Global number field 46.0.1380482837403389951188929417327974945597612959507252561395133063683075408426725855911571776236858989634125824.1

• Label: 46.0.13804828374...5824.1
• Degree: $46$
• Signature: $[0, 23]$
• Discriminant: $-\,2^{46}\cdot 139^{44}$
• Root discriminant: $224.32$
• Ramified primes: $2, 139$
• Class number: Not computed
• Class group: Not computed
• Galois group: $C_{46}$ (as 46T1)

Normalized defining polynomial

\( x^{46} + 133 x^{44} + 7910 x^{42} + 280979 x^{40} + 6711990 x^{38} + 114987064 x^{36} + 1469694259 x^{34} + 14379783234 x^{32} + 109546710767 x^{30} + 656889854778 x^{28} + 3119915278864 x^{26} + 11765458872927 x^{24} + 35196069562766 x^{22} + 83182641477483 x^{20} + 154201680196954 x^{18} + 221856965964565 x^{16} + 244193705300475 x^{14} + 201715739498828 x^{12} + 121843992775564 x^{10} + 51867928194453 x^{8} + 14702389784925 x^{6} + 2515252049816 x^{4} + 210633684685 x^{2} + 4088451481 \)

Invariants

Degree:		$46$
Signature:		$[0, 23]$
Discriminant:		\(-1380482837403389951188929417327974945597612959507252561395133063683075408426725855911571776236858989634125824=-\,2^{46}\cdot 139^{44}\)
Root discriminant:		$224.32$
Ramified primes:		$2, 139$
This field is Galois and abelian over $\Q$.
Conductor:		\(556=2^{2}\cdot 139\)
Dirichlet character group:		$\lbrace$$\chi_{556}(1,·)$, $\chi_{556}(131,·)$, $\chi_{556}(517,·)$, $\chi_{556}(129,·)$, $\chi_{556}(407,·)$, $\chi_{556}(369,·)$, $\chi_{556}(77,·)$, $\chi_{556}(45,·)$, $\chi_{556}(145,·)$, $\chi_{556}(403,·)$, $\chi_{556}(533,·)$, $\chi_{556}(279,·)$, $\chi_{556}(409,·)$, $\chi_{556}(91,·)$, $\chi_{556}(423,·)$, $\chi_{556}(255,·)$, $\chi_{556}(173,·)$, $\chi_{556}(175,·)$, $\chi_{556}(183,·)$, $\chi_{556}(57,·)$, $\chi_{556}(191,·)$, $\chi_{556}(65,·)$, $\chi_{556}(323,·)$, $\chi_{556}(453,·)$, $\chi_{556}(79,·)$, $\chi_{556}(203,·)$, $\chi_{556}(333,·)$, $\chi_{556}(461,·)$, $\chi_{556}(335,·)$, $\chi_{556}(341,·)$, $\chi_{556}(343,·)$, $\chi_{556}(219,·)$, $\chi_{556}(523,·)$, $\chi_{556}(481,·)$, $\chi_{556}(355,·)$, $\chi_{556}(357,·)$, $\chi_{556}(529,·)$, $\chi_{556}(451,·)$, $\chi_{556}(239,·)$, $\chi_{556}(497,·)$, $\chi_{556}(245,·)$, $\chi_{556}(251,·)$, $\chi_{556}(55,·)$, $\chi_{556}(63,·)$, $\chi_{556}(125,·)$, $\chi_{556}(469,·)$$\rbrace$
This is a CM field.

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

$1$, $a$, $a^{2}$, $a^{3}$, $a^{4}$, $a^{5}$, $a^{6}$, $a^{7}$, $a^{8}$, $a^{9}$, $a^{10}$, $a^{11}$, $a^{12}$, $a^{13}$, $a^{14}$, $a^{15}$, $a^{16}$, $a^{17}$, $a^{18}$, $a^{19}$, $a^{20}$, $a^{21}$, $a^{22}$, $a^{23}$, $a^{24}$, $a^{25}$, $a^{26}$, $a^{27}$, $a^{28}$, $a^{29}$, $a^{30}$, $\frac{1}{43} a^{31} + \frac{15}{43} a^{29} - \frac{11}{43} a^{27} + \frac{5}{43} a^{25} + \frac{15}{43} a^{23} - \frac{5}{43} a^{19} + \frac{15}{43} a^{17} - \frac{16}{43} a^{15} + \frac{19}{43} a^{13} + \frac{20}{43} a^{11} + \frac{1}{43} a^{9} - \frac{7}{43} a^{7} + \frac{13}{43} a^{5} - \frac{20}{43} a^{3} - \frac{5}{43} a$, $\frac{1}{43} a^{32} + \frac{15}{43} a^{30} - \frac{11}{43} a^{28} + \frac{5}{43} a^{26} + \frac{15}{43} a^{24} - \frac{5}{43} a^{20} + \frac{15}{43} a^{18} - \frac{16}{43} a^{16} + \frac{19}{43} a^{14} + \frac{20}{43} a^{12} + \frac{1}{43} a^{10} - \frac{7}{43} a^{8} + \frac{13}{43} a^{6} - \frac{20}{43} a^{4} - \frac{5}{43} a^{2}$, $\frac{1}{43} a^{33} - \frac{21}{43} a^{29} - \frac{2}{43} a^{27} - \frac{17}{43} a^{25} - \frac{10}{43} a^{23} - \frac{5}{43} a^{21} + \frac{4}{43} a^{19} + \frac{17}{43} a^{17} + \frac{1}{43} a^{15} - \frac{7}{43} a^{13} + \frac{2}{43} a^{11} + \frac{21}{43} a^{9} - \frac{11}{43} a^{7} - \frac{6}{43} a^{3} - \frac{11}{43} a$, $\frac{1}{4171} a^{34} - \frac{20}{4171} a^{32} - \frac{1181}{4171} a^{30} - \frac{1244}{4171} a^{28} - \frac{2009}{4171} a^{26} + \frac{937}{4171} a^{24} + \frac{1887}{4171} a^{22} - \frac{412}{4171} a^{20} + \frac{1308}{4171} a^{18} - \frac{1055}{4171} a^{16} - \frac{5}{97} a^{14} + \frac{376}{4171} a^{12} + \frac{2022}{4171} a^{10} - \frac{38}{97} a^{8} - \frac{8}{43} a^{6} + \frac{136}{4171} a^{4} + \frac{605}{4171} a^{2} - \frac{47}{97}$, $\frac{1}{4171} a^{35} - \frac{20}{4171} a^{33} - \frac{17}{4171} a^{31} - \frac{468}{4171} a^{29} + \frac{1871}{4171} a^{27} - \frac{1585}{4171} a^{25} - \frac{1508}{4171} a^{23} - \frac{412}{4171} a^{21} - \frac{341}{4171} a^{19} - \frac{279}{4171} a^{17} + \frac{2016}{4171} a^{15} + \frac{1637}{4171} a^{13} + \frac{276}{4171} a^{11} - \frac{470}{4171} a^{9} - \frac{6}{43} a^{7} - \frac{1416}{4171} a^{5} - \frac{1820}{4171} a^{3} + \frac{501}{4171} a$, $\frac{1}{4171} a^{36} - \frac{29}{4171} a^{32} - \frac{1584}{4171} a^{30} + \frac{1920}{4171} a^{28} + \frac{1885}{4171} a^{26} - \frac{1974}{4171} a^{24} - \frac{211}{4171} a^{22} + \frac{1992}{4171} a^{20} - \frac{1667}{4171} a^{18} - \frac{266}{4171} a^{16} + \frac{538}{4171} a^{14} - \frac{1128}{4171} a^{12} - \frac{1352}{4171} a^{10} + \frac{1561}{4171} a^{8} + \frac{621}{4171} a^{6} + \frac{1482}{4171} a^{4} - \frac{1852}{4171} a^{2} + \frac{30}{97}$, $\frac{1}{4171} a^{37} - \frac{29}{4171} a^{33} - \frac{32}{4171} a^{31} + \frac{174}{4171} a^{29} + \frac{1497}{4171} a^{27} + \frac{1615}{4171} a^{25} - \frac{1957}{4171} a^{23} + \frac{1992}{4171} a^{21} - \frac{1085}{4171} a^{19} - \frac{2012}{4171} a^{17} + \frac{732}{4171} a^{15} - \frac{837}{4171} a^{13} + \frac{491}{4171} a^{11} - \frac{1058}{4171} a^{9} - \frac{1901}{4171} a^{7} + \frac{803}{4171} a^{5} + \frac{476}{4171} a^{3} + \frac{1872}{4171} a$, $\frac{1}{4171} a^{38} - \frac{30}{4171} a^{32} - \frac{319}{4171} a^{30} + \frac{729}{4171} a^{28} + \frac{487}{4171} a^{26} + \frac{578}{4171} a^{24} - \frac{1679}{4171} a^{22} + \frac{741}{4171} a^{20} - \frac{1231}{4171} a^{18} - \frac{1636}{4171} a^{16} - \frac{185}{4171} a^{14} - \frac{1991}{4171} a^{12} - \frac{232}{4171} a^{10} + \frac{862}{4171} a^{8} - \frac{1622}{4171} a^{6} + \frac{1122}{4171} a^{4} - \frac{177}{4171} a^{2} - \frac{5}{97}$, $\frac{1}{4171} a^{39} - \frac{30}{4171} a^{33} - \frac{28}{4171} a^{31} + \frac{923}{4171} a^{29} + \frac{1457}{4171} a^{27} + \frac{2033}{4171} a^{25} - \frac{1485}{4171} a^{23} + \frac{741}{4171} a^{21} + \frac{1485}{4171} a^{19} - \frac{1442}{4171} a^{17} - \frac{670}{4171} a^{15} - \frac{633}{4171} a^{13} + \frac{1417}{4171} a^{11} + \frac{1153}{4171} a^{9} + \frac{512}{4171} a^{7} + \frac{734}{4171} a^{5} - \frac{1826}{4171} a^{3} - \frac{1670}{4171} a$, $\frac{1}{2498429} a^{40} + \frac{280}{2498429} a^{38} + \frac{265}{2498429} a^{36} - \frac{81}{2498429} a^{34} - \frac{18973}{2498429} a^{32} + \frac{365613}{2498429} a^{30} + \frac{40524}{2498429} a^{28} + \frac{754345}{2498429} a^{26} + \frac{1245539}{2498429} a^{24} - \frac{387955}{2498429} a^{22} + \frac{1211041}{2498429} a^{20} - \frac{191202}{2498429} a^{18} - \frac{1009808}{2498429} a^{16} + \frac{569612}{2498429} a^{14} + \frac{958559}{2498429} a^{12} + \frac{738895}{2498429} a^{10} - \frac{1206852}{2498429} a^{8} - \frac{74491}{2498429} a^{6} - \frac{659096}{2498429} a^{4} - \frac{1053985}{2498429} a^{2} - \frac{3954}{58103}$, $\frac{1}{2498429} a^{41} + \frac{280}{2498429} a^{39} + \frac{265}{2498429} a^{37} - \frac{81}{2498429} a^{35} - \frac{18973}{2498429} a^{33} + \frac{16995}{2498429} a^{31} - \frac{191888}{2498429} a^{29} - \frac{407715}{2498429} a^{27} - \frac{497551}{2498429} a^{25} - \frac{620367}{2498429} a^{23} + \frac{1211041}{2498429} a^{21} - \frac{946541}{2498429} a^{19} - \frac{1242220}{2498429} a^{17} + \frac{1150642}{2498429} a^{15} - \frac{668325}{2498429} a^{13} - \frac{1236607}{2498429} a^{11} + \frac{942959}{2498429} a^{9} - \frac{132594}{2498429} a^{7} - \frac{194272}{2498429} a^{5} + \frac{921517}{2498429} a^{3} - \frac{925361}{2498429} a$, $\frac{1}{145975663712849} a^{42} - \frac{28613691}{145975663712849} a^{40} - \frac{5691573102}{145975663712849} a^{38} - \frac{17439766729}{145975663712849} a^{36} - \frac{9524404111}{145975663712849} a^{34} + \frac{1212957976832}{145975663712849} a^{32} + \frac{42563703310036}{145975663712849} a^{30} + \frac{70123613297011}{145975663712849} a^{28} - \frac{11036261505221}{145975663712849} a^{26} + \frac{59126304611210}{145975663712849} a^{24} - \frac{30985359682358}{145975663712849} a^{22} + \frac{65640861250593}{145975663712849} a^{20} + \frac{42896878408843}{145975663712849} a^{18} - \frac{12310075776036}{145975663712849} a^{16} + \frac{27552792771966}{145975663712849} a^{14} - \frac{29175157235763}{145975663712849} a^{12} + \frac{33163517571468}{145975663712849} a^{10} + \frac{28596824574361}{145975663712849} a^{8} + \frac{1192795939939}{145975663712849} a^{6} - \frac{50799592209623}{145975663712849} a^{4} + \frac{48081963518602}{145975663712849} a^{2} + \frac{2781454457}{78948439001}$, $\frac{1}{217065811941006463} a^{43} + \frac{29126449828}{217065811941006463} a^{41} + \frac{17992097227157}{217065811941006463} a^{39} + \frac{23947613457022}{217065811941006463} a^{37} - \frac{10385571959901}{217065811941006463} a^{35} - \frac{1048984272682193}{217065811941006463} a^{33} + \frac{391903355294497}{217065811941006463} a^{31} - \frac{49860107598371965}{217065811941006463} a^{29} - \frac{7248505355308537}{217065811941006463} a^{27} + \frac{87378422761963837}{217065811941006463} a^{25} - \frac{11216581038361602}{217065811941006463} a^{23} + \frac{19669387548924573}{217065811941006463} a^{21} - \frac{94339654606420160}{217065811941006463} a^{19} - \frac{59195299225637063}{217065811941006463} a^{17} - \frac{87122922058038135}{217065811941006463} a^{15} + \frac{84402765710359455}{217065811941006463} a^{13} - \frac{79571756651768355}{217065811941006463} a^{11} + \frac{85170059232575690}{217065811941006463} a^{9} + \frac{45358988070069535}{217065811941006463} a^{7} + \frac{35183537138028990}{217065811941006463} a^{5} - \frac{60063113437977968}{217065811941006463} a^{3} + \frac{2480595160217167}{5048042138162941} a$, $\frac{1}{153921960452446439718003841610049386022803925538701508651047052568515566099441749} a^{44} - \frac{12834182579662482147705620702884762524190150671063724353780726238}{153921960452446439718003841610049386022803925538701508651047052568515566099441749} a^{42} - \frac{26922418720996524626972596975702675832958438346169716044772805168015140736}{153921960452446439718003841610049386022803925538701508651047052568515566099441749} a^{40} + \frac{14292497746737867817959910706164291302631530220575765038990338316602308279833}{153921960452446439718003841610049386022803925538701508651047052568515566099441749} a^{38} - \frac{5151105246008234400340055140550636607084691027566612421792562153368967780939}{153921960452446439718003841610049386022803925538701508651047052568515566099441749} a^{36} - \frac{9110756876094027969839391609843680704244775799062635876203808999535132805334}{153921960452446439718003841610049386022803925538701508651047052568515566099441749} a^{34} + \frac{1361220410225362692587803873111656738971897244981007306112262611101717704345561}{153921960452446439718003841610049386022803925538701508651047052568515566099441749} a^{32} + \frac{44338419634516341233716710761494151864433189698303655383003119702751346739951692}{153921960452446439718003841610049386022803925538701508651047052568515566099441749} a^{30} - \frac{38528785492758767641787506956555004877115600742240226666062161063404657377621842}{153921960452446439718003841610049386022803925538701508651047052568515566099441749} a^{28} + \frac{22473010637372801846816509011371928880551226972008381276224302676031095056157449}{153921960452446439718003841610049386022803925538701508651047052568515566099441749} a^{26} - \frac{71965591128877824703477067148893699455201866673858247871652810365293904135698863}{153921960452446439718003841610049386022803925538701508651047052568515566099441749} a^{24} - \frac{38786671735132699186448264008230215758312892314203802155870364904559805740600037}{153921960452446439718003841610049386022803925538701508651047052568515566099441749} a^{22} - \frac{57054285626911471780365587430508420180991503987899676820906229580681663910324974}{153921960452446439718003841610049386022803925538701508651047052568515566099441749} a^{20} + \frac{35992849387745582928824597837195588047607714829691319154766670485713470649616721}{153921960452446439718003841610049386022803925538701508651047052568515566099441749} a^{18} - \frac{29575779138324740571947102001298220792007980158305634540379089643781507361543878}{153921960452446439718003841610049386022803925538701508651047052568515566099441749} a^{16} + \frac{66325931489049874018937961066572980112266436515349287683525484450040486380946058}{153921960452446439718003841610049386022803925538701508651047052568515566099441749} a^{14} - \frac{7235159914114100968261672358477376251491652369526004428668170292456289420202245}{153921960452446439718003841610049386022803925538701508651047052568515566099441749} a^{12} + \frac{48929544794372923988810933923099670907597211838327265390028503517653973080882002}{153921960452446439718003841610049386022803925538701508651047052568515566099441749} a^{10} - \frac{46436706127208339367404301610489554357248776839713513775681996199548844897768004}{153921960452446439718003841610049386022803925538701508651047052568515566099441749} a^{8} + \frac{34157966099192039917787277216817858977840469353049455266749013423997184190560418}{153921960452446439718003841610049386022803925538701508651047052568515566099441749} a^{6} + \frac{24095488686707775790240067017011496390278831672920747077625737760602828064899830}{153921960452446439718003841610049386022803925538701508651047052568515566099441749} a^{4} + \frac{58994814301839556115643717815430404610218054197170732080155348621499966931584449}{153921960452446439718003841610049386022803925538701508651047052568515566099441749} a^{2} + \frac{22891779173635253039703771513310362534996843252629089451296540438211105425}{55982553848677519834965533855174405337625538346470386635880189174582660723}$, $\frac{1}{153921960452446439718003841610049386022803925538701508651047052568515566099441749} a^{45} - \frac{70333388629946243628440994631606101819259540282834964503979224}{153921960452446439718003841610049386022803925538701508651047052568515566099441749} a^{43} - \frac{24801795643814918428113816364867126089003184408876509204094835048796293630}{153921960452446439718003841610049386022803925538701508651047052568515566099441749} a^{41} - \frac{7171249820462239455899042989096735064135470858454563362235598221732568827125}{153921960452446439718003841610049386022803925538701508651047052568515566099441749} a^{39} + \frac{18042241548073302951739533786619272228981535644304512172930175983813099494984}{153921960452446439718003841610049386022803925538701508651047052568515566099441749} a^{37} - \frac{1020712440805145699636501277345250430990060031005401443604625100494944543025}{153921960452446439718003841610049386022803925538701508651047052568515566099441749} a^{35} - \frac{1029069972676929887326981821559713973354449827778315847904515494245908721585211}{153921960452446439718003841610049386022803925538701508651047052568515566099441749} a^{33} + \frac{25579318995930036966948927132168966392226998733143347032048109185183388223139}{3579580475638289295767531200233706651693114547411662991884815176011989909289343} a^{31} + \frac{38511002244945016590297381812961279681002091825272261973180015908683736898574525}{153921960452446439718003841610049386022803925538701508651047052568515566099441749} a^{29} + \frac{47082357252391325286865445482616495299068569728508336445935949131686081639896131}{153921960452446439718003841610049386022803925538701508651047052568515566099441749} a^{27} - \frac{43883443793204857683811464786921888989292138340872148226747924727189109756482314}{153921960452446439718003841610049386022803925538701508651047052568515566099441749} a^{25} + \frac{52639246446760951144208914868942032175169955452965927089076530994698545977379114}{153921960452446439718003841610049386022803925538701508651047052568515566099441749} a^{23} + \frac{11310333376104660407445404937225246765818600187716707094441579474139791804864542}{153921960452446439718003841610049386022803925538701508651047052568515566099441749} a^{21} - \frac{23076630192674051056182750775211018576890908309909914248567406661991538628101181}{153921960452446439718003841610049386022803925538701508651047052568515566099441749} a^{19} + \frac{30379068540166138538508626575972363715471549068465889318688076328634606877198624}{153921960452446439718003841610049386022803925538701508651047052568515566099441749} a^{17} - \frac{23990775768730041332938737364689533919382976093368530389615882619961614189221816}{153921960452446439718003841610049386022803925538701508651047052568515566099441749} a^{15} + \frac{49497677785131192918163120532421188812959995488983716292828309696270060198193425}{153921960452446439718003841610049386022803925538701508651047052568515566099441749} a^{13} + \frac{58808462968065837467719398744653394338846663364274199191384021591994571525548191}{153921960452446439718003841610049386022803925538701508651047052568515566099441749} a^{11} - \frac{75885059650607061080879242842127600823561218237090015092917782222048145069708327}{153921960452446439718003841610049386022803925538701508651047052568515566099441749} a^{9} + \frac{31676958676787407123478975955313327358851020608435453266210647547983144331648996}{153921960452446439718003841610049386022803925538701508651047052568515566099441749} a^{7} - \frac{58008724912882032117695165737498577104778053222266874268464329921541813752056578}{153921960452446439718003841610049386022803925538701508651047052568515566099441749} a^{5} - \frac{44295783624209784937837240664127643439011559210347505856268865953655677304040451}{153921960452446439718003841610049386022803925538701508651047052568515566099441749} a^{3} + \frac{278709663411448865340434334280869907576557231835214790991331532209490657567766}{3579580475638289295767531200233706651693114547411662991884815176011989909289343} a$

Class group and class number

Not computed

Unit group

Rank:		$22$
Torsion generator:		\( -\frac{96259495816406886775724441011588357578821797891008842}{2026075795400596295369374894695049709866648406116273837635103} a^{45} - \frac{12750858221704604499231436353541685435914943012406340768}{2026075795400596295369374894695049709866648406116273837635103} a^{43} - \frac{754490036776833370012854430924560935618957814737477082400}{2026075795400596295369374894695049709866648406116273837635103} a^{41} - \frac{26631700792861943101511378685424209194364857461319984712589}{2026075795400596295369374894695049709866648406116273837635103} a^{39} - \frac{631212011676111291169513493479649009390199944532775861339562}{2026075795400596295369374894695049709866648406116273837635103} a^{37} - \frac{10709914480741318744017098668868834979051423106580627600668892}{2026075795400596295369374894695049709866648406116273837635103} a^{35} - \frac{135274386745259274100295227129202808579020861625541647532505746}{2026075795400596295369374894695049709866648406116273837635103} a^{33} - \frac{1304378571944600451988616945858452521807450046223267256340713331}{2026075795400596295369374894695049709866648406116273837635103} a^{31} - \frac{9759525985093129024478370513655726859711445548124304820948753919}{2026075795400596295369374894695049709866648406116273837635103} a^{29} - \frac{57230547042471315019148946876382405151479060488106124853945411808}{2026075795400596295369374894695049709866648406116273837635103} a^{27} - \frac{264363273284497019453464305004213384599493942469018704129399361004}{2026075795400596295369374894695049709866648406116273837635103} a^{25} - \frac{962783244338751862595131693814934288152160491732682717199494183496}{2026075795400596295369374894695049709866648406116273837635103} a^{23} - \frac{2756166152281412911362441338643522884588710427867992723484891819526}{2026075795400596295369374894695049709866648406116273837635103} a^{21} - \frac{6159463861403006722275838902131099301393586692790026869067621394446}{2026075795400596295369374894695049709866648406116273837635103} a^{19} - \frac{10627997889248982622918080147649355843039843432642294829495152580728}{2026075795400596295369374894695049709866648406116273837635103} a^{17} - \frac{13937872222566807875262402464145426564111474092319171400175165212440}{2026075795400596295369374894695049709866648406116273837635103} a^{15} - \frac{13597900873685097529547499035909306042648671475250809599899043293239}{2026075795400596295369374894695049709866648406116273837635103} a^{13} - \frac{9587974269335040984381581176355621706685594019198094949757503980248}{2026075795400596295369374894695049709866648406116273837635103} a^{11} - \frac{4694612344645360114611661138741565077619109917327727854331083753696}{2026075795400596295369374894695049709866648406116273837635103} a^{9} - \frac{1504423207003757594363659033634871268656001618609066058164436319506}{2026075795400596295369374894695049709866648406116273837635103} a^{7} - \frac{285607437868387635938225783454611007810771137184238061937699168841}{2026075795400596295369374894695049709866648406116273837635103} a^{5} - \frac{26035601934584062700218691436119135923536898935608116381197713134}{2026075795400596295369374894695049709866648406116273837635103} a^{3} - \frac{12340663106433587011251157600229559179950366733859696866055565}{47118041753502239427194764992908132787596474560843577619421} a \) (order $4$)
Fundamental units:		Not computed
Regulator:		Not computed

Galois group

$C_{46}$ (as 46T1):

A cyclic group of order 46

The 46 conjugacy class representatives for $C_{46}$

Character table for $C_{46}$ is not computed

Intermediate fields

\(\Q(\sqrt{-1}) \), 23.23.140063703503689367173618364344202364099995564521.1

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	R	$46$	$23^{2}$	$46$	$46$	$23^{2}$	$23^{2}$	$46$	$46$	$23^{2}$	$46$	$23^{2}$	$23^{2}$	${\href{/LocalNumberField/43.2.0.1}{2} }^{23}$	$46$	$23^{2}$	$46$

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
2	Data not computed
139	Data not computed