Normalized defining polynomial
\( x^{23} - 2 x^{22} + 16 x^{21} - 34 x^{20} + 68 x^{19} - 63 x^{18} + 17 x^{17} + 43 x^{16} - 139 x^{15} + 165 x^{14} + 25 x^{13} - 228 x^{12} + 265 x^{11} - 270 x^{10} + 75 x^{9} + 246 x^{8} + \cdots + 1 \)
Invariants
Degree: | $23$ | sage: K.degree()
gp: poldegree(K.pol)
magma: Degree(K);
oscar: degree(K)
| |
Signature: | $[1, 11]$ | sage: K.signature()
gp: K.sign
magma: Signature(K);
oscar: signature(K)
| |
Discriminant: | \(-58230945563524325903440619509366903\) \(\medspace = -\,1447^{11}\) | sage: K.disc()
gp: K.disc
magma: OK := Integers(K); Discriminant(OK);
oscar: OK = ring_of_integers(K); discriminant(OK)
| |
Root discriminant: | \(32.47\) | 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: | $1447^{1/2}\approx 38.03945320322047$ | ||
Ramified primes: | \(1447\) | sage: K.disc().support()
gp: factor(abs(K.disc))[,1]~
magma: PrimeDivisors(Discriminant(OK));
oscar: prime_divisors(discriminant((OK)))
| |
Discriminant root field: | \(\Q(\sqrt{-1447}) \) | ||
$\card{ \Aut(K/\Q) }$: | $1$ | 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 \(a\))
$1$, $a$, $a^{2}$, $a^{3}$, $a^{4}$, $a^{5}$, $a^{6}$, $\frac{1}{3}a^{7}+\frac{1}{3}a^{6}+\frac{1}{3}a^{5}+\frac{1}{3}a^{4}+\frac{1}{3}a^{3}+\frac{1}{3}a^{2}+\frac{1}{3}a+\frac{1}{3}$, $\frac{1}{3}a^{8}-\frac{1}{3}$, $\frac{1}{3}a^{9}-\frac{1}{3}a$, $\frac{1}{3}a^{10}-\frac{1}{3}a^{2}$, $\frac{1}{3}a^{11}-\frac{1}{3}a^{3}$, $\frac{1}{3}a^{12}-\frac{1}{3}a^{4}$, $\frac{1}{3}a^{13}-\frac{1}{3}a^{5}$, $\frac{1}{9}a^{14}-\frac{1}{9}a^{13}+\frac{1}{9}a^{11}-\frac{1}{9}a^{10}+\frac{1}{9}a^{8}-\frac{1}{9}a^{7}-\frac{2}{9}a^{6}-\frac{1}{9}a^{4}-\frac{2}{9}a^{3}-\frac{1}{9}a-\frac{2}{9}$, $\frac{1}{27}a^{15}-\frac{1}{27}a^{13}+\frac{4}{27}a^{12}-\frac{1}{9}a^{11}-\frac{4}{27}a^{10}+\frac{1}{27}a^{9}+\frac{1}{9}a^{8}+\frac{10}{27}a^{6}-\frac{7}{27}a^{5}-\frac{4}{9}a^{4}+\frac{4}{27}a^{3}+\frac{5}{27}a^{2}+\frac{1}{3}a-\frac{2}{27}$, $\frac{1}{27}a^{16}-\frac{1}{27}a^{14}+\frac{4}{27}a^{13}-\frac{1}{9}a^{12}-\frac{4}{27}a^{11}+\frac{1}{27}a^{10}+\frac{1}{9}a^{9}+\frac{1}{27}a^{7}+\frac{11}{27}a^{6}+\frac{2}{9}a^{5}-\frac{5}{27}a^{4}-\frac{4}{27}a^{3}-\frac{11}{27}a-\frac{1}{3}$, $\frac{1}{27}a^{17}+\frac{1}{27}a^{14}-\frac{1}{27}a^{13}+\frac{4}{27}a^{11}+\frac{2}{27}a^{10}+\frac{1}{27}a^{9}+\frac{1}{27}a^{8}-\frac{4}{27}a^{7}+\frac{4}{27}a^{6}-\frac{1}{9}a^{5}-\frac{4}{27}a^{4}+\frac{10}{27}a^{3}+\frac{1}{9}a^{2}+\frac{4}{9}a+\frac{13}{27}$, $\frac{1}{135}a^{18}-\frac{2}{135}a^{17}+\frac{1}{135}a^{15}-\frac{19}{135}a^{13}+\frac{13}{135}a^{12}+\frac{1}{9}a^{11}+\frac{4}{45}a^{10}+\frac{17}{135}a^{9}-\frac{4}{45}a^{8}+\frac{1}{15}a^{7}+\frac{64}{135}a^{6}-\frac{7}{135}a^{5}-\frac{7}{45}a^{4}+\frac{8}{27}a^{3}-\frac{13}{45}a^{2}+\frac{49}{135}a+\frac{4}{135}$, $\frac{1}{135}a^{19}+\frac{1}{135}a^{17}+\frac{1}{135}a^{16}+\frac{2}{135}a^{15}+\frac{1}{135}a^{14}-\frac{4}{135}a^{12}-\frac{13}{135}a^{11}-\frac{1}{15}a^{10}-\frac{2}{15}a^{9}+\frac{1}{27}a^{8}+\frac{2}{135}a^{7}+\frac{22}{45}a^{6}-\frac{1}{27}a^{5}-\frac{37}{135}a^{4}-\frac{29}{135}a^{3}-\frac{14}{135}a^{2}+\frac{4}{45}a-\frac{2}{135}$, $\frac{1}{405}a^{20}-\frac{1}{405}a^{19}-\frac{1}{135}a^{17}+\frac{1}{405}a^{16}-\frac{2}{405}a^{15}-\frac{7}{135}a^{14}-\frac{11}{81}a^{13}-\frac{67}{405}a^{12}-\frac{1}{405}a^{11}-\frac{16}{405}a^{10}-\frac{44}{405}a^{9}+\frac{34}{405}a^{8}+\frac{1}{9}a^{7}+\frac{20}{81}a^{6}+\frac{7}{81}a^{5}+\frac{199}{405}a^{4}+\frac{1}{81}a^{2}+\frac{1}{15}a+\frac{8}{405}$, $\frac{1}{2025}a^{21}+\frac{2}{2025}a^{19}-\frac{1}{405}a^{17}+\frac{17}{2025}a^{16}-\frac{14}{2025}a^{15}+\frac{92}{2025}a^{14}+\frac{241}{2025}a^{13}-\frac{86}{2025}a^{12}+\frac{244}{2025}a^{11}-\frac{8}{75}a^{10}+\frac{32}{2025}a^{9}+\frac{103}{2025}a^{8}+\frac{13}{2025}a^{7}-\frac{32}{135}a^{6}+\frac{62}{225}a^{5}-\frac{46}{405}a^{4}-\frac{112}{2025}a^{3}-\frac{937}{2025}a^{2}-\frac{127}{2025}a-\frac{346}{2025}$, $\frac{1}{104470934408325}a^{22}-\frac{914858467}{6964728960555}a^{21}-\frac{32762334668}{104470934408325}a^{20}-\frac{56589028498}{20894186881665}a^{19}-\frac{32608635196}{20894186881665}a^{18}+\frac{298230323552}{104470934408325}a^{17}-\frac{175588356248}{34823644802775}a^{16}-\frac{965948654048}{104470934408325}a^{15}+\frac{50294744476}{104470934408325}a^{14}+\frac{8343057920609}{104470934408325}a^{13}-\frac{15682282111}{104470934408325}a^{12}+\frac{1391427574309}{104470934408325}a^{11}-\frac{401488707002}{11607881600925}a^{10}-\frac{737935559353}{11607881600925}a^{9}+\frac{5414916967156}{34823644802775}a^{8}-\frac{150434843501}{2321576320185}a^{7}-\frac{13838276284492}{104470934408325}a^{6}+\frac{3788513561851}{20894186881665}a^{5}+\frac{38665881240733}{104470934408325}a^{4}-\frac{1968498721702}{104470934408325}a^{3}+\frac{7920828501611}{34823644802775}a^{2}-\frac{8471973936001}{104470934408325}a+\frac{6111746943359}{20894186881665}$
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: | $11$ | 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: | $\frac{633691164013}{6964728960555}a^{22}-\frac{187652154623}{1392945792111}a^{21}+\frac{9635269559323}{6964728960555}a^{20}-\frac{16538481015637}{6964728960555}a^{19}+\frac{34234475496106}{6964728960555}a^{18}-\frac{21955353114377}{6964728960555}a^{17}-\frac{346603230763}{1392945792111}a^{16}+\frac{9085236501371}{2321576320185}a^{15}-\frac{76416663464029}{6964728960555}a^{14}+\frac{67082022822988}{6964728960555}a^{13}+\frac{50665909952251}{6964728960555}a^{12}-\frac{2658245781557}{154771754679}a^{11}+\frac{36654276033472}{2321576320185}a^{10}-\frac{121507848745502}{6964728960555}a^{9}-\frac{2590476189242}{1392945792111}a^{8}+\frac{155016079546184}{6964728960555}a^{7}-\frac{7615859221342}{6964728960555}a^{6}-\frac{95505354036952}{6964728960555}a^{5}+\frac{10156132525939}{773858773395}a^{4}-\frac{2489469923361}{85984308155}a^{3}+\frac{49567706279429}{1392945792111}a^{2}-\frac{6637329575035}{464315264037}a+\frac{1048384799716}{1392945792111}$, $\frac{7947616666166}{104470934408325}a^{22}-\frac{1098369443522}{11607881600925}a^{21}+\frac{116965795699367}{104470934408325}a^{20}-\frac{179953153150906}{104470934408325}a^{19}+\frac{73022582210377}{20894186881665}a^{18}-\frac{185442855163223}{104470934408325}a^{17}-\frac{7393178857577}{6964728960555}a^{16}+\frac{264528811181189}{104470934408325}a^{15}-\frac{173738952548759}{20894186881665}a^{14}+\frac{592329468504571}{104470934408325}a^{13}+\frac{918422801992882}{104470934408325}a^{12}-\frac{11\!\cdots\!03}{104470934408325}a^{11}+\frac{12722592151091}{1392945792111}a^{10}-\frac{133905245848672}{11607881600925}a^{9}-\frac{182552833288742}{34823644802775}a^{8}+\frac{601865817206227}{34823644802775}a^{7}+\frac{626680085384203}{104470934408325}a^{6}-\frac{10\!\cdots\!69}{104470934408325}a^{5}+\frac{715103529743048}{104470934408325}a^{4}-\frac{24\!\cdots\!16}{104470934408325}a^{3}+\frac{830072057011853}{34823644802775}a^{2}-\frac{109653275938822}{20894186881665}a-\frac{84907657231177}{104470934408325}$, $\frac{151490495887}{11607881600925}a^{22}-\frac{175567805237}{3869293866975}a^{21}+\frac{7140625923907}{34823644802775}a^{20}-\frac{24734157480661}{34823644802775}a^{19}+\frac{2142187953326}{2321576320185}a^{18}-\frac{15623019864301}{11607881600925}a^{17}-\frac{2865283207498}{6964728960555}a^{16}+\frac{21197177506204}{34823644802775}a^{15}-\frac{4723962955517}{2321576320185}a^{14}+\frac{104325825554696}{34823644802775}a^{13}+\frac{40135292076227}{34823644802775}a^{12}-\frac{176995501754758}{34823644802775}a^{11}+\frac{3445277207486}{1392945792111}a^{10}-\frac{80704023526943}{34823644802775}a^{9}+\frac{83809076477794}{34823644802775}a^{8}+\frac{56440365815542}{11607881600925}a^{7}-\frac{28655066753927}{34823644802775}a^{6}-\frac{269169983988184}{34823644802775}a^{5}+\frac{24952041265198}{34823644802775}a^{4}-\frac{24669994987532}{11607881600925}a^{3}+\frac{337034824310384}{34823644802775}a^{2}-\frac{16363591195594}{2321576320185}a+\frac{33019104036023}{34823644802775}$, $\frac{2617988812}{3869293866975}a^{22}+\frac{5773002847}{3869293866975}a^{21}+\frac{687542004491}{34823644802775}a^{20}+\frac{454294451626}{34823644802775}a^{19}+\frac{126827257786}{773858773395}a^{18}-\frac{22001254649}{429921540775}a^{17}+\frac{16056504855209}{34823644802775}a^{16}+\frac{3634529526209}{34823644802775}a^{15}+\frac{695411782433}{11607881600925}a^{14}+\frac{2990135338358}{6964728960555}a^{13}-\frac{17492131108691}{34823644802775}a^{12}+\frac{28712253494719}{34823644802775}a^{11}+\frac{61467559213738}{34823644802775}a^{10}+\frac{635939382313}{6964728960555}a^{9}+\frac{52328774181428}{34823644802775}a^{8}+\frac{190503491228}{11607881600925}a^{7}-\frac{4905368582281}{34823644802775}a^{6}+\frac{92790353680399}{34823644802775}a^{5}+\frac{95589718120919}{34823644802775}a^{4}+\frac{234067550237}{3869293866975}a^{3}+\frac{61853751019048}{34823644802775}a^{2}-\frac{24229661189738}{11607881600925}a+\frac{33886752644122}{34823644802775}$, $\frac{6328482818033}{104470934408325}a^{22}-\frac{1609010200327}{34823644802775}a^{21}+\frac{90937286045051}{104470934408325}a^{20}-\frac{98104721866567}{104470934408325}a^{19}+\frac{49240804583179}{20894186881665}a^{18}-\frac{11053118349929}{104470934408325}a^{17}-\frac{27816089729183}{34823644802775}a^{16}+\frac{38384152967719}{20894186881665}a^{15}-\frac{532740946914004}{104470934408325}a^{14}+\frac{181731321882826}{104470934408325}a^{13}+\frac{766587522100483}{104470934408325}a^{12}-\frac{620810832209242}{104470934408325}a^{11}+\frac{88879050113164}{34823644802775}a^{10}-\frac{215854698168001}{34823644802775}a^{9}-\frac{178629109738673}{34823644802775}a^{8}+\frac{107455453023148}{11607881600925}a^{7}+\frac{985783034455189}{104470934408325}a^{6}-\frac{629585784862208}{104470934408325}a^{5}+\frac{53968560873479}{104470934408325}a^{4}-\frac{13\!\cdots\!94}{104470934408325}a^{3}+\frac{520158096087857}{34823644802775}a^{2}-\frac{148185856308536}{104470934408325}a-\frac{111995219393389}{104470934408325}$, $\frac{426946931497}{20894186881665}a^{22}+\frac{1857050648}{11607881600925}a^{21}+\frac{6337028802064}{20894186881665}a^{20}-\frac{9208425636181}{104470934408325}a^{19}+\frac{18106554079573}{20894186881665}a^{18}+\frac{10879207894607}{20894186881665}a^{17}+\frac{18443696688703}{34823644802775}a^{16}+\frac{120196599501722}{104470934408325}a^{15}-\frac{84099283223341}{104470934408325}a^{14}+\frac{52256996203567}{104470934408325}a^{13}+\frac{256262736542938}{104470934408325}a^{12}+\frac{18048686665283}{104470934408325}a^{11}+\frac{28297432563427}{11607881600925}a^{10}-\frac{34419578475127}{34823644802775}a^{9}-\frac{23529302043056}{11607881600925}a^{8}+\frac{48352587880987}{34823644802775}a^{7}+\frac{61455578373932}{20894186881665}a^{6}+\frac{83845005913876}{104470934408325}a^{5}+\frac{48362445348649}{20894186881665}a^{4}-\frac{440044108012124}{104470934408325}a^{3}+\frac{7645810337158}{3869293866975}a^{2}+\frac{46122078649846}{104470934408325}a+\frac{94828209208403}{104470934408325}$, $\frac{837076225127}{20894186881665}a^{22}-\frac{1531999244039}{34823644802775}a^{21}+\frac{12136515055157}{20894186881665}a^{20}-\frac{84708618406649}{104470934408325}a^{19}+\frac{35175214697867}{20894186881665}a^{18}-\frac{10752477313937}{20894186881665}a^{17}-\frac{29508895816163}{34823644802775}a^{16}+\frac{160182695427688}{104470934408325}a^{15}-\frac{427236561817169}{104470934408325}a^{14}+\frac{210414094328453}{104470934408325}a^{13}+\frac{544421032279202}{104470934408325}a^{12}-\frac{650800196747723}{104470934408325}a^{11}+\frac{12645693077936}{3869293866975}a^{10}-\frac{50259616708081}{11607881600925}a^{9}-\frac{141934065653477}{34823644802775}a^{8}+\frac{36117152256422}{3869293866975}a^{7}+\frac{95060506169671}{20894186881665}a^{6}-\frac{725781683012506}{104470934408325}a^{5}+\frac{55473120101228}{20894186881665}a^{4}-\frac{10\!\cdots\!66}{104470934408325}a^{3}+\frac{361699599663623}{34823644802775}a^{2}-\frac{26561769457231}{104470934408325}a-\frac{256873622113508}{104470934408325}$, $\frac{593165404982}{104470934408325}a^{22}-\frac{11547511786}{773858773395}a^{21}+\frac{8494903688369}{104470934408325}a^{20}-\frac{4989454072931}{20894186881665}a^{19}+\frac{5639767870888}{20894186881665}a^{18}-\frac{38172277643876}{104470934408325}a^{17}-\frac{3353122137902}{11607881600925}a^{16}+\frac{12297165517889}{104470934408325}a^{15}-\frac{66011405657443}{104470934408325}a^{14}+\frac{104980909477438}{104470934408325}a^{13}+\frac{90556170922453}{104470934408325}a^{12}-\frac{145046685991492}{104470934408325}a^{11}+\frac{15159380309908}{34823644802775}a^{10}-\frac{29508864818018}{34823644802775}a^{9}+\frac{25778655818702}{34823644802775}a^{8}+\frac{2648622825661}{1392945792111}a^{7}+\frac{40950630643876}{104470934408325}a^{6}-\frac{26507751894538}{20894186881665}a^{5}-\frac{43221530068504}{104470934408325}a^{4}-\frac{336955089298469}{104470934408325}a^{3}+\frac{115514233353967}{34823644802775}a^{2}-\frac{11363505136652}{104470934408325}a-\frac{14541301408868}{20894186881665}$, $\frac{510737237161}{104470934408325}a^{22}-\frac{9882716008}{34823644802775}a^{21}+\frac{6849542042857}{104470934408325}a^{20}-\frac{3242429795603}{104470934408325}a^{19}+\frac{2284843336649}{20894186881665}a^{18}+\frac{6411566791832}{104470934408325}a^{17}-\frac{1031894126258}{11607881600925}a^{16}-\frac{20614730570762}{104470934408325}a^{15}-\frac{33339024020312}{104470934408325}a^{14}-\frac{6607379079191}{20894186881665}a^{13}+\frac{43522094596883}{104470934408325}a^{12}+\frac{82595478077443}{104470934408325}a^{11}-\frac{14695468671941}{11607881600925}a^{10}+\frac{3073880747659}{6964728960555}a^{9}-\frac{58291904948638}{34823644802775}a^{8}+\frac{35549506381081}{34823644802775}a^{7}+\frac{161259754324913}{104470934408325}a^{6}+\frac{161701349983553}{104470934408325}a^{5}-\frac{206490197772107}{104470934408325}a^{4}+\frac{38452162727636}{104470934408325}a^{3}-\frac{61772555300693}{34823644802775}a^{2}+\frac{209900478601922}{104470934408325}a-\frac{70458919710326}{104470934408325}$, $\frac{9324208177}{159012076725}a^{22}-\frac{45941699659}{477036230175}a^{21}+\frac{425620134937}{477036230175}a^{20}-\frac{265029910346}{159012076725}a^{19}+\frac{11403838379}{3533601705}a^{18}-\frac{1132668657013}{477036230175}a^{17}-\frac{127303413232}{477036230175}a^{16}+\frac{127105096637}{53004025575}a^{15}-\frac{3363790676852}{477036230175}a^{14}+\frac{647582276972}{95407246035}a^{13}+\frac{2362018550128}{477036230175}a^{12}-\frac{5650310202107}{477036230175}a^{11}+\frac{4618954084856}{477036230175}a^{10}-\frac{1079628038279}{95407246035}a^{9}-\frac{50428555738}{159012076725}a^{8}+\frac{7234985400143}{477036230175}a^{7}-\frac{356823870422}{477036230175}a^{6}-\frac{5545770348592}{477036230175}a^{5}+\frac{1265903807081}{159012076725}a^{4}-\frac{9202302183359}{477036230175}a^{3}+\frac{1395572284544}{53004025575}a^{2}-\frac{5026813939868}{477036230175}a+\frac{1951810228}{159012076725}$, $a$ (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: | \( 530761705.173 \) (assuming GRH) | sage: K.regulator()
gp: K.reg
magma: Regulator(K);
oscar: regulator(K)
|
Class number formula
\[ \begin{aligned}\lim_{s\to 1} (s-1)\zeta_K(s) =\mathstrut & \frac{2^{r_1}\cdot (2\pi)^{r_2}\cdot R\cdot h}{w\cdot\sqrt{|D|}}\cr \approx\mathstrut &\frac{2^{1}\cdot(2\pi)^{11}\cdot 530761705.173 \cdot 1}{2\cdot\sqrt{58230945563524325903440619509366903}}\cr\approx \mathstrut & 1.32526037075 \end{aligned}\] (assuming GRH)
Galois group
A solvable group of order 46 |
The 13 conjugacy class representatives for $D_{23}$ |
Character table for $D_{23}$ |
Intermediate fields
The extension is primitive: there are no intermediate fields between this field and $\Q$. |
Sibling fields
Galois closure: | data not computed |
Minimal sibling: | This field is its own minimal sibling |
Frobenius cycle types
$p$ | $2$ | $3$ | $5$ | $7$ | $11$ | $13$ | $17$ | $19$ | $23$ | $29$ | $31$ | $37$ | $41$ | $43$ | $47$ | $53$ | $59$ |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Cycle type | $23$ | ${\href{/padicField/3.2.0.1}{2} }^{11}{,}\,{\href{/padicField/3.1.0.1}{1} }$ | ${\href{/padicField/5.2.0.1}{2} }^{11}{,}\,{\href{/padicField/5.1.0.1}{1} }$ | $23$ | $23$ | $23$ | $23$ | $23$ | $23$ | ${\href{/padicField/29.2.0.1}{2} }^{11}{,}\,{\href{/padicField/29.1.0.1}{1} }$ | $23$ | $23$ | ${\href{/padicField/41.2.0.1}{2} }^{11}{,}\,{\href{/padicField/41.1.0.1}{1} }$ | $23$ | ${\href{/padicField/47.2.0.1}{2} }^{11}{,}\,{\href{/padicField/47.1.0.1}{1} }$ | $23$ | $23$ |
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 |
---|---|---|---|---|---|---|---|
\(1447\) | $\Q_{1447}$ | $x$ | $1$ | $1$ | $0$ | 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 $2$ | $2$ | $1$ | $1$ | $C_2$ | $[\ ]_{2}$ |