Normalized defining polynomial

\( x^{27} - 9 x^{26} + 41 x^{25} - 116 x^{24} + 234 x^{23} - 347 x^{22} + 380 x^{21} - 274 x^{20} + \cdots - 1 \) x^27 - 9*x^26 + 41*x^25 - 116*x^24 + 234*x^23 - 347*x^22 + 380*x^21 - 274*x^20 + 118*x^19 - 121*x^18 + 474*x^17 - 1071*x^16 + 1556*x^15 - 1531*x^14 + 964*x^13 - 256*x^12 + 122*x^11 - 700*x^10 + 1761*x^9 - 2620*x^8 + 2840*x^7 - 2483*x^6 + 1678*x^5 - 860*x^4 + 463*x^3 - 60*x^2 + 44*x - 1

Invariants

Degree:		$27$	sage: K.degree()   gp: poldegree(K.pol)   magma: Degree(K);   oscar: degree(K)
Signature:		$[1, 13]$	sage: K.signature()   gp: K.sign   magma: Signature(K);   oscar: signature(K)
Discriminant:		\(-800194812883861824535483445924579987063\) -800194812883861824535483445924579987063 \(\medspace = -\,983^{13}\)	sage: K.disc()   gp: K.disc   magma: OK := Integers(K); Discriminant(OK);   oscar: OK = ring_of_integers(K); discriminant(OK)
Root discriminant:		\(27.60\)	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:		$983^{1/2}\approx 31.352830813181765$
Ramified primes:		\(983\) 983	sage: K.disc().support()   gp: factor(abs(K.disc))[,1]~   magma: PrimeDivisors(Discriminant(OK));   oscar: prime_divisors(discriminant((OK)))
Discriminant root field:		\(\Q(\sqrt{-983}) \)
$\card{ \Aut(K/\Q) }$:		$1$	sage: K.automorphisms()   magma: Automorphisms(K);   oscar: automorphisms(K)
This field is not Galois over $\Q$.
This is not a CM field.

Integral basis (with respect to field generator \(a\))

$1$, $a$, $a^{2}$, $a^{3}$, $a^{4}$, $a^{5}$, $a^{6}$, $a^{7}$, $a^{8}$, $a^{9}$, $a^{10}$, $a^{11}$, $a^{12}$, $a^{13}$, $a^{14}$, $a^{15}$, $a^{16}$, $\frac{1}{5}a^{17}+\frac{2}{5}a^{16}-\frac{2}{5}a^{15}-\frac{2}{5}a^{14}+\frac{2}{5}a^{12}+\frac{2}{5}a^{11}-\frac{1}{5}a^{9}-\frac{2}{5}a^{7}+\frac{2}{5}a^{5}+\frac{2}{5}a^{4}-\frac{2}{5}a^{2}-\frac{1}{5}a+\frac{2}{5}$, $\frac{1}{5}a^{18}-\frac{1}{5}a^{16}+\frac{2}{5}a^{15}-\frac{1}{5}a^{14}+\frac{2}{5}a^{13}-\frac{2}{5}a^{12}+\frac{1}{5}a^{11}-\frac{1}{5}a^{10}+\frac{2}{5}a^{9}-\frac{2}{5}a^{8}-\frac{1}{5}a^{7}+\frac{2}{5}a^{6}-\frac{2}{5}a^{5}+\frac{1}{5}a^{4}-\frac{2}{5}a^{3}-\frac{2}{5}a^{2}-\frac{1}{5}a+\frac{1}{5}$, $\frac{1}{5}a^{19}-\frac{1}{5}a^{16}+\frac{2}{5}a^{15}-\frac{2}{5}a^{13}-\frac{2}{5}a^{12}+\frac{1}{5}a^{11}+\frac{2}{5}a^{10}+\frac{2}{5}a^{9}-\frac{1}{5}a^{8}-\frac{2}{5}a^{6}-\frac{2}{5}a^{5}-\frac{2}{5}a^{3}+\frac{2}{5}a^{2}+\frac{2}{5}$, $\frac{1}{5}a^{20}-\frac{1}{5}a^{16}-\frac{2}{5}a^{15}+\frac{1}{5}a^{14}-\frac{2}{5}a^{13}-\frac{2}{5}a^{12}-\frac{1}{5}a^{11}+\frac{2}{5}a^{10}-\frac{2}{5}a^{9}+\frac{1}{5}a^{7}-\frac{2}{5}a^{6}+\frac{2}{5}a^{5}+\frac{2}{5}a^{3}-\frac{2}{5}a^{2}+\frac{1}{5}a+\frac{2}{5}$, $\frac{1}{5}a^{21}-\frac{1}{5}a^{15}+\frac{1}{5}a^{14}-\frac{2}{5}a^{13}+\frac{1}{5}a^{12}-\frac{1}{5}a^{11}-\frac{2}{5}a^{10}-\frac{1}{5}a^{9}+\frac{1}{5}a^{8}+\frac{1}{5}a^{7}+\frac{2}{5}a^{6}+\frac{2}{5}a^{5}-\frac{1}{5}a^{4}-\frac{2}{5}a^{3}-\frac{1}{5}a^{2}+\frac{1}{5}a+\frac{2}{5}$, $\frac{1}{85}a^{22}+\frac{6}{85}a^{21}+\frac{7}{85}a^{20}-\frac{6}{85}a^{19}-\frac{6}{85}a^{17}-\frac{14}{85}a^{16}-\frac{14}{85}a^{15}-\frac{42}{85}a^{14}+\frac{12}{85}a^{13}-\frac{19}{85}a^{12}-\frac{28}{85}a^{11}-\frac{6}{85}a^{10}-\frac{4}{17}a^{9}+\frac{23}{85}a^{8}-\frac{13}{85}a^{7}+\frac{37}{85}a^{6}-\frac{3}{17}a^{5}-\frac{1}{17}a^{4}-\frac{37}{85}a^{3}-\frac{24}{85}a^{2}+\frac{21}{85}a+\frac{32}{85}$, $\frac{1}{1105}a^{23}-\frac{2}{1105}a^{22}+\frac{19}{221}a^{21}+\frac{6}{1105}a^{20}-\frac{54}{1105}a^{19}-\frac{23}{1105}a^{18}+\frac{6}{65}a^{17}-\frac{79}{221}a^{16}-\frac{236}{1105}a^{15}+\frac{433}{1105}a^{14}+\frac{72}{1105}a^{13}-\frac{97}{1105}a^{12}-\frac{394}{1105}a^{11}-\frac{42}{221}a^{10}+\frac{108}{221}a^{9}+\frac{66}{221}a^{8}+\frac{37}{85}a^{7}-\frac{4}{17}a^{6}-\frac{293}{1105}a^{5}+\frac{326}{1105}a^{4}-\frac{28}{65}a^{3}-\frac{5}{221}a^{2}+\frac{16}{65}a-\frac{103}{1105}$, $\frac{1}{5525}a^{24}+\frac{2}{5525}a^{23}+\frac{22}{5525}a^{22}-\frac{4}{5525}a^{21}-\frac{43}{5525}a^{20}-\frac{512}{5525}a^{19}-\frac{432}{5525}a^{18}-\frac{4}{85}a^{17}-\frac{2674}{5525}a^{16}-\frac{264}{5525}a^{15}-\frac{991}{5525}a^{14}+\frac{2284}{5525}a^{13}-\frac{652}{5525}a^{12}+\frac{93}{325}a^{11}-\frac{424}{1105}a^{10}+\frac{1359}{5525}a^{9}+\frac{44}{325}a^{8}+\frac{193}{425}a^{7}-\frac{173}{1105}a^{6}-\frac{1418}{5525}a^{5}+\frac{108}{221}a^{4}+\frac{16}{65}a^{3}-\frac{1583}{5525}a^{2}+\frac{1167}{5525}a-\frac{282}{5525}$, $\frac{1}{5525}a^{25}-\frac{2}{5525}a^{23}-\frac{8}{5525}a^{22}+\frac{11}{221}a^{21}-\frac{42}{425}a^{20}-\frac{538}{5525}a^{19}-\frac{41}{5525}a^{18}+\frac{226}{5525}a^{17}-\frac{2486}{5525}a^{16}-\frac{2373}{5525}a^{15}+\frac{87}{425}a^{14}+\frac{436}{1105}a^{13}+\frac{81}{1105}a^{12}+\frac{388}{5525}a^{11}+\frac{2064}{5525}a^{10}+\frac{319}{1105}a^{9}+\frac{1043}{5525}a^{8}+\frac{1072}{5525}a^{7}+\frac{84}{425}a^{6}-\frac{1864}{5525}a^{5}+\frac{98}{1105}a^{4}+\frac{1902}{5525}a^{3}+\frac{2623}{5525}a^{2}+\frac{1889}{5525}a-\frac{691}{5525}$, $\frac{1}{16\!\cdots\!75}a^{26}-\frac{11\!\cdots\!13}{14\!\cdots\!25}a^{25}+\frac{12\!\cdots\!39}{16\!\cdots\!75}a^{24}-\frac{26\!\cdots\!94}{29\!\cdots\!65}a^{23}-\frac{73\!\cdots\!39}{16\!\cdots\!75}a^{22}+\frac{74\!\cdots\!03}{32\!\cdots\!15}a^{21}+\frac{32\!\cdots\!27}{16\!\cdots\!75}a^{20}+\frac{94\!\cdots\!96}{16\!\cdots\!75}a^{19}+\frac{10\!\cdots\!92}{16\!\cdots\!75}a^{18}-\frac{12\!\cdots\!09}{16\!\cdots\!75}a^{17}-\frac{52\!\cdots\!89}{16\!\cdots\!75}a^{16}+\frac{30\!\cdots\!16}{16\!\cdots\!75}a^{15}-\frac{46\!\cdots\!59}{16\!\cdots\!75}a^{14}+\frac{24\!\cdots\!19}{16\!\cdots\!75}a^{13}+\frac{16\!\cdots\!73}{94\!\cdots\!75}a^{12}+\frac{36\!\cdots\!36}{16\!\cdots\!75}a^{11}-\frac{76\!\cdots\!22}{16\!\cdots\!75}a^{10}+\frac{45\!\cdots\!82}{16\!\cdots\!75}a^{9}+\frac{23\!\cdots\!21}{16\!\cdots\!75}a^{8}-\frac{97\!\cdots\!56}{32\!\cdots\!15}a^{7}-\frac{13\!\cdots\!17}{32\!\cdots\!15}a^{6}-\frac{47\!\cdots\!11}{14\!\cdots\!25}a^{5}+\frac{68\!\cdots\!22}{16\!\cdots\!75}a^{4}-\frac{29\!\cdots\!18}{16\!\cdots\!75}a^{3}-\frac{26\!\cdots\!63}{16\!\cdots\!75}a^{2}+\frac{75\!\cdots\!44}{16\!\cdots\!75}a-\frac{16\!\cdots\!69}{16\!\cdots\!75}$ 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, 1/5*a^17 + 2/5*a^16 - 2/5*a^15 - 2/5*a^14 + 2/5*a^12 + 2/5*a^11 - 1/5*a^9 - 2/5*a^7 + 2/5*a^5 + 2/5*a^4 - 2/5*a^2 - 1/5*a + 2/5, 1/5*a^18 - 1/5*a^16 + 2/5*a^15 - 1/5*a^14 + 2/5*a^13 - 2/5*a^12 + 1/5*a^11 - 1/5*a^10 + 2/5*a^9 - 2/5*a^8 - 1/5*a^7 + 2/5*a^6 - 2/5*a^5 + 1/5*a^4 - 2/5*a^3 - 2/5*a^2 - 1/5*a + 1/5, 1/5*a^19 - 1/5*a^16 + 2/5*a^15 - 2/5*a^13 - 2/5*a^12 + 1/5*a^11 + 2/5*a^10 + 2/5*a^9 - 1/5*a^8 - 2/5*a^6 - 2/5*a^5 - 2/5*a^3 + 2/5*a^2 + 2/5, 1/5*a^20 - 1/5*a^16 - 2/5*a^15 + 1/5*a^14 - 2/5*a^13 - 2/5*a^12 - 1/5*a^11 + 2/5*a^10 - 2/5*a^9 + 1/5*a^7 - 2/5*a^6 + 2/5*a^5 + 2/5*a^3 - 2/5*a^2 + 1/5*a + 2/5, 1/5*a^21 - 1/5*a^15 + 1/5*a^14 - 2/5*a^13 + 1/5*a^12 - 1/5*a^11 - 2/5*a^10 - 1/5*a^9 + 1/5*a^8 + 1/5*a^7 + 2/5*a^6 + 2/5*a^5 - 1/5*a^4 - 2/5*a^3 - 1/5*a^2 + 1/5*a + 2/5, 1/85*a^22 + 6/85*a^21 + 7/85*a^20 - 6/85*a^19 - 6/85*a^17 - 14/85*a^16 - 14/85*a^15 - 42/85*a^14 + 12/85*a^13 - 19/85*a^12 - 28/85*a^11 - 6/85*a^10 - 4/17*a^9 + 23/85*a^8 - 13/85*a^7 + 37/85*a^6 - 3/17*a^5 - 1/17*a^4 - 37/85*a^3 - 24/85*a^2 + 21/85*a + 32/85, 1/1105*a^23 - 2/1105*a^22 + 19/221*a^21 + 6/1105*a^20 - 54/1105*a^19 - 23/1105*a^18 + 6/65*a^17 - 79/221*a^16 - 236/1105*a^15 + 433/1105*a^14 + 72/1105*a^13 - 97/1105*a^12 - 394/1105*a^11 - 42/221*a^10 + 108/221*a^9 + 66/221*a^8 + 37/85*a^7 - 4/17*a^6 - 293/1105*a^5 + 326/1105*a^4 - 28/65*a^3 - 5/221*a^2 + 16/65*a - 103/1105, 1/5525*a^24 + 2/5525*a^23 + 22/5525*a^22 - 4/5525*a^21 - 43/5525*a^20 - 512/5525*a^19 - 432/5525*a^18 - 4/85*a^17 - 2674/5525*a^16 - 264/5525*a^15 - 991/5525*a^14 + 2284/5525*a^13 - 652/5525*a^12 + 93/325*a^11 - 424/1105*a^10 + 1359/5525*a^9 + 44/325*a^8 + 193/425*a^7 - 173/1105*a^6 - 1418/5525*a^5 + 108/221*a^4 + 16/65*a^3 - 1583/5525*a^2 + 1167/5525*a - 282/5525, 1/5525*a^25 - 2/5525*a^23 - 8/5525*a^22 + 11/221*a^21 - 42/425*a^20 - 538/5525*a^19 - 41/5525*a^18 + 226/5525*a^17 - 2486/5525*a^16 - 2373/5525*a^15 + 87/425*a^14 + 436/1105*a^13 + 81/1105*a^12 + 388/5525*a^11 + 2064/5525*a^10 + 319/1105*a^9 + 1043/5525*a^8 + 1072/5525*a^7 + 84/425*a^6 - 1864/5525*a^5 + 98/1105*a^4 + 1902/5525*a^3 + 2623/5525*a^2 + 1889/5525*a - 691/5525, 1/160497705249110837897575*a^26 - 1143171342020832313/14590700477191894354325*a^25 + 12042547297511383639/160497705249110837897575*a^24 - 261342174697961794/2918140095438378870865*a^23 - 739809879310502280739/160497705249110837897575*a^22 + 740811871484393469103/32099541049822167579515*a^21 + 3258012399365648422627/160497705249110837897575*a^20 + 9418735920655884211396/160497705249110837897575*a^19 + 10269350004228255221792/160497705249110837897575*a^18 - 12902260304265240580209/160497705249110837897575*a^17 - 52956548233273764927189/160497705249110837897575*a^16 + 30871640536410862160916/160497705249110837897575*a^15 - 46955886372723557565459/160497705249110837897575*a^14 + 2406294423568932068119/160497705249110837897575*a^13 + 1604046812257698793573/9441041485241813993975*a^12 + 36264304417158786945836/160497705249110837897575*a^11 - 76577735361570364878322/160497705249110837897575*a^10 + 45841298791240909448282/160497705249110837897575*a^9 + 23443617690375582435321/160497705249110837897575*a^8 - 9721655120203278319656/32099541049822167579515*a^7 - 13395596628200100868117/32099541049822167579515*a^6 - 4703429698717194610411/14590700477191894354325*a^5 + 68282674755647920441022/160497705249110837897575*a^4 - 29089499530605548866318/160497705249110837897575*a^3 - 26217258769654822472563/160497705249110837897575*a^2 + 75812345561325992011044/160497705249110837897575*a - 16548831501749163795569/160497705249110837897575

Class group and class number

Trivial group, which has order $1$ (assuming GRH)

Unit group

Rank:		$13$	sage: UK.rank()   gp: K.fu   magma: UnitRank(K);   oscar: rank(UK)
Torsion generator:		\( -1 \) -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:		$\frac{18\!\cdots\!04}{16\!\cdots\!75}a^{26}-\frac{20\!\cdots\!98}{14\!\cdots\!25}a^{25}+\frac{25\!\cdots\!18}{32\!\cdots\!15}a^{24}-\frac{15\!\cdots\!09}{58\!\cdots\!73}a^{23}+\frac{20\!\cdots\!06}{32\!\cdots\!15}a^{22}-\frac{16\!\cdots\!51}{16\!\cdots\!75}a^{21}+\frac{19\!\cdots\!72}{16\!\cdots\!75}a^{20}-\frac{14\!\cdots\!76}{16\!\cdots\!75}a^{19}+\frac{41\!\cdots\!01}{16\!\cdots\!75}a^{18}+\frac{64\!\cdots\!28}{16\!\cdots\!75}a^{17}+\frac{14\!\cdots\!04}{16\!\cdots\!75}a^{16}-\frac{48\!\cdots\!39}{16\!\cdots\!75}a^{15}+\frac{60\!\cdots\!43}{12\!\cdots\!75}a^{14}-\frac{79\!\cdots\!48}{16\!\cdots\!75}a^{13}+\frac{46\!\cdots\!31}{16\!\cdots\!75}a^{12}-\frac{94\!\cdots\!59}{32\!\cdots\!15}a^{11}-\frac{96\!\cdots\!27}{16\!\cdots\!75}a^{10}-\frac{25\!\cdots\!66}{16\!\cdots\!75}a^{9}+\frac{63\!\cdots\!31}{12\!\cdots\!75}a^{8}-\frac{12\!\cdots\!86}{16\!\cdots\!75}a^{7}+\frac{13\!\cdots\!13}{16\!\cdots\!75}a^{6}-\frac{10\!\cdots\!52}{14\!\cdots\!25}a^{5}+\frac{79\!\cdots\!88}{16\!\cdots\!75}a^{4}-\frac{39\!\cdots\!24}{16\!\cdots\!75}a^{3}+\frac{12\!\cdots\!73}{16\!\cdots\!75}a^{2}-\frac{13\!\cdots\!07}{32\!\cdots\!15}a-\frac{16\!\cdots\!83}{16\!\cdots\!75}$, $\frac{36\!\cdots\!46}{16\!\cdots\!75}a^{26}-\frac{27\!\cdots\!04}{14\!\cdots\!25}a^{25}+\frac{96\!\cdots\!79}{12\!\cdots\!75}a^{24}-\frac{21\!\cdots\!89}{11\!\cdots\!25}a^{23}+\frac{10\!\cdots\!41}{32\!\cdots\!15}a^{22}-\frac{56\!\cdots\!97}{16\!\cdots\!75}a^{21}+\frac{37\!\cdots\!84}{16\!\cdots\!75}a^{20}-\frac{64\!\cdots\!67}{16\!\cdots\!75}a^{19}-\frac{71\!\cdots\!53}{16\!\cdots\!75}a^{18}-\frac{65\!\cdots\!27}{18\!\cdots\!95}a^{17}+\frac{34\!\cdots\!28}{32\!\cdots\!15}a^{16}-\frac{24\!\cdots\!28}{16\!\cdots\!75}a^{15}+\frac{21\!\cdots\!02}{16\!\cdots\!75}a^{14}-\frac{85\!\cdots\!54}{16\!\cdots\!75}a^{13}-\frac{38\!\cdots\!39}{32\!\cdots\!15}a^{12}+\frac{12\!\cdots\!56}{16\!\cdots\!75}a^{11}+\frac{15\!\cdots\!84}{16\!\cdots\!75}a^{10}-\frac{23\!\cdots\!77}{12\!\cdots\!75}a^{9}+\frac{36\!\cdots\!32}{16\!\cdots\!75}a^{8}-\frac{66\!\cdots\!49}{32\!\cdots\!15}a^{7}+\frac{26\!\cdots\!03}{16\!\cdots\!75}a^{6}-\frac{12\!\cdots\!23}{85\!\cdots\!25}a^{5}+\frac{15\!\cdots\!27}{16\!\cdots\!75}a^{4}-\frac{10\!\cdots\!07}{32\!\cdots\!15}a^{3}+\frac{10\!\cdots\!17}{18\!\cdots\!95}a^{2}+\frac{65\!\cdots\!71}{16\!\cdots\!75}a+\frac{62\!\cdots\!11}{16\!\cdots\!75}$, $\frac{79\!\cdots\!66}{16\!\cdots\!75}a^{26}-\frac{64\!\cdots\!09}{14\!\cdots\!25}a^{25}+\frac{24\!\cdots\!02}{12\!\cdots\!75}a^{24}-\frac{81\!\cdots\!14}{14\!\cdots\!25}a^{23}+\frac{17\!\cdots\!28}{16\!\cdots\!75}a^{22}-\frac{26\!\cdots\!38}{16\!\cdots\!75}a^{21}+\frac{28\!\cdots\!57}{16\!\cdots\!75}a^{20}-\frac{40\!\cdots\!59}{32\!\cdots\!15}a^{19}+\frac{80\!\cdots\!79}{16\!\cdots\!75}a^{18}-\frac{17\!\cdots\!28}{32\!\cdots\!15}a^{17}+\frac{36\!\cdots\!44}{16\!\cdots\!75}a^{16}-\frac{81\!\cdots\!29}{16\!\cdots\!75}a^{15}+\frac{90\!\cdots\!21}{12\!\cdots\!75}a^{14}-\frac{11\!\cdots\!58}{16\!\cdots\!75}a^{13}+\frac{70\!\cdots\!52}{16\!\cdots\!75}a^{12}-\frac{60\!\cdots\!48}{64\!\cdots\!03}a^{11}+\frac{28\!\cdots\!87}{94\!\cdots\!75}a^{10}-\frac{10\!\cdots\!81}{32\!\cdots\!15}a^{9}+\frac{13\!\cdots\!74}{16\!\cdots\!75}a^{8}-\frac{20\!\cdots\!44}{16\!\cdots\!75}a^{7}+\frac{21\!\cdots\!88}{16\!\cdots\!75}a^{6}-\frac{16\!\cdots\!33}{14\!\cdots\!25}a^{5}+\frac{11\!\cdots\!72}{16\!\cdots\!75}a^{4}-\frac{64\!\cdots\!76}{18\!\cdots\!95}a^{3}+\frac{21\!\cdots\!61}{12\!\cdots\!75}a^{2}+\frac{83\!\cdots\!39}{16\!\cdots\!75}a+\frac{79\!\cdots\!21}{12\!\cdots\!75}$, $\frac{48\!\cdots\!66}{16\!\cdots\!75}a^{26}-\frac{30\!\cdots\!28}{11\!\cdots\!25}a^{25}+\frac{20\!\cdots\!28}{16\!\cdots\!75}a^{24}-\frac{10\!\cdots\!27}{29\!\cdots\!65}a^{23}+\frac{10\!\cdots\!82}{16\!\cdots\!75}a^{22}-\frac{10\!\cdots\!82}{12\!\cdots\!75}a^{21}+\frac{12\!\cdots\!41}{16\!\cdots\!75}a^{20}-\frac{37\!\cdots\!94}{16\!\cdots\!75}a^{19}-\frac{18\!\cdots\!18}{64\!\cdots\!03}a^{18}+\frac{12\!\cdots\!77}{24\!\cdots\!55}a^{17}+\frac{22\!\cdots\!56}{16\!\cdots\!75}a^{16}-\frac{53\!\cdots\!87}{16\!\cdots\!75}a^{15}+\frac{66\!\cdots\!16}{16\!\cdots\!75}a^{14}-\frac{17\!\cdots\!74}{64\!\cdots\!03}a^{13}+\frac{20\!\cdots\!88}{16\!\cdots\!75}a^{12}+\frac{29\!\cdots\!97}{16\!\cdots\!75}a^{11}-\frac{13\!\cdots\!11}{16\!\cdots\!75}a^{10}-\frac{38\!\cdots\!92}{16\!\cdots\!75}a^{9}+\frac{18\!\cdots\!69}{32\!\cdots\!15}a^{8}-\frac{85\!\cdots\!92}{12\!\cdots\!75}a^{7}+\frac{87\!\cdots\!03}{16\!\cdots\!75}a^{6}-\frac{41\!\cdots\!09}{14\!\cdots\!25}a^{5}+\frac{85\!\cdots\!27}{16\!\cdots\!75}a^{4}+\frac{58\!\cdots\!75}{64\!\cdots\!03}a^{3}-\frac{63\!\cdots\!99}{94\!\cdots\!75}a^{2}+\frac{69\!\cdots\!83}{16\!\cdots\!75}a-\frac{15\!\cdots\!96}{16\!\cdots\!75}$, $\frac{27\!\cdots\!87}{44\!\cdots\!25}a^{26}-\frac{15\!\cdots\!78}{27\!\cdots\!43}a^{25}+\frac{42\!\cdots\!28}{15\!\cdots\!65}a^{24}-\frac{58\!\cdots\!91}{69\!\cdots\!75}a^{23}+\frac{14\!\cdots\!01}{76\!\cdots\!25}a^{22}-\frac{24\!\cdots\!86}{76\!\cdots\!25}a^{21}+\frac{32\!\cdots\!24}{76\!\cdots\!25}a^{20}-\frac{13\!\cdots\!05}{30\!\cdots\!73}a^{19}+\frac{25\!\cdots\!38}{76\!\cdots\!25}a^{18}-\frac{19\!\cdots\!44}{76\!\cdots\!25}a^{17}+\frac{27\!\cdots\!76}{76\!\cdots\!25}a^{16}-\frac{57\!\cdots\!28}{76\!\cdots\!25}a^{15}+\frac{10\!\cdots\!77}{76\!\cdots\!25}a^{14}-\frac{13\!\cdots\!63}{76\!\cdots\!25}a^{13}+\frac{80\!\cdots\!08}{44\!\cdots\!25}a^{12}-\frac{99\!\cdots\!21}{76\!\cdots\!25}a^{11}+\frac{98\!\cdots\!59}{15\!\cdots\!65}a^{10}-\frac{30\!\cdots\!31}{76\!\cdots\!25}a^{9}+\frac{71\!\cdots\!67}{76\!\cdots\!25}a^{8}-\frac{32\!\cdots\!62}{15\!\cdots\!65}a^{7}+\frac{24\!\cdots\!89}{76\!\cdots\!25}a^{6}-\frac{15\!\cdots\!02}{40\!\cdots\!75}a^{5}+\frac{24\!\cdots\!43}{76\!\cdots\!25}a^{4}-\frac{11\!\cdots\!16}{58\!\cdots\!25}a^{3}+\frac{73\!\cdots\!52}{76\!\cdots\!25}a^{2}-\frac{23\!\cdots\!01}{58\!\cdots\!25}a-\frac{32\!\cdots\!46}{76\!\cdots\!25}$, $\frac{97\!\cdots\!74}{16\!\cdots\!75}a^{26}-\frac{75\!\cdots\!26}{14\!\cdots\!25}a^{25}+\frac{35\!\cdots\!09}{16\!\cdots\!75}a^{24}-\frac{80\!\cdots\!71}{14\!\cdots\!25}a^{23}+\frac{14\!\cdots\!37}{16\!\cdots\!75}a^{22}-\frac{16\!\cdots\!82}{16\!\cdots\!75}a^{21}+\frac{92\!\cdots\!33}{16\!\cdots\!75}a^{20}+\frac{11\!\cdots\!14}{32\!\cdots\!15}a^{19}-\frac{12\!\cdots\!44}{16\!\cdots\!75}a^{18}-\frac{19\!\cdots\!27}{64\!\cdots\!03}a^{17}+\frac{46\!\cdots\!81}{16\!\cdots\!75}a^{16}-\frac{80\!\cdots\!51}{16\!\cdots\!75}a^{15}+\frac{55\!\cdots\!19}{12\!\cdots\!75}a^{14}-\frac{16\!\cdots\!12}{16\!\cdots\!75}a^{13}-\frac{43\!\cdots\!67}{16\!\cdots\!75}a^{12}+\frac{11\!\cdots\!39}{32\!\cdots\!15}a^{11}+\frac{97\!\cdots\!31}{16\!\cdots\!75}a^{10}-\frac{19\!\cdots\!51}{32\!\cdots\!15}a^{9}+\frac{14\!\cdots\!31}{16\!\cdots\!75}a^{8}-\frac{11\!\cdots\!11}{16\!\cdots\!75}a^{7}+\frac{48\!\cdots\!52}{16\!\cdots\!75}a^{6}-\frac{35\!\cdots\!42}{14\!\cdots\!25}a^{5}-\frac{25\!\cdots\!37}{16\!\cdots\!75}a^{4}+\frac{56\!\cdots\!02}{32\!\cdots\!15}a^{3}+\frac{15\!\cdots\!57}{16\!\cdots\!75}a^{2}+\frac{52\!\cdots\!86}{16\!\cdots\!75}a+\frac{21\!\cdots\!42}{16\!\cdots\!75}$, $\frac{11\!\cdots\!56}{14\!\cdots\!25}a^{26}-\frac{79\!\cdots\!54}{11\!\cdots\!25}a^{25}+\frac{48\!\cdots\!61}{14\!\cdots\!25}a^{24}-\frac{14\!\cdots\!03}{14\!\cdots\!25}a^{23}+\frac{29\!\cdots\!97}{14\!\cdots\!25}a^{22}-\frac{44\!\cdots\!78}{14\!\cdots\!25}a^{21}+\frac{97\!\cdots\!02}{29\!\cdots\!65}a^{20}-\frac{35\!\cdots\!91}{14\!\cdots\!25}a^{19}+\frac{13\!\cdots\!47}{14\!\cdots\!25}a^{18}-\frac{11\!\cdots\!63}{14\!\cdots\!25}a^{17}+\frac{55\!\cdots\!27}{14\!\cdots\!25}a^{16}-\frac{54\!\cdots\!07}{58\!\cdots\!73}a^{15}+\frac{40\!\cdots\!58}{29\!\cdots\!65}a^{14}-\frac{15\!\cdots\!76}{11\!\cdots\!25}a^{13}+\frac{12\!\cdots\!37}{14\!\cdots\!25}a^{12}-\frac{23\!\cdots\!39}{14\!\cdots\!25}a^{11}+\frac{22\!\cdots\!32}{14\!\cdots\!25}a^{10}-\frac{16\!\cdots\!19}{29\!\cdots\!65}a^{9}+\frac{34\!\cdots\!14}{22\!\cdots\!05}a^{8}-\frac{10\!\cdots\!81}{44\!\cdots\!21}a^{7}+\frac{36\!\cdots\!32}{14\!\cdots\!25}a^{6}-\frac{30\!\cdots\!51}{14\!\cdots\!25}a^{5}+\frac{20\!\cdots\!52}{14\!\cdots\!25}a^{4}-\frac{10\!\cdots\!01}{14\!\cdots\!25}a^{3}+\frac{51\!\cdots\!19}{14\!\cdots\!25}a^{2}-\frac{11\!\cdots\!08}{14\!\cdots\!25}a+\frac{33\!\cdots\!36}{14\!\cdots\!25}$, $\frac{97\!\cdots\!16}{16\!\cdots\!75}a^{26}-\frac{84\!\cdots\!72}{14\!\cdots\!25}a^{25}+\frac{17\!\cdots\!77}{64\!\cdots\!03}a^{24}-\frac{22\!\cdots\!41}{29\!\cdots\!65}a^{23}+\frac{10\!\cdots\!40}{64\!\cdots\!03}a^{22}-\frac{37\!\cdots\!59}{16\!\cdots\!75}a^{21}+\frac{42\!\cdots\!53}{16\!\cdots\!75}a^{20}-\frac{37\!\cdots\!64}{16\!\cdots\!75}a^{19}+\frac{29\!\cdots\!04}{16\!\cdots\!75}a^{18}-\frac{36\!\cdots\!38}{16\!\cdots\!75}a^{17}+\frac{70\!\cdots\!16}{16\!\cdots\!75}a^{16}-\frac{11\!\cdots\!76}{16\!\cdots\!75}a^{15}+\frac{15\!\cdots\!41}{16\!\cdots\!75}a^{14}-\frac{15\!\cdots\!82}{16\!\cdots\!75}a^{13}+\frac{14\!\cdots\!54}{16\!\cdots\!75}a^{12}-\frac{25\!\cdots\!98}{32\!\cdots\!15}a^{11}+\frac{11\!\cdots\!27}{16\!\cdots\!75}a^{10}-\frac{13\!\cdots\!54}{16\!\cdots\!75}a^{9}+\frac{16\!\cdots\!87}{16\!\cdots\!75}a^{8}-\frac{22\!\cdots\!49}{16\!\cdots\!75}a^{7}+\frac{29\!\cdots\!97}{16\!\cdots\!75}a^{6}-\frac{32\!\cdots\!73}{14\!\cdots\!25}a^{5}+\frac{34\!\cdots\!42}{16\!\cdots\!75}a^{4}-\frac{25\!\cdots\!21}{16\!\cdots\!75}a^{3}+\frac{14\!\cdots\!02}{16\!\cdots\!75}a^{2}-\frac{12\!\cdots\!99}{24\!\cdots\!55}a+\frac{58\!\cdots\!18}{16\!\cdots\!75}$, $\frac{11\!\cdots\!38}{14\!\cdots\!15}a^{26}-\frac{10\!\cdots\!48}{14\!\cdots\!25}a^{25}+\frac{52\!\cdots\!51}{16\!\cdots\!75}a^{24}-\frac{13\!\cdots\!02}{14\!\cdots\!25}a^{23}+\frac{29\!\cdots\!56}{16\!\cdots\!75}a^{22}-\frac{42\!\cdots\!44}{16\!\cdots\!75}a^{21}+\frac{89\!\cdots\!32}{32\!\cdots\!15}a^{20}-\frac{13\!\cdots\!83}{72\!\cdots\!75}a^{19}+\frac{91\!\cdots\!36}{16\!\cdots\!75}a^{18}-\frac{11\!\cdots\!33}{16\!\cdots\!75}a^{17}+\frac{58\!\cdots\!54}{16\!\cdots\!75}a^{16}-\frac{26\!\cdots\!03}{32\!\cdots\!15}a^{15}+\frac{19\!\cdots\!21}{16\!\cdots\!75}a^{14}-\frac{80\!\cdots\!91}{72\!\cdots\!75}a^{13}+\frac{98\!\cdots\!63}{16\!\cdots\!75}a^{12}-\frac{80\!\cdots\!23}{16\!\cdots\!75}a^{11}+\frac{39\!\cdots\!19}{94\!\cdots\!75}a^{10}-\frac{50\!\cdots\!33}{94\!\cdots\!75}a^{9}+\frac{22\!\cdots\!59}{16\!\cdots\!75}a^{8}-\frac{32\!\cdots\!42}{16\!\cdots\!75}a^{7}+\frac{33\!\cdots\!54}{16\!\cdots\!75}a^{6}-\frac{14\!\cdots\!98}{85\!\cdots\!25}a^{5}+\frac{51\!\cdots\!19}{49\!\cdots\!31}a^{4}-\frac{73\!\cdots\!26}{16\!\cdots\!75}a^{3}+\frac{35\!\cdots\!63}{16\!\cdots\!75}a^{2}+\frac{16\!\cdots\!36}{64\!\cdots\!03}a+\frac{21\!\cdots\!96}{16\!\cdots\!75}$, $\frac{27\!\cdots\!81}{21\!\cdots\!75}a^{26}-\frac{18\!\cdots\!88}{19\!\cdots\!25}a^{25}+\frac{71\!\cdots\!12}{21\!\cdots\!75}a^{24}-\frac{12\!\cdots\!14}{19\!\cdots\!25}a^{23}+\frac{17\!\cdots\!62}{21\!\cdots\!75}a^{22}-\frac{69\!\cdots\!79}{16\!\cdots\!75}a^{21}-\frac{86\!\cdots\!72}{21\!\cdots\!75}a^{20}+\frac{11\!\cdots\!16}{87\!\cdots\!11}a^{19}-\frac{19\!\cdots\!54}{21\!\cdots\!75}a^{18}-\frac{13\!\cdots\!72}{12\!\cdots\!75}a^{17}+\frac{72\!\cdots\!19}{21\!\cdots\!75}a^{16}-\frac{71\!\cdots\!36}{21\!\cdots\!75}a^{15}+\frac{95\!\cdots\!23}{99\!\cdots\!75}a^{14}+\frac{59\!\cdots\!16}{21\!\cdots\!75}a^{13}-\frac{21\!\cdots\!83}{43\!\cdots\!55}a^{12}+\frac{84\!\cdots\!39}{21\!\cdots\!75}a^{11}+\frac{32\!\cdots\!93}{21\!\cdots\!75}a^{10}-\frac{84\!\cdots\!46}{21\!\cdots\!75}a^{9}+\frac{47\!\cdots\!70}{87\!\cdots\!11}a^{8}-\frac{79\!\cdots\!63}{21\!\cdots\!75}a^{7}-\frac{48\!\cdots\!19}{43\!\cdots\!55}a^{6}+\frac{16\!\cdots\!08}{39\!\cdots\!05}a^{5}-\frac{17\!\cdots\!53}{21\!\cdots\!75}a^{4}+\frac{16\!\cdots\!77}{21\!\cdots\!75}a^{3}-\frac{46\!\cdots\!62}{21\!\cdots\!75}a^{2}+\frac{18\!\cdots\!03}{43\!\cdots\!55}a+\frac{40\!\cdots\!44}{43\!\cdots\!55}$, $\frac{53\!\cdots\!27}{16\!\cdots\!75}a^{26}-\frac{25\!\cdots\!33}{85\!\cdots\!25}a^{25}+\frac{43\!\cdots\!72}{32\!\cdots\!15}a^{24}-\frac{55\!\cdots\!16}{14\!\cdots\!25}a^{23}+\frac{12\!\cdots\!26}{16\!\cdots\!75}a^{22}-\frac{18\!\cdots\!83}{16\!\cdots\!75}a^{21}+\frac{16\!\cdots\!11}{12\!\cdots\!75}a^{20}-\frac{12\!\cdots\!09}{12\!\cdots\!75}a^{19}+\frac{16\!\cdots\!78}{32\!\cdots\!15}a^{18}-\frac{67\!\cdots\!73}{16\!\cdots\!75}a^{17}+\frac{23\!\cdots\!39}{16\!\cdots\!75}a^{16}-\frac{54\!\cdots\!81}{16\!\cdots\!75}a^{15}+\frac{16\!\cdots\!48}{32\!\cdots\!15}a^{14}-\frac{87\!\cdots\!24}{16\!\cdots\!75}a^{13}+\frac{60\!\cdots\!48}{16\!\cdots\!75}a^{12}-\frac{19\!\cdots\!56}{16\!\cdots\!75}a^{11}+\frac{55\!\cdots\!11}{16\!\cdots\!75}a^{10}-\frac{30\!\cdots\!98}{16\!\cdots\!75}a^{9}+\frac{89\!\cdots\!33}{16\!\cdots\!75}a^{8}-\frac{14\!\cdots\!52}{16\!\cdots\!75}a^{7}+\frac{32\!\cdots\!42}{32\!\cdots\!15}a^{6}-\frac{13\!\cdots\!83}{14\!\cdots\!25}a^{5}+\frac{98\!\cdots\!89}{16\!\cdots\!75}a^{4}-\frac{49\!\cdots\!01}{16\!\cdots\!75}a^{3}+\frac{23\!\cdots\!58}{16\!\cdots\!75}a^{2}-\frac{13\!\cdots\!48}{16\!\cdots\!75}a+\frac{14\!\cdots\!58}{16\!\cdots\!75}$, $\frac{47\!\cdots\!44}{21\!\cdots\!75}a^{26}-\frac{25\!\cdots\!11}{19\!\cdots\!25}a^{25}+\frac{60\!\cdots\!69}{21\!\cdots\!75}a^{24}+\frac{53\!\cdots\!99}{19\!\cdots\!25}a^{23}-\frac{35\!\cdots\!74}{12\!\cdots\!75}a^{22}+\frac{17\!\cdots\!38}{21\!\cdots\!75}a^{21}-\frac{19\!\cdots\!06}{12\!\cdots\!75}a^{20}+\frac{82\!\cdots\!81}{43\!\cdots\!55}a^{19}-\frac{32\!\cdots\!94}{21\!\cdots\!75}a^{18}+\frac{17\!\cdots\!27}{43\!\cdots\!55}a^{17}+\frac{74\!\cdots\!06}{21\!\cdots\!75}a^{16}+\frac{16\!\cdots\!74}{21\!\cdots\!75}a^{15}-\frac{82\!\cdots\!43}{21\!\cdots\!75}a^{14}+\frac{15\!\cdots\!08}{21\!\cdots\!75}a^{13}-\frac{17\!\cdots\!57}{21\!\cdots\!75}a^{12}+\frac{48\!\cdots\!22}{87\!\cdots\!11}a^{11}-\frac{18\!\cdots\!69}{21\!\cdots\!75}a^{10}-\frac{57\!\cdots\!38}{43\!\cdots\!55}a^{9}-\frac{61\!\cdots\!92}{12\!\cdots\!75}a^{8}+\frac{13\!\cdots\!14}{21\!\cdots\!75}a^{7}-\frac{25\!\cdots\!18}{21\!\cdots\!75}a^{6}+\frac{26\!\cdots\!23}{19\!\cdots\!25}a^{5}-\frac{26\!\cdots\!27}{21\!\cdots\!75}a^{4}+\frac{35\!\cdots\!24}{43\!\cdots\!55}a^{3}-\frac{74\!\cdots\!33}{21\!\cdots\!75}a^{2}+\frac{44\!\cdots\!11}{21\!\cdots\!75}a+\frac{51\!\cdots\!57}{21\!\cdots\!75}$, $\frac{45\!\cdots\!16}{16\!\cdots\!75}a^{26}-\frac{37\!\cdots\!67}{14\!\cdots\!25}a^{25}+\frac{11\!\cdots\!82}{94\!\cdots\!75}a^{24}-\frac{50\!\cdots\!22}{14\!\cdots\!25}a^{23}+\frac{11\!\cdots\!48}{16\!\cdots\!75}a^{22}-\frac{34\!\cdots\!88}{32\!\cdots\!15}a^{21}+\frac{18\!\cdots\!31}{16\!\cdots\!75}a^{20}-\frac{13\!\cdots\!27}{16\!\cdots\!75}a^{19}+\frac{42\!\cdots\!47}{12\!\cdots\!75}a^{18}-\frac{47\!\cdots\!38}{16\!\cdots\!75}a^{17}+\frac{43\!\cdots\!27}{32\!\cdots\!15}a^{16}-\frac{30\!\cdots\!26}{94\!\cdots\!75}a^{15}+\frac{77\!\cdots\!97}{16\!\cdots\!75}a^{14}-\frac{45\!\cdots\!33}{94\!\cdots\!75}a^{13}+\frac{48\!\cdots\!11}{16\!\cdots\!75}a^{12}-\frac{10\!\cdots\!16}{16\!\cdots\!75}a^{11}+\frac{14\!\cdots\!07}{16\!\cdots\!75}a^{10}-\frac{30\!\cdots\!18}{16\!\cdots\!75}a^{9}+\frac{50\!\cdots\!37}{94\!\cdots\!75}a^{8}-\frac{13\!\cdots\!98}{16\!\cdots\!75}a^{7}+\frac{14\!\cdots\!22}{16\!\cdots\!75}a^{6}-\frac{44\!\cdots\!49}{58\!\cdots\!73}a^{5}+\frac{80\!\cdots\!07}{16\!\cdots\!75}a^{4}-\frac{38\!\cdots\!96}{16\!\cdots\!75}a^{3}+\frac{35\!\cdots\!78}{32\!\cdots\!15}a^{2}-\frac{10\!\cdots\!47}{16\!\cdots\!75}a-\frac{23\!\cdots\!32}{32\!\cdots\!15}$ 1870983275145255197704/160497705249110837897575*a^26 - 2084232795244502227098/14590700477191894354325*a^25 + 25745113149804019603218/32099541049822167579515*a^24 - 1595827098929615291209/583628019087675774173*a^23 + 201242115374597867499706/32099541049822167579515*a^22 - 1651004004263982895835151/160497705249110837897575*a^21 + 1924863295348657604001972/160497705249110837897575*a^20 - 1456696993571422039860576/160497705249110837897575*a^19 + 415764396043151475688001/160497705249110837897575*a^18 + 6487962608864153111428/160497705249110837897575*a^17 + 1492412334960151444412004/160497705249110837897575*a^16 - 4860519218172303842560739/160497705249110837897575*a^15 + 602441500563438161262343/12345977326854679838275*a^14 - 7931759283931385913692248/160497705249110837897575*a^13 + 4664451477023036355202031/160497705249110837897575*a^12 - 94808597650528238439159/32099541049822167579515*a^11 - 961057486955674710077027/160497705249110837897575*a^10 - 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44345057599100133482311/2198598702042614217775*a + 5109156061655247634657/2198598702042614217775, 45584223616268038274316/160497705249110837897575*a^26 - 37990800487332862396167/14590700477191894354325*a^25 + 113754881908868665034682/9441041485241813993975*a^24 - 505877508033735673660122/14590700477191894354325*a^23 + 11381025063296043532005848/160497705249110837897575*a^22 - 3419397742368989819053888/32099541049822167579515*a^21 + 18899054227662890768244231/160497705249110837897575*a^20 - 13708274393956111962372727/160497705249110837897575*a^19 + 422251078130012550088847/12345977326854679838275*a^18 - 4793845017191349489397438/160497705249110837897575*a^17 + 4335975898918472315598127/32099541049822167579515*a^16 - 3049546567806775339780626/9441041485241813993975*a^15 + 77182713311058718854296297/160497705249110837897575*a^14 - 4525468476393860151596533/9441041485241813993975*a^13 + 48085887303333557512232111/160497705249110837897575*a^12 - 10772545297651251363712416/160497705249110837897575*a^11 + 1481150914089440003487507/160497705249110837897575*a^10 - 30533286746745209390509718/160497705249110837897575*a^9 + 5004947569906328516920237/9441041485241813993975*a^8 - 130395204395846900549601398/160497705249110837897575*a^7 + 141907484703884161800740922/160497705249110837897575*a^6 - 444188219527821891623549/583628019087675774173*a^5 + 80405320661801886859852907/160497705249110837897575*a^4 - 38155556805022326699124996/160497705249110837897575*a^3 + 3556885054536170851261978/32099541049822167579515*a^2 - 1015167855099900304095547/160497705249110837897575*a - 2314373680553231295332/32099541049822167579515 (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:		\( 460164457.10213304 \) (assuming GRH)	sage: K.regulator()   gp: K.reg   magma: Regulator(K);   oscar: regulator(K)

Class number formula

\[ \begin{aligned}\lim_{s\to 1} (s-1)\zeta_K(s) =\mathstrut & \frac{2^{r_1}\cdot (2\pi)^{r_2}\cdot R\cdot h}{w\cdot\sqrt{|D|}}\cr \approx\mathstrut &\frac{2^{1}\cdot(2\pi)^{13}\cdot 460164457.10213304 \cdot 1}{2\cdot\sqrt{800194812883861824535483445924579987063}}\cr\approx \mathstrut & 0.386948790637645 \end{aligned}\] (assuming GRH)

Galois group

$D_{27}$ (as 27T8):

Intermediate fields

Fields in the database are given up to isomorphism. Isomorphic intermediate fields are shown with their multiplicities.

Frobenius cycle types

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
\(983\) 983	$\Q_{983}$	$x$	$1$	$1$	$0$	Trivial	$[\ ]$
		Deg $2$	$2$	$1$	$1$	$C_2$	$[\ ]_{2}$
		Deg $2$	$2$	$1$	$1$	$C_2$	$[\ ]_{2}$
		Deg $2$	$2$	$1$	$1$	$C_2$	$[\ ]_{2}$
		Deg $2$	$2$	$1$	$1$	$C_2$	$[\ ]_{2}$
		Deg $2$	$2$	$1$	$1$	$C_2$	$[\ ]_{2}$
		Deg $2$	$2$	$1$	$1$	$C_2$	$[\ ]_{2}$
		Deg $2$	$2$	$1$	$1$	$C_2$	$[\ ]_{2}$
		Deg $2$	$2$	$1$	$1$	$C_2$	$[\ ]_{2}$
		Deg $2$	$2$	$1$	$1$	$C_2$	$[\ ]_{2}$
		Deg $2$	$2$	$1$	$1$	$C_2$	$[\ ]_{2}$
		Deg $2$	$2$	$1$	$1$	$C_2$	$[\ ]_{2}$
		Deg $2$	$2$	$1$	$1$	$C_2$	$[\ ]_{2}$
		Deg $2$	$2$	$1$	$1$	$C_2$	$[\ ]_{2}$

Artin representations