Normalized defining polynomial
\( x^{29} - x^{28} + 33 x^{27} - 64 x^{26} + 535 x^{25} - 1144 x^{24} + 5145 x^{23} - 10327 x^{22} + 31220 x^{21} - 55583 x^{20} + 124455 x^{19} - 188951 x^{18} + 323227 x^{17} + \cdots - 1749375 \)
Invariants
Degree: | $29$ | sage: K.degree()
gp: poldegree(K.pol)
magma: Degree(K);
oscar: degree(K)
| |
Signature: | $[1, 14]$ | sage: K.signature()
gp: K.sign
magma: Signature(K);
oscar: signature(K)
| |
Discriminant: | \(142449251725173555024565249558533387292386826365409\) \(\medspace = 3823^{14}\) | sage: K.disc()
gp: K.disc
magma: OK := Integers(K); Discriminant(OK);
oscar: OK = ring_of_integers(K); discriminant(OK)
| |
Root discriminant: | \(53.63\) | 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: | $3823^{1/2}\approx 61.83041322844284$ | ||
Ramified primes: | \(3823\) | sage: K.disc().support()
gp: factor(abs(K.disc))[,1]~
magma: PrimeDivisors(Discriminant(OK));
oscar: prime_divisors(discriminant((OK)))
| |
Discriminant root field: | \(\Q\) | ||
$\card{ \Aut(K/\Q) }$: | $1$ | 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 \(a\))
$1$, $a$, $a^{2}$, $a^{3}$, $a^{4}$, $a^{5}$, $a^{6}$, $a^{7}$, $a^{8}$, $\frac{1}{3}a^{9}-\frac{1}{3}a$, $\frac{1}{3}a^{10}-\frac{1}{3}a^{2}$, $\frac{1}{3}a^{11}-\frac{1}{3}a^{3}$, $\frac{1}{3}a^{12}-\frac{1}{3}a^{4}$, $\frac{1}{3}a^{13}-\frac{1}{3}a^{5}$, $\frac{1}{3}a^{14}-\frac{1}{3}a^{6}$, $\frac{1}{3}a^{15}-\frac{1}{3}a^{7}$, $\frac{1}{15}a^{16}-\frac{1}{15}a^{15}-\frac{1}{15}a^{14}-\frac{2}{15}a^{13}-\frac{1}{15}a^{12}+\frac{1}{15}a^{11}+\frac{1}{15}a^{10}-\frac{1}{15}a^{9}+\frac{2}{15}a^{8}+\frac{7}{15}a^{7}+\frac{7}{15}a^{6}-\frac{7}{15}a^{5}+\frac{4}{15}a^{4}-\frac{4}{15}a^{3}+\frac{1}{3}a^{2}+\frac{4}{15}a$, $\frac{1}{15}a^{17}-\frac{2}{15}a^{15}+\frac{2}{15}a^{14}+\frac{2}{15}a^{13}+\frac{2}{15}a^{11}+\frac{1}{15}a^{9}-\frac{2}{5}a^{8}-\frac{1}{15}a^{7}-\frac{1}{3}a^{6}+\frac{7}{15}a^{5}+\frac{1}{15}a^{3}-\frac{2}{5}a^{2}+\frac{4}{15}a$, $\frac{1}{45}a^{18}+\frac{2}{15}a^{13}-\frac{1}{15}a^{11}-\frac{2}{45}a^{10}-\frac{1}{15}a^{9}+\frac{2}{5}a^{8}+\frac{1}{5}a^{7}-\frac{1}{5}a^{6}+\frac{7}{15}a^{5}+\frac{1}{5}a^{4}+\frac{7}{15}a^{3}+\frac{19}{45}a^{2}+\frac{1}{15}a$, $\frac{1}{45}a^{19}+\frac{2}{15}a^{14}-\frac{1}{15}a^{12}-\frac{2}{45}a^{11}-\frac{1}{15}a^{10}+\frac{1}{15}a^{9}+\frac{1}{5}a^{8}-\frac{1}{5}a^{7}+\frac{7}{15}a^{6}+\frac{1}{5}a^{5}+\frac{7}{15}a^{4}+\frac{19}{45}a^{3}+\frac{1}{15}a^{2}+\frac{1}{3}a$, $\frac{1}{315}a^{20}+\frac{1}{105}a^{19}+\frac{2}{315}a^{18}-\frac{2}{105}a^{17}+\frac{2}{105}a^{16}+\frac{2}{15}a^{15}-\frac{1}{7}a^{14}+\frac{1}{7}a^{13}-\frac{32}{315}a^{12}+\frac{1}{35}a^{11}+\frac{26}{315}a^{10}-\frac{2}{21}a^{9}+\frac{7}{15}a^{8}-\frac{4}{21}a^{7}-\frac{16}{35}a^{6}-\frac{1}{35}a^{5}+\frac{7}{45}a^{4}-\frac{31}{105}a^{3}+\frac{14}{45}a^{2}-\frac{6}{35}a-\frac{3}{7}$, $\frac{1}{315}a^{21}+\frac{2}{315}a^{18}+\frac{1}{105}a^{17}+\frac{1}{105}a^{16}-\frac{1}{105}a^{15}-\frac{1}{35}a^{14}+\frac{22}{315}a^{13}-\frac{1}{21}a^{11}+\frac{32}{315}a^{10}+\frac{2}{105}a^{9}-\frac{34}{105}a^{8}-\frac{44}{105}a^{7}-\frac{2}{35}a^{6}+\frac{13}{315}a^{5}+\frac{6}{35}a^{4}+\frac{44}{105}a^{3}+\frac{13}{63}a^{2}-\frac{11}{35}a+\frac{2}{7}$, $\frac{1}{315}a^{22}+\frac{2}{315}a^{19}+\frac{1}{105}a^{18}+\frac{1}{105}a^{17}-\frac{1}{105}a^{16}-\frac{1}{35}a^{15}+\frac{22}{315}a^{14}-\frac{1}{21}a^{12}+\frac{32}{315}a^{11}+\frac{2}{105}a^{10}+\frac{1}{105}a^{9}-\frac{44}{105}a^{8}-\frac{2}{35}a^{7}+\frac{13}{315}a^{6}+\frac{6}{35}a^{5}+\frac{44}{105}a^{4}+\frac{13}{63}a^{3}-\frac{11}{35}a^{2}-\frac{1}{21}a$, $\frac{1}{1575}a^{23}-\frac{1}{1575}a^{22}-\frac{1}{1575}a^{21}-\frac{1}{315}a^{19}+\frac{1}{105}a^{18}+\frac{8}{525}a^{17}-\frac{2}{75}a^{16}+\frac{34}{1575}a^{15}+\frac{7}{45}a^{14}-\frac{127}{1575}a^{13}-\frac{61}{525}a^{12}-\frac{71}{1575}a^{11}-\frac{1}{35}a^{10}-\frac{34}{525}a^{9}-\frac{166}{525}a^{8}-\frac{116}{1575}a^{7}+\frac{116}{1575}a^{6}-\frac{547}{1575}a^{5}-\frac{248}{525}a^{4}+\frac{436}{1575}a^{3}-\frac{248}{525}a^{2}-\frac{44}{105}a-\frac{2}{7}$, $\frac{1}{4725}a^{24}+\frac{1}{4725}a^{23}+\frac{2}{4725}a^{22}+\frac{1}{1575}a^{21}+\frac{1}{945}a^{20}-\frac{1}{189}a^{19}-\frac{41}{4725}a^{18}-\frac{8}{1575}a^{17}+\frac{2}{945}a^{16}-\frac{377}{4725}a^{15}+\frac{83}{4725}a^{14}-\frac{239}{1575}a^{13}+\frac{428}{4725}a^{12}-\frac{502}{4725}a^{11}-\frac{302}{4725}a^{10}-\frac{74}{1575}a^{9}+\frac{334}{675}a^{8}-\frac{1046}{4725}a^{7}+\frac{442}{945}a^{6}-\frac{146}{1575}a^{5}-\frac{262}{4725}a^{4}+\frac{113}{4725}a^{3}-\frac{8}{4725}a^{2}+\frac{19}{63}a-\frac{1}{21}$, $\frac{1}{70875}a^{25}-\frac{1}{70875}a^{24}+\frac{2}{23625}a^{23}-\frac{16}{10125}a^{22}+\frac{14}{10125}a^{21}-\frac{4}{14175}a^{20}+\frac{8}{23625}a^{19}-\frac{662}{70875}a^{18}-\frac{29}{10125}a^{17}+\frac{1016}{70875}a^{16}+\frac{137}{23625}a^{15}+\frac{2642}{70875}a^{14}+\frac{2266}{14175}a^{13}-\frac{4511}{70875}a^{12}+\frac{3392}{23625}a^{11}-\frac{2858}{70875}a^{10}-\frac{538}{14175}a^{9}-\frac{6908}{14175}a^{8}-\frac{6238}{23625}a^{7}-\frac{6112}{70875}a^{6}+\frac{17777}{70875}a^{5}-\frac{22307}{70875}a^{4}+\frac{167}{3375}a^{3}+\frac{21547}{70875}a^{2}-\frac{29}{945}a+\frac{44}{315}$, $\frac{1}{496125}a^{26}+\frac{2}{496125}a^{25}+\frac{2}{55125}a^{24}+\frac{8}{70875}a^{23}+\frac{107}{496125}a^{22}-\frac{41}{496125}a^{21}-\frac{62}{165375}a^{20}-\frac{913}{99225}a^{19}-\frac{47}{70875}a^{18}-\frac{4138}{496125}a^{17}+\frac{971}{55125}a^{16}-\frac{5783}{99225}a^{15}-\frac{47224}{496125}a^{14}-\frac{8678}{70875}a^{13}-\frac{16514}{165375}a^{12}+\frac{15026}{99225}a^{11}-\frac{32219}{496125}a^{10}+\frac{1693}{99225}a^{9}-\frac{947}{18375}a^{8}+\frac{243896}{496125}a^{7}-\frac{41749}{496125}a^{6}-\frac{21263}{70875}a^{5}-\frac{15503}{165375}a^{4}-\frac{60152}{496125}a^{3}+\frac{54727}{165375}a^{2}+\frac{866}{2205}a-\frac{12}{245}$, $\frac{1}{496125}a^{27}+\frac{34}{496125}a^{24}-\frac{89}{496125}a^{23}-\frac{262}{496125}a^{22}+\frac{11}{55125}a^{21}-\frac{109}{70875}a^{20}+\frac{748}{99225}a^{19}-\frac{512}{496125}a^{18}+\frac{319}{165375}a^{17}+\frac{808}{496125}a^{16}-\frac{51848}{496125}a^{15}+\frac{37664}{496125}a^{14}-\frac{946}{11025}a^{13}-\frac{5182}{496125}a^{12}+\frac{48332}{496125}a^{11}-\frac{1357}{99225}a^{10}+\frac{12562}{165375}a^{9}+\frac{65119}{496125}a^{8}-\frac{47839}{99225}a^{7}-\frac{8704}{19845}a^{6}-\frac{3484}{11025}a^{5}-\frac{152536}{496125}a^{4}+\frac{136162}{496125}a^{3}-\frac{22144}{99225}a^{2}+\frac{997}{6615}a+\frac{109}{441}$, $\frac{1}{10\!\cdots\!25}a^{28}-\frac{88\!\cdots\!66}{10\!\cdots\!25}a^{27}+\frac{39\!\cdots\!43}{47\!\cdots\!25}a^{26}+\frac{41\!\cdots\!36}{10\!\cdots\!25}a^{25}-\frac{14\!\cdots\!92}{40\!\cdots\!25}a^{24}+\frac{25\!\cdots\!96}{10\!\cdots\!25}a^{23}-\frac{34\!\cdots\!47}{67\!\cdots\!75}a^{22}+\frac{12\!\cdots\!23}{10\!\cdots\!25}a^{21}+\frac{99\!\cdots\!49}{20\!\cdots\!25}a^{20}-\frac{21\!\cdots\!18}{10\!\cdots\!25}a^{19}-\frac{54\!\cdots\!36}{67\!\cdots\!75}a^{18}+\frac{18\!\cdots\!79}{10\!\cdots\!25}a^{17}+\frac{13\!\cdots\!97}{10\!\cdots\!25}a^{16}+\frac{37\!\cdots\!28}{10\!\cdots\!25}a^{15}-\frac{40\!\cdots\!78}{33\!\cdots\!75}a^{14}-\frac{87\!\cdots\!39}{80\!\cdots\!05}a^{13}-\frac{75\!\cdots\!33}{10\!\cdots\!25}a^{12}-\frac{13\!\cdots\!26}{10\!\cdots\!25}a^{11}+\frac{46\!\cdots\!57}{33\!\cdots\!75}a^{10}+\frac{13\!\cdots\!68}{10\!\cdots\!25}a^{9}+\frac{67\!\cdots\!41}{20\!\cdots\!25}a^{8}+\frac{33\!\cdots\!74}{10\!\cdots\!25}a^{7}+\frac{16\!\cdots\!87}{33\!\cdots\!75}a^{6}-\frac{65\!\cdots\!81}{14\!\cdots\!75}a^{5}-\frac{11\!\cdots\!82}{33\!\cdots\!75}a^{4}-\frac{75\!\cdots\!02}{33\!\cdots\!75}a^{3}+\frac{42\!\cdots\!43}{95\!\cdots\!25}a^{2}-\frac{84\!\cdots\!16}{63\!\cdots\!75}a+\frac{82\!\cdots\!02}{29\!\cdots\!15}$
Monogenic: | No | |
Index: | Not computed | |
Inessential primes: | $3$, $5$ |
Class group and class number
Trivial group, which has order $1$ (assuming GRH)
Unit group
Rank: | $14$ | 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: | $\frac{69\!\cdots\!07}{10\!\cdots\!25}a^{28}-\frac{34\!\cdots\!69}{33\!\cdots\!75}a^{27}+\frac{31\!\cdots\!73}{14\!\cdots\!75}a^{26}-\frac{18\!\cdots\!96}{33\!\cdots\!75}a^{25}+\frac{23\!\cdots\!09}{67\!\cdots\!75}a^{24}-\frac{30\!\cdots\!26}{33\!\cdots\!75}a^{23}+\frac{14\!\cdots\!38}{44\!\cdots\!25}a^{22}-\frac{88\!\cdots\!66}{11\!\cdots\!25}a^{21}+\frac{13\!\cdots\!09}{67\!\cdots\!75}a^{20}-\frac{45\!\cdots\!59}{11\!\cdots\!25}a^{19}+\frac{17\!\cdots\!72}{22\!\cdots\!25}a^{18}-\frac{44\!\cdots\!49}{33\!\cdots\!75}a^{17}+\frac{63\!\cdots\!28}{33\!\cdots\!75}a^{16}-\frac{92\!\cdots\!63}{33\!\cdots\!75}a^{15}+\frac{10\!\cdots\!16}{37\!\cdots\!75}a^{14}-\frac{27\!\cdots\!69}{74\!\cdots\!75}a^{13}+\frac{96\!\cdots\!33}{33\!\cdots\!75}a^{12}-\frac{40\!\cdots\!63}{11\!\cdots\!25}a^{11}+\frac{91\!\cdots\!24}{33\!\cdots\!75}a^{10}-\frac{99\!\cdots\!23}{33\!\cdots\!75}a^{9}+\frac{66\!\cdots\!88}{47\!\cdots\!25}a^{8}-\frac{35\!\cdots\!29}{33\!\cdots\!75}a^{7}+\frac{28\!\cdots\!98}{11\!\cdots\!25}a^{6}-\frac{81\!\cdots\!14}{22\!\cdots\!25}a^{5}+\frac{56\!\cdots\!03}{10\!\cdots\!25}a^{4}-\frac{10\!\cdots\!09}{33\!\cdots\!75}a^{3}+\frac{15\!\cdots\!33}{28\!\cdots\!75}a^{2}-\frac{98\!\cdots\!36}{19\!\cdots\!25}a+\frac{16\!\cdots\!47}{89\!\cdots\!45}$, $\frac{24\!\cdots\!38}{47\!\cdots\!25}a^{28}+\frac{77\!\cdots\!83}{20\!\cdots\!25}a^{27}+\frac{24\!\cdots\!17}{14\!\cdots\!75}a^{26}-\frac{90\!\cdots\!91}{14\!\cdots\!75}a^{25}+\frac{74\!\cdots\!23}{28\!\cdots\!75}a^{24}-\frac{33\!\cdots\!21}{14\!\cdots\!75}a^{23}+\frac{74\!\cdots\!38}{31\!\cdots\!75}a^{22}-\frac{39\!\cdots\!18}{14\!\cdots\!75}a^{21}+\frac{40\!\cdots\!43}{28\!\cdots\!75}a^{20}-\frac{26\!\cdots\!82}{14\!\cdots\!75}a^{19}+\frac{56\!\cdots\!08}{95\!\cdots\!25}a^{18}-\frac{11\!\cdots\!74}{14\!\cdots\!75}a^{17}+\frac{35\!\cdots\!79}{20\!\cdots\!25}a^{16}-\frac{29\!\cdots\!93}{14\!\cdots\!75}a^{15}+\frac{23\!\cdots\!86}{76\!\cdots\!75}a^{14}-\frac{20\!\cdots\!19}{57\!\cdots\!75}a^{13}+\frac{34\!\cdots\!48}{14\!\cdots\!75}a^{12}-\frac{61\!\cdots\!24}{14\!\cdots\!75}a^{11}-\frac{42\!\cdots\!94}{15\!\cdots\!75}a^{10}-\frac{12\!\cdots\!93}{14\!\cdots\!75}a^{9}-\frac{26\!\cdots\!79}{14\!\cdots\!75}a^{8}-\frac{23\!\cdots\!84}{14\!\cdots\!75}a^{7}+\frac{58\!\cdots\!72}{52\!\cdots\!25}a^{6}-\frac{65\!\cdots\!28}{14\!\cdots\!75}a^{5}+\frac{35\!\cdots\!91}{14\!\cdots\!75}a^{4}-\frac{78\!\cdots\!71}{15\!\cdots\!75}a^{3}+\frac{23\!\cdots\!57}{41\!\cdots\!25}a^{2}-\frac{87\!\cdots\!59}{19\!\cdots\!25}a+\frac{48\!\cdots\!28}{12\!\cdots\!35}$, $\frac{59\!\cdots\!48}{10\!\cdots\!25}a^{28}-\frac{18\!\cdots\!72}{11\!\cdots\!25}a^{27}+\frac{91\!\cdots\!39}{47\!\cdots\!25}a^{26}-\frac{24\!\cdots\!57}{10\!\cdots\!25}a^{25}+\frac{57\!\cdots\!53}{20\!\cdots\!25}a^{24}-\frac{47\!\cdots\!07}{10\!\cdots\!25}a^{23}+\frac{17\!\cdots\!51}{67\!\cdots\!75}a^{22}-\frac{41\!\cdots\!46}{10\!\cdots\!25}a^{21}+\frac{56\!\cdots\!17}{40\!\cdots\!25}a^{20}-\frac{21\!\cdots\!04}{10\!\cdots\!25}a^{19}+\frac{33\!\cdots\!99}{67\!\cdots\!75}a^{18}-\frac{69\!\cdots\!13}{10\!\cdots\!25}a^{17}+\frac{11\!\cdots\!56}{10\!\cdots\!25}a^{16}-\frac{13\!\cdots\!76}{10\!\cdots\!25}a^{15}+\frac{47\!\cdots\!76}{33\!\cdots\!75}a^{14}-\frac{79\!\cdots\!87}{40\!\cdots\!25}a^{13}+\frac{68\!\cdots\!36}{10\!\cdots\!25}a^{12}-\frac{30\!\cdots\!43}{10\!\cdots\!25}a^{11}-\frac{33\!\cdots\!29}{33\!\cdots\!75}a^{10}-\frac{56\!\cdots\!66}{10\!\cdots\!25}a^{9}+\frac{60\!\cdots\!41}{14\!\cdots\!75}a^{8}-\frac{81\!\cdots\!33}{10\!\cdots\!25}a^{7}+\frac{50\!\cdots\!91}{33\!\cdots\!75}a^{6}-\frac{26\!\cdots\!48}{14\!\cdots\!75}a^{5}+\frac{24\!\cdots\!67}{10\!\cdots\!25}a^{4}-\frac{19\!\cdots\!18}{10\!\cdots\!25}a^{3}+\frac{16\!\cdots\!27}{71\!\cdots\!75}a^{2}-\frac{12\!\cdots\!08}{63\!\cdots\!75}a+\frac{39\!\cdots\!43}{59\!\cdots\!43}$, $\frac{16\!\cdots\!47}{21\!\cdots\!75}a^{28}+\frac{33\!\cdots\!92}{23\!\cdots\!75}a^{27}+\frac{76\!\cdots\!73}{30\!\cdots\!25}a^{26}+\frac{43\!\cdots\!62}{21\!\cdots\!75}a^{25}+\frac{94\!\cdots\!83}{28\!\cdots\!25}a^{24}+\frac{32\!\cdots\!17}{21\!\cdots\!75}a^{23}+\frac{10\!\cdots\!67}{42\!\cdots\!75}a^{22}+\frac{22\!\cdots\!46}{21\!\cdots\!75}a^{21}+\frac{47\!\cdots\!74}{47\!\cdots\!75}a^{20}+\frac{13\!\cdots\!49}{21\!\cdots\!75}a^{19}+\frac{98\!\cdots\!34}{42\!\cdots\!75}a^{18}+\frac{64\!\cdots\!98}{21\!\cdots\!75}a^{17}+\frac{12\!\cdots\!78}{71\!\cdots\!25}a^{16}+\frac{18\!\cdots\!56}{21\!\cdots\!75}a^{15}-\frac{14\!\cdots\!98}{21\!\cdots\!75}a^{14}+\frac{34\!\cdots\!11}{42\!\cdots\!75}a^{13}-\frac{21\!\cdots\!77}{71\!\cdots\!25}a^{12}-\frac{61\!\cdots\!82}{21\!\cdots\!75}a^{11}-\frac{19\!\cdots\!08}{21\!\cdots\!75}a^{10}-\frac{30\!\cdots\!74}{21\!\cdots\!75}a^{9}-\frac{14\!\cdots\!97}{10\!\cdots\!75}a^{8}-\frac{26\!\cdots\!72}{21\!\cdots\!75}a^{7}-\frac{29\!\cdots\!23}{21\!\cdots\!75}a^{6}-\frac{74\!\cdots\!91}{43\!\cdots\!75}a^{5}-\frac{85\!\cdots\!57}{21\!\cdots\!75}a^{4}+\frac{15\!\cdots\!73}{21\!\cdots\!75}a^{3}-\frac{19\!\cdots\!72}{87\!\cdots\!75}a^{2}+\frac{16\!\cdots\!29}{40\!\cdots\!75}a-\frac{39\!\cdots\!41}{19\!\cdots\!35}$, $\frac{14\!\cdots\!21}{10\!\cdots\!25}a^{28}-\frac{12\!\cdots\!49}{11\!\cdots\!25}a^{27}+\frac{95\!\cdots\!87}{20\!\cdots\!25}a^{26}-\frac{28\!\cdots\!88}{33\!\cdots\!75}a^{25}+\frac{29\!\cdots\!37}{40\!\cdots\!25}a^{24}-\frac{14\!\cdots\!59}{10\!\cdots\!25}a^{23}+\frac{13\!\cdots\!74}{20\!\cdots\!25}a^{22}-\frac{43\!\cdots\!49}{33\!\cdots\!75}a^{21}+\frac{75\!\cdots\!62}{20\!\cdots\!25}a^{20}-\frac{66\!\cdots\!33}{10\!\cdots\!25}a^{19}+\frac{28\!\cdots\!12}{20\!\cdots\!25}a^{18}-\frac{70\!\cdots\!47}{33\!\cdots\!75}a^{17}+\frac{33\!\cdots\!27}{10\!\cdots\!25}a^{16}-\frac{42\!\cdots\!42}{10\!\cdots\!25}a^{15}+\frac{46\!\cdots\!26}{10\!\cdots\!25}a^{14}-\frac{15\!\cdots\!11}{26\!\cdots\!35}a^{13}+\frac{35\!\cdots\!62}{10\!\cdots\!25}a^{12}-\frac{71\!\cdots\!01}{10\!\cdots\!25}a^{11}+\frac{56\!\cdots\!51}{10\!\cdots\!25}a^{10}-\frac{39\!\cdots\!34}{33\!\cdots\!75}a^{9}+\frac{22\!\cdots\!92}{14\!\cdots\!75}a^{8}-\frac{26\!\cdots\!91}{10\!\cdots\!25}a^{7}+\frac{34\!\cdots\!96}{99\!\cdots\!25}a^{6}-\frac{33\!\cdots\!82}{47\!\cdots\!25}a^{5}+\frac{73\!\cdots\!29}{10\!\cdots\!25}a^{4}-\frac{55\!\cdots\!51}{10\!\cdots\!25}a^{3}+\frac{15\!\cdots\!58}{19\!\cdots\!25}a^{2}-\frac{43\!\cdots\!06}{63\!\cdots\!75}a+\frac{43\!\cdots\!42}{19\!\cdots\!81}$, $\frac{10\!\cdots\!19}{67\!\cdots\!75}a^{28}+\frac{67\!\cdots\!02}{20\!\cdots\!25}a^{27}+\frac{16\!\cdots\!63}{28\!\cdots\!75}a^{26}+\frac{12\!\cdots\!17}{20\!\cdots\!25}a^{25}+\frac{16\!\cdots\!91}{20\!\cdots\!25}a^{24}+\frac{10\!\cdots\!41}{20\!\cdots\!25}a^{23}+\frac{42\!\cdots\!19}{67\!\cdots\!75}a^{22}+\frac{68\!\cdots\!27}{20\!\cdots\!25}a^{21}+\frac{64\!\cdots\!13}{20\!\cdots\!25}a^{20}+\frac{31\!\cdots\!84}{20\!\cdots\!25}a^{19}+\frac{69\!\cdots\!64}{67\!\cdots\!75}a^{18}+\frac{10\!\cdots\!56}{20\!\cdots\!25}a^{17}+\frac{42\!\cdots\!91}{20\!\cdots\!25}a^{16}+\frac{22\!\cdots\!99}{20\!\cdots\!25}a^{15}+\frac{14\!\cdots\!81}{67\!\cdots\!75}a^{14}-\frac{28\!\cdots\!43}{40\!\cdots\!25}a^{13}-\frac{72\!\cdots\!49}{20\!\cdots\!25}a^{12}-\frac{26\!\cdots\!84}{20\!\cdots\!25}a^{11}-\frac{17\!\cdots\!86}{67\!\cdots\!75}a^{10}-\frac{20\!\cdots\!22}{40\!\cdots\!25}a^{9}-\frac{18\!\cdots\!58}{28\!\cdots\!75}a^{8}-\frac{16\!\cdots\!87}{20\!\cdots\!25}a^{7}-\frac{41\!\cdots\!21}{66\!\cdots\!75}a^{6}-\frac{29\!\cdots\!46}{41\!\cdots\!25}a^{5}-\frac{86\!\cdots\!26}{20\!\cdots\!25}a^{4}-\frac{27\!\cdots\!28}{67\!\cdots\!75}a^{3}+\frac{28\!\cdots\!86}{82\!\cdots\!25}a^{2}+\frac{19\!\cdots\!01}{38\!\cdots\!05}a+\frac{34\!\cdots\!79}{17\!\cdots\!29}$, $\frac{25\!\cdots\!51}{33\!\cdots\!75}a^{28}-\frac{90\!\cdots\!06}{33\!\cdots\!75}a^{27}+\frac{58\!\cdots\!19}{22\!\cdots\!25}a^{26}-\frac{34\!\cdots\!52}{10\!\cdots\!25}a^{25}+\frac{81\!\cdots\!56}{20\!\cdots\!25}a^{24}-\frac{25\!\cdots\!31}{37\!\cdots\!75}a^{23}+\frac{75\!\cdots\!78}{20\!\cdots\!25}a^{22}-\frac{63\!\cdots\!31}{10\!\cdots\!25}a^{21}+\frac{90\!\cdots\!72}{40\!\cdots\!25}a^{20}-\frac{11\!\cdots\!93}{33\!\cdots\!75}a^{19}+\frac{18\!\cdots\!88}{20\!\cdots\!25}a^{18}-\frac{12\!\cdots\!63}{10\!\cdots\!25}a^{17}+\frac{24\!\cdots\!36}{10\!\cdots\!25}a^{16}-\frac{10\!\cdots\!03}{37\!\cdots\!75}a^{15}+\frac{40\!\cdots\!38}{10\!\cdots\!25}a^{14}-\frac{86\!\cdots\!79}{20\!\cdots\!25}a^{13}+\frac{32\!\cdots\!76}{10\!\cdots\!25}a^{12}-\frac{17\!\cdots\!06}{33\!\cdots\!75}a^{11}-\frac{18\!\cdots\!67}{10\!\cdots\!25}a^{10}-\frac{97\!\cdots\!91}{10\!\cdots\!25}a^{9}+\frac{95\!\cdots\!81}{14\!\cdots\!75}a^{8}-\frac{28\!\cdots\!62}{11\!\cdots\!25}a^{7}+\frac{16\!\cdots\!53}{99\!\cdots\!25}a^{6}-\frac{91\!\cdots\!03}{14\!\cdots\!75}a^{5}+\frac{40\!\cdots\!02}{10\!\cdots\!25}a^{4}-\frac{73\!\cdots\!72}{11\!\cdots\!25}a^{3}+\frac{13\!\cdots\!14}{28\!\cdots\!75}a^{2}-\frac{13\!\cdots\!22}{27\!\cdots\!75}a+\frac{99\!\cdots\!56}{89\!\cdots\!45}$, $\frac{34\!\cdots\!69}{10\!\cdots\!25}a^{28}+\frac{24\!\cdots\!11}{10\!\cdots\!25}a^{27}+\frac{30\!\cdots\!34}{29\!\cdots\!75}a^{26}-\frac{21\!\cdots\!71}{10\!\cdots\!25}a^{25}+\frac{26\!\cdots\!78}{20\!\cdots\!25}a^{24}-\frac{19\!\cdots\!32}{33\!\cdots\!75}a^{23}+\frac{18\!\cdots\!73}{20\!\cdots\!25}a^{22}-\frac{24\!\cdots\!28}{10\!\cdots\!25}a^{21}+\frac{68\!\cdots\!21}{20\!\cdots\!25}a^{20}+\frac{35\!\cdots\!41}{33\!\cdots\!75}a^{19}+\frac{10\!\cdots\!04}{20\!\cdots\!25}a^{18}+\frac{12\!\cdots\!36}{10\!\cdots\!25}a^{17}-\frac{54\!\cdots\!57}{10\!\cdots\!25}a^{16}+\frac{12\!\cdots\!49}{33\!\cdots\!75}a^{15}-\frac{22\!\cdots\!86}{10\!\cdots\!25}a^{14}+\frac{30\!\cdots\!94}{20\!\cdots\!25}a^{13}+\frac{19\!\cdots\!48}{10\!\cdots\!25}a^{12}-\frac{74\!\cdots\!93}{33\!\cdots\!75}a^{11}-\frac{34\!\cdots\!26}{10\!\cdots\!25}a^{10}-\frac{46\!\cdots\!18}{10\!\cdots\!25}a^{9}-\frac{53\!\cdots\!11}{20\!\cdots\!25}a^{8}-\frac{68\!\cdots\!18}{33\!\cdots\!75}a^{7}-\frac{11\!\cdots\!06}{99\!\cdots\!25}a^{6}-\frac{84\!\cdots\!19}{14\!\cdots\!75}a^{5}-\frac{40\!\cdots\!18}{33\!\cdots\!75}a^{4}-\frac{50\!\cdots\!99}{10\!\cdots\!25}a^{3}+\frac{93\!\cdots\!87}{95\!\cdots\!25}a^{2}-\frac{15\!\cdots\!06}{71\!\cdots\!75}a+\frac{25\!\cdots\!58}{29\!\cdots\!15}$, $\frac{22\!\cdots\!67}{14\!\cdots\!75}a^{28}-\frac{56\!\cdots\!41}{20\!\cdots\!25}a^{27}+\frac{24\!\cdots\!67}{47\!\cdots\!25}a^{26}-\frac{20\!\cdots\!33}{14\!\cdots\!75}a^{25}+\frac{81\!\cdots\!99}{95\!\cdots\!25}a^{24}-\frac{35\!\cdots\!53}{14\!\cdots\!75}a^{23}+\frac{24\!\cdots\!67}{28\!\cdots\!75}a^{22}-\frac{32\!\cdots\!29}{14\!\cdots\!75}a^{21}+\frac{59\!\cdots\!71}{10\!\cdots\!25}a^{20}-\frac{18\!\cdots\!86}{14\!\cdots\!75}a^{19}+\frac{68\!\cdots\!78}{28\!\cdots\!75}a^{18}-\frac{66\!\cdots\!77}{14\!\cdots\!75}a^{17}+\frac{45\!\cdots\!79}{68\!\cdots\!75}a^{16}-\frac{15\!\cdots\!49}{14\!\cdots\!75}a^{15}+\frac{23\!\cdots\!71}{20\!\cdots\!25}a^{14}-\frac{17\!\cdots\!51}{11\!\cdots\!15}a^{13}+\frac{51\!\cdots\!13}{47\!\cdots\!25}a^{12}-\frac{18\!\cdots\!67}{14\!\cdots\!75}a^{11}+\frac{11\!\cdots\!92}{14\!\cdots\!75}a^{10}-\frac{82\!\cdots\!84}{14\!\cdots\!75}a^{9}+\frac{20\!\cdots\!56}{47\!\cdots\!25}a^{8}-\frac{26\!\cdots\!37}{14\!\cdots\!75}a^{7}+\frac{16\!\cdots\!27}{14\!\cdots\!75}a^{6}-\frac{12\!\cdots\!79}{14\!\cdots\!75}a^{5}+\frac{38\!\cdots\!73}{14\!\cdots\!75}a^{4}-\frac{47\!\cdots\!74}{47\!\cdots\!25}a^{3}+\frac{16\!\cdots\!62}{58\!\cdots\!75}a^{2}-\frac{31\!\cdots\!17}{19\!\cdots\!25}a+\frac{22\!\cdots\!96}{12\!\cdots\!35}$, $\frac{23\!\cdots\!97}{67\!\cdots\!75}a^{28}-\frac{35\!\cdots\!24}{20\!\cdots\!25}a^{27}+\frac{40\!\cdots\!13}{35\!\cdots\!75}a^{26}-\frac{33\!\cdots\!23}{20\!\cdots\!25}a^{25}+\frac{36\!\cdots\!42}{20\!\cdots\!25}a^{24}-\frac{63\!\cdots\!89}{20\!\cdots\!25}a^{23}+\frac{11\!\cdots\!14}{67\!\cdots\!75}a^{22}-\frac{56\!\cdots\!17}{20\!\cdots\!25}a^{21}+\frac{19\!\cdots\!01}{20\!\cdots\!25}a^{20}-\frac{29\!\cdots\!33}{20\!\cdots\!25}a^{19}+\frac{24\!\cdots\!43}{67\!\cdots\!75}a^{18}-\frac{96\!\cdots\!66}{20\!\cdots\!25}a^{17}+\frac{35\!\cdots\!73}{40\!\cdots\!25}a^{16}-\frac{19\!\cdots\!78}{20\!\cdots\!25}a^{15}+\frac{86\!\cdots\!24}{67\!\cdots\!75}a^{14}-\frac{28\!\cdots\!58}{20\!\cdots\!25}a^{13}+\frac{19\!\cdots\!82}{20\!\cdots\!25}a^{12}-\frac{41\!\cdots\!47}{20\!\cdots\!25}a^{11}-\frac{29\!\cdots\!17}{67\!\cdots\!75}a^{10}-\frac{34\!\cdots\!42}{80\!\cdots\!05}a^{9}+\frac{70\!\cdots\!12}{57\!\cdots\!75}a^{8}-\frac{19\!\cdots\!73}{20\!\cdots\!25}a^{7}+\frac{35\!\cdots\!33}{66\!\cdots\!75}a^{6}-\frac{11\!\cdots\!67}{57\!\cdots\!75}a^{5}+\frac{56\!\cdots\!78}{40\!\cdots\!25}a^{4}-\frac{41\!\cdots\!53}{20\!\cdots\!25}a^{3}+\frac{15\!\cdots\!88}{95\!\cdots\!25}a^{2}-\frac{23\!\cdots\!79}{12\!\cdots\!35}a+\frac{95\!\cdots\!89}{99\!\cdots\!05}$, $\frac{88\!\cdots\!76}{10\!\cdots\!25}a^{28}-\frac{43\!\cdots\!81}{10\!\cdots\!25}a^{27}+\frac{13\!\cdots\!93}{47\!\cdots\!25}a^{26}-\frac{42\!\cdots\!14}{10\!\cdots\!25}a^{25}+\frac{11\!\cdots\!58}{24\!\cdots\!25}a^{24}-\frac{80\!\cdots\!69}{10\!\cdots\!25}a^{23}+\frac{16\!\cdots\!23}{40\!\cdots\!25}a^{22}-\frac{73\!\cdots\!62}{10\!\cdots\!25}a^{21}+\frac{16\!\cdots\!26}{67\!\cdots\!75}a^{20}-\frac{39\!\cdots\!68}{10\!\cdots\!25}a^{19}+\frac{18\!\cdots\!58}{20\!\cdots\!25}a^{18}-\frac{12\!\cdots\!01}{10\!\cdots\!25}a^{17}+\frac{25\!\cdots\!53}{11\!\cdots\!25}a^{16}-\frac{26\!\cdots\!27}{10\!\cdots\!25}a^{15}+\frac{31\!\cdots\!06}{10\!\cdots\!25}a^{14}-\frac{12\!\cdots\!57}{40\!\cdots\!25}a^{13}+\frac{60\!\cdots\!24}{33\!\cdots\!75}a^{12}-\frac{40\!\cdots\!06}{10\!\cdots\!25}a^{11}-\frac{14\!\cdots\!04}{10\!\cdots\!25}a^{10}-\frac{10\!\cdots\!72}{10\!\cdots\!25}a^{9}+\frac{22\!\cdots\!16}{53\!\cdots\!25}a^{8}-\frac{24\!\cdots\!01}{10\!\cdots\!25}a^{7}+\frac{17\!\cdots\!36}{99\!\cdots\!25}a^{6}-\frac{75\!\cdots\!81}{14\!\cdots\!75}a^{5}+\frac{31\!\cdots\!19}{10\!\cdots\!25}a^{4}-\frac{17\!\cdots\!62}{33\!\cdots\!75}a^{3}+\frac{92\!\cdots\!59}{28\!\cdots\!75}a^{2}-\frac{64\!\cdots\!73}{19\!\cdots\!25}a+\frac{82\!\cdots\!06}{89\!\cdots\!45}$, $\frac{51\!\cdots\!53}{33\!\cdots\!75}a^{28}-\frac{85\!\cdots\!04}{10\!\cdots\!25}a^{27}+\frac{21\!\cdots\!22}{47\!\cdots\!25}a^{26}-\frac{74\!\cdots\!36}{10\!\cdots\!25}a^{25}+\frac{42\!\cdots\!98}{67\!\cdots\!75}a^{24}-\frac{11\!\cdots\!66}{10\!\cdots\!25}a^{23}+\frac{10\!\cdots\!46}{20\!\cdots\!25}a^{22}-\frac{86\!\cdots\!08}{10\!\cdots\!25}a^{21}+\frac{30\!\cdots\!42}{13\!\cdots\!75}a^{20}-\frac{30\!\cdots\!82}{10\!\cdots\!25}a^{19}+\frac{10\!\cdots\!16}{20\!\cdots\!25}a^{18}-\frac{27\!\cdots\!49}{10\!\cdots\!25}a^{17}-\frac{74\!\cdots\!49}{33\!\cdots\!75}a^{16}+\frac{20\!\cdots\!52}{10\!\cdots\!25}a^{15}-\frac{49\!\cdots\!71}{10\!\cdots\!25}a^{14}+\frac{19\!\cdots\!43}{20\!\cdots\!25}a^{13}-\frac{48\!\cdots\!14}{33\!\cdots\!75}a^{12}+\frac{19\!\cdots\!16}{10\!\cdots\!25}a^{11}-\frac{24\!\cdots\!61}{10\!\cdots\!25}a^{10}+\frac{21\!\cdots\!52}{10\!\cdots\!25}a^{9}-\frac{39\!\cdots\!69}{47\!\cdots\!25}a^{8}+\frac{45\!\cdots\!71}{10\!\cdots\!25}a^{7}-\frac{24\!\cdots\!31}{99\!\cdots\!25}a^{6}-\frac{13\!\cdots\!02}{20\!\cdots\!25}a^{5}+\frac{13\!\cdots\!99}{11\!\cdots\!25}a^{4}-\frac{34\!\cdots\!04}{10\!\cdots\!25}a^{3}+\frac{52\!\cdots\!46}{28\!\cdots\!75}a^{2}-\frac{24\!\cdots\!02}{19\!\cdots\!25}a-\frac{71\!\cdots\!41}{89\!\cdots\!45}$, $\frac{14\!\cdots\!49}{10\!\cdots\!25}a^{28}+\frac{20\!\cdots\!57}{33\!\cdots\!75}a^{27}+\frac{48\!\cdots\!28}{97\!\cdots\!25}a^{26}+\frac{15\!\cdots\!64}{10\!\cdots\!25}a^{25}+\frac{37\!\cdots\!23}{67\!\cdots\!75}a^{24}+\frac{20\!\cdots\!19}{10\!\cdots\!25}a^{23}+\frac{57\!\cdots\!62}{20\!\cdots\!25}a^{22}+\frac{17\!\cdots\!92}{10\!\cdots\!25}a^{21}+\frac{15\!\cdots\!74}{44\!\cdots\!25}a^{20}+\frac{10\!\cdots\!48}{10\!\cdots\!25}a^{19}-\frac{70\!\cdots\!79}{20\!\cdots\!25}a^{18}+\frac{37\!\cdots\!01}{10\!\cdots\!25}a^{17}-\frac{65\!\cdots\!84}{33\!\cdots\!75}a^{16}+\frac{90\!\cdots\!02}{10\!\cdots\!25}a^{15}-\frac{52\!\cdots\!41}{10\!\cdots\!25}a^{14}+\frac{23\!\cdots\!07}{20\!\cdots\!25}a^{13}-\frac{38\!\cdots\!09}{33\!\cdots\!75}a^{12}-\frac{86\!\cdots\!19}{10\!\cdots\!25}a^{11}-\frac{36\!\cdots\!66}{10\!\cdots\!25}a^{10}-\frac{48\!\cdots\!88}{10\!\cdots\!25}a^{9}-\frac{46\!\cdots\!94}{47\!\cdots\!25}a^{8}-\frac{78\!\cdots\!39}{10\!\cdots\!25}a^{7}-\frac{18\!\cdots\!11}{99\!\cdots\!25}a^{6}-\frac{16\!\cdots\!19}{14\!\cdots\!75}a^{5}-\frac{34\!\cdots\!09}{10\!\cdots\!25}a^{4}-\frac{67\!\cdots\!24}{10\!\cdots\!25}a^{3}-\frac{88\!\cdots\!86}{28\!\cdots\!75}a^{2}-\frac{39\!\cdots\!61}{27\!\cdots\!75}a-\frac{23\!\cdots\!89}{89\!\cdots\!45}$, $\frac{41\!\cdots\!63}{53\!\cdots\!25}a^{28}-\frac{14\!\cdots\!71}{14\!\cdots\!75}a^{27}+\frac{35\!\cdots\!33}{14\!\cdots\!75}a^{26}-\frac{26\!\cdots\!43}{47\!\cdots\!25}a^{25}+\frac{38\!\cdots\!68}{95\!\cdots\!25}a^{24}-\frac{45\!\cdots\!68}{47\!\cdots\!25}a^{23}+\frac{36\!\cdots\!51}{95\!\cdots\!25}a^{22}-\frac{13\!\cdots\!28}{15\!\cdots\!75}a^{21}+\frac{21\!\cdots\!27}{95\!\cdots\!25}a^{20}-\frac{20\!\cdots\!56}{47\!\cdots\!25}a^{19}+\frac{16\!\cdots\!27}{19\!\cdots\!25}a^{18}-\frac{64\!\cdots\!07}{47\!\cdots\!25}a^{17}+\frac{96\!\cdots\!09}{47\!\cdots\!25}a^{16}-\frac{12\!\cdots\!19}{47\!\cdots\!25}a^{15}+\frac{13\!\cdots\!92}{47\!\cdots\!25}a^{14}-\frac{37\!\cdots\!33}{10\!\cdots\!25}a^{13}+\frac{16\!\cdots\!77}{68\!\cdots\!75}a^{12}-\frac{20\!\cdots\!87}{47\!\cdots\!25}a^{11}+\frac{83\!\cdots\!42}{47\!\cdots\!25}a^{10}-\frac{29\!\cdots\!04}{47\!\cdots\!25}a^{9}+\frac{56\!\cdots\!73}{47\!\cdots\!25}a^{8}-\frac{74\!\cdots\!82}{47\!\cdots\!25}a^{7}+\frac{12\!\cdots\!47}{47\!\cdots\!25}a^{6}-\frac{73\!\cdots\!94}{22\!\cdots\!25}a^{5}+\frac{27\!\cdots\!13}{47\!\cdots\!25}a^{4}-\frac{44\!\cdots\!76}{14\!\cdots\!75}a^{3}+\frac{14\!\cdots\!89}{28\!\cdots\!75}a^{2}-\frac{69\!\cdots\!06}{19\!\cdots\!25}a+\frac{49\!\cdots\!48}{12\!\cdots\!35}$ (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: | \( 254102374099303.56 \) (assuming GRH) | sage: K.regulator()
gp: K.reg
magma: Regulator(K);
oscar: regulator(K)
|
Class number formula
\[ \begin{aligned}\lim_{s\to 1} (s-1)\zeta_K(s) =\mathstrut & \frac{2^{r_1}\cdot (2\pi)^{r_2}\cdot R\cdot h}{w\cdot\sqrt{|D|}}\cr \approx\mathstrut &\frac{2^{1}\cdot(2\pi)^{14}\cdot 254102374099303.56 \cdot 1}{2\cdot\sqrt{142449251725173555024565249558533387292386826365409}}\cr\approx \mathstrut & 3.18197522288265 \end{aligned}\] (assuming GRH)
Galois group
A solvable group of order 58 |
The 16 conjugacy class representatives for $D_{29}$ |
Character table for $D_{29}$ |
Intermediate fields
The extension is primitive: there are no intermediate fields between this field and $\Q$. |
Frobenius cycle types
$p$ | $2$ | $3$ | $5$ | $7$ | $11$ | $13$ | $17$ | $19$ | $23$ | $29$ | $31$ | $37$ | $41$ | $43$ | $47$ | $53$ | $59$ |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Cycle type | $29$ | ${\href{/padicField/3.2.0.1}{2} }^{14}{,}\,{\href{/padicField/3.1.0.1}{1} }$ | ${\href{/padicField/5.2.0.1}{2} }^{14}{,}\,{\href{/padicField/5.1.0.1}{1} }$ | ${\href{/padicField/7.2.0.1}{2} }^{14}{,}\,{\href{/padicField/7.1.0.1}{1} }$ | $29$ | $29$ | $29$ | ${\href{/padicField/19.2.0.1}{2} }^{14}{,}\,{\href{/padicField/19.1.0.1}{1} }$ | $29$ | $29$ | ${\href{/padicField/31.2.0.1}{2} }^{14}{,}\,{\href{/padicField/31.1.0.1}{1} }$ | $29$ | $29$ | $29$ | ${\href{/padicField/47.2.0.1}{2} }^{14}{,}\,{\href{/padicField/47.1.0.1}{1} }$ | $29$ | $29$ |
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 |
---|---|---|---|---|---|---|---|
\(3823\) | $\Q_{3823}$ | $x$ | $1$ | $1$ | $0$ | 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 $2$ | $2$ | $1$ | $1$ | $C_2$ | $[\ ]_{2}$ | ||
Deg $2$ | $2$ | $1$ | $1$ | $C_2$ | $[\ ]_{2}$ |