452
$280$	5.79533e7	−	5.01890e7i	0.157770	−	0.136633i
$281$	4.30324e6			0.0115697			0.00578487	−	0.999983i	$-0.498159\pi$
$281$	4.30324e6			0.0115697			0.00578487	+	0.999983i	$0.498159\pi$
$282$	−9.23251e7	−	1.59912e8i	−0.245159	−	0.424628i
$283$	−1.90591e8	+	3.30114e8i	−0.499863	+	0.865787i	−1.00000		0.000158640i	$-0.999950\pi$
$283$	−1.90591e8	+	3.30114e8i	−0.499863	+	0.865787i	0.500137	+	0.865946i	$0.333283\pi$
$284$	−9.74989e7	+	1.68873e8i	−0.252572	+	0.437468i
$285$	−1.50401e7	−	2.60502e7i	−0.0384851	−	0.0666582i
$286$	4.47168e7			0.113029
$287$	8.42751e7	+	4.37906e8i	0.210432	+	1.09344i
$288$	−2.38879e7			−0.0589256
$289$	8.17987e7	+	1.41680e8i	0.199344	+	0.345275i
$290$	−7.80813e7	+	1.35241e8i	−0.187998	+	0.325623i
$291$	−1.80139e8	+	3.12010e8i	−0.428531	+	0.742238i
$292$	1.02692e8	+	1.77867e8i	0.241376	+	0.418076i
$293$	−5.26890e7			−0.122372			−0.0611862	−	0.998126i	$-0.519488\pi$
$293$	−5.26890e7			−0.122372			−0.0611862	+	0.998126i	$0.519488\pi$
$294$	1.65179e8	−	6.60228e7i	0.379088	−	0.151523i
$295$	−2.75680e7			−0.0625214
$296$	7.98034e7	+	1.38224e8i	0.178855	+	0.309785i
$297$	2.02243e7	−	3.50295e7i	0.0447946	−	0.0775865i
$298$	−8.95826e7	+	1.55162e8i	−0.196095	+	0.339647i
$299$	−4.19261e7	−	7.26181e7i	−0.0907058	−	0.157107i
$300$	−8.79552e7			−0.188078
$301$	9.89853e7	+	5.14343e8i	0.209213	+	1.08710i
$302$	6.31952e8			1.32026
$303$	−1.43574e8	−	2.48677e8i	−0.296501	−	0.513554i
$304$	−1.38281e7	+	2.39510e7i	−0.0282296	+	0.0488951i
$305$	−8.47501e7	+	1.46791e8i	−0.171037	+	0.296245i
$306$	−4.58045e7	−	7.93358e7i	−0.0913868	−	0.158287i
$307$	−4.67610e8			−0.922358			−0.461179	−	0.887307i	$-0.652573\pi$
$307$	−4.67610e8			−0.922358			−0.461179	+	0.887307i	$0.652573\pi$
$308$	9.02227e7	−	7.81352e7i	0.175950	−	0.152377i
$309$	−3.06540e8			−0.591061
$310$	−9.73612e7	−	1.68635e8i	−0.185618	−	0.321500i
$311$	7.61608e7	−	1.31914e8i	0.143572	−	0.248674i	−0.785267	−	0.619157i	$-0.787474\pi$
$311$	7.61608e7	−	1.31914e8i	0.143572	−	0.248674i	0.928839	+	0.370483i	$0.120808\pi$
$312$	1.88006e7	−	3.25637e7i	0.0350454	−	0.0607005i
$313$	−9.87334e7	−	1.71011e8i	−0.181995	−	0.315224i	0.760565	−	0.649262i	$-0.224922\pi$
$313$	−9.87334e7	−	1.71011e8i	−0.181995	−	0.315224i	−0.942560	+	0.334038i	$0.891589\pi$
$314$	−4.99374e8			−0.910273
$315$	1.03144e8	+	3.57303e7i	0.185934	+	0.0644094i
$316$	4.56191e8			0.813284
$317$	−4.07837e8	−	7.06394e8i	−0.719083	−	1.24549i	−0.961363	−	0.275283i	$-0.911229\pi$
$317$	−4.07837e8	−	7.06394e8i	−0.719083	−	1.24549i	0.242280	−	0.970206i	$-0.422105\pi$
$318$	1.26023e8	−	2.18279e8i	0.219764	−	0.380642i
$319$	−1.21558e8	+	2.10545e8i	−0.209661	+	0.363143i
$320$	−2.16269e7	−	3.74589e7i	−0.0368951	−	0.0639042i
$321$	−3.77884e7			−0.0637662
$322$	−2.11480e8	−	7.32588e7i	−0.352999	−	0.122283i
$323$	−1.06060e8			−0.175124
$324$	−1.70061e7	−	2.94555e7i	−0.0277778	−	0.0481125i
$325$	6.92240e7	−	1.19899e8i	0.111857	−	0.193743i
$326$	−7.36005e7	+	1.27480e8i	−0.117657	+	0.203789i
$327$	−2.61185e7	−	4.52385e7i	−0.0413077	−	0.0715470i
$328$	2.51597e8			0.393683
$329$	5.86435e8	−	5.07868e8i	0.907893	−	0.786258i
$330$	7.32402e7			0.112189
$331$	3.73390e8	+	6.46731e8i	0.565933	+	0.980225i	0.996962	+	0.0778868i	$0.0248173\pi$
$331$	3.73390e8	+	6.46731e8i	0.565933	+	0.980225i	−0.431029	+	0.902338i	$0.641849\pi$
$332$	−1.39709e8	+	2.41983e8i	−0.209528	+	0.362913i
$333$	−1.13626e8	+	1.96807e8i	−0.168626	+	0.292069i
$334$	−1.72720e8	−	2.99160e8i	−0.253647	−	0.439330i
$335$	−5.39239e8			−0.783654
$336$	−1.89665e7	−	9.85530e7i	−0.0272772	−	0.141737i
$337$	5.55804e8			0.791074			0.395537	−	0.918450i	$-0.370558\pi$
$337$	5.55804e8			0.791074			0.395537	+	0.918450i	$0.370558\pi$
$338$	−2.21400e8	−	3.83477e8i	−0.311867	−	0.540170i
$339$	3.56210e8	−	6.16973e8i	0.496600	−	0.860137i
$340$	8.29382e7	−	1.43653e8i	0.114440	−	0.198216i
$341$	−1.51574e8	−	2.62533e8i	−0.207006	−	0.358545i
$342$	−3.93777e7			−0.0532303
$343$	4.03536e8	+	6.29050e8i	0.539949	+	0.841698i
$344$	2.95513e8			0.391401
$345$	−6.86694e7	−	1.18939e8i	−0.0900319	−	0.155940i
$346$	−3.41928e8	+	5.92237e8i	−0.443781	+	0.768652i
$347$	−3.63350e8	+	6.29340e8i	−0.466844	+	0.808598i	−0.999283	−	0.0378710i	$-0.987942\pi$
$347$	−3.63350e8	+	6.29340e8i	−0.466844	+	0.808598i	0.532439	+	0.846469i	$0.321276\pi$
$348$	1.02216e8	+	1.77042e8i	0.130014	+	0.225191i
$349$	4.65885e8			0.586664			0.293332	−	0.956011i	$-0.405236\pi$
$349$	4.65885e8			0.586664			0.293332	+	0.956011i	$0.405236\pi$
$350$	−6.98348e7	−	3.62872e8i	−0.0870630	−	0.452393i
$351$	5.35378e7			0.0660823
$352$	−3.36691e7	−	5.83166e7i	−0.0411465	−	0.0712678i
$353$	7.73776e8	−	1.34022e9i	0.936276	−	1.62168i	0.163933	−	0.986472i	$-0.447582\pi$
$353$	7.73776e8	−	1.34022e9i	0.936276	−	1.62168i	0.772343	−	0.635205i	$-0.219085\pi$
$354$	−1.80445e7	+	3.12540e7i	−0.0216189	+	0.0374451i
$355$	−2.51364e8	−	4.35376e8i	−0.298198	−	0.516494i
$356$	−7.67758e8			−0.901881
$357$	2.90944e8	−	2.51965e8i	0.338431	−	0.293090i
$358$	1.03005e9			1.18650
$359$	−7.99283e6	−	1.38440e7i	−0.00911737	−	0.0157918i	0.861431	−	0.507875i	$-0.169569\pi$
$359$	−7.99283e6	−	1.38440e7i	−0.00911737	−	0.0157918i	−0.870548	+	0.492083i	$0.836236\pi$
$360$	3.07930e7	−	5.33350e7i	0.0347851	−	0.0602495i
$361$	4.24141e8	−	7.34634e8i	0.474499	−	0.821856i
$362$	−4.32885e7	−	7.49778e7i	−0.0479615	−	0.0830717i
$363$	−4.12132e8			−0.452234
$364$	1.49274e8	+	5.17099e7i	0.162229	+	0.0561977i
$365$	−5.29503e8			−0.569959
$366$	1.10946e8	+	1.92163e8i	0.118284	+	0.204874i
$367$	−4.56083e7	+	7.89958e7i	−0.0481629	+	0.0834205i	−0.889102	−	0.457709i	$-0.848670\pi$
$367$	−4.56083e7	+	7.89958e7i	−0.0481629	+	0.0834205i	0.840939	+	0.541130i	$0.182003\pi$
$368$	−6.31357e7	+	1.09354e8i	−0.0660401	+	0.114385i
$369$	1.79115e8	+	3.10237e8i	0.185584	+	0.321441i
$370$	−4.11486e8			−0.422327
$371$	1.00060e9	+	3.46619e8i	1.01731	+	0.352406i
$372$	−2.54909e8			−0.256735
$373$	6.89851e8	+	1.19486e9i	0.688294	+	1.19216i	0.972389	+	0.233365i	$0.0749736\pi$
$373$	6.89851e8	+	1.19486e9i	0.688294	+	1.19216i	−0.284095	+	0.958796i	$0.591693\pi$
$374$	1.29120e8	−	2.23642e8i	0.127627	−	0.221056i
$375$	2.87403e8	−	4.97797e8i	0.281438	−	0.487464i
$376$	−2.18845e8	−	3.79050e8i	−0.212314	−	0.367739i
$377$	−3.21790e8			−0.309298
$378$	1.08020e8	−	9.35483e7i	0.102869	−	0.0890871i
$379$	6.28208e8			0.592743			0.296371	−	0.955073i	$-0.404223\pi$
$379$	6.28208e8			0.592743			0.296371	+	0.955073i	$0.404223\pi$
$380$	−3.56506e7	−	6.17486e7i	−0.0333291	−	0.0577277i
$381$	2.49733e8	−	4.32550e8i	0.231333	−	0.400681i
$382$	−1.84832e8	+	3.20138e8i	−0.169650	+	0.293843i
$383$	4.93247e8	+	8.54329e8i	0.448610	+	0.777015i	0.998296	−	0.0583564i	$-0.0185860\pi$
$383$	4.93247e8	+	8.54329e8i	0.448610	+	0.777015i	−0.549686	+	0.835371i	$0.685253\pi$
$384$	−5.66231e7			−0.0510310
$385$	5.81514e7	+	3.02163e8i	0.0519335	+	0.269854i
$386$	−2.67957e8			−0.237143
$387$	2.10380e8	+	3.64389e8i	0.184508	+	0.319578i
$388$	−4.26996e8	+	7.39580e8i	−0.371119	+	0.642797i
$389$	4.42663e8	−	7.66715e8i	0.381285	−	0.660405i	−0.609961	−	0.792431i	$-0.708815\pi$
$389$	4.42663e8	−	7.66715e8i	0.381285	−	0.660405i	0.991246	+	0.132026i	$0.0421484\pi$
$390$	4.84704e7	+	8.39532e7i	0.0413762	+	0.0716657i
$391$	−4.84246e8			−0.409683
$392$	3.91536e8	−	1.56498e8i	0.328300	−	0.131223i
$393$	−1.00669e8			−0.0836612
$394$	−5.38925e8	−	9.33445e8i	−0.443906	−	0.768868i
$395$	−5.88059e8	+	1.01855e9i	−0.480099	+	0.831556i
$396$	4.79390e7	−	8.30329e7i	0.0387933	−	0.0671919i
$397$	−1.04501e9	−	1.81001e9i	−0.838211	−	1.45182i	−0.891389	−	0.453240i	$-0.850268\pi$
$397$	−1.04501e9	−	1.81001e9i	−0.838211	−	1.45182i	0.0531772	−	0.998585i	$-0.483065\pi$
$398$	6.29228e8			0.500285
$399$	−3.12651e7	−	1.62458e8i	−0.0246408	−	0.128037i
$400$	−2.08486e8			−0.162880
$401$	4.31222e8	+	7.46898e8i	0.333961	+	0.578437i	0.983285	−	0.182075i	$-0.0582814\pi$
$401$	4.31222e8	+	7.46898e8i	0.333961	+	0.578437i	−0.649324	+	0.760512i	$0.724948\pi$
$402$	−3.52956e8	+	6.11338e8i	−0.270975	+	0.469343i
$403$	2.00623e8	−	3.47489e8i	0.152691	−	0.264468i
$404$	−3.40323e8	−	5.89457e8i	−0.256777	−	0.444751i
$405$	8.76878e7			0.0655913
$406$	−6.49258e8	+	5.62274e8i	−0.481478	+	0.416972i
$407$	−6.40609e8			−0.470991
$408$	−1.08574e8	−	1.88055e8i	−0.0791433	−	0.137080i
$409$	−2.23578e8	+	3.87248e8i	−0.161584	+	0.279871i	−0.935437	−	0.353494i	$-0.884993\pi$
$409$	−2.23578e8	+	3.87248e8i	−0.161584	+	0.279871i	0.773853	+	0.633365i	$0.218327\pi$
$410$	−3.24324e8	+	5.61746e8i	−0.232400	+	0.402528i
$411$	4.92862e8	+	8.53662e8i	0.350170	+	0.606513i
$412$	−7.26614e8			−0.511874
$413$	−1.43270e8	−	4.96303e7i	−0.100076	−	0.0346674i
$414$	−1.79789e8			−0.124526
$415$	−3.60187e8	−	6.23863e8i	−0.247378	−	0.428470i
$416$	4.45645e7	−	7.71879e7i	0.0303502	−	0.0525682i
$417$	−6.09766e8	+	1.05615e9i	−0.411800	+	0.713259i
$418$	−5.55014e7	−	9.61313e7i	−0.0371695	−	0.0643795i
$419$	3.22182e8			0.213970			0.106985	−	0.994261i	$-0.465880\pi$
$419$	3.22182e8			0.213970			0.106985	+	0.994261i	$0.465880\pi$
$420$	2.44490e8	+	8.46940e7i	0.161024	+	0.0557802i
$421$	6.51038e8			0.425225			0.212613	−	0.977137i	$-0.431803\pi$
$421$	6.51038e8			0.425225			0.212613	+	0.977137i	$0.431803\pi$
$422$	3.57765e8	+	6.19667e8i	0.231742	+	0.401389i
$423$	3.11597e8	−	5.39702e8i	0.200172	−	0.346707i
$424$	2.98722e8	−	5.17402e8i	0.190321	−	0.329646i
$425$	−3.99769e8	−	6.92420e8i	−0.252608	−	0.437530i
$426$	−6.58118e8			−0.412449
$427$	−7.04710e8	+	6.10297e8i	−0.438039	+	0.379353i
$428$	−8.95724e7			−0.0552231
$429$	7.54596e7	+	1.30700e8i	0.0461439	+	0.0799235i
$430$	−3.80935e8	+	6.59798e8i	−0.231053	+	0.400195i
$431$	−1.49813e9	+	2.59484e9i	−0.901322	+	1.56114i	−0.0755420	+	0.997143i	$0.524069\pi$
$431$	−1.49813e9	+	2.59484e9i	−0.901322	+	1.56114i	−0.825780	+	0.563993i	$0.809265\pi$
$432$	−4.03108e7	−	6.98203e7i	−0.0240563	−	0.0416667i
$433$	4.59956e8			0.272275			0.136138	−	0.990690i	$-0.456531\pi$
$433$	4.59956e8			0.272275			0.136138	+	0.990690i	$0.456531\pi$
$434$	−2.02393e8	−	1.05167e9i	−0.118845	−	0.617538i
$435$	−5.27049e8			−0.307000
$436$	−6.19105e7	−	1.07232e8i	−0.0357735	−	0.0619615i
$437$	−1.04075e8	+	1.80264e8i	−0.0596572	+	0.103329i
$438$	−3.46584e8	+	6.00301e8i	−0.197083	+	0.341358i
$439$	−1.72768e9	−	2.99243e9i	−0.974624	−	1.68810i	−0.681170	−	0.732125i	$-0.738529\pi$
$439$	−1.72768e9	−	2.99243e9i	−0.974624	−	1.68810i	−0.293454	−	0.955973i	$-0.594805\pi$
$440$	1.73606e8			0.0971586
$441$	4.71714e8	+	3.71378e8i	0.261905	+	0.206197i
$442$	3.41806e8			0.188279
$443$	1.39501e9	+	2.41623e9i	0.762367	+	1.32046i	0.941627	+	0.336657i	$0.109296\pi$
$443$	1.39501e9	+	2.41623e9i	0.762367	+	1.32046i	−0.179260	+	0.983802i	$0.557370\pi$
$444$	−2.69336e8	+	4.66504e8i	−0.146034	+	0.252939i
$445$	9.89688e8	−	1.71419e9i	0.532400	−	0.922144i
$446$	6.40544e8	+	1.10945e9i	0.341883	+	0.592158i
$447$	−6.04682e8			−0.320222
$448$	−4.49577e7	−	2.33607e8i	−0.0236228	−	0.122748i
$449$	−3.29958e9			−1.72027			−0.860134	−	0.510068i	$-0.829620\pi$
$449$	−3.29958e9			−1.72027			−0.860134	+	0.510068i	$0.829620\pi$
$450$	−1.48424e8	−	2.57079e8i	−0.0767824	−	0.132991i
$451$	−5.04914e8	+	8.74536e8i	−0.259179	+	0.448910i
$452$	8.44349e8	−	1.46246e9i	0.430068	−	0.744900i
$453$	1.06642e9	+	1.84709e9i	0.538994	+	0.933566i
$454$	1.74198e9			0.873669
$455$	−3.07877e8	+	2.66629e8i	−0.153228	+	0.132699i
$456$	−9.33396e7			−0.0460988
$457$	3.89405e8	+	6.74470e8i	0.190851	+	0.330564i	0.945533	−	0.325527i	$-0.105542\pi$
$457$	3.89405e8	+	6.74470e8i	0.190851	+	0.330564i	−0.754681	+	0.656092i	$0.772208\pi$
$458$	6.36235e8	−	1.10199e9i	0.309449	−	0.535981i
$459$	1.54590e8	−	2.67758e8i	0.0746170	−	0.129240i
$460$	−1.62772e8	−	2.81929e8i	−0.0779699	−	0.135048i
$461$	3.58706e9			1.70524			0.852619	−	0.522533i	$-0.175013\pi$
$461$	3.58706e9			1.70524			0.852619	+	0.522533i	$0.175013\pi$
$462$	3.80627e8	+	1.31853e8i	0.179578	+	0.0622076i
$463$	4.82745e8			0.226040			0.113020	−	0.993593i	$-0.463948\pi$
$463$	4.82745e8			0.226040			0.113020	+	0.993593i	$0.463948\pi$
$464$	2.42289e8	+	4.19656e8i	0.112595	+	0.195021i
$465$	3.28594e8	−	5.69142e8i	0.151556	−	0.262503i
$466$	3.79017e7	−	6.56477e7i	0.0173503	−	0.0300517i
$467$	1.83154e9	+	3.17232e9i	0.832161	+	1.44135i	0.896321	+	0.443406i	$0.146230\pi$
$467$	1.83154e9	+	3.17232e9i	0.832161	+	1.44135i	−0.0641595	+	0.997940i	$0.520437\pi$
$468$	1.26904e8			0.0572290
$469$	−2.80241e9	−	9.70783e8i	−1.25437	−	0.434527i
$470$	1.12842e9			0.501334
$471$	−8.42693e8	−	1.45959e9i	−0.371617	−	0.643660i
$472$	−4.27722e7	+	7.40837e7i	−0.0187225	+	0.0324284i
$473$	−5.93046e8	+	1.02719e9i	−0.257676	+	0.446309i
$474$	7.69823e8	+	1.33337e9i	0.332022	+	0.575078i
$475$	−3.43677e8			−0.147137
$476$	6.89644e8	−	5.97249e8i	0.293090	−	0.253823i
$477$	8.50658e8			0.358873
$478$	3.05565e8	+	5.29254e8i	0.127969	+	0.221649i
$479$	1.26969e9	−	2.19917e9i	0.527866	−	0.914290i	−0.471607	−	0.881809i	$-0.656326\pi$
$479$	1.26969e9	−	2.19917e9i	0.527866	−	0.914290i	0.999472	−	0.0324812i	$-0.0103409\pi$
$480$	7.29907e7	−	1.26424e8i	0.0301247	−	0.0521776i
$481$	−4.23956e8	−	7.34313e8i	−0.173705	−	0.300866i
$482$	1.82892e9			0.743925
$483$	−1.42749e8	−	7.41746e8i	−0.0576446	−	0.299530i
$484$	−9.76905e8			−0.391646
$485$	−1.10085e9	−	1.90673e9i	−0.438159	−	0.758914i
$486$	5.73956e7	−	9.94121e7i	0.0226805	−	0.0392837i
$487$	1.63342e9	−	2.82917e9i	0.640836	−	1.10996i	−0.344410	−	0.938819i	$-0.611921\pi$
$487$	1.63342e9	−	2.82917e9i	0.640836	−	1.10996i	0.985246	−	0.171142i	$-0.0547456\pi$
$488$	2.62982e8	+	4.55498e8i	0.102437	+	0.177426i
$489$	−4.96804e8			−0.192134
$490$	−1.55297e8	+	1.07593e9i	−0.0596315	+	0.413139i
$491$	−1.62704e9			−0.620318			−0.310159	−	0.950685i	$-0.600382\pi$
$491$	−1.62704e9			−0.620318			−0.310159	+	0.950685i	$0.600382\pi$
$492$	4.24570e8	+	7.35376e8i	0.160720	+	0.278376i
$493$	−9.29167e8	+	1.60937e9i	−0.349245	+	0.604910i
$494$	7.34618e7	−	1.27240e8i	0.0274168	−	0.0474873i
$495$	1.23593e8	+	2.14069e8i	0.0458010	+	0.0793297i
$496$	−6.04230e8			−0.222339
$497$	−5.22533e8	−	2.71516e9i	−0.190927	−	0.992084i
$498$	−9.43036e8			−0.342157
$499$	−1.88131e9	−	3.25852e9i	−0.677810	−	1.17400i	−0.975639	−	0.219383i	$-0.929596\pi$
$499$	−1.88131e9	−	3.25852e9i	−0.677810	−	1.17400i	0.297828	−	0.954619i	$-0.403738\pi$
$500$	6.81252e8	−	1.17996e9i	0.243732	−	0.422156i
$501$	5.82931e8	−	1.00967e9i	0.207102	−	0.358712i
$502$	4.52772e8	+	7.84225e8i	0.159741	+	0.276680i
$503$	1.26437e8			0.0442984			0.0221492	−	0.999755i	$-0.492949\pi$
$503$	1.26437e8			0.0442984			0.0221492	+	0.999755i	$0.492949\pi$
$504$	2.56048e8	−	2.21744e8i	0.0890871	−	0.0771517i
$505$	1.75479e9			0.606325
$506$	−2.53406e8	−	4.38912e8i	−0.0869542	−	0.150609i
$507$	7.47227e8	−	1.29423e9i	0.254639	−	0.441047i
$508$	5.91959e8	−	1.02530e9i	0.200341	−	0.347000i
$509$	−1.14378e9	−	1.98109e9i	−0.384443	−	0.665875i	0.607249	−	0.794512i	$-0.292273\pi$
$509$	−1.14378e9	−	1.98109e9i	−0.384443	−	0.665875i	−0.991692	+	0.128637i	$0.958940\pi$
$510$	5.59833e8			0.186880
$511$	−2.75181e9	−	9.53256e8i	−0.912317	−	0.316036i
$512$	−1.34218e8			−0.0441942
$513$	−6.64498e7	−	1.15094e8i	−0.0217312	−	0.0376395i
$514$	6.21626e8	−	1.07669e9i	0.201910	−	0.349718i
$515$	9.36650e8	−	1.62233e9i	0.302171	−	0.523375i
$516$	4.98678e8	+	8.63736e8i	0.159789	+	0.276762i
$517$	1.75674e9			0.559102
$518$	−2.13848e9	−	7.40792e8i	−0.676007	−	0.234176i
$519$	−2.30802e9			−0.724692
$520$	1.14893e8	+	1.99000e8i	0.0358328	+	0.0620643i
$521$	−2.73830e9	+	4.74288e9i	−0.848299	+	1.46930i	0.0344257	+	0.999407i	$0.489040\pi$
$521$	−2.73830e9	+	4.74288e9i	−0.848299	+	1.46930i	−0.882725	+	0.469890i	$0.844294\pi$
$522$	−3.44977e8	+	5.97518e8i	−0.106156	+	0.183867i
$523$	2.46514e9	+	4.26975e9i	0.753505	+	1.30511i	0.946114	+	0.323833i	$0.104972\pi$
$523$	2.46514e9	+	4.26975e9i	0.753505	+	1.30511i	−0.192609	+	0.981276i	$0.561695\pi$
$524$	−2.38624e8			−0.0724527
$525$	9.42770e8	−	8.16463e8i	0.284347	−	0.246251i
$526$	6.46065e8			0.193565
$527$	−1.15860e9	−	2.00675e9i	−0.344823	−	0.597250i
$528$	1.13633e8	−	1.96819e8i	0.0335959	−	0.0581899i
$529$	1.22723e9	−	2.12562e9i	0.360438	−	0.624298i
$530$	7.70143e8	+	1.33393e9i	0.224701	+	0.389194i
$531$	−1.21801e8			−0.0353036
$532$	−7.41100e7	−	3.85087e8i	−0.0213396	−	0.110884i
$533$	−1.33661e9			−0.382348
$534$	−1.29559e9	−	2.24403e9i	−0.368191	−	0.637726i
$535$	1.15464e8	−	1.99990e8i	0.0325994	−	0.0564639i
$536$	−8.36637e8	+	1.44910e9i	−0.234672	+	0.406463i
$537$	1.73821e9	+	3.01067e9i	0.484388	+	0.838984i
$538$	2.18407e9			0.604685
$539$	−2.41769e8	+	1.67502e9i	−0.0665027	+	0.460744i
$540$	2.07852e8			0.0568038
$541$	2.99276e9	+	5.18362e9i	0.812610	+	1.40748i	0.911032	+	0.412337i	$0.135287\pi$
$541$	2.99276e9	+	5.18362e9i	0.812610	+	1.40748i	−0.0984219	+	0.995145i	$0.531379\pi$
$542$	2.32840e9	−	4.03290e9i	0.628144	−	1.08798i
$543$	1.46099e8	−	2.53050e8i	0.0391604	−	0.0678277i
$544$	−2.57360e8	−	4.45760e8i	−0.0685401	−	0.118715i
$545$	3.19226e8			0.0844715
$546$	1.00760e8	+	5.23563e8i	0.0264919	+	0.137656i
$547$	6.64499e9			1.73596			0.867978	−	0.496603i	$-0.165419\pi$
$547$	6.64499e9			1.73596			0.867978	+	0.496603i	$0.165419\pi$
$548$	1.16827e9	+	2.02350e9i	0.303256	+	0.525255i
$549$	−3.74441e8	+	6.48551e8i	−0.0965785	+	0.167279i
$550$	4.18398e8	−	7.24687e8i	0.107231	−	0.185729i
$551$	3.99398e8	+	6.91777e8i	0.101713	+	0.176171i
$552$	−4.26166e8			−0.107843
$553$	−4.88980e9	+	4.23469e9i	−1.22957	+	1.06484i
$554$	−4.67389e9			−1.16787
$555$	−6.94383e8	−	1.20271e9i	−0.172414	−	0.298631i
$556$	−1.44537e9	+	2.50346e9i	−0.356630	+	0.617701i
$557$	−2.48158e8	+	4.29822e8i	−0.0608465	+	0.105389i	−0.894844	−	0.446379i	$-0.852713\pi$
$557$	−2.48158e8	+	4.29822e8i	−0.0608465	+	0.105389i	0.833998	+	0.551768i	$0.186047\pi$
$558$	−4.30160e8	−	7.45058e8i	−0.104812	−	0.181539i
$559$	−1.56991e9			−0.380132
$560$	5.79533e8	+	2.00756e8i	0.139450	+	0.0483071i
$561$	8.71558e8			0.208414
$562$	1.72130e7	+	2.98137e7i	0.00409052	+	0.00708499i
$563$	−3.23848e9	+	5.60922e9i	−0.764826	+	1.32472i	0.175513	+	0.984477i	$0.443842\pi$
$563$	−3.23848e9	+	5.60922e9i	−0.764826	+	1.32472i	−0.940339	+	0.340240i	$0.889492\pi$
$564$	7.38601e8	−	1.27929e9i	0.173354	−	0.300257i
$565$	2.17684e9	+	3.77039e9i	0.507758	+	0.879462i
$566$	−3.04946e9			−0.706912
$567$	4.55711e8	+	1.57863e8i	0.104990	+	0.0363696i
$568$	−1.55998e9			−0.357191
$569$	−3.53796e9	−	6.12793e9i	−0.805119	−	1.39451i	−0.916211	−	0.400696i	$-0.868768\pi$
$569$	−3.53796e9	−	6.12793e9i	−0.805119	−	1.39451i	0.111092	−	0.993810i	$-0.464565\pi$
$570$	1.20321e8	−	2.08401e8i	0.0272131	−	0.0471345i
$571$	2.15407e8	−	3.73096e8i	0.0484210	−	0.0838676i	−0.840799	−	0.541347i	$-0.817914\pi$
$571$	2.15407e8	−	3.73096e8i	0.0484210	−	0.0838676i	0.889220	+	0.457480i	$0.151248\pi$
$572$	1.78867e8	+	3.09807e8i	0.0399618	+	0.0692158i
$573$	−1.24761e9			−0.277038
$574$	−2.69680e9	+	2.33550e9i	−0.595193	+	0.515452i
$575$	−1.56915e9			−0.344212
$576$	−9.55515e7	−	1.65500e8i	−0.0208333	−	0.0360844i
$577$	−2.84140e9	+	4.92144e9i	−0.615767	+	1.06654i	0.374482	+	0.927234i	$0.377820\pi$
$577$	−2.84140e9	+	4.92144e9i	−0.615767	+	1.06654i	−0.990249	+	0.139306i	$0.955513\pi$
$578$	−6.54390e8	+	1.13344e9i	−0.140958	+	0.244146i
$579$	−4.52178e8	−	7.83195e8i	−0.0968131	−	0.167685i
$580$	−1.24930e9			−0.265870
$581$	−7.48753e8	−	3.89064e9i	−0.158388	−	0.823008i
$582$	−2.88223e9			−0.606035
$583$	1.19897e9	+	2.07668e9i	0.250593	+	0.434040i
$584$	−8.21532e8	+	1.42294e9i	−0.170679	+	0.295624i
$585$	−1.63588e8	+	2.83342e8i	−0.0337835	+	0.0585148i
$586$	−2.10756e8	−	3.65040e8i	−0.0432652	−	0.0749375i
$587$	8.04091e9			1.64086			0.820430	−	0.571747i	$-0.193734\pi$
$587$	8.04091e9			1.64086			0.820430	+	0.571747i	$0.193734\pi$
$588$	1.11814e9	+	8.80304e8i	0.226816	+	0.178571i
$589$	−9.96035e8			−0.200850
$590$	−1.10272e8	−	1.90997e8i	−0.0221047	−	0.0382864i
$591$	1.81887e9	−	3.15038e9i	0.362448	−	0.627778i
$592$	−6.38427e8	+	1.10579e9i	−0.126469	+	0.219051i
$593$	2.86879e9	+	4.96889e9i	0.564947	+	0.978516i	0.997055	+	0.0766944i	$0.0244366\pi$
$593$	2.86879e9	+	4.96889e9i	0.564947	+	0.978516i	−0.432108	+	0.901822i	$0.642230\pi$
$594$	3.23589e8			0.0633491
$595$	4.44497e8	+	2.30967e9i	0.0865087	+	0.449512i
$596$	−1.43332e9			−0.277320
$597$	1.06182e9	+	1.83913e9i	0.204240	+	0.353755i
$598$	3.35409e8	−	5.80945e8i	0.0641387	−	0.111091i
$599$	2.64100e9	−	4.57434e9i	0.502081	−	0.869630i	−0.497916	−	0.867225i	$-0.665901\pi$
$599$	2.64100e9	−	4.57434e9i	0.502081	−	0.869630i	0.999997	−	0.00240467i	$-0.000765431\pi$
$600$	−3.51821e8	−	6.09372e8i	−0.0664955	−	0.115174i
$601$	2.13403e9			0.400997			0.200498	−	0.979694i	$-0.435744\pi$
$601$	2.13403e9			0.400997			0.200498	+	0.979694i	$0.435744\pi$
$602$	−3.16753e9	+	2.74316e9i	−0.591743	+	0.512464i
$603$	−2.38246e9			−0.442501
$604$	2.52781e9	+	4.37829e9i	0.466783	+	0.808492i
$605$	1.25929e9	−	2.18116e9i	0.231197	−	0.400445i
$606$	1.14859e9	−	1.98942e9i	0.209658	−	0.363138i
$607$	−3.29681e9	−	5.71025e9i	−0.598321	−	1.03632i	−0.993069	−	0.117532i	$-0.962502\pi$
$607$	−3.29681e9	−	5.71025e9i	−0.598321	−	1.03632i	0.394749	−	0.918789i	$-0.370832\pi$
$608$	−2.21250e8			−0.0399227
$609$	−2.73906e9	−	9.48837e8i	−0.491406	−	0.170228i
$610$	−1.35600e9			−0.241883
$611$	1.16261e9	+	2.01370e9i	0.206201	+	0.357151i
$612$	3.66436e8	−	6.34686e8i	0.0646202	−	0.111926i
$613$	−1.47304e9	+	2.55137e9i	−0.258287	+	0.447366i	−0.965783	−	0.259351i	$-0.916491\pi$
$613$	−1.47304e9	+	2.55137e9i	−0.258287	+	0.447366i	0.707496	+	0.706717i	$0.249825\pi$
$614$	−1.87044e9	−	3.23970e9i	−0.326103	−	0.564827i
$615$	−2.18919e9			−0.379507
$616$	9.02227e8	+	3.12541e8i	0.155519	+	0.0538734i
$617$	2.45529e9			0.420828			0.210414	−	0.977612i	$-0.432519\pi$
$617$	2.45529e9			0.420828			0.210414	+	0.977612i	$0.432519\pi$
$618$	−1.22616e9	−	2.12377e9i	−0.208972	−	0.361950i
$619$	1.62017e9	−	2.80622e9i	0.274564	−	0.475559i	−0.695461	−	0.718564i	$-0.744800\pi$
$619$	1.62017e9	−	2.80622e9i	0.274564	−	0.475559i	0.970025	+	0.243005i	$0.0781331\pi$
$620$	7.78890e8	−	1.34908e9i	0.131252	−	0.227335i
$621$	−3.03394e8	−	5.25493e8i	−0.0508377	−	0.0880535i
$622$	1.21857e9			0.203042
$623$	8.22940e9	−	7.12687e9i	1.36352	−	1.18084i
$624$	3.00810e8			0.0495617
$625$	−2.31928e8	−	4.01712e8i	−0.0379992	−	0.0658165i
$626$	7.89867e8	−	1.36809e9i	0.128690	−	0.222897i
$627$	1.87317e8	−	3.24443e8i	0.0303488	−	0.0525657i
$628$	−1.99749e9	−	3.45976e9i	−0.321830	−	0.557426i
$629$	−4.89669e9			−0.784558
$630$	1.65031e8	+	8.57526e8i	0.0262950	+	0.136633i
$631$	6.13521e9			0.972135			0.486067	−	0.873921i	$-0.338431\pi$
$631$	6.13521e9			0.972135			0.486067	+	0.873921i	$0.338431\pi$
$632$	1.82476e9	+	3.16059e9i	0.287539	+	0.498033i
$633$	−1.20746e9	+	2.09138e9i	−0.189216	+	0.327732i
$634$	3.26270e9	−	5.65116e9i	0.508469	−	0.880694i
$635$	1.52614e9	+	2.64336e9i	0.236531	+	0.409683i
$636$	2.01637e9			0.310793
$637$	−2.08003e9	+	8.31398e8i	−0.318847	+	0.127444i
$638$	−1.94493e9			−0.296505
$639$	−1.11057e9	−	1.92357e9i	−0.168382	−	0.291645i
$640$	1.73015e8	−	2.99671e8i	0.0260888	−	0.0451871i
$641$	5.33639e9	−	9.24290e9i	0.800285	−	1.38613i	−0.119144	−	0.992877i	$-0.538015\pi$
$641$	5.33639e9	−	9.24290e9i	0.800285	−	1.38613i	0.919429	−	0.393257i	$-0.128652\pi$
$642$	−1.51153e8	−	2.61805e8i	−0.0225448	−	0.0390487i
$643$	−1.43004e9			−0.212133			−0.106067	−	0.994359i	$-0.533826\pi$
$643$	−1.43004e9			−0.212133			−0.106067	+	0.994359i	$0.533826\pi$
$644$	−3.38368e8	−	1.75821e9i	−0.0499216	−	0.259400i
$645$	−2.57131e9			−0.377308
$646$	−4.24242e8	−	7.34808e8i	−0.0619155	−	0.107241i
$647$	1.36120e9	−	2.35766e9i	0.197586	−	0.342229i	−0.750159	−	0.661257i	$-0.770023\pi$
$647$	1.36120e9	−	2.35766e9i	0.197586	−	0.342229i	0.947745	+	0.319028i	$0.103357\pi$
$648$	1.36049e8	−	2.35644e8i	0.0196419	−	0.0340207i
$649$	−1.71674e8	−	2.97348e8i	−0.0246517	−	0.0426980i
$650$	1.10758e9			0.158190
$651$	2.73231e9	−	2.36625e9i	0.388147	−	0.336145i
$652$	−1.17761e9			−0.166393
$653$	−3.86201e8	−	6.68920e8i	−0.0542772	−	0.0940108i	0.837610	−	0.546268i	$-0.183952\pi$
$653$	−3.86201e8	−	6.68920e8i	−0.0542772	−	0.0940108i	−0.891887	+	0.452258i	$0.850619\pi$
$654$	2.08948e8	−	3.61908e8i	0.0292089	−	0.0505914i
$655$	3.07601e8	−	5.32781e8i	0.0427704	−	0.0740805i
$656$	1.00639e9	+	1.74311e9i	0.139188	+	0.241081i
$657$	−2.33944e9			−0.321835
$658$	5.86435e9	+	2.03147e9i	0.802471	+	0.277984i
$659$	6.83410e9			0.930213			0.465107	−	0.885255i	$-0.346016\pi$
$659$	6.83410e9			0.930213			0.465107	+	0.885255i	$0.346016\pi$
$660$	2.92961e8	+	5.07423e8i	0.0396648	+	0.0687015i
$661$	−2.15728e8	+	3.73651e8i	−0.0290536	+	0.0503224i	−0.880187	−	0.474628i	$-0.842583\pi$
$661$	−2.15728e8	+	3.73651e8i	−0.0290536	+	0.0503224i	0.851133	+	0.524950i	$0.175916\pi$
$662$	−2.98712e9	+	5.17385e9i	−0.400175	+	0.693124i
$663$	5.76798e8	+	9.99043e8i	0.0768646	+	0.133133i
$664$	−2.23535e9			−0.296317
$665$	9.55324e8	+	3.30934e8i	0.125972	+	0.0436381i
$666$	−1.81802e9			−0.238473
$667$	1.82355e9	+	3.15849e9i	0.237946	+	0.412134i
$668$	1.38176e9	−	2.39328e9i	0.179356	−	0.310653i
$669$	−2.16184e9	+	3.74441e9i	−0.279146	+	0.483495i
$670$	−2.15696e9	−	3.73596e9i	−0.277064	−	0.479888i
$671$	−2.11105e9			−0.269755
$672$	6.06929e8	−	5.25616e8i	0.0771517	−	0.0668153i
$673$	3.88077e7			0.00490755			0.00245378	−	0.999997i	$-0.499219\pi$
$673$	3.88077e7			0.00490755			0.00245378	+	0.999997i	$0.499219\pi$
$674$	2.22322e9	+	3.85073e9i	0.279687	+	0.484432i
$675$	5.00932e8	−	8.67640e8i	0.0626925	−	0.108587i
$676$	1.77120e9	−	3.06781e9i	0.220524	−	0.381958i
$677$	−1.07723e9	−	1.86582e9i	−0.133428	−	0.231105i	0.791568	−	0.611082i	$-0.209265\pi$
$677$	−1.07723e9	−	1.86582e9i	−0.133428	−	0.231105i	−0.924996	+	0.379977i	$0.875932\pi$
$678$	5.69936e9			0.702299
$679$	−2.28843e9	−	1.18911e10i	−0.280540	−	1.45773i
$680$	1.32701e9			0.161843
$681$	2.93959e9	+	5.09151e9i	0.356674	+	0.617778i
$682$	1.21259e9	−	2.10027e9i	0.146376	−	0.253530i
$683$	−6.86330e9	+	1.18876e10i	−0.824253	+	1.42765i	0.0782350	+	0.996935i	$0.475072\pi$
$683$	−6.86330e9	+	1.18876e10i	−0.824253	+	1.42765i	−0.902489	+	0.430714i	$0.858262\pi$
$684$	−1.57511e8	−	2.72816e8i	−0.0188197	−	0.0325967i
$685$	−6.02387e9			−0.716075
$686$	−2.74405e9	+	5.31198e9i	−0.324532	+	0.628235i
$687$	4.29459e9			0.505328
$688$	1.18205e9	+	2.04737e9i	0.138381	+	0.239683i
$689$	−1.58696e9	+	2.74870e9i	−0.184841	+	0.320154i
$690$	5.49355e8	−	9.51511e8i	0.0636621	−	0.110266i
$691$	−2.12534e9	−	3.68119e9i	−0.245050	−	0.424439i	0.717096	−	0.696975i	$-0.245471\pi$
$691$	−2.12534e9	−	3.68119e9i	−0.245050	−	0.424439i	−0.962146	+	0.272536i	$0.912138\pi$
$692$	−5.47086e9			−0.627601
$693$	2.56923e8	+	1.33501e9i	0.0293249	+	0.152377i
$694$	−5.81360e9			−0.660217
$695$	−3.72635e9	−	6.45422e9i	−0.421053	−	0.729285i
$696$	−8.17724e8	+	1.41634e9i	−0.0919336	+	0.159234i
$697$	−3.85946e9	+	6.68477e9i	−0.431729	+	0.747777i
$698$	1.86354e9	+	3.22774e9i	0.207417	+	0.359257i
$699$	2.55837e8			0.0283330
$700$	2.23471e9	−	1.93532e9i	0.246251	−	0.213260i
$701$	−2.59521e9			−0.284550			−0.142275	−	0.989827i	$-0.545442\pi$
$701$	−2.59521e9			−0.284550			−0.142275	+	0.989827i	$0.545442\pi$
$702$	2.14151e8	+	3.70920e8i	0.0233636	+	0.0404670i
$703$	−1.05241e9	+	1.82282e9i	−0.114246	+	0.197880i
$704$	2.69353e8	−	4.66533e8i	0.0290949	−	0.0503939i
$705$	1.90421e9	+	3.29818e9i	0.204669	+	0.354497i
$706$	1.23804e10			1.32409
$707$	9.11959e9	+	3.15912e9i	0.970526	+	0.336200i
$708$	−2.88713e8			−0.0305738
$709$	−1.97756e8	−	3.42524e8i	−0.0208386	−	0.0360935i	0.855418	−	0.517938i	$-0.173300\pi$
$709$	−1.97756e8	−	3.42524e8i	−0.0208386	−	0.0360935i	−0.876257	+	0.481845i	$0.839967\pi$
$710$	2.01092e9	−	3.48301e9i	0.210858	−	0.365216i
$711$	−2.59815e9	+	4.50013e9i	−0.271095	+	0.469550i
$712$	−3.07103e9	−	5.31918e9i	−0.318863	−	0.552287i
$713$	−4.54765e9			−0.469866
$714$	2.90944e9	+	1.00786e9i	0.299133	+	0.103623i
$715$	−9.22284e8			−0.0943612
$716$	4.12021e9	+	7.13641e9i	0.419492	+	0.726581i
$717$	−1.03128e9	+	1.78623e9i	−0.104486	+	0.180976i
$718$	6.39426e7	−	1.10752e8i	0.00644696	−	0.0111665i
$719$	−4.45139e9	−	7.71004e9i	−0.446627	−	0.773581i	0.551537	−	0.834150i	$-0.314042\pi$
$719$	−4.45139e9	−	7.71004e9i	−0.446627	−	0.773581i	−0.998164	+	0.0605698i	$0.980708\pi$
$720$	4.92687e8			0.0491935
$721$	7.78839e9	−	6.74494e9i	0.773881	−	0.670201i
$722$	6.78626e9			0.671043
$723$	3.08630e9	+	5.34562e9i	0.303706	+	0.526035i
$724$	3.46308e8	−	5.99823e8i	0.0339139	−	0.0587405i
$725$	−3.01086e9	+	5.21497e9i	−0.293432	+	0.508240i
$726$	−1.64853e9	−	2.85533e9i	−0.159889	−	0.276936i
$727$	−9.81918e9			−0.947774			−0.473887	−	0.880586i	$-0.657150\pi$
$727$	−9.81918e9			−0.947774			−0.473887	+	0.880586i	$0.657150\pi$
$728$	2.38838e8	+	1.24104e9i	0.0229426	+	0.119213i
$729$	3.87420e8			0.0370370
$730$	−2.11801e9	−	3.66851e9i	−0.201511	−	0.349027i
$731$	−4.53312e9	+	7.85160e9i	−0.429227	+	0.743443i
$732$	−8.87565e8	+	1.53731e9i	−0.0836395	+	0.144868i
$733$	1.14693e8	+	1.98654e8i	0.0107566	+	0.0186309i	0.871354	−	0.490656i	$-0.163243\pi$
$733$	1.14693e8	+	1.98654e8i	0.0107566	+	0.0186309i	−0.860597	+	0.509287i	$0.829909\pi$
$734$	−7.29732e8			−0.0681126
$735$	−3.40682e9	+	1.36172e9i	−0.316478	+	0.126498i
$736$	−1.01017e9			−0.0933949
$737$	−3.35799e9	−	5.81620e9i	−0.308989	−	0.535184i
$738$	−1.43292e9	+	2.48189e9i	−0.131228	+	0.227293i
$739$	−7.12423e9	+	1.23395e10i	−0.649356	+	1.12472i	0.333921	+	0.942601i	$0.391628\pi$
$739$	−7.12423e9	+	1.23395e10i	−0.649356	+	1.12472i	−0.983277	+	0.182116i	$0.941705\pi$
$740$	−1.64594e9	−	2.85086e9i	−0.149315	−	0.258622i
$741$	4.95867e8			0.0447715
$742$	1.60096e9	+	8.31885e9i	0.143869	+	0.747566i
$743$	1.83025e9			0.163700			0.0818502	−	0.996645i	$-0.473917\pi$
$743$	1.83025e9			0.163700			0.0818502	+	0.996645i	$0.473917\pi$
$744$	−1.01964e9	−	1.76606e9i	−0.0907696	−	0.157218i
$745$	1.84764e9	−	3.20021e9i	0.163708	−	0.283551i
$746$	−5.51881e9	+	9.55885e9i	−0.486698	+	0.842985i
$747$	−1.59137e9	−	2.75634e9i	−0.139685	−	0.241942i
$748$	2.06592e9			0.180492
$749$	9.60104e8	−	8.31475e8i	0.0834895	−	0.0723041i
$750$	4.59845e9			0.398013
$751$	−1.06585e10	−	1.84611e10i	−0.918242	−	1.59044i	−0.802084	−	0.597212i	$-0.796275\pi$
$751$	−1.06585e10	−	1.84611e10i	−0.918242	−	1.59044i	−0.116159	−	0.993231i	$-0.537058\pi$
$752$	1.75076e9	−	3.03240e9i	0.150129	−	0.260030i
$753$	−1.52811e9	+	2.64676e9i	−0.130428	+	0.225908i
$754$	−1.28716e9	−	2.22942e9i	−0.109353	−	0.189406i
$755$	−1.30340e10			−1.10221
$756$	1.08020e9	+	3.74193e8i	0.0909241	+	0.0314970i
$757$	−2.31635e9			−0.194075			−0.0970373	−	0.995281i	$-0.530937\pi$
$757$	−2.31635e9			−0.194075			−0.0970373	+	0.995281i	$0.530937\pi$
$758$	2.51283e9	+	4.35235e9i	0.209566	+	0.362979i
$759$	8.55246e8	−	1.48133e9i	0.0709978	−	0.122972i
$760$	2.85204e8	−	4.93989e8i	0.0235672	−	0.0408197i
$761$	7.20962e8	+	1.24874e9i	0.0593015	+	0.102713i	0.894152	−	0.447763i	$-0.147779\pi$
$761$	7.20962e8	+	1.24874e9i	0.0593015	+	0.102713i	−0.834851	+	0.550477i	$0.814446\pi$
$762$	3.99573e9			0.327155
$763$	1.65901e9	+	5.74697e8i	0.135211	+	0.0468385i
$764$	−2.95731e9			−0.239922
$765$	9.44718e8	+	1.63630e9i	0.0762935	+	0.132144i
$766$	−3.94598e9	+	6.83463e9i	−0.317215	+	0.549433i
$767$	2.27227e8	−	3.93569e8i	0.0181835	−	0.0314947i
$768$	−2.26492e8	−	3.92296e8i	−0.0180422	−	0.0312500i
$769$	−6.48046e8			−0.0513882			−0.0256941	−	0.999670i	$-0.508180\pi$
$769$	−6.48046e8			−0.0513882			−0.0256941	+	0.999670i	$0.508180\pi$
$770$	−1.86084e9	+	1.61154e9i	−0.146890	+	0.127211i
$771$	4.19597e9			0.329718
$772$	−1.07183e9	−	1.85646e9i	−0.0838426	−	0.145220i
$773$	−5.31902e9	+	9.21282e9i	−0.414194	+	0.717405i	−0.995343	−	0.0963919i	$-0.969270\pi$
$773$	−5.31902e9	+	9.21282e9i	−0.414194	+	0.717405i	0.581150	+	0.813797i	$0.302603\pi$
$774$	−1.68304e9	+	2.91511e9i	−0.130467	+	0.225976i
$775$	−3.75431e9	−	6.50265e9i	−0.289717	−	0.501804i
$776$	−6.83194e9			−0.524842
$777$	−1.44348e9	−	7.50052e9i	−0.110392	−	0.573611i
$778$	7.08261e9			0.539218
$779$	1.65897e9	+	2.87341e9i	0.125735	+	0.217780i
$780$	−3.87763e8	+	6.71626e8i	−0.0292574	+	0.0506753i
$781$	3.13063e9	−	5.42241e9i	0.235154	−	0.407299i
$782$	−1.93698e9	−	3.35496e9i	−0.144845	−	0.250878i
$783$	−2.32860e9			−0.173352
$784$	2.65040e9	+	2.08665e9i	0.196429	+	0.154647i
$785$	1.02996e10			0.759934
$786$	−4.02678e8	−	6.97459e8i	−0.0295787	−	0.0512318i
$787$	−1.08062e9	+	1.87169e9i	−0.0790246	+	0.136875i	−0.902829	−	0.429999i	$-0.858514\pi$
$787$	−1.08062e9	+	1.87169e9i	−0.0790246	+	0.136875i	0.823805	+	0.566874i	$0.191847\pi$
$788$	4.31140e9	−	7.46756e9i	0.313889	−	0.543672i
$789$	1.09023e9	+	1.88834e9i	0.0790224	+	0.136871i
$790$	−9.40894e9			−0.678963
$791$	4.52518e9	+	2.35135e10i	0.325101	+	1.68928i
$792$	7.67025e8			0.0548619
$793$	−1.39709e9	−	2.41984e9i	−0.0994876	−	0.172318i
$794$	8.36008e9	−	1.44801e10i	0.592705	−	1.02660i
$795$	−2.59923e9	+	4.50200e9i	−0.183468	+	0.317776i
$796$	2.51691e9	+	4.35942e9i	0.176877	+	0.306361i
$797$	1.02799e10			0.719258			0.359629	−	0.933095i	$-0.382903\pi$
$797$	1.02799e10			0.719258			0.359629	+	0.933095i	$0.382903\pi$
$798$	1.00048e9	−	8.66445e8i	0.0696948	−	0.0603574i
$799$	1.34282e10			0.931329
$800$	−8.33946e8	−	1.44444e9i	−0.0575868	−	0.0997432i
$801$	4.37262e9	−	7.57360e9i	0.300627	−	0.520701i
$802$	−3.44977e9	+	5.97518e9i	−0.236146	+	0.409016i
$803$	−3.29736e9	−	5.71120e9i	−0.224731	−	0.389245i
$804$	−5.64730e9			−0.383217
$805$	4.36178e9	+	1.51096e9i	0.294698	+	0.102087i
$806$	3.20997e9			0.215938
$807$	3.68563e9	+	6.38369e9i	0.246862	+	0.427577i
$808$	2.72258e9	−	4.71565e9i	0.181569	−	0.314486i
$809$	1.08055e10	−	1.87158e10i	0.717508	−	1.24276i	−0.244476	−	0.969655i	$-0.578616\pi$
$809$	1.08055e10	−	1.87158e10i	0.717508	−	1.24276i	0.961984	−	0.273105i	$-0.0880507\pi$
$810$	3.50751e8	+	6.07519e8i	0.0231900	+	0.0401663i
$811$	9.72617e9			0.640278			0.320139	−	0.947371i	$-0.396270\pi$
$811$	9.72617e9			0.640278			0.320139	+	0.947371i	$0.396270\pi$
$812$	−6.49258e9	−	2.24910e9i	−0.425570	−	0.147422i
$813$	1.57167e10			1.02576
$814$	−2.56244e9	−	4.43827e9i	−0.166521	−	0.288422i
$815$	1.51801e9	−	2.62927e9i	0.0982253	−	0.170131i
$816$	8.68590e8	−	1.50444e9i	0.0559628	−	0.0969303i
$817$	1.94854e9	+	3.37497e9i	0.125006	+	0.216517i
$818$	−3.57724e9			−0.228514
$819$	−1.36026e9	+	1.17802e9i	−0.0865221	+	0.0749303i
$820$	−5.18918e9			−0.328663
$821$	−7.37933e9	−	1.27814e10i	−0.465389	−	0.806077i	0.533830	−	0.845592i	$-0.320752\pi$
$821$	−7.37933e9	−	1.27814e10i	−0.465389	−	0.806077i	−0.999219	+	0.0395149i	$0.987419\pi$
$822$	−3.94290e9	+	6.82930e9i	−0.247608	+	0.428869i
$823$	−1.18766e10	+	2.05708e10i	−0.742663	+	1.28633i	0.208616	+	0.977998i	$0.433104\pi$
$823$	−1.18766e10	+	2.05708e10i	−0.742663	+	1.28633i	−0.951279	+	0.308332i	$0.900229\pi$
$824$	−2.90645e9	−	5.03413e9i	−0.180975	−	0.313458i
$825$	2.82419e9			0.175107
$826$	−2.29232e8	−	1.19113e9i	−0.0141529	−	0.0735407i
$827$	2.00552e10			1.23298			0.616492	−	0.787361i	$-0.288553\pi$
$827$	2.00552e10			1.23298			0.616492	+	0.787361i	$0.288553\pi$
$828$	−7.19156e8	−	1.24561e9i	−0.0440268	−	0.0762566i
$829$	1.04369e10	−	1.80773e10i	0.636256	−	1.10203i	−0.349991	−	0.936753i	$-0.613815\pi$
$829$	1.04369e10	−	1.80773e10i	0.636256	−	1.10203i	0.986247	−	0.165275i	$-0.0528513\pi$
$830$	2.88150e9	−	4.99090e9i	0.174922	−	0.302974i
$831$	−7.88719e9	−	1.36610e10i	−0.476780	−	0.825808i
$832$	7.13032e8			0.0429217
$833$	−1.84803e9	+	1.28035e10i	−0.110778	+	0.767489i
$834$	−9.75625e9			−0.582374
$835$	3.56235e9	+	6.17018e9i	0.211755	+	0.366771i
$836$	4.44012e8	−	7.69051e8i	0.0262828	−	0.0455232i
$837$	1.45179e9	−	2.51457e9i	0.0855784	−	0.148226i
$838$	1.28873e9	+	2.23214e9i	0.0756497	+	0.131029i
$839$	6.49929e9			0.379926			0.189963	−	0.981791i	$-0.439163\pi$
$839$	6.49929e9			0.379926			0.189963	+	0.981791i	$0.439163\pi$
$840$	3.91185e8	+	2.03266e9i	0.0227722	+	0.118328i
$841$	−3.25380e9			−0.188628
$842$	2.60415e9	+	4.51052e9i	0.150340	+	0.260396i
$843$	−5.80938e7	+	1.00621e8i	−0.00333990	+	0.00578487i
$844$	−2.86212e9	+	4.95734e9i	−0.163866	+	0.283825i
$845$	4.56638e9	+	7.90921e9i	0.260360	+	0.450956i
$846$	4.98556e9			0.283085
$847$	1.04712e10	−	9.06833e9i	0.592113	−	0.512785i
$848$	4.77955e9			0.269155
$849$	−5.14597e9	−	8.91308e9i	−0.288596	−	0.499863i
$850$	3.19815e9	−	5.53936e9i	0.178621	−	0.309381i
$851$	−4.80504e9	+	8.32257e9i	−0.267266	+	0.462918i
$852$	−2.63247e9	−	4.55957e9i	−0.145823	−	0.252572i
$853$	2.02423e10			1.11670			0.558352	−	0.829604i	$-0.311434\pi$
$853$	2.02423e10			1.11670			0.558352	+	0.829604i	$0.311434\pi$
$854$	−7.04710e9	−	2.44119e9i	−0.387175	−	0.134122i
$855$	8.12164e8			0.0444388
$856$	−3.58290e8	−	6.20576e8i	−0.0195243	−	0.0338171i
$857$	6.16520e9	−	1.06784e10i	0.334591	−	0.579529i	−0.648815	−	0.760946i	$-0.724735\pi$
$857$	6.16520e9	−	1.06784e10i	0.334591	−	0.579529i	0.983406	+	0.181417i	$0.0580685\pi$
$858$	−6.03677e8	+	1.04560e9i	−0.0326286	+	0.0565145i
$859$	9.48793e9	+	1.64336e10i	0.510735	+	0.884618i	0.999923	+	0.0124400i	$0.00395988\pi$
$859$	9.48793e9	+	1.64336e10i	0.510735	+	0.884618i	−0.489188	+	0.872178i	$0.662707\pi$
$860$	−6.09496e9			−0.326758
$861$	−1.13771e10	−	3.94116e9i	−0.607466	−	0.210432i
$862$	−2.39701e10			−1.27466
$863$	−8.19494e9	−	1.41941e10i	−0.434018	−	0.751742i	0.563197	−	0.826323i	$-0.309571\pi$
$863$	−8.19494e9	−	1.41941e10i	−0.434018	−	0.751742i	−0.997215	+	0.0745810i	$0.976238\pi$
$864$	3.22486e8	−	5.58563e8i	0.0170103	−	0.0294628i
$865$	7.05227e9	−	1.22149e10i	0.370487	−	0.641702i
$866$	1.83982e9	+	3.18667e9i	0.0962638	+	0.166734i
$867$	−4.41713e9			−0.230183
$868$	6.47659e9	−	5.60889e9i	0.336145	−	0.291110i
$869$	−1.46480e10			−0.757198
$870$	−2.10820e9	−	3.65150e9i	−0.108541	−	0.187998i
$871$	4.44464e9	−	7.69833e9i	0.227915	−	0.394760i
$872$	4.95284e8	−	8.57857e8i	0.0252957	−	0.0438134i
$873$	−4.86376e9	−	8.42427e9i	−0.247413	−	0.428531i
$874$	−1.66521e9			−0.0843680
$875$	3.65108e9	+	1.89716e10i	0.184244	+	0.957361i
$876$	−5.54534e9			−0.278717
$877$	4.47514e8	+	7.75118e8i	0.0224031	+	0.0388033i	0.877010	−	0.480473i	$-0.159535\pi$
$877$	4.47514e8	+	7.75118e8i	0.0224031	+	0.0388033i	−0.854606	+	0.519276i	$0.826202\pi$
$878$	1.38214e10	−	2.39394e10i	0.689163	−	1.19367i
$879$	7.11302e8	−	1.23201e9i	0.0353259	−	0.0611862i
$880$	6.94426e8	+	1.20278e9i	0.0343508	+	0.0594973i
$881$	−7.75707e8			−0.0382192			−0.0191096	−	0.999817i	$-0.506083\pi$
$881$	−7.75707e8			−0.0382192			−0.0191096	+	0.999817i	$0.506083\pi$
$882$	−6.86129e8	+	4.75364e9i	−0.0336718	+	0.233285i
$883$	−3.01054e9			−0.147157			−0.0735787	−	0.997289i	$-0.523442\pi$
$883$	−3.01054e9			−0.147157			−0.0735787	+	0.997289i	$0.523442\pi$
$884$	1.36722e9	+	2.36810e9i	0.0665667	+	0.115297i
$885$	3.72168e8	−	6.44615e8i	0.0180484	−	0.0312607i
$886$	−1.11601e10	+	1.93298e10i	−0.539075	+	0.933705i
$887$	−1.63120e10	−	2.82532e10i	−0.784829	−	1.35936i	−0.929101	−	0.369825i	$-0.879418\pi$
$887$	−1.63120e10	−	2.82532e10i	−0.784829	−	1.35936i	0.144273	−	0.989538i	$-0.453916\pi$
$888$	−4.30938e9			−0.206524
$889$	3.17253e9	+	1.64850e10i	0.151443	+	0.786922i
$890$	1.58350e10			0.752927
$891$	5.46056e8	+	9.45796e8i	0.0258622	+	0.0447946i
$892$	−5.12435e9	+	8.87564e9i	−0.241747	+	0.418719i
$893$	2.88601e9	−	4.99872e9i	0.135618	−	0.234898i
$894$	−2.41873e9	−	4.18936e9i	−0.113216	−	0.196095i
$895$	−2.12448e10			−0.990541
$896$	1.43865e9	−	1.24590e9i	0.0668153	−	0.0578638i
$897$	2.26401e9			0.104738
$898$	−1.31983e10	−	2.28601e10i	−0.608207	−	1.05344i
$899$	−8.72600e9	+	1.51139e10i	−0.400550	+	0.693772i
$900$	1.18740e9	−	2.05663e9i	0.0542933	−	0.0940388i
$901$	9.16470e9	+	1.58737e10i	0.417428	+	0.723006i
$902$	−8.07862e9			−0.366534
$903$	−1.33630e10	−	4.62909e9i	−0.603945	−	0.209213i
$904$	1.35096e10			0.608209
$905$	8.92825e8	+	1.54642e9i	0.0400402	+	0.0693517i
$906$	−8.53135e9	+	1.47767e10i	−0.381127	+	0.660131i
$907$	−1.74439e10	+	3.02137e10i	−0.776278	+	1.34455i	0.157796	+	0.987472i	$0.449561\pi$
$907$	−1.74439e10	+	3.02137e10i	−0.776278	+	1.34455i	−0.934073	+	0.357081i	$0.883772\pi$
$908$	6.96791e9	+	1.20688e10i	0.308889	+	0.535011i
$909$	7.75298e9			0.342370
$910$	−3.07877e9	−	1.06652e9i	−0.135435	−	0.0469162i
$911$	−2.24983e10			−0.985904			−0.492952	−	0.870056i	$-0.664082\pi$
$911$	−2.24983e10			−0.985904			−0.492952	+	0.870056i	$0.664082\pi$
$912$	−3.73359e8	−	6.46676e8i	−0.0162984	−	0.0282296i
$913$	4.48597e9	−	7.76993e9i	0.195078	−	0.337885i
$914$	−3.11524e9	+	5.39576e9i	−0.134952	+	0.233744i
$915$	−2.28825e9	−	3.96337e9i	−0.0987484	−	0.171037i
$916$	1.01798e10			0.437626
$917$	2.55775e9	−	2.21508e9i	0.109538	−	0.0948628i
$918$	2.47344e9			0.105524
$919$	1.78860e10	+	3.09795e10i	0.760169	+	1.31665i	0.942763	+	0.333463i	$0.108217\pi$
$919$	1.78860e10	+	3.09795e10i	0.760169	+	1.31665i	−0.182595	+	0.983188i	$0.558450\pi$
$920$	1.30217e9	−	2.25543e9i	0.0551330	−	0.0954932i
$921$	6.31274e9	−	1.09340e10i	0.266262	−	0.461179i
$922$	1.43482e10	+	2.48519e10i	0.602893	+	1.04424i
$923$	8.28741e9			0.346907
$924$	6.09003e8	+	3.16447e9i	0.0253961	+	0.131962i
$925$	−1.58672e10			−0.659179
$926$	1.93098e9	+	3.34456e9i	0.0799171	+	0.138420i
$927$	4.13829e9	−	7.16773e9i	0.170625	−	0.295531i
$928$	−1.93831e9	+	3.35725e9i	−0.0796169	+	0.137900i
$929$	1.16756e10	+	2.02228e10i	0.477776	+	0.827533i	0.999675	−	0.0254742i	$-0.00810957\pi$
$929$	1.16756e10	+	2.02228e10i	0.477776	+	0.827533i	−0.521899	+	0.853007i	$0.674776\pi$
$930$	5.25751e9			0.214333
$931$	4.36901e9	+	3.43971e9i	0.177443	+	0.139700i
$932$	6.06427e8			0.0245371
$933$	2.05634e9	+	3.56169e9i	0.0828914	+	0.143572i
$934$	−1.46523e10	+	2.53786e10i	−0.588427	+	1.01919i
$935$	−2.66310e9	+	4.61262e9i	−0.106548	+	0.184547i
$936$	5.07617e8	+	8.79219e8i	0.0202335	+	0.0350454i
$937$	−2.92882e10			−1.16307			−0.581533	−	0.813522i	$-0.697547\pi$
$937$	−2.92882e10			−1.16307			−0.581533	+	0.813522i	$0.697547\pi$
$938$	−4.48385e9	−	2.32988e10i	−0.177395	−	0.921771i
$939$	5.33160e9			0.210149
$940$	4.51367e9	+	7.81791e9i	0.177248	+	0.307003i
$941$	−1.97120e10	+	3.41422e10i	−0.771201	+	1.33576i	0.165705	+	0.986175i	$0.447010\pi$
$941$	−1.97120e10	+	3.41422e10i	−0.771201	+	1.33576i	−0.936905	+	0.349583i	$0.886323\pi$
$942$	6.74154e9	−	1.16767e10i	0.262773	−	0.455137i
$943$	7.57444e9	+	1.31193e10i	0.294144	+	0.509472i
$944$	−6.84356e8			−0.0264777
$945$	−2.22792e9	+	1.92943e9i	−0.0858792	+	0.0743736i
$946$	−9.48874e9			−0.364409
$947$	−1.96279e9	−	3.39965e9i	−0.0751015	−	0.130080i	0.826029	−	0.563628i	$-0.190595\pi$
$947$	−1.96279e9	−	3.39965e9i	−0.0751015	−	0.130080i	−0.901130	+	0.433548i	$0.857261\pi$
$948$	−6.15858e9	+	1.06670e10i	−0.234775	+	0.406642i
$949$	4.36439e9	−	7.55934e9i	0.165765	−	0.287113i
$950$	−1.37471e9	−	2.38106e9i	−0.0520209	−	0.0901028i
$951$	2.20232e10			0.830326
$952$	6.89644e9	+	2.38900e9i	0.259057	+	0.0897400i
$953$	−1.03211e10			−0.386280			−0.193140	−	0.981171i	$-0.561867\pi$
$953$	−1.03211e10			−0.386280			−0.193140	+	0.981171i	$0.561867\pi$
$954$	3.40263e9	+	5.89353e9i	0.126881	+	0.219764i
$955$	3.81215e9	−	6.60284e9i	0.141631	−	0.245312i
$956$	−2.44452e9	+	4.23403e9i	−0.0904879	+	0.156730i
$957$	−3.28208e9	−	5.68472e9i	−0.121048	−	0.209661i
$958$	2.03150e10			0.746515
$959$	−3.13059e10	−	1.08447e10i	−1.14620	−	0.397056i
$960$	1.16785e9			0.0426028
$961$	2.87567e9	+	4.98081e9i	0.104522	+	0.181037i
$962$	3.39164e9	−	5.87450e9i	0.122828	−	0.212744i
$963$	5.10143e8	−	8.83593e8i	0.0184077	−	0.0318831i
$964$	7.31567e9	+	1.26711e10i	0.263017	+	0.455559i
$965$	5.52662e9			0.197977
$966$	4.56797e9	−	3.95598e9i	0.163043	−	0.141200i
$967$	−2.54805e10			−0.906181			−0.453091	−	0.891464i	$-0.649679\pi$
$967$	−2.54805e10			−0.906181			−0.453091	+	0.891464i	$0.649679\pi$
$968$	−3.90762e9	−	6.76820e9i	−0.138468	−	0.239833i
$969$	1.43182e9	−	2.47998e9i	0.0505538	−	0.0875618i
$970$	8.80680e9	−	1.52538e10i	0.309825	−	0.536633i
$971$	−1.27182e10	−	2.20286e10i	−0.445819	−	0.772181i	0.552290	−	0.833652i	$-0.313754\pi$
$971$	−1.27182e10	−	2.20286e10i	−0.445819	−	0.772181i	−0.998109	+	0.0614711i	$0.980421\pi$
$972$	9.18330e8			0.0320750
$973$	−7.74628e9	−	4.02509e10i	−0.269587	−	1.40081i
$974$	2.61348e10			0.906279
$975$	1.86905e9	+	3.23729e9i	0.0645809	+	0.111857i
$976$	−2.10386e9	+	3.64399e9i	−0.0724339	+	0.125459i
$977$	1.03560e10	−	1.79371e10i	0.355271	−	0.615347i	−0.631894	−	0.775055i	$-0.717722\pi$
$977$	1.03560e10	−	1.79371e10i	0.355271	−	0.615347i	0.987164	+	0.159708i	$0.0510553\pi$
$978$	−1.98721e9	−	3.44196e9i	−0.0679295	−	0.117657i
$979$	2.46522e10			0.839685
$980$	−8.07543e9	+	3.22778e9i	−0.274078	+	0.109550i
$981$	1.41040e9			0.0476980
$982$	−6.50818e9	−	1.12725e10i	−0.219315	−	0.379865i
$983$	−1.76779e10	+	3.06190e10i	−0.593598	+	1.02814i	0.400145	+	0.916452i	$0.368960\pi$
$983$	−1.76779e10	+	3.06190e10i	−0.593598	+	1.02814i	−0.993743	+	0.111690i	$0.964374\pi$
$984$	−3.39656e9	+	5.88301e9i	−0.113646	+	0.196841i
$985$	1.11153e10	+	1.92523e10i	0.370591	+	0.641883i
$986$	−1.48667e10			−0.493907
$987$	3.95844e9	+	2.05686e10i	0.131043	+	0.680919i
$988$	1.17539e9			0.0387732
$989$	8.89656e9	+	1.54093e10i	0.292439	+	0.506519i
$990$	−9.88743e8	+	1.71255e9i	−0.0323862	+	0.0560946i
$991$	1.12571e10	−	1.94979e10i	0.367426	−	0.636400i	−0.621737	−	0.783226i	$-0.713573\pi$
$991$	1.12571e10	−	1.94979e10i	0.367426	−	0.636400i	0.989162	+	0.146827i	$0.0469059\pi$
$992$	−2.41692e9	−	4.18623e9i	−0.0786088	−	0.136154i
$993$	−2.01631e10			−0.653483
$994$	1.67211e10	−	1.44809e10i	0.540022	−	0.467673i
$995$	−1.29778e10			−0.417658
$996$	−3.77215e9	−	6.53355e9i	−0.120971	−	0.209528i
$997$	1.45334e10	−	2.51726e10i	0.464445	−	0.804443i	−0.534731	−	0.845022i	$-0.679587\pi$
$997$	1.45334e10	−	2.51726e10i	0.464445	−	0.804443i	0.999176	+	0.0405793i	$0.0129203\pi$
$998$	1.50505e10	−	2.60682e10i	0.479284	−	0.830145i
$999$	−3.06791e9	−	5.31378e9i	−0.0973562	−	0.168626i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	42.8.e.a.25.1	✓	2
3.2	odd	2		126.8.g.b.109.1		2
7.2	even	3	inner	42.8.e.a.37.1	yes	2
7.3	odd	6		294.8.a.b.1.1		1
7.4	even	3		294.8.a.i.1.1		1
7.5	odd	6		294.8.e.p.79.1		2
7.6	odd	2		294.8.e.p.67.1		2
21.2	odd	6		126.8.g.b.37.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.8.e.a.25.1	✓	2	1.1	even	1	trivial
42.8.e.a.37.1	yes	2	7.2	even	3	inner
126.8.g.b.37.1		2	21.2	odd	6
126.8.g.b.109.1		2	3.2	odd	2
294.8.a.b.1.1		1	7.3	odd	6
294.8.a.i.1.1		1	7.4	even	3
294.8.e.p.67.1		2	7.6	odd	2
294.8.e.p.79.1		2	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 42 = 2 \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	42.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(4.00000 + 6.92820i) q^{2} +(-13.5000 + 23.3827i) q^{3} +(-32.0000 + 55.4256i) q^{4} +(-82.5000 - 142.894i) q^{5} -216.000 q^{6} +(-171.500 - 891.140i) q^{7} -512.000 q^{8} +(-364.500 - 631.333i) q^{9} +O(q^{10})\)	\(q+(4.00000 + 6.92820i) q^{2} +(-13.5000 + 23.3827i) q^{3} +(-32.0000 + 55.4256i) q^{4} +(-82.5000 - 142.894i) q^{5} -216.000 q^{6} +(-171.500 - 891.140i) q^{7} -512.000 q^{8} +(-364.500 - 631.333i) q^{9} +(660.000 - 1143.15i) q^{10} +(1027.50 - 1779.68i) q^{11} +(-864.000 - 1496.49i) q^{12} +2720.00 q^{13} +(5488.00 - 4752.75i) q^{14} +4455.00 q^{15} +(-2048.00 - 3547.24i) q^{16} +(7854.00 - 13603.5i) q^{17} +(2916.00 - 5050.66i) q^{18} +(-3376.00 - 5847.40i) q^{19} +10560.0 q^{20} +(23152.5 + 8020.26i) q^{21} +16440.0 q^{22} +(-15414.0 - 26697.8i) q^{23} +(6912.00 - 11971.9i) q^{24} +(25450.0 - 44080.7i) q^{25} +(10880.0 + 18844.7i) q^{26} +19683.0 q^{27} +(54880.0 + 19011.0i) q^{28} -118305. q^{29} +(17820.0 + 30865.1i) q^{30} +(73758.5 - 127753. i) q^{31} +(16384.0 - 28377.9i) q^{32} +(27742.5 + 48051.4i) q^{33} +125664. q^{34} +(-113190. + 98025.4i) q^{35} +46656.0 q^{36} +(-155866. - 269968. i) q^{37} +(27008.0 - 46779.2i) q^{38} +(-36720.0 + 63600.9i) q^{39} +(42240.0 + 73161.8i) q^{40} -491400. q^{41} +(37044.0 + 192486. i) q^{42} -577174. q^{43} +(65760.0 + 113900. i) q^{44} +(-60142.5 + 104170. i) q^{45} +(123312. - 213583. i) q^{46} +(427431. + 740332. i) q^{47} +110592. q^{48} +(-764718. + 305661. i) q^{49} +407200. q^{50} +(212058. + 367295. i) q^{51} +(-87040.0 + 150758. i) q^{52} +(-583442. + 1.01055e6i) q^{53} +(78732.0 + 136368. i) q^{54} -339075. q^{55} +(87808.0 + 456264. i) q^{56} +182304. q^{57} +(-473220. - 819641. i) q^{58} +(83539.5 - 144695. i) q^{59} +(-142560. + 246921. i) q^{60} +(-513637. - 889645. i) q^{61} +1.18014e6 q^{62} +(-500094. + 433094. i) q^{63} +262144. q^{64} +(-224400. - 388672. i) q^{65} +(-221940. + 384411. i) q^{66} +(1.63406e6 - 2.83027e6i) q^{67} +(502656. + 870626. i) q^{68} +832356. q^{69} +(-1.13190e6 - 392102. i) q^{70} +3.04684e6 q^{71} +(186624. + 323242. i) q^{72} +(1.60456e6 - 2.77917e6i) q^{73} +(1.24693e6 - 2.15974e6i) q^{74} +(687150. + 1.19018e6i) q^{75} +432128. q^{76} +(-1.76216e6 - 610431. i) q^{77} -587520. q^{78} +(-3.56399e6 - 6.17302e6i) q^{79} +(-337920. + 585295. i) q^{80} +(-265720. + 460241. i) q^{81} +(-1.96560e6 - 3.40452e6i) q^{82} +4.36591e6 q^{83} +(-1.18541e6 + 1.02659e6i) q^{84} -2.59182e6 q^{85} +(-2.30870e6 - 3.99878e6i) q^{86} +(1.59712e6 - 2.76629e6i) q^{87} +(-526080. + 911197. i) q^{88} +(5.99811e6 + 1.03890e7i) q^{89} -962280. q^{90} +(-466480. - 2.42390e6i) q^{91} +1.97299e6 q^{92} +(1.99148e6 + 3.44934e6i) q^{93} +(-3.41945e6 + 5.92266e6i) q^{94} +(-557040. + 964822. i) q^{95} +(442368. + 766204. i) q^{96} +1.33436e7 q^{97} +(-5.17656e6 - 4.07548e6i) q^{98} -1.49810e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 8 q^{2} - 27 q^{3} - 64 q^{4} - 165 q^{5} - 432 q^{6} - 343 q^{7} - 1024 q^{8} - 729 q^{9}+O(q^{10}) \) 2 * q + 8 * q^2 - 27 * q^3 - 64 * q^4 - 165 * q^5 - 432 * q^6 - 343 * q^7 - 1024 * q^8 - 729 * q^9	\( 2 q + 8 q^{2} - 27 q^{3} - 64 q^{4} - 165 q^{5} - 432 q^{6} - 343 q^{7} - 1024 q^{8} - 729 q^{9} + 1320 q^{10} + 2055 q^{11} - 1728 q^{12} + 5440 q^{13} + 10976 q^{14} + 8910 q^{15} - 4096 q^{16} + 15708 q^{17} + 5832 q^{18} - 6752 q^{19} + 21120 q^{20} + 46305 q^{21} + 32880 q^{22} - 30828 q^{23} + 13824 q^{24} + 50900 q^{25} + 21760 q^{26} + 39366 q^{27} + 109760 q^{28} - 236610 q^{29} + 35640 q^{30} + 147517 q^{31} + 32768 q^{32} + 55485 q^{33} + 251328 q^{34} - 226380 q^{35} + 93312 q^{36} - 311732 q^{37} + 54016 q^{38} - 73440 q^{39} + 84480 q^{40} - 982800 q^{41} + 74088 q^{42} - 1154348 q^{43} + 131520 q^{44} - 120285 q^{45} + 246624 q^{46} + 854862 q^{47} + 221184 q^{48} - 1529437 q^{49} + 814400 q^{50} + 424116 q^{51} - 174080 q^{52} - 1166883 q^{53} + 157464 q^{54} - 678150 q^{55} + 175616 q^{56} + 364608 q^{57} - 946440 q^{58} + 167079 q^{59} - 285120 q^{60} - 1027274 q^{61} + 2360272 q^{62} - 1000188 q^{63} + 524288 q^{64} - 448800 q^{65} - 443880 q^{66} + 3268114 q^{67} + 1005312 q^{68} + 1664712 q^{69} - 2263800 q^{70} + 6093684 q^{71} + 373248 q^{72} + 3209110 q^{73} + 2493856 q^{74} + 1374300 q^{75} + 864256 q^{76} - 3524325 q^{77} - 1175040 q^{78} - 7127987 q^{79} - 675840 q^{80} - 531441 q^{81} - 3931200 q^{82} + 8731818 q^{83} - 2370816 q^{84} - 5183640 q^{85} - 4617392 q^{86} + 3194235 q^{87} - 1052160 q^{88} + 11996214 q^{89} - 1924560 q^{90} - 932960 q^{91} + 3945984 q^{92} + 3982959 q^{93} - 6838896 q^{94} - 1114080 q^{95} + 884736 q^{96} + 26687278 q^{97} - 10353112 q^{98} - 2996190 q^{99}+O(q^{100}) \) 2 * q + 8 * q^2 - 27 * q^3 - 64 * q^4 - 165 * q^5 - 432 * q^6 - 343 * q^7 - 1024 * q^8 - 729 * q^9 + 1320 * q^10 + 2055 * q^11 - 1728 * q^12 + 5440 * q^13 + 10976 * q^14 + 8910 * q^15 - 4096 * q^16 + 15708 * q^17 + 5832 * q^18 - 6752 * q^19 + 21120 * q^20 + 46305 * q^21 + 32880 * q^22 - 30828 * q^23 + 13824 * q^24 + 50900 * q^25 + 21760 * q^26 + 39366 * q^27 + 109760 * q^28 - 236610 * q^29 + 35640 * q^30 + 147517 * q^31 + 32768 * q^32 + 55485 * q^33 + 251328 * q^34 - 226380 * q^35 + 93312 * q^36 - 311732 * q^37 + 54016 * q^38 - 73440 * q^39 + 84480 * q^40 - 982800 * q^41 + 74088 * q^42 - 1154348 * q^43 + 131520 * q^44 - 120285 * q^45 + 246624 * q^46 + 854862 * q^47 + 221184 * q^48 - 1529437 * q^49 + 814400 * q^50 + 424116 * q^51 - 174080 * q^52 - 1166883 * q^53 + 157464 * q^54 - 678150 * q^55 + 175616 * q^56 + 364608 * q^57 - 946440 * q^58 + 167079 * q^59 - 285120 * q^60 - 1027274 * q^61 + 2360272 * q^62 - 1000188 * q^63 + 524288 * q^64 - 448800 * q^65 - 443880 * q^66 + 3268114 * q^67 + 1005312 * q^68 + 1664712 * q^69 - 2263800 * q^70 + 6093684 * q^71 + 373248 * q^72 + 3209110 * q^73 + 2493856 * q^74 + 1374300 * q^75 + 864256 * q^76 - 3524325 * q^77 - 1175040 * q^78 - 7127987 * q^79 - 675840 * q^80 - 531441 * q^81 - 3931200 * q^82 + 8731818 * q^83 - 2370816 * q^84 - 5183640 * q^85 - 4617392 * q^86 + 3194235 * q^87 - 1052160 * q^88 + 11996214 * q^89 - 1924560 * q^90 - 932960 * q^91 + 3945984 * q^92 + 3982959 * q^93 - 6838896 * q^94 - 1114080 * q^95 + 884736 * q^96 + 26687278 * q^97 - 10353112 * q^98 - 2996190 * q^99

Introduction

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