Normalized defining polynomial
\( x^{39} - 10 x^{38} - 55 x^{37} + 838 x^{36} + 433 x^{35} - 29490 x^{34} + 36492 x^{33} + 574075 x^{32} + \cdots - 17513 \)
Invariants
Degree: | $39$ | sage: K.degree()
gp: poldegree(K.pol)
magma: Degree(K);
oscar: degree(K)
| |
Signature: | $[39, 0]$ | sage: K.signature()
gp: K.sign
magma: Signature(K);
oscar: signature(K)
| |
Discriminant: | \(111\!\cdots\!929\) \(\medspace = 7^{26}\cdot 53^{36}\) | sage: K.disc()
gp: K.disc
magma: OK := Integers(K); Discriminant(OK);
oscar: OK = ring_of_integers(K); discriminant(OK)
| |
Root discriminant: | \(142.90\) | sage: (K.disc().abs())^(1./K.degree())
gp: abs(K.disc)^(1/poldegree(K.pol))
magma: Abs(Discriminant(OK))^(1/Degree(K));
oscar: (1.0 * dK)^(1/degree(K))
| |
Galois root discriminant: | $7^{2/3}53^{12/13}\approx 142.90188501299207$ | ||
Ramified primes: | \(7\), \(53\) | sage: K.disc().support()
gp: factor(abs(K.disc))[,1]~
magma: PrimeDivisors(Discriminant(OK));
oscar: prime_divisors(discriminant((OK)))
| |
Discriminant root field: | \(\Q\) | ||
$\card{ \Gal(K/\Q) }$: | $39$ | sage: K.automorphisms()
magma: Automorphisms(K);
oscar: automorphisms(K)
| |
This field is Galois and abelian over $\Q$. | |||
Conductor: | \(371=7\cdot 53\) | ||
Dirichlet character group: | $\lbrace$$\chi_{371}(256,·)$, $\chi_{371}(1,·)$, $\chi_{371}(130,·)$, $\chi_{371}(261,·)$, $\chi_{371}(134,·)$, $\chi_{371}(44,·)$, $\chi_{371}(142,·)$, $\chi_{371}(15,·)$, $\chi_{371}(16,·)$, $\chi_{371}(275,·)$, $\chi_{371}(148,·)$, $\chi_{371}(281,·)$, $\chi_{371}(155,·)$, $\chi_{371}(289,·)$, $\chi_{371}(36,·)$, $\chi_{371}(169,·)$, $\chi_{371}(172,·)$, $\chi_{371}(46,·)$, $\chi_{371}(309,·)$, $\chi_{371}(183,·)$, $\chi_{371}(312,·)$, $\chi_{371}(319,·)$, $\chi_{371}(331,·)$, $\chi_{371}(333,·)$, $\chi_{371}(205,·)$, $\chi_{371}(81,·)$, $\chi_{371}(100,·)$, $\chi_{371}(95,·)$, $\chi_{371}(225,·)$, $\chi_{371}(354,·)$, $\chi_{371}(99,·)$, $\chi_{371}(228,·)$, $\chi_{371}(102,·)$, $\chi_{371}(107,·)$, $\chi_{371}(365,·)$, $\chi_{371}(240,·)$, $\chi_{371}(116,·)$, $\chi_{371}(121,·)$, $\chi_{371}(254,·)$$\rbrace$ | ||
This is not a CM field. |
Integral basis (with respect to field generator \(a\))
$1$, $a$, $a^{2}$, $a^{3}$, $a^{4}$, $a^{5}$, $a^{6}$, $a^{7}$, $a^{8}$, $a^{9}$, $a^{10}$, $a^{11}$, $a^{12}$, $a^{13}$, $a^{14}$, $a^{15}$, $a^{16}$, $a^{17}$, $a^{18}$, $a^{19}$, $a^{20}$, $a^{21}$, $a^{22}$, $a^{23}$, $a^{24}$, $a^{25}$, $a^{26}$, $a^{27}$, $a^{28}$, $a^{29}$, $a^{30}$, $\frac{1}{83}a^{31}-\frac{11}{83}a^{30}-\frac{37}{83}a^{29}+\frac{37}{83}a^{28}+\frac{11}{83}a^{27}-\frac{9}{83}a^{26}+\frac{11}{83}a^{25}-\frac{27}{83}a^{24}+\frac{16}{83}a^{23}-\frac{41}{83}a^{22}-\frac{3}{83}a^{21}-\frac{3}{83}a^{20}-\frac{8}{83}a^{19}+\frac{6}{83}a^{18}-\frac{13}{83}a^{17}+\frac{13}{83}a^{16}-\frac{39}{83}a^{15}+\frac{10}{83}a^{13}-\frac{27}{83}a^{12}-\frac{1}{83}a^{11}+\frac{22}{83}a^{10}-\frac{33}{83}a^{9}-\frac{18}{83}a^{8}-\frac{41}{83}a^{7}+\frac{27}{83}a^{6}+\frac{30}{83}a^{5}-\frac{28}{83}a^{4}+\frac{12}{83}a^{3}-\frac{27}{83}a^{2}+\frac{4}{83}a$, $\frac{1}{83}a^{32}+\frac{8}{83}a^{30}-\frac{38}{83}a^{29}+\frac{3}{83}a^{28}+\frac{29}{83}a^{27}-\frac{5}{83}a^{26}+\frac{11}{83}a^{25}-\frac{32}{83}a^{24}-\frac{31}{83}a^{23}-\frac{39}{83}a^{22}-\frac{36}{83}a^{21}-\frac{41}{83}a^{20}+\frac{1}{83}a^{19}-\frac{30}{83}a^{18}+\frac{36}{83}a^{17}+\frac{21}{83}a^{16}-\frac{14}{83}a^{15}+\frac{10}{83}a^{14}+\frac{34}{83}a^{12}+\frac{11}{83}a^{11}-\frac{40}{83}a^{10}+\frac{34}{83}a^{9}+\frac{10}{83}a^{8}-\frac{9}{83}a^{7}-\frac{5}{83}a^{6}-\frac{30}{83}a^{5}+\frac{36}{83}a^{4}+\frac{22}{83}a^{3}+\frac{39}{83}a^{2}-\frac{39}{83}a$, $\frac{1}{1909}a^{33}-\frac{2}{1909}a^{32}-\frac{8}{1909}a^{31}-\frac{44}{1909}a^{30}+\frac{754}{1909}a^{29}-\frac{901}{1909}a^{28}-\frac{73}{1909}a^{27}-\frac{250}{1909}a^{26}-\frac{396}{1909}a^{25}+\frac{133}{1909}a^{24}+\frac{763}{1909}a^{23}-\frac{879}{1909}a^{22}+\frac{328}{1909}a^{21}+\frac{214}{1909}a^{20}+\frac{511}{1909}a^{19}+\frac{7}{23}a^{18}+\frac{74}{1909}a^{17}+\frac{21}{83}a^{16}+\frac{579}{1909}a^{15}-\frac{767}{1909}a^{14}-\frac{541}{1909}a^{13}-\frac{123}{1909}a^{12}-\frac{710}{1909}a^{11}+\frac{426}{1909}a^{10}-\frac{28}{1909}a^{9}+\frac{674}{1909}a^{8}+\frac{5}{1909}a^{7}+\frac{710}{1909}a^{6}+\frac{114}{1909}a^{5}-\frac{681}{1909}a^{4}+\frac{633}{1909}a^{3}-\frac{349}{1909}a^{2}+\frac{678}{1909}a-\frac{3}{23}$, $\frac{1}{1909}a^{34}+\frac{11}{1909}a^{32}+\frac{9}{1909}a^{31}+\frac{91}{1909}a^{30}-\frac{911}{1909}a^{29}+\frac{9}{23}a^{28}-\frac{879}{1909}a^{27}+\frac{277}{1909}a^{26}+\frac{353}{1909}a^{25}+\frac{339}{1909}a^{24}-\frac{871}{1909}a^{23}+\frac{571}{1909}a^{22}-\frac{165}{1909}a^{21}-\frac{211}{1909}a^{20}-\frac{835}{1909}a^{19}-\frac{949}{1909}a^{18}+\frac{562}{1909}a^{17}-\frac{893}{1909}a^{16}-\frac{31}{83}a^{15}+\frac{64}{1909}a^{14}-\frac{515}{1909}a^{13}-\frac{128}{1909}a^{12}-\frac{810}{1909}a^{11}-\frac{487}{1909}a^{10}-\frac{877}{1909}a^{9}+\frac{341}{1909}a^{8}-\frac{407}{1909}a^{7}-\frac{536}{1909}a^{6}+\frac{927}{1909}a^{5}+\frac{76}{1909}a^{4}+\frac{342}{1909}a^{3}+\frac{923}{1909}a^{2}+\frac{486}{1909}a-\frac{6}{23}$, $\frac{1}{1909}a^{35}+\frac{8}{1909}a^{32}-\frac{5}{1909}a^{31}-\frac{496}{1909}a^{30}+\frac{135}{1909}a^{29}+\frac{246}{1909}a^{28}+\frac{298}{1909}a^{27}-\frac{853}{1909}a^{26}+\frac{509}{1909}a^{25}-\frac{448}{1909}a^{24}-\frac{508}{1909}a^{23}+\frac{764}{1909}a^{22}-\frac{530}{1909}a^{21}+\frac{215}{1909}a^{20}+\frac{606}{1909}a^{19}-\frac{516}{1909}a^{18}-\frac{143}{1909}a^{17}+\frac{28}{83}a^{16}-\frac{716}{1909}a^{15}+\frac{56}{1909}a^{14}+\frac{165}{1909}a^{13}+\frac{911}{1909}a^{12}-\frac{382}{1909}a^{11}+\frac{854}{1909}a^{10}+\frac{212}{1909}a^{9}-\frac{921}{1909}a^{8}-\frac{476}{1909}a^{7}-\frac{282}{1909}a^{6}-\frac{281}{1909}a^{5}+\frac{703}{1909}a^{4}+\frac{791}{1909}a^{3}+\frac{760}{1909}a^{2}-\frac{159}{1909}a+\frac{10}{23}$, $\frac{1}{435105007}a^{36}-\frac{67040}{435105007}a^{35}-\frac{30321}{435105007}a^{34}+\frac{31397}{435105007}a^{33}-\frac{1039630}{435105007}a^{32}-\frac{1023346}{435105007}a^{31}-\frac{9195197}{435105007}a^{30}+\frac{215300484}{435105007}a^{29}+\frac{169782691}{435105007}a^{28}-\frac{68429824}{435105007}a^{27}-\frac{140508366}{435105007}a^{26}-\frac{137646052}{435105007}a^{25}-\frac{106071776}{435105007}a^{24}+\frac{2539541}{435105007}a^{23}+\frac{71864732}{435105007}a^{22}-\frac{99371206}{435105007}a^{21}-\frac{153190109}{435105007}a^{20}-\frac{187434909}{435105007}a^{19}+\frac{82001253}{435105007}a^{18}+\frac{210533319}{435105007}a^{17}+\frac{64883935}{435105007}a^{16}+\frac{24542742}{435105007}a^{15}+\frac{96463632}{435105007}a^{14}+\frac{26757242}{435105007}a^{13}-\frac{143868370}{435105007}a^{12}+\frac{197499317}{435105007}a^{11}+\frac{108238735}{435105007}a^{10}+\frac{124499006}{435105007}a^{9}-\frac{45506248}{435105007}a^{8}+\frac{193725523}{435105007}a^{7}-\frac{73753079}{435105007}a^{6}+\frac{202595629}{435105007}a^{5}+\frac{48451495}{435105007}a^{4}+\frac{30075163}{435105007}a^{3}-\frac{131065835}{435105007}a^{2}-\frac{177748284}{435105007}a+\frac{876341}{5242229}$, $\frac{1}{435105007}a^{37}+\frac{21716}{435105007}a^{35}-\frac{71129}{435105007}a^{34}+\frac{85960}{435105007}a^{33}+\frac{351085}{435105007}a^{32}-\frac{2194501}{435105007}a^{31}+\frac{146020964}{435105007}a^{30}+\frac{3523052}{435105007}a^{29}-\frac{74177341}{435105007}a^{28}+\frac{40742800}{435105007}a^{27}+\frac{79769131}{435105007}a^{26}+\frac{79451432}{435105007}a^{25}+\frac{130042661}{435105007}a^{24}-\frac{189693850}{435105007}a^{23}+\frac{94922077}{435105007}a^{22}-\frac{80550796}{435105007}a^{21}-\frac{113190639}{435105007}a^{20}+\frac{200126464}{435105007}a^{19}+\frac{202374318}{435105007}a^{18}-\frac{20992884}{435105007}a^{17}-\frac{95400233}{435105007}a^{16}-\frac{158070074}{435105007}a^{15}-\frac{99808568}{435105007}a^{14}-\frac{4630692}{18917609}a^{13}-\frac{149613492}{435105007}a^{12}+\frac{146431275}{435105007}a^{11}-\frac{61982782}{435105007}a^{10}+\frac{94721748}{435105007}a^{9}-\frac{183482420}{435105007}a^{8}-\frac{153104798}{435105007}a^{7}+\frac{70786412}{435105007}a^{6}-\frac{17337296}{435105007}a^{5}+\frac{106772495}{435105007}a^{4}-\frac{172615444}{435105007}a^{3}-\frac{169930300}{435105007}a^{2}+\frac{72535567}{435105007}a+\frac{12314}{5242229}$, $\frac{1}{36\!\cdots\!71}a^{38}-\frac{38\!\cdots\!11}{36\!\cdots\!71}a^{37}+\frac{14\!\cdots\!70}{36\!\cdots\!71}a^{36}-\frac{45\!\cdots\!35}{36\!\cdots\!71}a^{35}+\frac{67\!\cdots\!56}{36\!\cdots\!71}a^{34}+\frac{94\!\cdots\!84}{36\!\cdots\!71}a^{33}+\frac{20\!\cdots\!63}{36\!\cdots\!71}a^{32}+\frac{24\!\cdots\!33}{36\!\cdots\!71}a^{31}+\frac{72\!\cdots\!67}{36\!\cdots\!71}a^{30}-\frac{60\!\cdots\!70}{36\!\cdots\!71}a^{29}+\frac{35\!\cdots\!66}{36\!\cdots\!71}a^{28}-\frac{14\!\cdots\!21}{36\!\cdots\!71}a^{27}-\frac{15\!\cdots\!12}{36\!\cdots\!71}a^{26}-\frac{13\!\cdots\!43}{36\!\cdots\!71}a^{25}-\frac{95\!\cdots\!70}{36\!\cdots\!71}a^{24}+\frac{25\!\cdots\!44}{36\!\cdots\!71}a^{23}+\frac{80\!\cdots\!13}{36\!\cdots\!71}a^{22}-\frac{60\!\cdots\!03}{36\!\cdots\!71}a^{21}+\frac{13\!\cdots\!00}{36\!\cdots\!71}a^{20}+\frac{91\!\cdots\!99}{36\!\cdots\!71}a^{19}-\frac{92\!\cdots\!35}{36\!\cdots\!71}a^{18}+\frac{68\!\cdots\!03}{15\!\cdots\!77}a^{17}-\frac{12\!\cdots\!81}{36\!\cdots\!71}a^{16}-\frac{10\!\cdots\!93}{36\!\cdots\!71}a^{15}+\frac{13\!\cdots\!70}{36\!\cdots\!71}a^{14}-\frac{45\!\cdots\!87}{15\!\cdots\!77}a^{13}-\frac{16\!\cdots\!75}{36\!\cdots\!71}a^{12}-\frac{96\!\cdots\!67}{36\!\cdots\!71}a^{11}-\frac{12\!\cdots\!37}{36\!\cdots\!71}a^{10}-\frac{17\!\cdots\!08}{36\!\cdots\!71}a^{9}+\frac{25\!\cdots\!24}{36\!\cdots\!71}a^{8}-\frac{83\!\cdots\!32}{36\!\cdots\!71}a^{7}-\frac{21\!\cdots\!13}{36\!\cdots\!71}a^{6}+\frac{99\!\cdots\!14}{36\!\cdots\!71}a^{5}-\frac{72\!\cdots\!97}{36\!\cdots\!71}a^{4}+\frac{12\!\cdots\!68}{36\!\cdots\!71}a^{3}-\frac{79\!\cdots\!26}{36\!\cdots\!71}a^{2}+\frac{13\!\cdots\!26}{36\!\cdots\!71}a-\frac{17\!\cdots\!83}{43\!\cdots\!37}$
Monogenic: | Not computed | |
Index: | $1$ | |
Inessential primes: | None |
Class group and class number
Trivial group, which has order $1$ (assuming GRH)
Unit group
Rank: | $38$ | sage: UK.rank()
gp: K.fu
magma: UnitRank(K);
oscar: rank(UK)
| |
Torsion generator: | \( -1 \) (order $2$) | sage: UK.torsion_generator()
gp: K.tu[2]
magma: K!f(TU.1) where TU,f is TorsionUnitGroup(K);
oscar: torsion_units_generator(OK)
| |
Fundamental units: | $\frac{30\!\cdots\!94}{69\!\cdots\!99}a^{38}-\frac{28\!\cdots\!70}{69\!\cdots\!99}a^{37}-\frac{18\!\cdots\!09}{69\!\cdots\!99}a^{36}+\frac{24\!\cdots\!87}{69\!\cdots\!99}a^{35}+\frac{26\!\cdots\!12}{69\!\cdots\!99}a^{34}-\frac{87\!\cdots\!81}{69\!\cdots\!99}a^{33}+\frac{59\!\cdots\!61}{69\!\cdots\!99}a^{32}+\frac{17\!\cdots\!62}{69\!\cdots\!99}a^{31}-\frac{29\!\cdots\!73}{69\!\cdots\!99}a^{30}-\frac{22\!\cdots\!63}{69\!\cdots\!99}a^{29}+\frac{52\!\cdots\!24}{69\!\cdots\!99}a^{28}+\frac{18\!\cdots\!50}{69\!\cdots\!99}a^{27}-\frac{55\!\cdots\!15}{69\!\cdots\!99}a^{26}-\frac{97\!\cdots\!49}{69\!\cdots\!99}a^{25}+\frac{38\!\cdots\!18}{69\!\cdots\!99}a^{24}+\frac{33\!\cdots\!06}{69\!\cdots\!99}a^{23}-\frac{18\!\cdots\!85}{69\!\cdots\!99}a^{22}-\frac{59\!\cdots\!79}{69\!\cdots\!99}a^{21}+\frac{63\!\cdots\!05}{69\!\cdots\!99}a^{20}-\frac{17\!\cdots\!72}{69\!\cdots\!99}a^{19}-\frac{15\!\cdots\!07}{69\!\cdots\!99}a^{18}+\frac{38\!\cdots\!79}{69\!\cdots\!99}a^{17}+\frac{26\!\cdots\!96}{69\!\cdots\!99}a^{16}-\frac{10\!\cdots\!96}{69\!\cdots\!99}a^{15}-\frac{30\!\cdots\!99}{69\!\cdots\!99}a^{14}+\frac{14\!\cdots\!68}{69\!\cdots\!99}a^{13}+\frac{25\!\cdots\!70}{69\!\cdots\!99}a^{12}-\frac{12\!\cdots\!44}{69\!\cdots\!99}a^{11}-\frac{13\!\cdots\!23}{69\!\cdots\!99}a^{10}+\frac{60\!\cdots\!58}{69\!\cdots\!99}a^{9}+\frac{47\!\cdots\!98}{69\!\cdots\!99}a^{8}-\frac{17\!\cdots\!94}{69\!\cdots\!99}a^{7}-\frac{99\!\cdots\!45}{69\!\cdots\!99}a^{6}+\frac{27\!\cdots\!81}{69\!\cdots\!99}a^{5}+\frac{10\!\cdots\!35}{69\!\cdots\!99}a^{4}-\frac{20\!\cdots\!14}{69\!\cdots\!99}a^{3}-\frac{47\!\cdots\!98}{69\!\cdots\!99}a^{2}+\frac{63\!\cdots\!57}{69\!\cdots\!99}a+\frac{86\!\cdots\!67}{83\!\cdots\!53}$, $\frac{30\!\cdots\!94}{69\!\cdots\!99}a^{38}-\frac{28\!\cdots\!70}{69\!\cdots\!99}a^{37}-\frac{18\!\cdots\!09}{69\!\cdots\!99}a^{36}+\frac{24\!\cdots\!87}{69\!\cdots\!99}a^{35}+\frac{26\!\cdots\!12}{69\!\cdots\!99}a^{34}-\frac{87\!\cdots\!81}{69\!\cdots\!99}a^{33}+\frac{59\!\cdots\!61}{69\!\cdots\!99}a^{32}+\frac{17\!\cdots\!62}{69\!\cdots\!99}a^{31}-\frac{29\!\cdots\!73}{69\!\cdots\!99}a^{30}-\frac{22\!\cdots\!63}{69\!\cdots\!99}a^{29}+\frac{52\!\cdots\!24}{69\!\cdots\!99}a^{28}+\frac{18\!\cdots\!50}{69\!\cdots\!99}a^{27}-\frac{55\!\cdots\!15}{69\!\cdots\!99}a^{26}-\frac{97\!\cdots\!49}{69\!\cdots\!99}a^{25}+\frac{38\!\cdots\!18}{69\!\cdots\!99}a^{24}+\frac{33\!\cdots\!06}{69\!\cdots\!99}a^{23}-\frac{18\!\cdots\!85}{69\!\cdots\!99}a^{22}-\frac{59\!\cdots\!79}{69\!\cdots\!99}a^{21}+\frac{63\!\cdots\!05}{69\!\cdots\!99}a^{20}-\frac{17\!\cdots\!72}{69\!\cdots\!99}a^{19}-\frac{15\!\cdots\!07}{69\!\cdots\!99}a^{18}+\frac{38\!\cdots\!79}{69\!\cdots\!99}a^{17}+\frac{26\!\cdots\!96}{69\!\cdots\!99}a^{16}-\frac{10\!\cdots\!96}{69\!\cdots\!99}a^{15}-\frac{30\!\cdots\!99}{69\!\cdots\!99}a^{14}+\frac{14\!\cdots\!68}{69\!\cdots\!99}a^{13}+\frac{25\!\cdots\!70}{69\!\cdots\!99}a^{12}-\frac{12\!\cdots\!44}{69\!\cdots\!99}a^{11}-\frac{13\!\cdots\!23}{69\!\cdots\!99}a^{10}+\frac{60\!\cdots\!58}{69\!\cdots\!99}a^{9}+\frac{47\!\cdots\!98}{69\!\cdots\!99}a^{8}-\frac{17\!\cdots\!94}{69\!\cdots\!99}a^{7}-\frac{99\!\cdots\!45}{69\!\cdots\!99}a^{6}+\frac{27\!\cdots\!81}{69\!\cdots\!99}a^{5}+\frac{10\!\cdots\!35}{69\!\cdots\!99}a^{4}-\frac{20\!\cdots\!14}{69\!\cdots\!99}a^{3}-\frac{47\!\cdots\!98}{69\!\cdots\!99}a^{2}+\frac{63\!\cdots\!57}{69\!\cdots\!99}a+\frac{95\!\cdots\!20}{83\!\cdots\!53}$, $\frac{96\!\cdots\!47}{18\!\cdots\!19}a^{38}-\frac{21\!\cdots\!82}{43\!\cdots\!37}a^{37}-\frac{13\!\cdots\!81}{43\!\cdots\!37}a^{36}+\frac{17\!\cdots\!78}{43\!\cdots\!37}a^{35}+\frac{19\!\cdots\!60}{43\!\cdots\!37}a^{34}-\frac{64\!\cdots\!74}{43\!\cdots\!37}a^{33}+\frac{46\!\cdots\!71}{43\!\cdots\!37}a^{32}+\frac{13\!\cdots\!72}{43\!\cdots\!37}a^{31}-\frac{22\!\cdots\!62}{43\!\cdots\!37}a^{30}-\frac{16\!\cdots\!41}{43\!\cdots\!37}a^{29}+\frac{39\!\cdots\!09}{43\!\cdots\!37}a^{28}+\frac{13\!\cdots\!65}{43\!\cdots\!37}a^{27}-\frac{41\!\cdots\!06}{43\!\cdots\!37}a^{26}-\frac{70\!\cdots\!42}{43\!\cdots\!37}a^{25}+\frac{29\!\cdots\!36}{43\!\cdots\!37}a^{24}+\frac{23\!\cdots\!01}{43\!\cdots\!37}a^{23}-\frac{13\!\cdots\!70}{43\!\cdots\!37}a^{22}-\frac{38\!\cdots\!41}{43\!\cdots\!37}a^{21}+\frac{47\!\cdots\!10}{43\!\cdots\!37}a^{20}-\frac{29\!\cdots\!48}{43\!\cdots\!37}a^{19}-\frac{59\!\cdots\!87}{22\!\cdots\!93}a^{18}+\frac{32\!\cdots\!90}{43\!\cdots\!37}a^{17}+\frac{19\!\cdots\!66}{43\!\cdots\!37}a^{16}-\frac{81\!\cdots\!90}{43\!\cdots\!37}a^{15}-\frac{22\!\cdots\!64}{43\!\cdots\!37}a^{14}+\frac{11\!\cdots\!18}{43\!\cdots\!37}a^{13}+\frac{18\!\cdots\!88}{43\!\cdots\!37}a^{12}-\frac{95\!\cdots\!19}{43\!\cdots\!37}a^{11}-\frac{10\!\cdots\!63}{43\!\cdots\!37}a^{10}+\frac{20\!\cdots\!98}{18\!\cdots\!19}a^{9}+\frac{34\!\cdots\!80}{43\!\cdots\!37}a^{8}-\frac{13\!\cdots\!92}{43\!\cdots\!37}a^{7}-\frac{72\!\cdots\!53}{43\!\cdots\!37}a^{6}+\frac{21\!\cdots\!21}{43\!\cdots\!37}a^{5}+\frac{79\!\cdots\!21}{43\!\cdots\!37}a^{4}-\frac{71\!\cdots\!18}{18\!\cdots\!19}a^{3}-\frac{35\!\cdots\!93}{43\!\cdots\!37}a^{2}+\frac{48\!\cdots\!76}{43\!\cdots\!37}a+\frac{76\!\cdots\!80}{52\!\cdots\!39}$, $\frac{67\!\cdots\!22}{36\!\cdots\!71}a^{38}-\frac{60\!\cdots\!42}{36\!\cdots\!71}a^{37}-\frac{43\!\cdots\!25}{36\!\cdots\!71}a^{36}+\frac{52\!\cdots\!90}{36\!\cdots\!71}a^{35}+\frac{81\!\cdots\!13}{36\!\cdots\!71}a^{34}-\frac{19\!\cdots\!65}{36\!\cdots\!71}a^{33}+\frac{56\!\cdots\!65}{36\!\cdots\!71}a^{32}+\frac{38\!\cdots\!23}{36\!\cdots\!71}a^{31}-\frac{49\!\cdots\!01}{36\!\cdots\!71}a^{30}-\frac{50\!\cdots\!87}{36\!\cdots\!71}a^{29}+\frac{95\!\cdots\!16}{36\!\cdots\!71}a^{28}+\frac{42\!\cdots\!40}{36\!\cdots\!71}a^{27}-\frac{10\!\cdots\!52}{36\!\cdots\!71}a^{26}-\frac{24\!\cdots\!69}{36\!\cdots\!71}a^{25}+\frac{73\!\cdots\!30}{36\!\cdots\!71}a^{24}+\frac{93\!\cdots\!85}{36\!\cdots\!71}a^{23}-\frac{35\!\cdots\!94}{36\!\cdots\!71}a^{22}-\frac{23\!\cdots\!06}{36\!\cdots\!71}a^{21}+\frac{12\!\cdots\!74}{36\!\cdots\!71}a^{20}+\frac{32\!\cdots\!08}{36\!\cdots\!71}a^{19}-\frac{29\!\cdots\!81}{36\!\cdots\!71}a^{18}-\frac{54\!\cdots\!65}{36\!\cdots\!71}a^{17}+\frac{21\!\cdots\!90}{15\!\cdots\!77}a^{16}-\frac{63\!\cdots\!36}{36\!\cdots\!71}a^{15}-\frac{57\!\cdots\!54}{36\!\cdots\!71}a^{14}+\frac{50\!\cdots\!82}{15\!\cdots\!77}a^{13}+\frac{45\!\cdots\!62}{36\!\cdots\!71}a^{12}-\frac{94\!\cdots\!38}{36\!\cdots\!71}a^{11}-\frac{22\!\cdots\!09}{36\!\cdots\!71}a^{10}+\frac{36\!\cdots\!24}{36\!\cdots\!71}a^{9}+\frac{68\!\cdots\!33}{36\!\cdots\!71}a^{8}-\frac{43\!\cdots\!49}{36\!\cdots\!71}a^{7}-\frac{96\!\cdots\!06}{36\!\cdots\!71}a^{6}-\frac{51\!\cdots\!99}{36\!\cdots\!71}a^{5}+\frac{16\!\cdots\!70}{36\!\cdots\!71}a^{4}+\frac{73\!\cdots\!29}{36\!\cdots\!71}a^{3}+\frac{50\!\cdots\!47}{36\!\cdots\!71}a^{2}+\frac{18\!\cdots\!93}{36\!\cdots\!71}a-\frac{33\!\cdots\!87}{43\!\cdots\!37}$, $\frac{92\!\cdots\!19}{36\!\cdots\!71}a^{38}-\frac{86\!\cdots\!94}{36\!\cdots\!71}a^{37}-\frac{55\!\cdots\!84}{36\!\cdots\!71}a^{36}+\frac{73\!\cdots\!20}{36\!\cdots\!71}a^{35}+\frac{83\!\cdots\!15}{36\!\cdots\!71}a^{34}-\frac{26\!\cdots\!33}{36\!\cdots\!71}a^{33}+\frac{17\!\cdots\!27}{36\!\cdots\!71}a^{32}+\frac{53\!\cdots\!87}{36\!\cdots\!71}a^{31}-\frac{88\!\cdots\!67}{36\!\cdots\!71}a^{30}-\frac{67\!\cdots\!40}{36\!\cdots\!71}a^{29}+\frac{15\!\cdots\!03}{36\!\cdots\!71}a^{28}+\frac{55\!\cdots\!83}{36\!\cdots\!71}a^{27}-\frac{73\!\cdots\!22}{15\!\cdots\!77}a^{26}-\frac{30\!\cdots\!27}{36\!\cdots\!71}a^{25}+\frac{11\!\cdots\!69}{36\!\cdots\!71}a^{24}+\frac{10\!\cdots\!48}{36\!\cdots\!71}a^{23}-\frac{56\!\cdots\!98}{36\!\cdots\!71}a^{22}-\frac{19\!\cdots\!65}{36\!\cdots\!71}a^{21}+\frac{19\!\cdots\!10}{36\!\cdots\!71}a^{20}-\frac{15\!\cdots\!74}{36\!\cdots\!71}a^{19}-\frac{46\!\cdots\!04}{36\!\cdots\!71}a^{18}+\frac{10\!\cdots\!18}{36\!\cdots\!71}a^{17}+\frac{79\!\cdots\!84}{36\!\cdots\!71}a^{16}-\frac{29\!\cdots\!02}{36\!\cdots\!71}a^{15}-\frac{94\!\cdots\!98}{36\!\cdots\!71}a^{14}+\frac{41\!\cdots\!30}{36\!\cdots\!71}a^{13}+\frac{76\!\cdots\!06}{36\!\cdots\!71}a^{12}-\frac{34\!\cdots\!01}{36\!\cdots\!71}a^{11}-\frac{41\!\cdots\!59}{36\!\cdots\!71}a^{10}+\frac{17\!\cdots\!86}{36\!\cdots\!71}a^{9}+\frac{14\!\cdots\!14}{36\!\cdots\!71}a^{8}-\frac{48\!\cdots\!71}{36\!\cdots\!71}a^{7}-\frac{29\!\cdots\!79}{36\!\cdots\!71}a^{6}+\frac{72\!\cdots\!02}{36\!\cdots\!71}a^{5}+\frac{31\!\cdots\!02}{36\!\cdots\!71}a^{4}-\frac{53\!\cdots\!80}{36\!\cdots\!71}a^{3}-\frac{13\!\cdots\!72}{36\!\cdots\!71}a^{2}+\frac{15\!\cdots\!76}{36\!\cdots\!71}a+\frac{33\!\cdots\!34}{43\!\cdots\!37}$, $\frac{12\!\cdots\!30}{36\!\cdots\!71}a^{38}-\frac{12\!\cdots\!54}{36\!\cdots\!71}a^{37}-\frac{76\!\cdots\!35}{36\!\cdots\!71}a^{36}+\frac{10\!\cdots\!63}{36\!\cdots\!71}a^{35}+\frac{10\!\cdots\!20}{36\!\cdots\!71}a^{34}-\frac{36\!\cdots\!99}{36\!\cdots\!71}a^{33}+\frac{26\!\cdots\!34}{36\!\cdots\!71}a^{32}+\frac{74\!\cdots\!69}{36\!\cdots\!71}a^{31}-\frac{12\!\cdots\!64}{36\!\cdots\!71}a^{30}-\frac{93\!\cdots\!12}{36\!\cdots\!71}a^{29}+\frac{22\!\cdots\!45}{36\!\cdots\!71}a^{28}+\frac{76\!\cdots\!84}{36\!\cdots\!71}a^{27}-\frac{23\!\cdots\!78}{36\!\cdots\!71}a^{26}-\frac{40\!\cdots\!89}{36\!\cdots\!71}a^{25}+\frac{16\!\cdots\!41}{36\!\cdots\!71}a^{24}+\frac{13\!\cdots\!57}{36\!\cdots\!71}a^{23}-\frac{80\!\cdots\!29}{36\!\cdots\!71}a^{22}-\frac{23\!\cdots\!90}{36\!\cdots\!71}a^{21}+\frac{27\!\cdots\!89}{36\!\cdots\!71}a^{20}-\frac{14\!\cdots\!97}{36\!\cdots\!71}a^{19}-\frac{65\!\cdots\!41}{36\!\cdots\!71}a^{18}+\frac{18\!\cdots\!89}{36\!\cdots\!71}a^{17}+\frac{11\!\cdots\!63}{36\!\cdots\!71}a^{16}-\frac{46\!\cdots\!32}{36\!\cdots\!71}a^{15}-\frac{13\!\cdots\!14}{36\!\cdots\!71}a^{14}+\frac{65\!\cdots\!08}{36\!\cdots\!71}a^{13}+\frac{10\!\cdots\!11}{36\!\cdots\!71}a^{12}-\frac{55\!\cdots\!41}{36\!\cdots\!71}a^{11}-\frac{59\!\cdots\!25}{36\!\cdots\!71}a^{10}+\frac{27\!\cdots\!74}{36\!\cdots\!71}a^{9}+\frac{20\!\cdots\!04}{36\!\cdots\!71}a^{8}-\frac{81\!\cdots\!66}{36\!\cdots\!71}a^{7}-\frac{44\!\cdots\!28}{36\!\cdots\!71}a^{6}+\frac{12\!\cdots\!66}{36\!\cdots\!71}a^{5}+\frac{49\!\cdots\!77}{36\!\cdots\!71}a^{4}-\frac{10\!\cdots\!42}{36\!\cdots\!71}a^{3}-\frac{22\!\cdots\!25}{36\!\cdots\!71}a^{2}+\frac{29\!\cdots\!90}{36\!\cdots\!71}a+\frac{49\!\cdots\!89}{43\!\cdots\!37}$, $\frac{62\!\cdots\!11}{36\!\cdots\!71}a^{38}-\frac{58\!\cdots\!56}{36\!\cdots\!71}a^{37}-\frac{38\!\cdots\!19}{36\!\cdots\!71}a^{36}+\frac{50\!\cdots\!26}{36\!\cdots\!71}a^{35}+\frac{60\!\cdots\!26}{36\!\cdots\!71}a^{34}-\frac{18\!\cdots\!46}{36\!\cdots\!71}a^{33}+\frac{10\!\cdots\!22}{36\!\cdots\!71}a^{32}+\frac{36\!\cdots\!00}{36\!\cdots\!71}a^{31}-\frac{57\!\cdots\!46}{36\!\cdots\!71}a^{30}-\frac{46\!\cdots\!77}{36\!\cdots\!71}a^{29}+\frac{10\!\cdots\!24}{36\!\cdots\!71}a^{28}+\frac{38\!\cdots\!09}{36\!\cdots\!71}a^{27}-\frac{11\!\cdots\!11}{36\!\cdots\!71}a^{26}-\frac{21\!\cdots\!33}{36\!\cdots\!71}a^{25}+\frac{79\!\cdots\!78}{36\!\cdots\!71}a^{24}+\frac{75\!\cdots\!79}{36\!\cdots\!71}a^{23}-\frac{38\!\cdots\!68}{36\!\cdots\!71}a^{22}-\frac{15\!\cdots\!58}{36\!\cdots\!71}a^{21}+\frac{13\!\cdots\!89}{36\!\cdots\!71}a^{20}+\frac{72\!\cdots\!75}{36\!\cdots\!71}a^{19}-\frac{31\!\cdots\!93}{36\!\cdots\!71}a^{18}+\frac{53\!\cdots\!01}{36\!\cdots\!71}a^{17}+\frac{54\!\cdots\!52}{36\!\cdots\!71}a^{16}-\frac{16\!\cdots\!68}{36\!\cdots\!71}a^{15}-\frac{65\!\cdots\!43}{36\!\cdots\!71}a^{14}+\frac{24\!\cdots\!32}{36\!\cdots\!71}a^{13}+\frac{53\!\cdots\!78}{36\!\cdots\!71}a^{12}-\frac{20\!\cdots\!78}{36\!\cdots\!71}a^{11}-\frac{29\!\cdots\!30}{36\!\cdots\!71}a^{10}+\frac{98\!\cdots\!03}{36\!\cdots\!71}a^{9}+\frac{10\!\cdots\!71}{36\!\cdots\!71}a^{8}-\frac{26\!\cdots\!83}{36\!\cdots\!71}a^{7}-\frac{22\!\cdots\!76}{36\!\cdots\!71}a^{6}+\frac{37\!\cdots\!05}{36\!\cdots\!71}a^{5}+\frac{23\!\cdots\!12}{36\!\cdots\!71}a^{4}-\frac{26\!\cdots\!88}{36\!\cdots\!71}a^{3}-\frac{10\!\cdots\!96}{36\!\cdots\!71}a^{2}+\frac{83\!\cdots\!79}{36\!\cdots\!71}a+\frac{31\!\cdots\!81}{18\!\cdots\!19}$, $\frac{45\!\cdots\!70}{36\!\cdots\!71}a^{38}-\frac{42\!\cdots\!42}{36\!\cdots\!71}a^{37}-\frac{27\!\cdots\!45}{36\!\cdots\!71}a^{36}+\frac{36\!\cdots\!73}{36\!\cdots\!71}a^{35}+\frac{41\!\cdots\!20}{36\!\cdots\!71}a^{34}-\frac{13\!\cdots\!99}{36\!\cdots\!71}a^{33}+\frac{87\!\cdots\!91}{36\!\cdots\!71}a^{32}+\frac{26\!\cdots\!44}{36\!\cdots\!71}a^{31}-\frac{43\!\cdots\!53}{36\!\cdots\!71}a^{30}-\frac{33\!\cdots\!57}{36\!\cdots\!71}a^{29}+\frac{78\!\cdots\!32}{36\!\cdots\!71}a^{28}+\frac{27\!\cdots\!18}{36\!\cdots\!71}a^{27}-\frac{83\!\cdots\!67}{36\!\cdots\!71}a^{26}-\frac{14\!\cdots\!45}{36\!\cdots\!71}a^{25}+\frac{58\!\cdots\!62}{36\!\cdots\!71}a^{24}+\frac{51\!\cdots\!04}{36\!\cdots\!71}a^{23}-\frac{28\!\cdots\!21}{36\!\cdots\!71}a^{22}-\frac{94\!\cdots\!51}{36\!\cdots\!71}a^{21}+\frac{95\!\cdots\!73}{36\!\cdots\!71}a^{20}-\frac{63\!\cdots\!66}{36\!\cdots\!71}a^{19}-\frac{23\!\cdots\!43}{36\!\cdots\!71}a^{18}+\frac{53\!\cdots\!09}{36\!\cdots\!71}a^{17}+\frac{39\!\cdots\!02}{36\!\cdots\!71}a^{16}-\frac{14\!\cdots\!50}{36\!\cdots\!71}a^{15}-\frac{47\!\cdots\!21}{36\!\cdots\!71}a^{14}+\frac{20\!\cdots\!14}{36\!\cdots\!71}a^{13}+\frac{38\!\cdots\!54}{36\!\cdots\!71}a^{12}-\frac{17\!\cdots\!48}{36\!\cdots\!71}a^{11}-\frac{21\!\cdots\!49}{36\!\cdots\!71}a^{10}+\frac{88\!\cdots\!34}{36\!\cdots\!71}a^{9}+\frac{74\!\cdots\!23}{36\!\cdots\!71}a^{8}-\frac{25\!\cdots\!46}{36\!\cdots\!71}a^{7}-\frac{15\!\cdots\!53}{36\!\cdots\!71}a^{6}+\frac{39\!\cdots\!91}{36\!\cdots\!71}a^{5}+\frac{17\!\cdots\!69}{36\!\cdots\!71}a^{4}-\frac{31\!\cdots\!28}{36\!\cdots\!71}a^{3}-\frac{74\!\cdots\!40}{36\!\cdots\!71}a^{2}+\frac{96\!\cdots\!69}{36\!\cdots\!71}a+\frac{14\!\cdots\!92}{43\!\cdots\!37}$, $\frac{54\!\cdots\!43}{36\!\cdots\!71}a^{38}-\frac{51\!\cdots\!42}{36\!\cdots\!71}a^{37}-\frac{33\!\cdots\!09}{36\!\cdots\!71}a^{36}+\frac{43\!\cdots\!57}{36\!\cdots\!71}a^{35}+\frac{49\!\cdots\!73}{36\!\cdots\!71}a^{34}-\frac{15\!\cdots\!92}{36\!\cdots\!71}a^{33}+\frac{10\!\cdots\!01}{36\!\cdots\!71}a^{32}+\frac{31\!\cdots\!53}{36\!\cdots\!71}a^{31}-\frac{52\!\cdots\!66}{36\!\cdots\!71}a^{30}-\frac{40\!\cdots\!49}{36\!\cdots\!71}a^{29}+\frac{94\!\cdots\!18}{36\!\cdots\!71}a^{28}+\frac{33\!\cdots\!61}{36\!\cdots\!71}a^{27}-\frac{10\!\cdots\!64}{36\!\cdots\!71}a^{26}-\frac{17\!\cdots\!45}{36\!\cdots\!71}a^{25}+\frac{70\!\cdots\!79}{36\!\cdots\!71}a^{24}+\frac{61\!\cdots\!40}{36\!\cdots\!71}a^{23}-\frac{33\!\cdots\!59}{36\!\cdots\!71}a^{22}-\frac{11\!\cdots\!75}{36\!\cdots\!71}a^{21}+\frac{11\!\cdots\!76}{36\!\cdots\!71}a^{20}-\frac{32\!\cdots\!59}{36\!\cdots\!71}a^{19}-\frac{27\!\cdots\!27}{36\!\cdots\!71}a^{18}+\frac{63\!\cdots\!56}{36\!\cdots\!71}a^{17}+\frac{47\!\cdots\!19}{36\!\cdots\!71}a^{16}-\frac{17\!\cdots\!08}{36\!\cdots\!71}a^{15}-\frac{57\!\cdots\!14}{36\!\cdots\!71}a^{14}+\frac{24\!\cdots\!52}{36\!\cdots\!71}a^{13}+\frac{46\!\cdots\!02}{36\!\cdots\!71}a^{12}-\frac{21\!\cdots\!84}{36\!\cdots\!71}a^{11}-\frac{25\!\cdots\!85}{36\!\cdots\!71}a^{10}+\frac{10\!\cdots\!31}{36\!\cdots\!71}a^{9}+\frac{90\!\cdots\!72}{36\!\cdots\!71}a^{8}-\frac{30\!\cdots\!92}{36\!\cdots\!71}a^{7}-\frac{19\!\cdots\!51}{36\!\cdots\!71}a^{6}+\frac{47\!\cdots\!95}{36\!\cdots\!71}a^{5}+\frac{20\!\cdots\!45}{36\!\cdots\!71}a^{4}-\frac{37\!\cdots\!28}{36\!\cdots\!71}a^{3}-\frac{92\!\cdots\!09}{36\!\cdots\!71}a^{2}+\frac{11\!\cdots\!95}{36\!\cdots\!71}a+\frac{21\!\cdots\!75}{43\!\cdots\!37}$, $\frac{52\!\cdots\!48}{36\!\cdots\!71}a^{38}-\frac{49\!\cdots\!48}{36\!\cdots\!71}a^{37}-\frac{31\!\cdots\!51}{36\!\cdots\!71}a^{36}+\frac{41\!\cdots\!21}{36\!\cdots\!71}a^{35}+\frac{46\!\cdots\!48}{36\!\cdots\!71}a^{34}-\frac{15\!\cdots\!87}{36\!\cdots\!71}a^{33}+\frac{10\!\cdots\!28}{36\!\cdots\!71}a^{32}+\frac{30\!\cdots\!73}{36\!\cdots\!71}a^{31}-\frac{50\!\cdots\!08}{36\!\cdots\!71}a^{30}-\frac{38\!\cdots\!16}{36\!\cdots\!71}a^{29}+\frac{90\!\cdots\!13}{36\!\cdots\!71}a^{28}+\frac{31\!\cdots\!64}{36\!\cdots\!71}a^{27}-\frac{96\!\cdots\!48}{36\!\cdots\!71}a^{26}-\frac{16\!\cdots\!81}{36\!\cdots\!71}a^{25}+\frac{67\!\cdots\!34}{36\!\cdots\!71}a^{24}+\frac{57\!\cdots\!03}{36\!\cdots\!71}a^{23}-\frac{32\!\cdots\!31}{36\!\cdots\!71}a^{22}-\frac{10\!\cdots\!34}{36\!\cdots\!71}a^{21}+\frac{11\!\cdots\!47}{36\!\cdots\!71}a^{20}-\frac{20\!\cdots\!05}{36\!\cdots\!71}a^{19}-\frac{26\!\cdots\!35}{36\!\cdots\!71}a^{18}+\frac{64\!\cdots\!62}{36\!\cdots\!71}a^{17}+\frac{45\!\cdots\!61}{36\!\cdots\!71}a^{16}-\frac{17\!\cdots\!42}{36\!\cdots\!71}a^{15}-\frac{53\!\cdots\!94}{36\!\cdots\!71}a^{14}+\frac{24\!\cdots\!14}{36\!\cdots\!71}a^{13}+\frac{44\!\cdots\!36}{36\!\cdots\!71}a^{12}-\frac{20\!\cdots\!01}{36\!\cdots\!71}a^{11}-\frac{23\!\cdots\!85}{36\!\cdots\!71}a^{10}+\frac{10\!\cdots\!25}{36\!\cdots\!71}a^{9}+\frac{83\!\cdots\!85}{36\!\cdots\!71}a^{8}-\frac{29\!\cdots\!02}{36\!\cdots\!71}a^{7}-\frac{17\!\cdots\!66}{36\!\cdots\!71}a^{6}+\frac{45\!\cdots\!01}{36\!\cdots\!71}a^{5}+\frac{18\!\cdots\!47}{36\!\cdots\!71}a^{4}-\frac{34\!\cdots\!44}{36\!\cdots\!71}a^{3}-\frac{81\!\cdots\!10}{36\!\cdots\!71}a^{2}+\frac{10\!\cdots\!11}{36\!\cdots\!71}a+\frac{16\!\cdots\!22}{43\!\cdots\!37}$, $\frac{37\!\cdots\!68}{36\!\cdots\!71}a^{38}-\frac{34\!\cdots\!68}{36\!\cdots\!71}a^{37}-\frac{22\!\cdots\!92}{36\!\cdots\!71}a^{36}+\frac{29\!\cdots\!74}{36\!\cdots\!71}a^{35}+\frac{34\!\cdots\!50}{36\!\cdots\!71}a^{34}-\frac{10\!\cdots\!72}{36\!\cdots\!71}a^{33}+\frac{70\!\cdots\!83}{36\!\cdots\!71}a^{32}+\frac{21\!\cdots\!63}{36\!\cdots\!71}a^{31}-\frac{35\!\cdots\!57}{36\!\cdots\!71}a^{30}-\frac{27\!\cdots\!61}{36\!\cdots\!71}a^{29}+\frac{63\!\cdots\!98}{36\!\cdots\!71}a^{28}+\frac{22\!\cdots\!50}{36\!\cdots\!71}a^{27}-\frac{67\!\cdots\!56}{36\!\cdots\!71}a^{26}-\frac{12\!\cdots\!95}{36\!\cdots\!71}a^{25}+\frac{47\!\cdots\!73}{36\!\cdots\!71}a^{24}+\frac{42\!\cdots\!13}{36\!\cdots\!71}a^{23}-\frac{22\!\cdots\!16}{36\!\cdots\!71}a^{22}-\frac{80\!\cdots\!86}{36\!\cdots\!71}a^{21}+\frac{78\!\cdots\!68}{36\!\cdots\!71}a^{20}+\frac{60\!\cdots\!60}{36\!\cdots\!71}a^{19}-\frac{18\!\cdots\!49}{36\!\cdots\!71}a^{18}+\frac{40\!\cdots\!10}{36\!\cdots\!71}a^{17}+\frac{32\!\cdots\!12}{36\!\cdots\!71}a^{16}-\frac{11\!\cdots\!02}{36\!\cdots\!71}a^{15}-\frac{38\!\cdots\!34}{36\!\cdots\!71}a^{14}+\frac{16\!\cdots\!34}{36\!\cdots\!71}a^{13}+\frac{13\!\cdots\!31}{15\!\cdots\!77}a^{12}-\frac{13\!\cdots\!86}{36\!\cdots\!71}a^{11}-\frac{17\!\cdots\!95}{36\!\cdots\!71}a^{10}+\frac{70\!\cdots\!83}{36\!\cdots\!71}a^{9}+\frac{61\!\cdots\!48}{36\!\cdots\!71}a^{8}-\frac{19\!\cdots\!93}{36\!\cdots\!71}a^{7}-\frac{12\!\cdots\!03}{36\!\cdots\!71}a^{6}+\frac{30\!\cdots\!59}{36\!\cdots\!71}a^{5}+\frac{14\!\cdots\!13}{36\!\cdots\!71}a^{4}-\frac{24\!\cdots\!81}{36\!\cdots\!71}a^{3}-\frac{60\!\cdots\!41}{36\!\cdots\!71}a^{2}+\frac{77\!\cdots\!10}{36\!\cdots\!71}a+\frac{12\!\cdots\!71}{43\!\cdots\!37}$, $\frac{30\!\cdots\!96}{36\!\cdots\!71}a^{38}-\frac{28\!\cdots\!76}{36\!\cdots\!71}a^{37}-\frac{18\!\cdots\!26}{36\!\cdots\!71}a^{36}+\frac{24\!\cdots\!60}{36\!\cdots\!71}a^{35}+\frac{30\!\cdots\!28}{36\!\cdots\!71}a^{34}-\frac{87\!\cdots\!50}{36\!\cdots\!71}a^{33}+\frac{46\!\cdots\!35}{36\!\cdots\!71}a^{32}+\frac{17\!\cdots\!29}{36\!\cdots\!71}a^{31}-\frac{26\!\cdots\!53}{36\!\cdots\!71}a^{30}-\frac{22\!\cdots\!15}{36\!\cdots\!71}a^{29}+\frac{49\!\cdots\!51}{36\!\cdots\!71}a^{28}+\frac{18\!\cdots\!66}{36\!\cdots\!71}a^{27}-\frac{52\!\cdots\!57}{36\!\cdots\!71}a^{26}-\frac{10\!\cdots\!32}{36\!\cdots\!71}a^{25}+\frac{36\!\cdots\!81}{36\!\cdots\!71}a^{24}+\frac{37\!\cdots\!17}{36\!\cdots\!71}a^{23}-\frac{17\!\cdots\!36}{36\!\cdots\!71}a^{22}-\frac{79\!\cdots\!01}{36\!\cdots\!71}a^{21}+\frac{60\!\cdots\!56}{36\!\cdots\!71}a^{20}+\frac{52\!\cdots\!09}{36\!\cdots\!71}a^{19}-\frac{14\!\cdots\!62}{36\!\cdots\!71}a^{18}+\frac{20\!\cdots\!02}{36\!\cdots\!71}a^{17}+\frac{24\!\cdots\!21}{36\!\cdots\!71}a^{16}-\frac{70\!\cdots\!52}{36\!\cdots\!71}a^{15}-\frac{29\!\cdots\!57}{36\!\cdots\!71}a^{14}+\frac{10\!\cdots\!64}{36\!\cdots\!71}a^{13}+\frac{23\!\cdots\!19}{36\!\cdots\!71}a^{12}-\frac{86\!\cdots\!35}{36\!\cdots\!71}a^{11}-\frac{12\!\cdots\!42}{36\!\cdots\!71}a^{10}+\frac{40\!\cdots\!08}{36\!\cdots\!71}a^{9}+\frac{42\!\cdots\!38}{36\!\cdots\!71}a^{8}-\frac{10\!\cdots\!60}{36\!\cdots\!71}a^{7}-\frac{79\!\cdots\!77}{36\!\cdots\!71}a^{6}+\frac{13\!\cdots\!83}{36\!\cdots\!71}a^{5}+\frac{71\!\cdots\!38}{36\!\cdots\!71}a^{4}-\frac{90\!\cdots\!64}{36\!\cdots\!71}a^{3}-\frac{21\!\cdots\!17}{36\!\cdots\!71}a^{2}+\frac{34\!\cdots\!92}{36\!\cdots\!71}a-\frac{44\!\cdots\!46}{43\!\cdots\!37}$, $\frac{36\!\cdots\!45}{36\!\cdots\!71}a^{38}-\frac{14\!\cdots\!04}{15\!\cdots\!77}a^{37}-\frac{21\!\cdots\!32}{36\!\cdots\!71}a^{36}+\frac{29\!\cdots\!45}{36\!\cdots\!71}a^{35}+\frac{32\!\cdots\!06}{36\!\cdots\!71}a^{34}-\frac{10\!\cdots\!69}{36\!\cdots\!71}a^{33}+\frac{74\!\cdots\!54}{36\!\cdots\!71}a^{32}+\frac{21\!\cdots\!02}{36\!\cdots\!71}a^{31}-\frac{35\!\cdots\!83}{36\!\cdots\!71}a^{30}-\frac{26\!\cdots\!72}{36\!\cdots\!71}a^{29}+\frac{63\!\cdots\!31}{36\!\cdots\!71}a^{28}+\frac{21\!\cdots\!33}{36\!\cdots\!71}a^{27}-\frac{67\!\cdots\!43}{36\!\cdots\!71}a^{26}-\frac{11\!\cdots\!27}{36\!\cdots\!71}a^{25}+\frac{46\!\cdots\!14}{36\!\cdots\!71}a^{24}+\frac{38\!\cdots\!69}{36\!\cdots\!71}a^{23}-\frac{97\!\cdots\!39}{15\!\cdots\!77}a^{22}-\frac{66\!\cdots\!60}{36\!\cdots\!71}a^{21}+\frac{75\!\cdots\!21}{36\!\cdots\!71}a^{20}-\frac{14\!\cdots\!02}{15\!\cdots\!77}a^{19}-\frac{18\!\cdots\!08}{36\!\cdots\!71}a^{18}+\frac{48\!\cdots\!27}{36\!\cdots\!71}a^{17}+\frac{30\!\cdots\!35}{36\!\cdots\!71}a^{16}-\frac{12\!\cdots\!92}{36\!\cdots\!71}a^{15}-\frac{35\!\cdots\!23}{36\!\cdots\!71}a^{14}+\frac{16\!\cdots\!36}{36\!\cdots\!71}a^{13}+\frac{28\!\cdots\!54}{36\!\cdots\!71}a^{12}-\frac{13\!\cdots\!17}{36\!\cdots\!71}a^{11}-\frac{15\!\cdots\!02}{36\!\cdots\!71}a^{10}+\frac{66\!\cdots\!02}{36\!\cdots\!71}a^{9}+\frac{51\!\cdots\!50}{36\!\cdots\!71}a^{8}-\frac{76\!\cdots\!04}{15\!\cdots\!77}a^{7}-\frac{10\!\cdots\!04}{36\!\cdots\!71}a^{6}+\frac{24\!\cdots\!48}{36\!\cdots\!71}a^{5}+\frac{10\!\cdots\!49}{36\!\cdots\!71}a^{4}-\frac{16\!\cdots\!14}{36\!\cdots\!71}a^{3}-\frac{45\!\cdots\!97}{36\!\cdots\!71}a^{2}+\frac{49\!\cdots\!59}{36\!\cdots\!71}a+\frac{19\!\cdots\!89}{43\!\cdots\!37}$, $\frac{33\!\cdots\!25}{36\!\cdots\!71}a^{38}-\frac{31\!\cdots\!42}{36\!\cdots\!71}a^{37}-\frac{20\!\cdots\!28}{36\!\cdots\!71}a^{36}+\frac{26\!\cdots\!47}{36\!\cdots\!71}a^{35}+\frac{30\!\cdots\!68}{36\!\cdots\!71}a^{34}-\frac{97\!\cdots\!45}{36\!\cdots\!71}a^{33}+\frac{63\!\cdots\!35}{36\!\cdots\!71}a^{32}+\frac{19\!\cdots\!97}{36\!\cdots\!71}a^{31}-\frac{32\!\cdots\!62}{36\!\cdots\!71}a^{30}-\frac{24\!\cdots\!13}{36\!\cdots\!71}a^{29}+\frac{58\!\cdots\!66}{36\!\cdots\!71}a^{28}+\frac{20\!\cdots\!69}{36\!\cdots\!71}a^{27}-\frac{61\!\cdots\!50}{36\!\cdots\!71}a^{26}-\frac{11\!\cdots\!95}{36\!\cdots\!71}a^{25}+\frac{43\!\cdots\!46}{36\!\cdots\!71}a^{24}+\frac{38\!\cdots\!20}{36\!\cdots\!71}a^{23}-\frac{20\!\cdots\!21}{36\!\cdots\!71}a^{22}-\frac{72\!\cdots\!31}{36\!\cdots\!71}a^{21}+\frac{30\!\cdots\!79}{15\!\cdots\!77}a^{20}+\frac{38\!\cdots\!79}{36\!\cdots\!71}a^{19}-\frac{17\!\cdots\!46}{36\!\cdots\!71}a^{18}+\frac{37\!\cdots\!92}{36\!\cdots\!71}a^{17}+\frac{29\!\cdots\!83}{36\!\cdots\!71}a^{16}-\frac{10\!\cdots\!72}{36\!\cdots\!71}a^{15}-\frac{34\!\cdots\!82}{36\!\cdots\!71}a^{14}+\frac{14\!\cdots\!20}{36\!\cdots\!71}a^{13}+\frac{28\!\cdots\!32}{36\!\cdots\!71}a^{12}-\frac{12\!\cdots\!24}{36\!\cdots\!71}a^{11}-\frac{15\!\cdots\!56}{36\!\cdots\!71}a^{10}+\frac{63\!\cdots\!43}{36\!\cdots\!71}a^{9}+\frac{54\!\cdots\!45}{36\!\cdots\!71}a^{8}-\frac{17\!\cdots\!66}{36\!\cdots\!71}a^{7}-\frac{11\!\cdots\!67}{36\!\cdots\!71}a^{6}+\frac{27\!\cdots\!58}{36\!\cdots\!71}a^{5}+\frac{12\!\cdots\!04}{36\!\cdots\!71}a^{4}-\frac{21\!\cdots\!82}{36\!\cdots\!71}a^{3}-\frac{52\!\cdots\!91}{36\!\cdots\!71}a^{2}+\frac{28\!\cdots\!61}{15\!\cdots\!77}a+\frac{10\!\cdots\!19}{43\!\cdots\!37}$, $\frac{35\!\cdots\!71}{36\!\cdots\!71}a^{38}-\frac{34\!\cdots\!12}{36\!\cdots\!71}a^{37}-\frac{20\!\cdots\!99}{36\!\cdots\!71}a^{36}+\frac{29\!\cdots\!36}{36\!\cdots\!71}a^{35}+\frac{10\!\cdots\!93}{15\!\cdots\!77}a^{34}-\frac{10\!\cdots\!01}{36\!\cdots\!71}a^{33}+\frac{95\!\cdots\!37}{36\!\cdots\!71}a^{32}+\frac{20\!\cdots\!97}{36\!\cdots\!71}a^{31}-\frac{39\!\cdots\!99}{36\!\cdots\!71}a^{30}-\frac{25\!\cdots\!30}{36\!\cdots\!71}a^{29}+\frac{68\!\cdots\!39}{36\!\cdots\!71}a^{28}+\frac{19\!\cdots\!08}{36\!\cdots\!71}a^{27}-\frac{70\!\cdots\!94}{36\!\cdots\!71}a^{26}-\frac{99\!\cdots\!50}{36\!\cdots\!71}a^{25}+\frac{48\!\cdots\!43}{36\!\cdots\!71}a^{24}+\frac{28\!\cdots\!35}{36\!\cdots\!71}a^{23}-\frac{23\!\cdots\!59}{36\!\cdots\!71}a^{22}-\frac{75\!\cdots\!40}{15\!\cdots\!77}a^{21}+\frac{76\!\cdots\!99}{36\!\cdots\!71}a^{20}-\frac{19\!\cdots\!00}{36\!\cdots\!71}a^{19}-\frac{17\!\cdots\!39}{36\!\cdots\!71}a^{18}+\frac{87\!\cdots\!65}{36\!\cdots\!71}a^{17}+\frac{29\!\cdots\!49}{36\!\cdots\!71}a^{16}-\frac{18\!\cdots\!26}{36\!\cdots\!71}a^{15}-\frac{33\!\cdots\!37}{36\!\cdots\!71}a^{14}+\frac{25\!\cdots\!53}{36\!\cdots\!71}a^{13}+\frac{25\!\cdots\!85}{36\!\cdots\!71}a^{12}-\frac{20\!\cdots\!55}{36\!\cdots\!71}a^{11}-\frac{12\!\cdots\!61}{36\!\cdots\!71}a^{10}+\frac{10\!\cdots\!66}{36\!\cdots\!71}a^{9}+\frac{39\!\cdots\!89}{36\!\cdots\!71}a^{8}-\frac{29\!\cdots\!01}{36\!\cdots\!71}a^{7}-\frac{73\!\cdots\!47}{36\!\cdots\!71}a^{6}+\frac{46\!\cdots\!34}{36\!\cdots\!71}a^{5}+\frac{70\!\cdots\!32}{36\!\cdots\!71}a^{4}-\frac{32\!\cdots\!71}{36\!\cdots\!71}a^{3}-\frac{26\!\cdots\!72}{36\!\cdots\!71}a^{2}+\frac{55\!\cdots\!91}{36\!\cdots\!71}a+\frac{11\!\cdots\!32}{43\!\cdots\!37}$, $\frac{95\!\cdots\!50}{36\!\cdots\!71}a^{38}-\frac{89\!\cdots\!96}{36\!\cdots\!71}a^{37}-\frac{58\!\cdots\!76}{36\!\cdots\!71}a^{36}+\frac{76\!\cdots\!58}{36\!\cdots\!71}a^{35}+\frac{88\!\cdots\!27}{36\!\cdots\!71}a^{34}-\frac{12\!\cdots\!62}{15\!\cdots\!77}a^{33}+\frac{18\!\cdots\!02}{36\!\cdots\!71}a^{32}+\frac{56\!\cdots\!54}{36\!\cdots\!71}a^{31}-\frac{91\!\cdots\!33}{36\!\cdots\!71}a^{30}-\frac{70\!\cdots\!80}{36\!\cdots\!71}a^{29}+\frac{16\!\cdots\!21}{36\!\cdots\!71}a^{28}+\frac{58\!\cdots\!45}{36\!\cdots\!71}a^{27}-\frac{17\!\cdots\!05}{36\!\cdots\!71}a^{26}-\frac{31\!\cdots\!14}{36\!\cdots\!71}a^{25}+\frac{12\!\cdots\!27}{36\!\cdots\!71}a^{24}+\frac{11\!\cdots\!30}{36\!\cdots\!71}a^{23}-\frac{59\!\cdots\!56}{36\!\cdots\!71}a^{22}-\frac{21\!\cdots\!23}{36\!\cdots\!71}a^{21}+\frac{20\!\cdots\!86}{36\!\cdots\!71}a^{20}+\frac{19\!\cdots\!27}{36\!\cdots\!71}a^{19}-\frac{48\!\cdots\!01}{36\!\cdots\!71}a^{18}+\frac{10\!\cdots\!70}{36\!\cdots\!71}a^{17}+\frac{83\!\cdots\!87}{36\!\cdots\!71}a^{16}-\frac{29\!\cdots\!61}{36\!\cdots\!71}a^{15}-\frac{10\!\cdots\!73}{36\!\cdots\!71}a^{14}+\frac{42\!\cdots\!46}{36\!\cdots\!71}a^{13}+\frac{35\!\cdots\!66}{15\!\cdots\!77}a^{12}-\frac{36\!\cdots\!19}{36\!\cdots\!71}a^{11}-\frac{45\!\cdots\!10}{36\!\cdots\!71}a^{10}+\frac{18\!\cdots\!19}{36\!\cdots\!71}a^{9}+\frac{15\!\cdots\!59}{36\!\cdots\!71}a^{8}-\frac{51\!\cdots\!89}{36\!\cdots\!71}a^{7}-\frac{33\!\cdots\!38}{36\!\cdots\!71}a^{6}+\frac{79\!\cdots\!62}{36\!\cdots\!71}a^{5}+\frac{36\!\cdots\!05}{36\!\cdots\!71}a^{4}-\frac{62\!\cdots\!16}{36\!\cdots\!71}a^{3}-\frac{15\!\cdots\!20}{36\!\cdots\!71}a^{2}+\frac{19\!\cdots\!65}{36\!\cdots\!71}a+\frac{33\!\cdots\!13}{43\!\cdots\!37}$, $\frac{70\!\cdots\!97}{36\!\cdots\!71}a^{38}-\frac{65\!\cdots\!64}{36\!\cdots\!71}a^{37}-\frac{43\!\cdots\!95}{36\!\cdots\!71}a^{36}+\frac{55\!\cdots\!67}{36\!\cdots\!71}a^{35}+\frac{68\!\cdots\!04}{36\!\cdots\!71}a^{34}-\frac{20\!\cdots\!96}{36\!\cdots\!71}a^{33}+\frac{11\!\cdots\!84}{36\!\cdots\!71}a^{32}+\frac{41\!\cdots\!25}{36\!\cdots\!71}a^{31}-\frac{27\!\cdots\!18}{15\!\cdots\!77}a^{30}-\frac{52\!\cdots\!97}{36\!\cdots\!71}a^{29}+\frac{11\!\cdots\!59}{36\!\cdots\!71}a^{28}+\frac{43\!\cdots\!57}{36\!\cdots\!71}a^{27}-\frac{54\!\cdots\!55}{15\!\cdots\!77}a^{26}-\frac{24\!\cdots\!75}{36\!\cdots\!71}a^{25}+\frac{88\!\cdots\!17}{36\!\cdots\!71}a^{24}+\frac{86\!\cdots\!24}{36\!\cdots\!71}a^{23}-\frac{42\!\cdots\!14}{36\!\cdots\!71}a^{22}-\frac{18\!\cdots\!30}{36\!\cdots\!71}a^{21}+\frac{14\!\cdots\!69}{36\!\cdots\!71}a^{20}+\frac{11\!\cdots\!17}{36\!\cdots\!71}a^{19}-\frac{35\!\cdots\!21}{36\!\cdots\!71}a^{18}+\frac{54\!\cdots\!12}{36\!\cdots\!71}a^{17}+\frac{62\!\cdots\!75}{36\!\cdots\!71}a^{16}-\frac{18\!\cdots\!69}{36\!\cdots\!71}a^{15}-\frac{75\!\cdots\!97}{36\!\cdots\!71}a^{14}+\frac{27\!\cdots\!60}{36\!\cdots\!71}a^{13}+\frac{62\!\cdots\!55}{36\!\cdots\!71}a^{12}-\frac{23\!\cdots\!45}{36\!\cdots\!71}a^{11}-\frac{35\!\cdots\!31}{36\!\cdots\!71}a^{10}+\frac{12\!\cdots\!31}{36\!\cdots\!71}a^{9}+\frac{12\!\cdots\!46}{36\!\cdots\!71}a^{8}-\frac{35\!\cdots\!26}{36\!\cdots\!71}a^{7}-\frac{26\!\cdots\!88}{36\!\cdots\!71}a^{6}+\frac{55\!\cdots\!11}{36\!\cdots\!71}a^{5}+\frac{29\!\cdots\!97}{36\!\cdots\!71}a^{4}-\frac{45\!\cdots\!59}{36\!\cdots\!71}a^{3}-\frac{12\!\cdots\!68}{36\!\cdots\!71}a^{2}+\frac{15\!\cdots\!99}{36\!\cdots\!71}a+\frac{25\!\cdots\!68}{43\!\cdots\!37}$, $\frac{87\!\cdots\!84}{36\!\cdots\!71}a^{38}-\frac{82\!\cdots\!47}{36\!\cdots\!71}a^{37}-\frac{52\!\cdots\!53}{36\!\cdots\!71}a^{36}+\frac{70\!\cdots\!08}{36\!\cdots\!71}a^{35}+\frac{74\!\cdots\!84}{36\!\cdots\!71}a^{34}-\frac{25\!\cdots\!79}{36\!\cdots\!71}a^{33}+\frac{18\!\cdots\!11}{36\!\cdots\!71}a^{32}+\frac{51\!\cdots\!07}{36\!\cdots\!71}a^{31}-\frac{87\!\cdots\!39}{36\!\cdots\!71}a^{30}-\frac{63\!\cdots\!34}{36\!\cdots\!71}a^{29}+\frac{15\!\cdots\!41}{36\!\cdots\!71}a^{28}+\frac{22\!\cdots\!71}{15\!\cdots\!77}a^{27}-\frac{16\!\cdots\!80}{36\!\cdots\!71}a^{26}-\frac{27\!\cdots\!67}{36\!\cdots\!71}a^{25}+\frac{11\!\cdots\!03}{36\!\cdots\!71}a^{24}+\frac{92\!\cdots\!35}{36\!\cdots\!71}a^{23}-\frac{54\!\cdots\!47}{36\!\cdots\!71}a^{22}-\frac{21\!\cdots\!37}{49\!\cdots\!81}a^{21}+\frac{18\!\cdots\!87}{36\!\cdots\!71}a^{20}-\frac{10\!\cdots\!36}{36\!\cdots\!71}a^{19}-\frac{44\!\cdots\!37}{36\!\cdots\!71}a^{18}+\frac{12\!\cdots\!70}{36\!\cdots\!71}a^{17}+\frac{75\!\cdots\!30}{36\!\cdots\!71}a^{16}-\frac{31\!\cdots\!91}{36\!\cdots\!71}a^{15}-\frac{89\!\cdots\!82}{36\!\cdots\!71}a^{14}+\frac{43\!\cdots\!96}{36\!\cdots\!71}a^{13}+\frac{72\!\cdots\!41}{36\!\cdots\!71}a^{12}-\frac{36\!\cdots\!62}{36\!\cdots\!71}a^{11}-\frac{39\!\cdots\!71}{36\!\cdots\!71}a^{10}+\frac{25\!\cdots\!61}{50\!\cdots\!09}a^{9}+\frac{13\!\cdots\!50}{36\!\cdots\!71}a^{8}-\frac{51\!\cdots\!66}{36\!\cdots\!71}a^{7}-\frac{28\!\cdots\!49}{36\!\cdots\!71}a^{6}+\frac{79\!\cdots\!71}{36\!\cdots\!71}a^{5}+\frac{30\!\cdots\!86}{36\!\cdots\!71}a^{4}-\frac{59\!\cdots\!30}{36\!\cdots\!71}a^{3}-\frac{13\!\cdots\!80}{36\!\cdots\!71}a^{2}+\frac{17\!\cdots\!94}{36\!\cdots\!71}a+\frac{19\!\cdots\!98}{43\!\cdots\!37}$, $\frac{24\!\cdots\!90}{36\!\cdots\!71}a^{38}-\frac{22\!\cdots\!55}{36\!\cdots\!71}a^{37}-\frac{14\!\cdots\!62}{36\!\cdots\!71}a^{36}+\frac{19\!\cdots\!02}{36\!\cdots\!71}a^{35}+\frac{21\!\cdots\!83}{36\!\cdots\!71}a^{34}-\frac{69\!\cdots\!84}{36\!\cdots\!71}a^{33}+\frac{20\!\cdots\!83}{15\!\cdots\!77}a^{32}+\frac{14\!\cdots\!77}{36\!\cdots\!71}a^{31}-\frac{23\!\cdots\!02}{36\!\cdots\!71}a^{30}-\frac{17\!\cdots\!30}{36\!\cdots\!71}a^{29}+\frac{42\!\cdots\!58}{36\!\cdots\!71}a^{28}+\frac{14\!\cdots\!04}{36\!\cdots\!71}a^{27}-\frac{44\!\cdots\!98}{36\!\cdots\!71}a^{26}-\frac{79\!\cdots\!33}{36\!\cdots\!71}a^{25}+\frac{31\!\cdots\!26}{36\!\cdots\!71}a^{24}+\frac{27\!\cdots\!06}{36\!\cdots\!71}a^{23}-\frac{15\!\cdots\!98}{36\!\cdots\!71}a^{22}-\frac{50\!\cdots\!27}{36\!\cdots\!71}a^{21}+\frac{51\!\cdots\!24}{36\!\cdots\!71}a^{20}-\frac{35\!\cdots\!29}{36\!\cdots\!71}a^{19}-\frac{12\!\cdots\!36}{36\!\cdots\!71}a^{18}+\frac{28\!\cdots\!76}{36\!\cdots\!71}a^{17}+\frac{21\!\cdots\!63}{36\!\cdots\!71}a^{16}-\frac{78\!\cdots\!66}{36\!\cdots\!71}a^{15}-\frac{25\!\cdots\!31}{36\!\cdots\!71}a^{14}+\frac{11\!\cdots\!66}{36\!\cdots\!71}a^{13}+\frac{20\!\cdots\!05}{36\!\cdots\!71}a^{12}-\frac{41\!\cdots\!93}{15\!\cdots\!77}a^{11}-\frac{11\!\cdots\!30}{36\!\cdots\!71}a^{10}+\frac{47\!\cdots\!54}{36\!\cdots\!71}a^{9}+\frac{40\!\cdots\!64}{36\!\cdots\!71}a^{8}-\frac{13\!\cdots\!62}{36\!\cdots\!71}a^{7}-\frac{86\!\cdots\!29}{36\!\cdots\!71}a^{6}+\frac{21\!\cdots\!65}{36\!\cdots\!71}a^{5}+\frac{94\!\cdots\!28}{36\!\cdots\!71}a^{4}-\frac{16\!\cdots\!05}{36\!\cdots\!71}a^{3}-\frac{41\!\cdots\!24}{36\!\cdots\!71}a^{2}+\frac{53\!\cdots\!52}{36\!\cdots\!71}a+\frac{83\!\cdots\!60}{43\!\cdots\!37}$, $\frac{15\!\cdots\!93}{36\!\cdots\!71}a^{38}-\frac{14\!\cdots\!85}{36\!\cdots\!71}a^{37}-\frac{97\!\cdots\!76}{36\!\cdots\!71}a^{36}+\frac{12\!\cdots\!51}{36\!\cdots\!71}a^{35}+\frac{15\!\cdots\!79}{36\!\cdots\!71}a^{34}-\frac{46\!\cdots\!44}{36\!\cdots\!71}a^{33}+\frac{27\!\cdots\!59}{36\!\cdots\!71}a^{32}+\frac{40\!\cdots\!23}{15\!\cdots\!77}a^{31}-\frac{14\!\cdots\!33}{36\!\cdots\!71}a^{30}-\frac{11\!\cdots\!83}{36\!\cdots\!71}a^{29}+\frac{26\!\cdots\!26}{36\!\cdots\!71}a^{28}+\frac{98\!\cdots\!71}{36\!\cdots\!71}a^{27}-\frac{28\!\cdots\!26}{36\!\cdots\!71}a^{26}-\frac{54\!\cdots\!29}{36\!\cdots\!71}a^{25}+\frac{20\!\cdots\!85}{36\!\cdots\!71}a^{24}+\frac{19\!\cdots\!01}{36\!\cdots\!71}a^{23}-\frac{97\!\cdots\!48}{36\!\cdots\!71}a^{22}-\frac{40\!\cdots\!64}{36\!\cdots\!71}a^{21}+\frac{33\!\cdots\!03}{36\!\cdots\!71}a^{20}+\frac{22\!\cdots\!29}{36\!\cdots\!71}a^{19}-\frac{80\!\cdots\!81}{36\!\cdots\!71}a^{18}+\frac{12\!\cdots\!92}{36\!\cdots\!71}a^{17}+\frac{13\!\cdots\!27}{36\!\cdots\!71}a^{16}-\frac{40\!\cdots\!14}{36\!\cdots\!71}a^{15}-\frac{16\!\cdots\!86}{36\!\cdots\!71}a^{14}+\frac{60\!\cdots\!90}{36\!\cdots\!71}a^{13}+\frac{13\!\cdots\!80}{36\!\cdots\!71}a^{12}-\frac{22\!\cdots\!81}{15\!\cdots\!77}a^{11}-\frac{76\!\cdots\!54}{36\!\cdots\!71}a^{10}+\frac{25\!\cdots\!88}{36\!\cdots\!71}a^{9}+\frac{26\!\cdots\!35}{36\!\cdots\!71}a^{8}-\frac{68\!\cdots\!52}{36\!\cdots\!71}a^{7}-\frac{55\!\cdots\!75}{36\!\cdots\!71}a^{6}+\frac{98\!\cdots\!09}{36\!\cdots\!71}a^{5}+\frac{57\!\cdots\!12}{36\!\cdots\!71}a^{4}-\frac{74\!\cdots\!69}{36\!\cdots\!71}a^{3}-\frac{23\!\cdots\!13}{36\!\cdots\!71}a^{2}+\frac{25\!\cdots\!90}{36\!\cdots\!71}a+\frac{67\!\cdots\!93}{43\!\cdots\!37}$, $\frac{50\!\cdots\!44}{36\!\cdots\!71}a^{38}-\frac{47\!\cdots\!42}{36\!\cdots\!71}a^{37}-\frac{30\!\cdots\!68}{36\!\cdots\!71}a^{36}+\frac{40\!\cdots\!26}{36\!\cdots\!71}a^{35}+\frac{45\!\cdots\!89}{36\!\cdots\!71}a^{34}-\frac{14\!\cdots\!36}{36\!\cdots\!71}a^{33}+\frac{96\!\cdots\!67}{36\!\cdots\!71}a^{32}+\frac{29\!\cdots\!69}{36\!\cdots\!71}a^{31}-\frac{48\!\cdots\!17}{36\!\cdots\!71}a^{30}-\frac{37\!\cdots\!23}{36\!\cdots\!71}a^{29}+\frac{87\!\cdots\!32}{36\!\cdots\!71}a^{28}+\frac{30\!\cdots\!01}{36\!\cdots\!71}a^{27}-\frac{92\!\cdots\!50}{36\!\cdots\!71}a^{26}-\frac{16\!\cdots\!18}{36\!\cdots\!71}a^{25}+\frac{28\!\cdots\!93}{15\!\cdots\!77}a^{24}+\frac{57\!\cdots\!50}{36\!\cdots\!71}a^{23}-\frac{31\!\cdots\!07}{36\!\cdots\!71}a^{22}-\frac{10\!\cdots\!55}{36\!\cdots\!71}a^{21}+\frac{10\!\cdots\!12}{36\!\cdots\!71}a^{20}-\frac{28\!\cdots\!88}{36\!\cdots\!71}a^{19}-\frac{25\!\cdots\!36}{36\!\cdots\!71}a^{18}+\frac{58\!\cdots\!74}{36\!\cdots\!71}a^{17}+\frac{43\!\cdots\!77}{36\!\cdots\!71}a^{16}-\frac{16\!\cdots\!01}{36\!\cdots\!71}a^{15}-\frac{52\!\cdots\!13}{36\!\cdots\!71}a^{14}+\frac{23\!\cdots\!08}{36\!\cdots\!71}a^{13}+\frac{43\!\cdots\!70}{36\!\cdots\!71}a^{12}-\frac{19\!\cdots\!44}{36\!\cdots\!71}a^{11}-\frac{23\!\cdots\!76}{36\!\cdots\!71}a^{10}+\frac{98\!\cdots\!65}{36\!\cdots\!71}a^{9}+\frac{83\!\cdots\!68}{36\!\cdots\!71}a^{8}-\frac{28\!\cdots\!63}{36\!\cdots\!71}a^{7}-\frac{17\!\cdots\!50}{36\!\cdots\!71}a^{6}+\frac{43\!\cdots\!53}{36\!\cdots\!71}a^{5}+\frac{19\!\cdots\!37}{36\!\cdots\!71}a^{4}-\frac{34\!\cdots\!90}{36\!\cdots\!71}a^{3}-\frac{83\!\cdots\!68}{36\!\cdots\!71}a^{2}+\frac{10\!\cdots\!80}{36\!\cdots\!71}a+\frac{18\!\cdots\!13}{43\!\cdots\!37}$, $\frac{65\!\cdots\!93}{36\!\cdots\!71}a^{38}-\frac{61\!\cdots\!76}{36\!\cdots\!71}a^{37}-\frac{39\!\cdots\!51}{36\!\cdots\!71}a^{36}+\frac{52\!\cdots\!02}{36\!\cdots\!71}a^{35}+\frac{59\!\cdots\!29}{36\!\cdots\!71}a^{34}-\frac{18\!\cdots\!35}{36\!\cdots\!71}a^{33}+\frac{12\!\cdots\!47}{36\!\cdots\!71}a^{32}+\frac{38\!\cdots\!21}{36\!\cdots\!71}a^{31}-\frac{62\!\cdots\!43}{36\!\cdots\!71}a^{30}-\frac{48\!\cdots\!11}{36\!\cdots\!71}a^{29}+\frac{11\!\cdots\!40}{36\!\cdots\!71}a^{28}+\frac{39\!\cdots\!61}{36\!\cdots\!71}a^{27}-\frac{12\!\cdots\!85}{36\!\cdots\!71}a^{26}-\frac{21\!\cdots\!25}{36\!\cdots\!71}a^{25}+\frac{84\!\cdots\!91}{36\!\cdots\!71}a^{24}+\frac{74\!\cdots\!14}{36\!\cdots\!71}a^{23}-\frac{40\!\cdots\!94}{36\!\cdots\!71}a^{22}-\frac{14\!\cdots\!50}{36\!\cdots\!71}a^{21}+\frac{13\!\cdots\!05}{36\!\cdots\!71}a^{20}+\frac{66\!\cdots\!12}{36\!\cdots\!71}a^{19}-\frac{33\!\cdots\!91}{36\!\cdots\!71}a^{18}+\frac{74\!\cdots\!42}{36\!\cdots\!71}a^{17}+\frac{57\!\cdots\!68}{36\!\cdots\!71}a^{16}-\frac{20\!\cdots\!72}{36\!\cdots\!71}a^{15}-\frac{68\!\cdots\!59}{36\!\cdots\!71}a^{14}+\frac{29\!\cdots\!17}{36\!\cdots\!71}a^{13}+\frac{56\!\cdots\!52}{36\!\cdots\!71}a^{12}-\frac{25\!\cdots\!45}{36\!\cdots\!71}a^{11}-\frac{31\!\cdots\!08}{36\!\cdots\!71}a^{10}+\frac{55\!\cdots\!16}{15\!\cdots\!77}a^{9}+\frac{10\!\cdots\!27}{36\!\cdots\!71}a^{8}-\frac{36\!\cdots\!71}{36\!\cdots\!71}a^{7}-\frac{22\!\cdots\!88}{36\!\cdots\!71}a^{6}+\frac{56\!\cdots\!99}{36\!\cdots\!71}a^{5}+\frac{25\!\cdots\!20}{36\!\cdots\!71}a^{4}-\frac{44\!\cdots\!90}{36\!\cdots\!71}a^{3}-\frac{10\!\cdots\!41}{36\!\cdots\!71}a^{2}+\frac{13\!\cdots\!41}{36\!\cdots\!71}a+\frac{23\!\cdots\!38}{43\!\cdots\!37}$, $\frac{86\!\cdots\!95}{36\!\cdots\!71}a^{38}-\frac{81\!\cdots\!64}{36\!\cdots\!71}a^{37}-\frac{52\!\cdots\!17}{36\!\cdots\!71}a^{36}+\frac{69\!\cdots\!39}{36\!\cdots\!71}a^{35}+\frac{78\!\cdots\!93}{36\!\cdots\!71}a^{34}-\frac{24\!\cdots\!62}{36\!\cdots\!71}a^{33}+\frac{16\!\cdots\!03}{36\!\cdots\!71}a^{32}+\frac{50\!\cdots\!87}{36\!\cdots\!71}a^{31}-\frac{82\!\cdots\!58}{36\!\cdots\!71}a^{30}-\frac{63\!\cdots\!74}{36\!\cdots\!71}a^{29}+\frac{14\!\cdots\!72}{36\!\cdots\!71}a^{28}+\frac{52\!\cdots\!22}{36\!\cdots\!71}a^{27}-\frac{15\!\cdots\!69}{36\!\cdots\!71}a^{26}-\frac{28\!\cdots\!72}{36\!\cdots\!71}a^{25}+\frac{11\!\cdots\!44}{36\!\cdots\!71}a^{24}+\frac{98\!\cdots\!97}{36\!\cdots\!71}a^{23}-\frac{53\!\cdots\!95}{36\!\cdots\!71}a^{22}-\frac{18\!\cdots\!83}{36\!\cdots\!71}a^{21}+\frac{79\!\cdots\!57}{15\!\cdots\!77}a^{20}+\frac{35\!\cdots\!74}{36\!\cdots\!71}a^{19}-\frac{44\!\cdots\!26}{36\!\cdots\!71}a^{18}+\frac{97\!\cdots\!46}{36\!\cdots\!71}a^{17}+\frac{75\!\cdots\!28}{36\!\cdots\!71}a^{16}-\frac{27\!\cdots\!02}{36\!\cdots\!71}a^{15}-\frac{90\!\cdots\!81}{36\!\cdots\!71}a^{14}+\frac{39\!\cdots\!47}{36\!\cdots\!71}a^{13}+\frac{74\!\cdots\!31}{36\!\cdots\!71}a^{12}-\frac{33\!\cdots\!28}{36\!\cdots\!71}a^{11}-\frac{40\!\cdots\!94}{36\!\cdots\!71}a^{10}+\frac{16\!\cdots\!69}{36\!\cdots\!71}a^{9}+\frac{14\!\cdots\!73}{36\!\cdots\!71}a^{8}-\frac{47\!\cdots\!81}{36\!\cdots\!71}a^{7}-\frac{30\!\cdots\!07}{36\!\cdots\!71}a^{6}+\frac{73\!\cdots\!11}{36\!\cdots\!71}a^{5}+\frac{32\!\cdots\!90}{36\!\cdots\!71}a^{4}-\frac{57\!\cdots\!86}{36\!\cdots\!71}a^{3}-\frac{14\!\cdots\!29}{36\!\cdots\!71}a^{2}+\frac{78\!\cdots\!72}{15\!\cdots\!77}a+\frac{30\!\cdots\!53}{43\!\cdots\!37}$, $\frac{76\!\cdots\!46}{36\!\cdots\!71}a^{38}-\frac{72\!\cdots\!47}{36\!\cdots\!71}a^{37}-\frac{20\!\cdots\!82}{15\!\cdots\!77}a^{36}+\frac{26\!\cdots\!79}{15\!\cdots\!77}a^{35}+\frac{69\!\cdots\!86}{36\!\cdots\!71}a^{34}-\frac{22\!\cdots\!41}{36\!\cdots\!71}a^{33}+\frac{14\!\cdots\!72}{36\!\cdots\!71}a^{32}+\frac{44\!\cdots\!31}{36\!\cdots\!71}a^{31}-\frac{73\!\cdots\!36}{36\!\cdots\!71}a^{30}-\frac{56\!\cdots\!59}{36\!\cdots\!71}a^{29}+\frac{13\!\cdots\!83}{36\!\cdots\!71}a^{28}+\frac{20\!\cdots\!80}{15\!\cdots\!77}a^{27}-\frac{14\!\cdots\!87}{36\!\cdots\!71}a^{26}-\frac{10\!\cdots\!19}{15\!\cdots\!77}a^{25}+\frac{98\!\cdots\!49}{36\!\cdots\!71}a^{24}+\frac{86\!\cdots\!24}{36\!\cdots\!71}a^{23}-\frac{47\!\cdots\!91}{36\!\cdots\!71}a^{22}-\frac{16\!\cdots\!50}{36\!\cdots\!71}a^{21}+\frac{16\!\cdots\!58}{36\!\cdots\!71}a^{20}-\frac{10\!\cdots\!74}{36\!\cdots\!71}a^{19}-\frac{39\!\cdots\!67}{36\!\cdots\!71}a^{18}+\frac{89\!\cdots\!49}{36\!\cdots\!71}a^{17}+\frac{66\!\cdots\!25}{36\!\cdots\!71}a^{16}-\frac{24\!\cdots\!20}{36\!\cdots\!71}a^{15}-\frac{79\!\cdots\!23}{36\!\cdots\!71}a^{14}+\frac{35\!\cdots\!26}{36\!\cdots\!71}a^{13}+\frac{65\!\cdots\!09}{36\!\cdots\!71}a^{12}-\frac{29\!\cdots\!02}{36\!\cdots\!71}a^{11}-\frac{35\!\cdots\!88}{36\!\cdots\!71}a^{10}+\frac{14\!\cdots\!85}{36\!\cdots\!71}a^{9}+\frac{12\!\cdots\!72}{36\!\cdots\!71}a^{8}-\frac{42\!\cdots\!22}{36\!\cdots\!71}a^{7}-\frac{26\!\cdots\!18}{36\!\cdots\!71}a^{6}+\frac{66\!\cdots\!68}{36\!\cdots\!71}a^{5}+\frac{28\!\cdots\!39}{36\!\cdots\!71}a^{4}-\frac{51\!\cdots\!23}{36\!\cdots\!71}a^{3}-\frac{12\!\cdots\!24}{36\!\cdots\!71}a^{2}+\frac{16\!\cdots\!96}{36\!\cdots\!71}a+\frac{26\!\cdots\!02}{43\!\cdots\!37}$, $\frac{96\!\cdots\!73}{36\!\cdots\!71}a^{38}-\frac{90\!\cdots\!59}{36\!\cdots\!71}a^{37}-\frac{58\!\cdots\!25}{36\!\cdots\!71}a^{36}+\frac{77\!\cdots\!23}{36\!\cdots\!71}a^{35}+\frac{88\!\cdots\!11}{36\!\cdots\!71}a^{34}-\frac{27\!\cdots\!74}{36\!\cdots\!71}a^{33}+\frac{18\!\cdots\!13}{36\!\cdots\!71}a^{32}+\frac{56\!\cdots\!66}{36\!\cdots\!71}a^{31}-\frac{91\!\cdots\!61}{36\!\cdots\!71}a^{30}-\frac{71\!\cdots\!06}{36\!\cdots\!71}a^{29}+\frac{16\!\cdots\!49}{36\!\cdots\!71}a^{28}+\frac{58\!\cdots\!88}{36\!\cdots\!71}a^{27}-\frac{17\!\cdots\!48}{36\!\cdots\!71}a^{26}-\frac{31\!\cdots\!67}{36\!\cdots\!71}a^{25}+\frac{12\!\cdots\!04}{36\!\cdots\!71}a^{24}+\frac{11\!\cdots\!08}{36\!\cdots\!71}a^{23}-\frac{59\!\cdots\!83}{36\!\cdots\!71}a^{22}-\frac{21\!\cdots\!11}{36\!\cdots\!71}a^{21}+\frac{20\!\cdots\!39}{36\!\cdots\!71}a^{20}+\frac{15\!\cdots\!54}{36\!\cdots\!71}a^{19}-\frac{49\!\cdots\!40}{36\!\cdots\!71}a^{18}+\frac{10\!\cdots\!59}{36\!\cdots\!71}a^{17}+\frac{84\!\cdots\!07}{36\!\cdots\!71}a^{16}-\frac{12\!\cdots\!09}{15\!\cdots\!77}a^{15}-\frac{10\!\cdots\!89}{36\!\cdots\!71}a^{14}+\frac{43\!\cdots\!20}{36\!\cdots\!71}a^{13}+\frac{82\!\cdots\!40}{36\!\cdots\!71}a^{12}-\frac{36\!\cdots\!21}{36\!\cdots\!71}a^{11}-\frac{45\!\cdots\!11}{36\!\cdots\!71}a^{10}+\frac{18\!\cdots\!05}{36\!\cdots\!71}a^{9}+\frac{16\!\cdots\!90}{36\!\cdots\!71}a^{8}-\frac{22\!\cdots\!88}{15\!\cdots\!77}a^{7}-\frac{33\!\cdots\!95}{36\!\cdots\!71}a^{6}+\frac{82\!\cdots\!13}{36\!\cdots\!71}a^{5}+\frac{36\!\cdots\!58}{36\!\cdots\!71}a^{4}-\frac{64\!\cdots\!93}{36\!\cdots\!71}a^{3}-\frac{15\!\cdots\!17}{36\!\cdots\!71}a^{2}+\frac{20\!\cdots\!53}{36\!\cdots\!71}a+\frac{29\!\cdots\!48}{43\!\cdots\!37}$, $\frac{12\!\cdots\!69}{36\!\cdots\!71}a^{38}-\frac{11\!\cdots\!79}{36\!\cdots\!71}a^{37}-\frac{72\!\cdots\!29}{36\!\cdots\!71}a^{36}+\frac{98\!\cdots\!50}{36\!\cdots\!71}a^{35}+\frac{99\!\cdots\!99}{36\!\cdots\!71}a^{34}-\frac{35\!\cdots\!41}{36\!\cdots\!71}a^{33}+\frac{27\!\cdots\!96}{36\!\cdots\!71}a^{32}+\frac{70\!\cdots\!44}{36\!\cdots\!71}a^{31}-\frac{12\!\cdots\!06}{36\!\cdots\!71}a^{30}-\frac{88\!\cdots\!66}{36\!\cdots\!71}a^{29}+\frac{22\!\cdots\!75}{36\!\cdots\!71}a^{28}+\frac{71\!\cdots\!45}{36\!\cdots\!71}a^{27}-\frac{23\!\cdots\!95}{36\!\cdots\!71}a^{26}-\frac{37\!\cdots\!02}{36\!\cdots\!71}a^{25}+\frac{16\!\cdots\!66}{36\!\cdots\!71}a^{24}+\frac{12\!\cdots\!80}{36\!\cdots\!71}a^{23}-\frac{77\!\cdots\!22}{36\!\cdots\!71}a^{22}-\frac{17\!\cdots\!43}{36\!\cdots\!71}a^{21}+\frac{26\!\cdots\!31}{36\!\cdots\!71}a^{20}-\frac{29\!\cdots\!35}{36\!\cdots\!71}a^{19}-\frac{62\!\cdots\!45}{36\!\cdots\!71}a^{18}+\frac{21\!\cdots\!36}{36\!\cdots\!71}a^{17}+\frac{10\!\cdots\!91}{36\!\cdots\!71}a^{16}-\frac{50\!\cdots\!12}{36\!\cdots\!71}a^{15}-\frac{12\!\cdots\!85}{36\!\cdots\!71}a^{14}+\frac{70\!\cdots\!34}{36\!\cdots\!71}a^{13}+\frac{10\!\cdots\!13}{36\!\cdots\!71}a^{12}-\frac{59\!\cdots\!18}{36\!\cdots\!71}a^{11}-\frac{54\!\cdots\!08}{36\!\cdots\!71}a^{10}+\frac{13\!\cdots\!30}{15\!\cdots\!77}a^{9}+\frac{19\!\cdots\!27}{36\!\cdots\!71}a^{8}-\frac{90\!\cdots\!44}{36\!\cdots\!71}a^{7}-\frac{41\!\cdots\!04}{36\!\cdots\!71}a^{6}+\frac{14\!\cdots\!45}{36\!\cdots\!71}a^{5}+\frac{47\!\cdots\!58}{36\!\cdots\!71}a^{4}-\frac{11\!\cdots\!02}{36\!\cdots\!71}a^{3}-\frac{22\!\cdots\!83}{36\!\cdots\!71}a^{2}+\frac{31\!\cdots\!05}{36\!\cdots\!71}a+\frac{60\!\cdots\!49}{43\!\cdots\!37}$, $\frac{17\!\cdots\!35}{36\!\cdots\!71}a^{38}-\frac{16\!\cdots\!74}{36\!\cdots\!71}a^{37}-\frac{10\!\cdots\!22}{36\!\cdots\!71}a^{36}+\frac{14\!\cdots\!34}{36\!\cdots\!71}a^{35}+\frac{16\!\cdots\!97}{36\!\cdots\!71}a^{34}-\frac{51\!\cdots\!29}{36\!\cdots\!71}a^{33}+\frac{35\!\cdots\!21}{36\!\cdots\!71}a^{32}+\frac{10\!\cdots\!11}{36\!\cdots\!71}a^{31}-\frac{17\!\cdots\!91}{36\!\cdots\!71}a^{30}-\frac{13\!\cdots\!27}{36\!\cdots\!71}a^{29}+\frac{31\!\cdots\!77}{36\!\cdots\!71}a^{28}+\frac{10\!\cdots\!82}{36\!\cdots\!71}a^{27}-\frac{32\!\cdots\!15}{36\!\cdots\!71}a^{26}-\frac{58\!\cdots\!44}{36\!\cdots\!71}a^{25}+\frac{23\!\cdots\!11}{36\!\cdots\!71}a^{24}+\frac{19\!\cdots\!75}{36\!\cdots\!71}a^{23}-\frac{11\!\cdots\!64}{36\!\cdots\!71}a^{22}-\frac{36\!\cdots\!13}{36\!\cdots\!71}a^{21}+\frac{37\!\cdots\!68}{36\!\cdots\!71}a^{20}-\frac{59\!\cdots\!97}{36\!\cdots\!71}a^{19}-\frac{90\!\cdots\!83}{36\!\cdots\!71}a^{18}+\frac{21\!\cdots\!87}{36\!\cdots\!71}a^{17}+\frac{15\!\cdots\!85}{36\!\cdots\!71}a^{16}-\frac{57\!\cdots\!62}{36\!\cdots\!71}a^{15}-\frac{18\!\cdots\!87}{36\!\cdots\!71}a^{14}+\frac{81\!\cdots\!01}{36\!\cdots\!71}a^{13}+\frac{14\!\cdots\!08}{36\!\cdots\!71}a^{12}-\frac{68\!\cdots\!95}{36\!\cdots\!71}a^{11}-\frac{79\!\cdots\!68}{36\!\cdots\!71}a^{10}+\frac{33\!\cdots\!03}{36\!\cdots\!71}a^{9}+\frac{27\!\cdots\!90}{36\!\cdots\!71}a^{8}-\frac{92\!\cdots\!34}{36\!\cdots\!71}a^{7}-\frac{56\!\cdots\!79}{36\!\cdots\!71}a^{6}+\frac{13\!\cdots\!87}{36\!\cdots\!71}a^{5}+\frac{58\!\cdots\!14}{36\!\cdots\!71}a^{4}-\frac{97\!\cdots\!58}{36\!\cdots\!71}a^{3}-\frac{24\!\cdots\!26}{36\!\cdots\!71}a^{2}+\frac{27\!\cdots\!60}{36\!\cdots\!71}a+\frac{87\!\cdots\!95}{43\!\cdots\!37}$, $\frac{18\!\cdots\!42}{36\!\cdots\!71}a^{38}-\frac{17\!\cdots\!83}{36\!\cdots\!71}a^{37}-\frac{11\!\cdots\!93}{36\!\cdots\!71}a^{36}+\frac{14\!\cdots\!13}{36\!\cdots\!71}a^{35}+\frac{16\!\cdots\!22}{36\!\cdots\!71}a^{34}-\frac{54\!\cdots\!95}{36\!\cdots\!71}a^{33}+\frac{36\!\cdots\!62}{36\!\cdots\!71}a^{32}+\frac{10\!\cdots\!92}{36\!\cdots\!71}a^{31}-\frac{18\!\cdots\!31}{36\!\cdots\!71}a^{30}-\frac{13\!\cdots\!10}{36\!\cdots\!71}a^{29}+\frac{32\!\cdots\!68}{36\!\cdots\!71}a^{28}+\frac{11\!\cdots\!29}{36\!\cdots\!71}a^{27}-\frac{34\!\cdots\!34}{36\!\cdots\!71}a^{26}-\frac{61\!\cdots\!44}{36\!\cdots\!71}a^{25}+\frac{24\!\cdots\!70}{36\!\cdots\!71}a^{24}+\frac{21\!\cdots\!30}{36\!\cdots\!71}a^{23}-\frac{11\!\cdots\!66}{36\!\cdots\!71}a^{22}-\frac{39\!\cdots\!86}{36\!\cdots\!71}a^{21}+\frac{39\!\cdots\!53}{36\!\cdots\!71}a^{20}-\frac{30\!\cdots\!85}{36\!\cdots\!71}a^{19}-\frac{95\!\cdots\!05}{36\!\cdots\!71}a^{18}+\frac{22\!\cdots\!02}{36\!\cdots\!71}a^{17}+\frac{71\!\cdots\!85}{15\!\cdots\!77}a^{16}-\frac{60\!\cdots\!11}{36\!\cdots\!71}a^{15}-\frac{19\!\cdots\!19}{36\!\cdots\!71}a^{14}+\frac{86\!\cdots\!58}{36\!\cdots\!71}a^{13}+\frac{16\!\cdots\!33}{36\!\cdots\!71}a^{12}-\frac{73\!\cdots\!55}{36\!\cdots\!71}a^{11}-\frac{38\!\cdots\!99}{15\!\cdots\!77}a^{10}+\frac{37\!\cdots\!44}{36\!\cdots\!71}a^{9}+\frac{31\!\cdots\!00}{36\!\cdots\!71}a^{8}-\frac{10\!\cdots\!62}{36\!\cdots\!71}a^{7}-\frac{65\!\cdots\!34}{36\!\cdots\!71}a^{6}+\frac{16\!\cdots\!58}{36\!\cdots\!71}a^{5}+\frac{72\!\cdots\!89}{36\!\cdots\!71}a^{4}-\frac{13\!\cdots\!66}{36\!\cdots\!71}a^{3}-\frac{31\!\cdots\!71}{36\!\cdots\!71}a^{2}+\frac{41\!\cdots\!14}{36\!\cdots\!71}a+\frac{70\!\cdots\!18}{43\!\cdots\!37}$, $\frac{39\!\cdots\!92}{36\!\cdots\!71}a^{38}-\frac{37\!\cdots\!23}{36\!\cdots\!71}a^{37}-\frac{23\!\cdots\!48}{36\!\cdots\!71}a^{36}+\frac{31\!\cdots\!81}{36\!\cdots\!71}a^{35}+\frac{34\!\cdots\!08}{36\!\cdots\!71}a^{34}-\frac{49\!\cdots\!03}{15\!\cdots\!77}a^{33}+\frac{79\!\cdots\!05}{36\!\cdots\!71}a^{32}+\frac{23\!\cdots\!46}{36\!\cdots\!71}a^{31}-\frac{38\!\cdots\!93}{36\!\cdots\!71}a^{30}-\frac{28\!\cdots\!29}{36\!\cdots\!71}a^{29}+\frac{69\!\cdots\!49}{36\!\cdots\!71}a^{28}+\frac{23\!\cdots\!11}{36\!\cdots\!71}a^{27}-\frac{73\!\cdots\!22}{36\!\cdots\!71}a^{26}-\frac{12\!\cdots\!19}{36\!\cdots\!71}a^{25}+\frac{50\!\cdots\!17}{36\!\cdots\!71}a^{24}+\frac{42\!\cdots\!04}{36\!\cdots\!71}a^{23}-\frac{24\!\cdots\!75}{36\!\cdots\!71}a^{22}-\frac{75\!\cdots\!70}{36\!\cdots\!71}a^{21}+\frac{83\!\cdots\!64}{36\!\cdots\!71}a^{20}-\frac{28\!\cdots\!13}{36\!\cdots\!71}a^{19}-\frac{20\!\cdots\!71}{36\!\cdots\!71}a^{18}+\frac{51\!\cdots\!80}{36\!\cdots\!71}a^{17}+\frac{33\!\cdots\!73}{36\!\cdots\!71}a^{16}-\frac{13\!\cdots\!80}{36\!\cdots\!71}a^{15}-\frac{40\!\cdots\!26}{36\!\cdots\!71}a^{14}+\frac{19\!\cdots\!27}{36\!\cdots\!71}a^{13}+\frac{32\!\cdots\!15}{36\!\cdots\!71}a^{12}-\frac{15\!\cdots\!74}{36\!\cdots\!71}a^{11}-\frac{17\!\cdots\!52}{36\!\cdots\!71}a^{10}+\frac{79\!\cdots\!76}{36\!\cdots\!71}a^{9}+\frac{61\!\cdots\!55}{36\!\cdots\!71}a^{8}-\frac{22\!\cdots\!32}{36\!\cdots\!71}a^{7}-\frac{12\!\cdots\!43}{36\!\cdots\!71}a^{6}+\frac{34\!\cdots\!05}{36\!\cdots\!71}a^{5}+\frac{13\!\cdots\!47}{36\!\cdots\!71}a^{4}-\frac{26\!\cdots\!53}{36\!\cdots\!71}a^{3}-\frac{59\!\cdots\!64}{36\!\cdots\!71}a^{2}+\frac{78\!\cdots\!16}{36\!\cdots\!71}a+\frac{13\!\cdots\!22}{43\!\cdots\!37}$, $\frac{55\!\cdots\!08}{36\!\cdots\!71}a^{38}-\frac{52\!\cdots\!38}{36\!\cdots\!71}a^{37}-\frac{33\!\cdots\!54}{36\!\cdots\!71}a^{36}+\frac{44\!\cdots\!46}{36\!\cdots\!71}a^{35}+\frac{50\!\cdots\!47}{36\!\cdots\!71}a^{34}-\frac{16\!\cdots\!18}{36\!\cdots\!71}a^{33}+\frac{10\!\cdots\!33}{36\!\cdots\!71}a^{32}+\frac{32\!\cdots\!28}{36\!\cdots\!71}a^{31}-\frac{53\!\cdots\!53}{36\!\cdots\!71}a^{30}-\frac{41\!\cdots\!18}{36\!\cdots\!71}a^{29}+\frac{97\!\cdots\!39}{36\!\cdots\!71}a^{28}+\frac{33\!\cdots\!34}{36\!\cdots\!71}a^{27}-\frac{10\!\cdots\!48}{36\!\cdots\!71}a^{26}-\frac{18\!\cdots\!24}{36\!\cdots\!71}a^{25}+\frac{71\!\cdots\!29}{36\!\cdots\!71}a^{24}+\frac{62\!\cdots\!13}{36\!\cdots\!71}a^{23}-\frac{34\!\cdots\!47}{36\!\cdots\!71}a^{22}-\frac{11\!\cdots\!41}{36\!\cdots\!71}a^{21}+\frac{11\!\cdots\!18}{36\!\cdots\!71}a^{20}-\frac{16\!\cdots\!62}{36\!\cdots\!71}a^{19}-\frac{28\!\cdots\!16}{36\!\cdots\!71}a^{18}+\frac{67\!\cdots\!76}{36\!\cdots\!71}a^{17}+\frac{48\!\cdots\!50}{36\!\cdots\!71}a^{16}-\frac{78\!\cdots\!67}{15\!\cdots\!77}a^{15}-\frac{57\!\cdots\!92}{36\!\cdots\!71}a^{14}+\frac{25\!\cdots\!74}{36\!\cdots\!71}a^{13}+\frac{47\!\cdots\!83}{36\!\cdots\!71}a^{12}-\frac{21\!\cdots\!85}{36\!\cdots\!71}a^{11}-\frac{25\!\cdots\!81}{36\!\cdots\!71}a^{10}+\frac{10\!\cdots\!94}{36\!\cdots\!71}a^{9}+\frac{90\!\cdots\!54}{36\!\cdots\!71}a^{8}-\frac{30\!\cdots\!27}{36\!\cdots\!71}a^{7}-\frac{18\!\cdots\!13}{36\!\cdots\!71}a^{6}+\frac{20\!\cdots\!34}{15\!\cdots\!77}a^{5}+\frac{64\!\cdots\!16}{11\!\cdots\!63}a^{4}-\frac{37\!\cdots\!93}{36\!\cdots\!71}a^{3}-\frac{89\!\cdots\!72}{36\!\cdots\!71}a^{2}+\frac{11\!\cdots\!94}{36\!\cdots\!71}a+\frac{19\!\cdots\!78}{43\!\cdots\!37}$, $\frac{44\!\cdots\!43}{36\!\cdots\!71}a^{38}-\frac{41\!\cdots\!86}{36\!\cdots\!71}a^{37}-\frac{26\!\cdots\!43}{36\!\cdots\!71}a^{36}+\frac{35\!\cdots\!32}{36\!\cdots\!71}a^{35}+\frac{39\!\cdots\!70}{36\!\cdots\!71}a^{34}-\frac{12\!\cdots\!18}{36\!\cdots\!71}a^{33}+\frac{86\!\cdots\!34}{36\!\cdots\!71}a^{32}+\frac{25\!\cdots\!01}{36\!\cdots\!71}a^{31}-\frac{42\!\cdots\!47}{36\!\cdots\!71}a^{30}-\frac{32\!\cdots\!30}{36\!\cdots\!71}a^{29}+\frac{76\!\cdots\!75}{36\!\cdots\!71}a^{28}+\frac{26\!\cdots\!39}{36\!\cdots\!71}a^{27}-\frac{81\!\cdots\!70}{36\!\cdots\!71}a^{26}-\frac{14\!\cdots\!91}{36\!\cdots\!71}a^{25}+\frac{56\!\cdots\!27}{36\!\cdots\!71}a^{24}+\frac{49\!\cdots\!91}{36\!\cdots\!71}a^{23}-\frac{27\!\cdots\!81}{36\!\cdots\!71}a^{22}-\frac{91\!\cdots\!67}{36\!\cdots\!71}a^{21}+\frac{93\!\cdots\!49}{36\!\cdots\!71}a^{20}-\frac{92\!\cdots\!62}{36\!\cdots\!71}a^{19}-\frac{22\!\cdots\!94}{36\!\cdots\!71}a^{18}+\frac{52\!\cdots\!45}{36\!\cdots\!71}a^{17}+\frac{38\!\cdots\!45}{36\!\cdots\!71}a^{16}-\frac{14\!\cdots\!39}{36\!\cdots\!71}a^{15}-\frac{45\!\cdots\!89}{36\!\cdots\!71}a^{14}+\frac{20\!\cdots\!88}{36\!\cdots\!71}a^{13}+\frac{37\!\cdots\!99}{36\!\cdots\!71}a^{12}-\frac{17\!\cdots\!04}{36\!\cdots\!71}a^{11}-\frac{20\!\cdots\!60}{36\!\cdots\!71}a^{10}+\frac{86\!\cdots\!60}{36\!\cdots\!71}a^{9}+\frac{72\!\cdots\!38}{36\!\cdots\!71}a^{8}-\frac{24\!\cdots\!90}{36\!\cdots\!71}a^{7}-\frac{15\!\cdots\!91}{36\!\cdots\!71}a^{6}+\frac{38\!\cdots\!54}{36\!\cdots\!71}a^{5}+\frac{16\!\cdots\!16}{36\!\cdots\!71}a^{4}-\frac{29\!\cdots\!23}{36\!\cdots\!71}a^{3}-\frac{73\!\cdots\!58}{36\!\cdots\!71}a^{2}+\frac{91\!\cdots\!00}{36\!\cdots\!71}a+\frac{18\!\cdots\!47}{43\!\cdots\!37}$, $\frac{81\!\cdots\!44}{36\!\cdots\!71}a^{38}-\frac{77\!\cdots\!13}{36\!\cdots\!71}a^{37}-\frac{49\!\cdots\!84}{36\!\cdots\!71}a^{36}+\frac{65\!\cdots\!12}{36\!\cdots\!71}a^{35}+\frac{70\!\cdots\!77}{36\!\cdots\!71}a^{34}-\frac{23\!\cdots\!65}{36\!\cdots\!71}a^{33}+\frac{17\!\cdots\!55}{36\!\cdots\!71}a^{32}+\frac{47\!\cdots\!84}{36\!\cdots\!71}a^{31}-\frac{81\!\cdots\!46}{36\!\cdots\!71}a^{30}-\frac{59\!\cdots\!31}{36\!\cdots\!71}a^{29}+\frac{14\!\cdots\!14}{36\!\cdots\!71}a^{28}+\frac{48\!\cdots\!18}{36\!\cdots\!71}a^{27}-\frac{15\!\cdots\!59}{36\!\cdots\!71}a^{26}-\frac{26\!\cdots\!14}{36\!\cdots\!71}a^{25}+\frac{10\!\cdots\!42}{36\!\cdots\!71}a^{24}+\frac{87\!\cdots\!67}{36\!\cdots\!71}a^{23}-\frac{51\!\cdots\!28}{36\!\cdots\!71}a^{22}-\frac{14\!\cdots\!06}{36\!\cdots\!71}a^{21}+\frac{17\!\cdots\!18}{36\!\cdots\!71}a^{20}-\frac{93\!\cdots\!73}{36\!\cdots\!71}a^{19}-\frac{41\!\cdots\!45}{36\!\cdots\!71}a^{18}+\frac{11\!\cdots\!39}{36\!\cdots\!71}a^{17}+\frac{71\!\cdots\!76}{36\!\cdots\!71}a^{16}-\frac{29\!\cdots\!58}{36\!\cdots\!71}a^{15}-\frac{84\!\cdots\!21}{36\!\cdots\!71}a^{14}+\frac{41\!\cdots\!74}{36\!\cdots\!71}a^{13}+\frac{29\!\cdots\!72}{15\!\cdots\!77}a^{12}-\frac{34\!\cdots\!75}{36\!\cdots\!71}a^{11}-\frac{37\!\cdots\!65}{36\!\cdots\!71}a^{10}+\frac{17\!\cdots\!23}{36\!\cdots\!71}a^{9}+\frac{12\!\cdots\!78}{36\!\cdots\!71}a^{8}-\frac{51\!\cdots\!70}{36\!\cdots\!71}a^{7}-\frac{27\!\cdots\!36}{36\!\cdots\!71}a^{6}+\frac{80\!\cdots\!03}{36\!\cdots\!71}a^{5}+\frac{29\!\cdots\!06}{36\!\cdots\!71}a^{4}-\frac{63\!\cdots\!49}{36\!\cdots\!71}a^{3}-\frac{12\!\cdots\!30}{36\!\cdots\!71}a^{2}+\frac{19\!\cdots\!38}{36\!\cdots\!71}a+\frac{24\!\cdots\!00}{43\!\cdots\!37}$, $\frac{67\!\cdots\!64}{36\!\cdots\!71}a^{38}-\frac{63\!\cdots\!92}{36\!\cdots\!71}a^{37}-\frac{41\!\cdots\!21}{36\!\cdots\!71}a^{36}+\frac{54\!\cdots\!41}{36\!\cdots\!71}a^{35}+\frac{61\!\cdots\!42}{36\!\cdots\!71}a^{34}-\frac{19\!\cdots\!83}{36\!\cdots\!71}a^{33}+\frac{13\!\cdots\!67}{36\!\cdots\!71}a^{32}+\frac{39\!\cdots\!51}{36\!\cdots\!71}a^{31}-\frac{65\!\cdots\!16}{36\!\cdots\!71}a^{30}-\frac{49\!\cdots\!53}{36\!\cdots\!71}a^{29}+\frac{11\!\cdots\!42}{36\!\cdots\!71}a^{28}+\frac{40\!\cdots\!61}{36\!\cdots\!71}a^{27}-\frac{12\!\cdots\!06}{36\!\cdots\!71}a^{26}-\frac{22\!\cdots\!49}{36\!\cdots\!71}a^{25}+\frac{87\!\cdots\!55}{36\!\cdots\!71}a^{24}+\frac{75\!\cdots\!20}{36\!\cdots\!71}a^{23}-\frac{42\!\cdots\!57}{36\!\cdots\!71}a^{22}-\frac{13\!\cdots\!59}{36\!\cdots\!71}a^{21}+\frac{14\!\cdots\!64}{36\!\cdots\!71}a^{20}-\frac{25\!\cdots\!95}{36\!\cdots\!71}a^{19}-\frac{15\!\cdots\!25}{15\!\cdots\!77}a^{18}+\frac{83\!\cdots\!58}{36\!\cdots\!71}a^{17}+\frac{58\!\cdots\!53}{36\!\cdots\!71}a^{16}-\frac{22\!\cdots\!58}{36\!\cdots\!71}a^{15}-\frac{70\!\cdots\!22}{36\!\cdots\!71}a^{14}+\frac{13\!\cdots\!89}{15\!\cdots\!77}a^{13}+\frac{57\!\cdots\!48}{36\!\cdots\!71}a^{12}-\frac{26\!\cdots\!82}{36\!\cdots\!71}a^{11}-\frac{31\!\cdots\!60}{36\!\cdots\!71}a^{10}+\frac{13\!\cdots\!51}{36\!\cdots\!71}a^{9}+\frac{10\!\cdots\!21}{36\!\cdots\!71}a^{8}-\frac{37\!\cdots\!34}{36\!\cdots\!71}a^{7}-\frac{22\!\cdots\!43}{36\!\cdots\!71}a^{6}+\frac{58\!\cdots\!90}{36\!\cdots\!71}a^{5}+\frac{24\!\cdots\!10}{36\!\cdots\!71}a^{4}-\frac{44\!\cdots\!82}{36\!\cdots\!71}a^{3}-\frac{10\!\cdots\!43}{36\!\cdots\!71}a^{2}+\frac{13\!\cdots\!14}{36\!\cdots\!71}a+\frac{22\!\cdots\!22}{43\!\cdots\!37}$, $\frac{15\!\cdots\!98}{36\!\cdots\!71}a^{38}-\frac{14\!\cdots\!88}{36\!\cdots\!71}a^{37}-\frac{96\!\cdots\!68}{36\!\cdots\!71}a^{36}+\frac{12\!\cdots\!83}{36\!\cdots\!71}a^{35}+\frac{15\!\cdots\!78}{36\!\cdots\!71}a^{34}-\frac{45\!\cdots\!45}{36\!\cdots\!71}a^{33}+\frac{27\!\cdots\!16}{36\!\cdots\!71}a^{32}+\frac{92\!\cdots\!35}{36\!\cdots\!71}a^{31}-\frac{14\!\cdots\!26}{36\!\cdots\!71}a^{30}-\frac{11\!\cdots\!94}{36\!\cdots\!71}a^{29}+\frac{26\!\cdots\!08}{36\!\cdots\!71}a^{28}+\frac{97\!\cdots\!47}{36\!\cdots\!71}a^{27}-\frac{28\!\cdots\!65}{36\!\cdots\!71}a^{26}-\frac{54\!\cdots\!55}{36\!\cdots\!71}a^{25}+\frac{20\!\cdots\!90}{36\!\cdots\!71}a^{24}+\frac{19\!\cdots\!66}{36\!\cdots\!71}a^{23}-\frac{97\!\cdots\!90}{36\!\cdots\!71}a^{22}-\frac{40\!\cdots\!82}{36\!\cdots\!71}a^{21}+\frac{33\!\cdots\!99}{36\!\cdots\!71}a^{20}+\frac{22\!\cdots\!24}{36\!\cdots\!71}a^{19}-\frac{81\!\cdots\!87}{36\!\cdots\!71}a^{18}+\frac{12\!\cdots\!36}{36\!\cdots\!71}a^{17}+\frac{14\!\cdots\!04}{36\!\cdots\!71}a^{16}-\frac{40\!\cdots\!13}{36\!\cdots\!71}a^{15}-\frac{17\!\cdots\!26}{36\!\cdots\!71}a^{14}+\frac{61\!\cdots\!76}{36\!\cdots\!71}a^{13}+\frac{61\!\cdots\!02}{15\!\cdots\!77}a^{12}-\frac{52\!\cdots\!60}{36\!\cdots\!71}a^{11}-\frac{79\!\cdots\!20}{36\!\cdots\!71}a^{10}+\frac{26\!\cdots\!51}{36\!\cdots\!71}a^{9}+\frac{28\!\cdots\!90}{36\!\cdots\!71}a^{8}-\frac{72\!\cdots\!73}{36\!\cdots\!71}a^{7}-\frac{59\!\cdots\!34}{36\!\cdots\!71}a^{6}+\frac{10\!\cdots\!37}{36\!\cdots\!71}a^{5}+\frac{64\!\cdots\!01}{36\!\cdots\!71}a^{4}-\frac{87\!\cdots\!19}{36\!\cdots\!71}a^{3}-\frac{27\!\cdots\!91}{36\!\cdots\!71}a^{2}+\frac{31\!\cdots\!28}{36\!\cdots\!71}a+\frac{71\!\cdots\!27}{43\!\cdots\!37}$, $\frac{47\!\cdots\!62}{36\!\cdots\!71}a^{38}-\frac{44\!\cdots\!72}{36\!\cdots\!71}a^{37}-\frac{28\!\cdots\!53}{36\!\cdots\!71}a^{36}+\frac{38\!\cdots\!26}{36\!\cdots\!71}a^{35}+\frac{42\!\cdots\!48}{36\!\cdots\!71}a^{34}-\frac{13\!\cdots\!99}{36\!\cdots\!71}a^{33}+\frac{93\!\cdots\!95}{36\!\cdots\!71}a^{32}+\frac{27\!\cdots\!93}{36\!\cdots\!71}a^{31}-\frac{45\!\cdots\!37}{36\!\cdots\!71}a^{30}-\frac{34\!\cdots\!56}{36\!\cdots\!71}a^{29}+\frac{82\!\cdots\!61}{36\!\cdots\!71}a^{28}+\frac{28\!\cdots\!83}{36\!\cdots\!71}a^{27}-\frac{87\!\cdots\!63}{36\!\cdots\!71}a^{26}-\frac{15\!\cdots\!33}{36\!\cdots\!71}a^{25}+\frac{61\!\cdots\!02}{36\!\cdots\!71}a^{24}+\frac{52\!\cdots\!28}{36\!\cdots\!71}a^{23}-\frac{29\!\cdots\!79}{36\!\cdots\!71}a^{22}-\frac{95\!\cdots\!49}{36\!\cdots\!71}a^{21}+\frac{43\!\cdots\!68}{15\!\cdots\!77}a^{20}-\frac{20\!\cdots\!52}{36\!\cdots\!71}a^{19}-\frac{24\!\cdots\!93}{36\!\cdots\!71}a^{18}+\frac{58\!\cdots\!48}{36\!\cdots\!71}a^{17}+\frac{41\!\cdots\!62}{36\!\cdots\!71}a^{16}-\frac{15\!\cdots\!55}{36\!\cdots\!71}a^{15}-\frac{48\!\cdots\!43}{36\!\cdots\!71}a^{14}+\frac{22\!\cdots\!08}{36\!\cdots\!71}a^{13}+\frac{39\!\cdots\!94}{36\!\cdots\!71}a^{12}-\frac{18\!\cdots\!78}{36\!\cdots\!71}a^{11}-\frac{21\!\cdots\!99}{36\!\cdots\!71}a^{10}+\frac{93\!\cdots\!03}{36\!\cdots\!71}a^{9}+\frac{75\!\cdots\!24}{36\!\cdots\!71}a^{8}-\frac{26\!\cdots\!47}{36\!\cdots\!71}a^{7}-\frac{15\!\cdots\!12}{36\!\cdots\!71}a^{6}+\frac{40\!\cdots\!24}{36\!\cdots\!71}a^{5}+\frac{16\!\cdots\!27}{36\!\cdots\!71}a^{4}-\frac{31\!\cdots\!01}{36\!\cdots\!71}a^{3}-\frac{71\!\cdots\!22}{36\!\cdots\!71}a^{2}+\frac{95\!\cdots\!75}{36\!\cdots\!71}a+\frac{12\!\cdots\!11}{43\!\cdots\!37}$, $\frac{12\!\cdots\!03}{36\!\cdots\!71}a^{38}-\frac{11\!\cdots\!14}{36\!\cdots\!71}a^{37}-\frac{74\!\cdots\!99}{36\!\cdots\!71}a^{36}+\frac{98\!\cdots\!14}{36\!\cdots\!71}a^{35}+\frac{11\!\cdots\!67}{36\!\cdots\!71}a^{34}-\frac{35\!\cdots\!34}{36\!\cdots\!71}a^{33}+\frac{10\!\cdots\!77}{15\!\cdots\!77}a^{32}+\frac{72\!\cdots\!83}{36\!\cdots\!71}a^{31}-\frac{11\!\cdots\!54}{36\!\cdots\!71}a^{30}-\frac{91\!\cdots\!76}{36\!\cdots\!71}a^{29}+\frac{21\!\cdots\!76}{36\!\cdots\!71}a^{28}+\frac{32\!\cdots\!44}{15\!\cdots\!77}a^{27}-\frac{22\!\cdots\!03}{36\!\cdots\!71}a^{26}-\frac{40\!\cdots\!34}{36\!\cdots\!71}a^{25}+\frac{15\!\cdots\!47}{36\!\cdots\!71}a^{24}+\frac{14\!\cdots\!02}{36\!\cdots\!71}a^{23}-\frac{76\!\cdots\!16}{36\!\cdots\!71}a^{22}-\frac{26\!\cdots\!68}{36\!\cdots\!71}a^{21}+\frac{25\!\cdots\!24}{36\!\cdots\!71}a^{20}+\frac{21\!\cdots\!46}{36\!\cdots\!71}a^{19}-\frac{62\!\cdots\!46}{36\!\cdots\!71}a^{18}+\frac{13\!\cdots\!72}{36\!\cdots\!71}a^{17}+\frac{46\!\cdots\!69}{15\!\cdots\!77}a^{16}-\frac{38\!\cdots\!54}{36\!\cdots\!71}a^{15}-\frac{12\!\cdots\!28}{36\!\cdots\!71}a^{14}+\frac{54\!\cdots\!07}{36\!\cdots\!71}a^{13}+\frac{10\!\cdots\!12}{36\!\cdots\!71}a^{12}-\frac{46\!\cdots\!66}{36\!\cdots\!71}a^{11}-\frac{58\!\cdots\!65}{36\!\cdots\!71}a^{10}+\frac{23\!\cdots\!83}{36\!\cdots\!71}a^{9}+\frac{20\!\cdots\!66}{36\!\cdots\!71}a^{8}-\frac{66\!\cdots\!22}{36\!\cdots\!71}a^{7}-\frac{42\!\cdots\!23}{36\!\cdots\!71}a^{6}+\frac{10\!\cdots\!66}{36\!\cdots\!71}a^{5}+\frac{46\!\cdots\!55}{36\!\cdots\!71}a^{4}-\frac{81\!\cdots\!51}{36\!\cdots\!71}a^{3}-\frac{20\!\cdots\!85}{36\!\cdots\!71}a^{2}+\frac{25\!\cdots\!42}{36\!\cdots\!71}a+\frac{42\!\cdots\!90}{43\!\cdots\!37}$, $\frac{14\!\cdots\!48}{36\!\cdots\!71}a^{38}-\frac{14\!\cdots\!20}{36\!\cdots\!71}a^{37}-\frac{88\!\cdots\!62}{36\!\cdots\!71}a^{36}+\frac{12\!\cdots\!64}{36\!\cdots\!71}a^{35}+\frac{12\!\cdots\!66}{36\!\cdots\!71}a^{34}-\frac{43\!\cdots\!98}{36\!\cdots\!71}a^{33}+\frac{33\!\cdots\!38}{36\!\cdots\!71}a^{32}+\frac{86\!\cdots\!03}{36\!\cdots\!71}a^{31}-\frac{15\!\cdots\!17}{36\!\cdots\!71}a^{30}-\frac{10\!\cdots\!66}{36\!\cdots\!71}a^{29}+\frac{27\!\cdots\!19}{36\!\cdots\!71}a^{28}+\frac{87\!\cdots\!70}{36\!\cdots\!71}a^{27}-\frac{28\!\cdots\!66}{36\!\cdots\!71}a^{26}-\frac{20\!\cdots\!08}{15\!\cdots\!77}a^{25}+\frac{19\!\cdots\!21}{36\!\cdots\!71}a^{24}+\frac{14\!\cdots\!03}{36\!\cdots\!71}a^{23}-\frac{94\!\cdots\!95}{36\!\cdots\!71}a^{22}-\frac{21\!\cdots\!78}{36\!\cdots\!71}a^{21}+\frac{32\!\cdots\!60}{36\!\cdots\!71}a^{20}-\frac{33\!\cdots\!92}{36\!\cdots\!71}a^{19}-\frac{76\!\cdots\!25}{36\!\cdots\!71}a^{18}+\frac{25\!\cdots\!02}{36\!\cdots\!71}a^{17}+\frac{12\!\cdots\!22}{36\!\cdots\!71}a^{16}-\frac{61\!\cdots\!65}{36\!\cdots\!71}a^{15}-\frac{15\!\cdots\!27}{36\!\cdots\!71}a^{14}+\frac{84\!\cdots\!05}{36\!\cdots\!71}a^{13}+\frac{12\!\cdots\!82}{36\!\cdots\!71}a^{12}-\frac{71\!\cdots\!49}{36\!\cdots\!71}a^{11}-\frac{67\!\cdots\!12}{36\!\cdots\!71}a^{10}+\frac{36\!\cdots\!95}{36\!\cdots\!71}a^{9}+\frac{23\!\cdots\!85}{36\!\cdots\!71}a^{8}-\frac{10\!\cdots\!81}{36\!\cdots\!71}a^{7}-\frac{50\!\cdots\!72}{36\!\cdots\!71}a^{6}+\frac{17\!\cdots\!82}{36\!\cdots\!71}a^{5}+\frac{58\!\cdots\!98}{36\!\cdots\!71}a^{4}-\frac{13\!\cdots\!94}{36\!\cdots\!71}a^{3}-\frac{27\!\cdots\!95}{36\!\cdots\!71}a^{2}+\frac{37\!\cdots\!52}{36\!\cdots\!71}a+\frac{49\!\cdots\!70}{43\!\cdots\!37}$, $\frac{29\!\cdots\!42}{36\!\cdots\!71}a^{38}-\frac{27\!\cdots\!81}{36\!\cdots\!71}a^{37}-\frac{17\!\cdots\!87}{36\!\cdots\!71}a^{36}+\frac{23\!\cdots\!74}{36\!\cdots\!71}a^{35}+\frac{26\!\cdots\!91}{36\!\cdots\!71}a^{34}-\frac{84\!\cdots\!97}{36\!\cdots\!71}a^{33}+\frac{56\!\cdots\!78}{36\!\cdots\!71}a^{32}+\frac{17\!\cdots\!84}{36\!\cdots\!71}a^{31}-\frac{28\!\cdots\!22}{36\!\cdots\!71}a^{30}-\frac{21\!\cdots\!83}{36\!\cdots\!71}a^{29}+\frac{50\!\cdots\!84}{36\!\cdots\!71}a^{28}+\frac{17\!\cdots\!61}{36\!\cdots\!71}a^{27}-\frac{53\!\cdots\!40}{36\!\cdots\!71}a^{26}-\frac{95\!\cdots\!07}{36\!\cdots\!71}a^{25}+\frac{37\!\cdots\!84}{36\!\cdots\!71}a^{24}+\frac{33\!\cdots\!25}{36\!\cdots\!71}a^{23}-\frac{18\!\cdots\!10}{36\!\cdots\!71}a^{22}-\frac{61\!\cdots\!57}{36\!\cdots\!71}a^{21}+\frac{61\!\cdots\!09}{36\!\cdots\!71}a^{20}-\frac{34\!\cdots\!29}{36\!\cdots\!71}a^{19}-\frac{14\!\cdots\!68}{36\!\cdots\!71}a^{18}+\frac{34\!\cdots\!51}{36\!\cdots\!71}a^{17}+\frac{25\!\cdots\!80}{36\!\cdots\!71}a^{16}-\frac{93\!\cdots\!67}{36\!\cdots\!71}a^{15}-\frac{30\!\cdots\!59}{36\!\cdots\!71}a^{14}+\frac{13\!\cdots\!52}{36\!\cdots\!71}a^{13}+\frac{25\!\cdots\!75}{36\!\cdots\!71}a^{12}-\frac{11\!\cdots\!63}{36\!\cdots\!71}a^{11}-\frac{13\!\cdots\!11}{36\!\cdots\!71}a^{10}+\frac{57\!\cdots\!88}{36\!\cdots\!71}a^{9}+\frac{48\!\cdots\!37}{36\!\cdots\!71}a^{8}-\frac{16\!\cdots\!59}{36\!\cdots\!71}a^{7}-\frac{10\!\cdots\!38}{36\!\cdots\!71}a^{6}+\frac{25\!\cdots\!66}{36\!\cdots\!71}a^{5}+\frac{11\!\cdots\!87}{36\!\cdots\!71}a^{4}-\frac{20\!\cdots\!35}{36\!\cdots\!71}a^{3}-\frac{47\!\cdots\!48}{36\!\cdots\!71}a^{2}+\frac{64\!\cdots\!31}{36\!\cdots\!71}a+\frac{55\!\cdots\!16}{43\!\cdots\!37}$ (assuming GRH) | sage: UK.fundamental_units()
gp: K.fu
magma: [K|fUK(g): g in Generators(UK)];
oscar: [K(fUK(a)) for a in gens(UK)]
| |
Regulator: | \( 688762923023490700000000000000 \) (assuming GRH) | sage: K.regulator()
gp: K.reg
magma: Regulator(K);
oscar: regulator(K)
|
Class number formula
\[ \begin{aligned}\lim_{s\to 1} (s-1)\zeta_K(s) =\mathstrut & \frac{2^{r_1}\cdot (2\pi)^{r_2}\cdot R\cdot h}{w\cdot\sqrt{|D|}}\cr \approx\mathstrut &\frac{2^{39}\cdot(2\pi)^{0}\cdot 688762923023490700000000000000 \cdot 1}{2\cdot\sqrt{1112962024555065990379787974028986797706599025588599389261176471461970163669515376929}}\cr\approx \mathstrut & 0.179460726971272 \end{aligned}\] (assuming GRH)
Galois group
A cyclic group of order 39 |
The 39 conjugacy class representatives for $C_{39}$ |
Character table for $C_{39}$ |
Intermediate fields
\(\Q(\zeta_{7})^+\), 13.13.491258904256726154641.1 |
Fields in the database are given up to isomorphism. Isomorphic intermediate fields are shown with their multiplicities.
Frobenius cycle types
$p$ | $2$ | $3$ | $5$ | $7$ | $11$ | $13$ | $17$ | $19$ | $23$ | $29$ | $31$ | $37$ | $41$ | $43$ | $47$ | $53$ | $59$ |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Cycle type | $39$ | $39$ | $39$ | R | $39$ | ${\href{/padicField/13.13.0.1}{13} }^{3}$ | $39$ | $39$ | ${\href{/padicField/23.3.0.1}{3} }^{13}$ | ${\href{/padicField/29.13.0.1}{13} }^{3}$ | $39$ | $39$ | ${\href{/padicField/41.13.0.1}{13} }^{3}$ | ${\href{/padicField/43.13.0.1}{13} }^{3}$ | $39$ | R | $39$ |
In the table, R denotes a ramified prime. Cycle lengths which are repeated in a cycle type are indicated by exponents.
Local algebras for ramified primes
$p$ | Label | Polynomial | $e$ | $f$ | $c$ | Galois group | Slope content |
---|---|---|---|---|---|---|---|
\(7\) | Deg $39$ | $3$ | $13$ | $26$ | |||
\(53\) | Deg $39$ | $13$ | $3$ | $36$ |