Number field 46.46.165269405800315006446654642733283089940652236420810887453559572571427563258244528313989.1: \(\Q(\zeta_{141})^+\)

• Label: 46.46.165...989.1
• Degree: $46$
• Signature: $[46, 0]$
• Discriminant: $1.653\times 10^{86}$
• Root discriminant: \(74.87\)
• Ramified primes: $3,47$
• Class number: $1$ (GRH)
• Class group: trivial (GRH)
• Galois group: $C_{46}$ (as 46T1)

Normalized defining polynomial

x^46 - x^45 - 46*x^44 + 46*x^43 + 988*x^42 - 988*x^41 - 13159*x^40 + 13159*x^39 + 121731*x^38 - 121731*x^37 - 830207*x^36 + 830207*x^35 + 4324189*x^34 - 4324189*x^33 - 17581994*x^32 + 17581994*x^31 + 56562010*x^30 - 56562010*x^29 - 145057650*x^28 + 145057650*x^27 + 297415766*x^26 - 297415766*x^25 - 486968926*x^24 + 486968926*x^23 + 633580634*x^22 - 633580634*x^21 - 649220446*x^20 + 649220446*x^19 + 516962354*x^18 - 516962354*x^17 - 313942891*x^16 + 313942891*x^15 + 141714824*x^14 - 141714824*x^13 - 45908941*x^12 + 45908941*x^11 + 10162529*x^10 - 10162529*x^9 - 1431196*x^8 + 1431196*x^7 + 114634*x^6 - 114634*x^5 - 4276*x^4 + 4276*x^3 + 48*x^2 - 48*x + 1

Invariants

Degree:		$46$
Signature:		$[46, 0]$
Discriminant:		165269405800315006446654642733283089940652236420810887453559572571427563258244528313989
Root discriminant:		\(74.87\)
Galois root discriminant:		$3^{1/2}47^{45/46}\approx 74.87012045804902$
Ramified primes:		\(3\), \(47\)
Discriminant root field:		\(\Q(\sqrt{141}) \)
$\card{ \Gal(K/\Q) }$:		$46$
This field is Galois and abelian over $\Q$.
Conductor:		\(141=3\cdot 47\)
Dirichlet character group:		$\lbrace$$\chi_{141}(1,·)$, $\chi_{141}(130,·)$, $\chi_{141}(4,·)$, $\chi_{141}(5,·)$, $\chi_{141}(134,·)$, $\chi_{141}(7,·)$, $\chi_{141}(136,·)$, $\chi_{141}(137,·)$, $\chi_{141}(11,·)$, $\chi_{141}(140,·)$, $\chi_{141}(16,·)$, $\chi_{141}(20,·)$, $\chi_{141}(23,·)$, $\chi_{141}(25,·)$, $\chi_{141}(26,·)$, $\chi_{141}(28,·)$, $\chi_{141}(29,·)$, $\chi_{141}(34,·)$, $\chi_{141}(35,·)$, $\chi_{141}(37,·)$, $\chi_{141}(38,·)$, $\chi_{141}(41,·)$, $\chi_{141}(44,·)$, $\chi_{141}(49,·)$, $\chi_{141}(55,·)$, $\chi_{141}(61,·)$, $\chi_{141}(62,·)$, $\chi_{141}(64,·)$, $\chi_{141}(77,·)$, $\chi_{141}(79,·)$, $\chi_{141}(80,·)$, $\chi_{141}(86,·)$, $\chi_{141}(92,·)$, $\chi_{141}(97,·)$, $\chi_{141}(100,·)$, $\chi_{141}(103,·)$, $\chi_{141}(104,·)$, $\chi_{141}(106,·)$, $\chi_{141}(107,·)$, $\chi_{141}(112,·)$, $\chi_{141}(113,·)$, $\chi_{141}(115,·)$, $\chi_{141}(116,·)$, $\chi_{141}(118,·)$, $\chi_{141}(121,·)$, $\chi_{141}(125,·)$$\rbrace$
This is not a CM field.

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

$1$, $a$, $a^{2}$, $a^{3}$, $a^{4}$, $a^{5}$, $a^{6}$, $a^{7}$, $a^{8}$, $a^{9}$, $a^{10}$, $a^{11}$, $a^{12}$, $a^{13}$, $a^{14}$, $a^{15}$, $a^{16}$, $a^{17}$, $a^{18}$, $a^{19}$, $a^{20}$, $a^{21}$, $a^{22}$, $a^{23}$, $a^{24}$, $a^{25}$, $a^{26}$, $a^{27}$, $a^{28}$, $a^{29}$, $a^{30}$, $a^{31}$, $a^{32}$, $a^{33}$, $a^{34}$, $a^{35}$, $a^{36}$, $a^{37}$, $a^{38}$, $a^{39}$, $a^{40}$, $a^{41}$, $a^{42}$, $a^{43}$, $a^{44}$, $a^{45}$

Monogenic:		Yes
Index:		$1$
Inessential primes:		None

Class group and class number

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

Unit group

Rank:		$45$
Torsion generator:		\( -1 \)  (order $2$)
Fundamental units:		$a^{45}-46a^{43}+a^{42}+988a^{41}-43a^{40}-13159a^{39}+859a^{38}+121731a^{37}-10581a^{36}-830207a^{35}+89948a^{34}+4324189a^{33}-559624a^{32}-17581994a^{31}+2636954a^{30}+56562010a^{29}-9606310a^{28}-145057650a^{27}+27378550a^{26}+297415766a^{25}-61385114a^{24}-486968926a^{23}+108310126a^{22}+633580634a^{21}-149738834a^{20}-649220446a^{19}+160726321a^{18}+516962354a^{17}-132019979a^{16}-313942891a^{15}+81266611a^{14}+141714824a^{13}-36408749a^{12}-45908941a^{11}+11396866a^{10}+10162529a^{9}-2351154a^{8}-1431196a^{7}+292696a^{6}+114634a^{5}-19000a^{4}-4276a^{3}+481a^{2}+49a-3$, $a^{45}-46a^{43}+a^{42}+988a^{41}-42a^{40}-13160a^{39}+819a^{38}+121770a^{37}-9841a^{36}-830909a^{35}+81548a^{34}+4331923a^{33}-494174a^{32}-17640304a^{31}+2265945a^{30}+56880660a^{29}-8024040a^{28}-146361694a^{27}+22199905a^{26}+301487250a^{25}-48233990a^{24}-496757496a^{23}+82279901a^{22}+651739984a^{21}-109615332a^{20}-675104602a^{19}+112839405a^{18}+545005214a^{17}-88247494a^{16}-336613616a^{15}+51132973a^{14}+155009043a^{13}-21163505a^{12}-51327951a^{11}+5927831a^{10}+11601019a^{9}-1034112a^{8}-1655092a^{7}+98250a^{6}+131714a^{5}-4084a^{4}-4756a^{3}+48a^{2}+48a$, $a^{3}-3a$, $a^{43}-43a^{41}+860a^{39}-10621a^{37}+90687a^{35}-567987a^{33}+2701776a^{31}-9970840a^{29}+28915436a^{27}-66335412a^{25}+120609840a^{23}-173376645a^{21}+195747825a^{19}-171655785a^{17}+115000920a^{15}-57500460a^{13}+20764055a^{11}-5167525a^{9}+826804a^{7}-76153a^{5}+a^{4}+3311a^{3}-4a^{2}-43a+1$, $a^{6}-6a^{4}+9a^{2}-2$, $a^{25}-25a^{23}+a^{22}+275a^{21}-22a^{20}-1750a^{19}+209a^{18}+7125a^{17}-1122a^{16}-19380a^{15}+3740a^{14}+35700a^{13}-8008a^{12}-44200a^{11}+11011a^{10}+35750a^{9}-9438a^{8}-17875a^{7}+4719a^{6}+5005a^{5}-1210a^{4}-650a^{3}+121a^{2}+25a-2$, $a^{36}-36a^{34}+594a^{32}-5952a^{30}+40455a^{28}-197316a^{26}+712530a^{24}-1937520a^{22}+3996135a^{20}-6249100a^{18}+7354710a^{16}-6418656a^{14}+4056234a^{12}-1790712a^{10}+523260a^{8}-93024a^{6}+8721a^{4}-324a^{2}+2$, $a^{12}-12a^{10}+54a^{8}-112a^{6}+105a^{4}-36a^{2}+3$, $a^{34}-34a^{32}+527a^{30}-4930a^{28}+31059a^{26}-139230a^{24}+457470a^{22}-1118260a^{20}+2042975a^{18}-2778446a^{16}+2778446a^{14}+a^{13}-1998724a^{12}-13a^{11}+999362a^{10}+65a^{9}-329460a^{8}-156a^{7}+65892a^{6}+182a^{5}-6936a^{4}-91a^{3}+289a^{2}+13a-3$, $a^{30}-30a^{28}+405a^{26}-3250a^{24}+17250a^{22}-63756a^{20}+168245a^{18}-319770a^{16}+436050a^{14}-419900a^{12}+277134a^{10}-119340a^{8}+30940a^{6}-4200a^{4}+225a^{2}-2$, $a^{42}-42a^{40}+819a^{38}-a^{37}-9842a^{36}+37a^{35}+81585a^{34}-629a^{33}-494802a^{32}+6512a^{31}+2272424a^{30}-45880a^{29}-8069424a^{28}+232842a^{27}+22428252a^{26}-878814a^{25}-49085400a^{24}+2511144a^{23}+84672315a^{22}-5478462a^{21}-114717330a^{20}+9137370a^{19}+121090515a^{18}-11593154a^{17}-98285670a^{16}+11064689a^{15}+60174900a^{14}-7801111a^{13}-27041560a^{12}+3955718a^{11}+8580494a^{10}-1387815a^{9}-1817036a^{8}+318162a^{7}+235508a^{6}-43602a^{5}-16120a^{4}+3068a^{3}+416a^{2}-79a+1$, $a^{42}-42a^{40}+819a^{38}-9842a^{36}+81585a^{34}+a^{33}-494802a^{32}-33a^{31}+2272424a^{30}+495a^{29}-8069425a^{28}-4466a^{27}+22428280a^{26}+27027a^{25}-49085750a^{24}-115830a^{23}+84674891a^{22}+361790a^{21}-114729727a^{20}-834901a^{19}+121131479a^{18}+1427698a^{17}-98380632a^{16}-1797970a^{15}+60329940a^{14}+1642151a^{13}-27217918a^{12}-1059877a^{11}+8716631a^{10}+464607a^{9}-1885114a^{8}-130416a^{7}+255927a^{6}+21450a^{5}-19355a^{4}-1781a^{3}+637a^{2}+52a-3$, $a^{40}-40a^{38}+740a^{36}-8400a^{34}-a^{33}+65450a^{32}+33a^{31}-371008a^{30}-495a^{29}+1582240a^{28}+4466a^{27}-5178240a^{26}-27027a^{25}+13147875a^{24}+115830a^{23}-26013000a^{22}-361791a^{21}+40060020a^{20}+834921a^{19}-47720400a^{18}-1427868a^{17}+43459650a^{16}+1798770a^{15}-29716000a^{14}-1644426a^{13}+14858000a^{12}+1063881a^{11}-5230016a^{10}-468897a^{9}+1225785a^{8}+133057a^{7}-175560a^{6}-22282a^{5}+13300a^{4}+1895a^{3}-400a^{2}-61a+1$, $a^{43}-43a^{41}+859a^{39}-10582a^{37}+89985a^{35}-560252a^{33}+2643432a^{31}-9651664a^{29}+27606492a^{27}-62233275a^{25}+110685315a^{23}-154777350a^{21}+168810915a^{19}-141745320a^{17}+89890900a^{15}-41899560a^{13}+13810511a^{11}-3042831a^{9}+411103a^{7}-29470a^{5}+a^{4}+841a^{3}-4a^{2}-4a+1$, $a^{43}-43a^{41}+a^{40}+860a^{39}-40a^{38}-10620a^{37}+740a^{36}+90650a^{35}-8399a^{34}-567359a^{33}+65416a^{32}+2695297a^{31}-370482a^{30}-9925455a^{29}+1577340a^{28}+28687060a^{27}-5147586a^{26}-65483625a^{25}+13011894a^{24}+118214526a^{23}-25572756a^{22}-168259973a^{21}+39005264a^{20}+187445355a^{19}-45844150a^{18}-161490310a^{17}+40995160a^{16}+105734050a^{15}-27358916a^{14}-51340849a^{13}+13254424a^{12}+17866562a^{11}-4480331a^{10}-4241810a^{9}+996350a^{8}+636845a^{7}-132565a^{6}-52950a^{5}+8799a^{4}+1801a^{3}-171a^{2}-3a-1$, $a^{6}-6a^{4}+9a^{2}-1$, $a^{28}-28a^{26}+350a^{24}-2576a^{22}+12397a^{20}+a^{19}-40964a^{18}-19a^{17}+94962a^{16}+152a^{15}-155040a^{14}-665a^{13}+176358a^{12}+1729a^{11}-136136a^{10}-2717a^{9}+68068a^{8}+2508a^{7}-20384a^{6}-1254a^{5}+3185a^{4}+285a^{3}-196a^{2}-19a+2$, $a^{43}-43a^{41}+859a^{39}-10582a^{37}+89985a^{35}-560252a^{33}+2643432a^{31}-9651664a^{29}+27606492a^{27}-62233275a^{25}+110685315a^{23}-154777350a^{21}+168810915a^{19}-141745320a^{17}+89890900a^{15}-41899560a^{13}-a^{12}+13810511a^{11}+12a^{10}-3042831a^{9}-54a^{8}+411103a^{7}+112a^{6}-29470a^{5}-104a^{4}+841a^{3}+32a^{2}-4a-1$, $a^{24}-24a^{22}+252a^{20}-1520a^{18}+5814a^{16}-14688a^{14}+24752a^{12}-27456a^{10}+19305a^{8}-8008a^{6}+1716a^{4}-144a^{2}+2$, $a^{30}-30a^{28}+405a^{26}-3250a^{24}+17250a^{22}-63756a^{20}+168245a^{18}-319770a^{16}+436050a^{14}-419900a^{12}+277134a^{10}-119340a^{8}+30940a^{6}-4200a^{4}+225a^{2}-1$, $a^{31}-31a^{29}+434a^{27}-3627a^{25}+20150a^{23}-78430a^{21}+219604a^{19}-447051a^{17}+a^{16}+660858a^{15}-16a^{14}-700910a^{13}+104a^{12}+520676a^{11}-352a^{10}-260338a^{9}+660a^{8}+82212a^{7}-672a^{6}-14756a^{5}+336a^{4}+1240a^{3}-64a^{2}-31a+2$, $a^{43}-43a^{41}+860a^{39}-10621a^{37}+90687a^{35}-567987a^{33}+2701776a^{31}-9970840a^{29}+28915436a^{27}-66335412a^{25}+120609840a^{23}-173376645a^{21}+195747825a^{19}-171655785a^{17}+115000920a^{15}-57500460a^{13}+20764055a^{11}-5167525a^{9}+826804a^{7}-76153a^{5}+a^{4}+3311a^{3}-4a^{2}-43a+2$, $a^{2}-2$, $a^{43}-43a^{41}+860a^{39}-10621a^{37}+90687a^{35}-567987a^{33}+2701776a^{31}-9970840a^{29}+28915436a^{27}-66335412a^{25}+120609840a^{23}-173376645a^{21}+195747825a^{19}-171655785a^{17}+115000920a^{15}-57500460a^{13}+20764055a^{11}-5167525a^{9}+826804a^{7}-76153a^{5}+3311a^{3}-43a$, $a$, $a^{23}-23a^{21}+230a^{19}-1311a^{17}+4692a^{15}-10948a^{13}+16744a^{11}-16445a^{9}+9867a^{7}-3289a^{5}+506a^{3}-23a$, $a^{35}-35a^{33}+560a^{31}-5425a^{29}+35525a^{27}-166257a^{25}+573300a^{23}-1480050a^{21}+2877875a^{19}-4206125a^{17}+4576264a^{15}-3640210a^{13}+a^{12}+2057510a^{11}-12a^{10}-791350a^{9}+54a^{8}+193800a^{7}-112a^{6}-27132a^{5}+105a^{4}+1785a^{3}-36a^{2}-35a+2$, $a^{41}-41a^{39}+779a^{37}-9102a^{35}+73185a^{33}-429352a^{31}+1901416a^{29}-6487184a^{27}+17250012a^{25}-35937525a^{23}+58659315a^{21}-74657310a^{19}+73370115a^{17}-54826020a^{15}+30458900a^{13}-12183560a^{11}+3350479a^{9}-591261a^{7}+59983a^{5}-2870a^{3}+41a$, $a^{44}-44a^{42}+902a^{40}-11440a^{38}+100529a^{36}-649572a^{34}+3196578a^{32}-12243264a^{30}+36984860a^{28}-88763664a^{26}+169695240a^{24}-258048960a^{22}+310465155a^{20}-292746300a^{18}+213286590a^{16}-117675360a^{14}+47805615a^{12}-13748020a^{10}+2643850a^{8}-311696a^{6}+19481a^{4}+a^{3}-484a^{2}-3a+2$, $a^{37}-37a^{35}+629a^{33}-6512a^{31}+45880a^{29}-232841a^{27}+878787a^{25}-2510820a^{23}+5476185a^{21}-9126975a^{19}+11560835a^{17}-10994920a^{15}+7696444a^{13}-3848222a^{11}+1314610a^{9}-286824a^{7}+35853a^{5}-2109a^{3}+37a$, $a^{33}-33a^{31}+495a^{29}-4466a^{27}+27027a^{25}-115830a^{23}+361790a^{21}-834900a^{19}+1427679a^{17}-1797818a^{15}+a^{14}+1641486a^{13}-14a^{12}-1058148a^{11}+77a^{10}+461890a^{9}-210a^{8}-127908a^{7}+295a^{6}+20196a^{5}-202a^{4}-1496a^{3}+58a^{2}+33a-4$, $a^{39}-39a^{37}+702a^{35}-7735a^{33}+58343a^{31}-319145a^{29}+1308510a^{27}-4098510a^{25}+9904375a^{23}-18520865a^{21}+26717306a^{19}-29463414a^{17}+24449162a^{15}-14899990a^{13}+6432868a^{11}-1864356a^{9}+a^{8}+333489a^{7}-8a^{6}-31927a^{5}+20a^{4}+1230a^{3}-16a^{2}-8a+1$, $a^{5}-5a^{3}+5a$, $a^{30}-30a^{28}+405a^{26}-a^{25}-3250a^{24}+25a^{23}+17249a^{22}-275a^{21}-63734a^{20}+1750a^{19}+168036a^{18}-7124a^{17}-318648a^{16}+19363a^{15}+432310a^{14}-35581a^{13}-411892a^{12}+43758a^{11}+266123a^{10}-34815a^{9}-109902a^{8}+16753a^{7}+26221a^{6}-4291a^{5}-2990a^{4}+446a^{3}+104a^{2}-8a$, $a^{30}-30a^{28}+405a^{26}-3250a^{24}+17250a^{22}-63756a^{20}+168245a^{18}+a^{17}-319770a^{16}-17a^{15}+436050a^{14}+119a^{13}-419900a^{12}-442a^{11}+277134a^{10}+936a^{9}-119340a^{8}-1131a^{7}+30940a^{6}+741a^{5}-4200a^{4}-234a^{3}+225a^{2}+26a-2$, $a^{39}-39a^{37}+702a^{35}-7735a^{33}+58344a^{31}-319176a^{29}+1308944a^{27}-4102137a^{25}+9924525a^{23}-18599295a^{21}+26936910a^{19}-29910465a^{17}+25110020a^{15}-15600900a^{13}+6953544a^{11}-2124694a^{9}+a^{8}+415701a^{7}-8a^{6}-46683a^{5}+20a^{4}+2470a^{3}-16a^{2}-39a+2$, $a^{39}-39a^{37}+702a^{35}-7735a^{33}+58344a^{31}-319176a^{29}+1308944a^{27}-4102137a^{25}-a^{24}+9924525a^{23}+24a^{22}-18599295a^{21}-252a^{20}+26936910a^{19}+1520a^{18}-29910465a^{17}-5814a^{16}+25110020a^{15}+14688a^{14}-15600900a^{13}-24752a^{12}+6953544a^{11}+27456a^{10}-2124694a^{9}-19304a^{8}+415701a^{7}+8000a^{6}-46683a^{5}-1696a^{4}+2470a^{3}+128a^{2}-39a$, $a^{34}-34a^{32}+527a^{30}-4930a^{28}+31059a^{26}-139230a^{24}+457470a^{22}-a^{21}-1118260a^{20}+21a^{19}+2042975a^{18}-189a^{17}-2778446a^{16}+952a^{15}+2778446a^{14}-2940a^{13}-1998724a^{12}+5733a^{11}+999362a^{10}-7007a^{9}-329460a^{8}+5148a^{7}+65892a^{6}-2079a^{5}-6936a^{4}+385a^{3}+289a^{2}-21a-2$, $a^{25}-25a^{23}+275a^{21}-1750a^{19}+7125a^{17}-19380a^{15}+35700a^{13}-44200a^{11}+35750a^{9}-17875a^{7}+5005a^{5}-650a^{3}+25a$, $a^{38}-38a^{36}+666a^{34}-7140a^{32}+52359a^{30}-278226a^{28}+1107162a^{26}-3362580a^{24}+7871175a^{22}-14241370a^{20}+19852910a^{18}-21128076a^{16}+16893546a^{14}+a^{13}-9903180a^{12}-13a^{11}+4104684a^{10}+65a^{9}-1139544a^{8}-156a^{7}+194769a^{6}+182a^{5}-17766a^{4}-91a^{3}+650a^{2}+13a-4$, $a^{22}-22a^{20}+209a^{18}-1122a^{16}+3740a^{14}-8008a^{12}+a^{11}+11011a^{10}-11a^{9}-9438a^{8}+44a^{7}+4719a^{6}-77a^{5}-1210a^{4}+55a^{3}+121a^{2}-11a-1$, $a^{36}-36a^{34}+594a^{32}-5952a^{30}+40455a^{28}-197316a^{26}+712530a^{24}-1937520a^{22}+3996135a^{20}-6249100a^{18}+7354710a^{16}-6418656a^{14}+4056234a^{12}-1790712a^{10}+523260a^{8}-a^{7}-93024a^{6}+7a^{5}+8721a^{4}-14a^{3}-324a^{2}+7a+2$, $a^{39}-38a^{37}+665a^{35}-7106a^{33}+51832a^{31}-a^{30}-273296a^{29}+29a^{28}+1076103a^{27}-377a^{26}-3223350a^{25}+2900a^{24}+7413705a^{23}-14674a^{22}-13123110a^{21}+51359a^{20}+17809935a^{19}-127281a^{18}-18349630a^{17}+224808a^{16}+14115100a^{15}-281010a^{14}-7904456a^{13}+243542a^{12}+3105322a^{11}-140997a^{10}-810084a^{9}+51263a^{8}+128877a^{7}-10529a^{6}-10830a^{5}+985a^{4}+361a^{3}-20a^{2}-3a$, $a^{43}-43a^{41}+859a^{39}-10582a^{37}+89985a^{35}-560252a^{33}+2643432a^{31}-9651664a^{29}+27606492a^{27}-62233275a^{25}+110685315a^{23}-154777350a^{21}+168810915a^{19}-141745320a^{17}+89890900a^{15}-41899560a^{13}+a^{12}+13810511a^{11}-12a^{10}-3042831a^{9}+53a^{8}+411103a^{7}-104a^{6}-29470a^{5}+85a^{4}+841a^{3}-20a^{2}-4a+1$, $a^{27}-27a^{25}+324a^{23}-2277a^{21}+a^{20}+10395a^{19}-20a^{18}-32319a^{17}+170a^{16}+69768a^{15}-800a^{14}-104652a^{13}+2275a^{12}+107406a^{11}-4004a^{10}-72930a^{9}+4290a^{8}+30888a^{7}-2640a^{6}-7371a^{5}+825a^{4}+819a^{3}-100a^{2}-27a+2$ (assuming GRH)
Regulator:		\( 45504514750422600000000000000 \) (assuming GRH)

Class number formula

\[ \begin{aligned}\lim_{s\to 1} (s-1)\zeta_K(s) =\mathstrut & \frac{2^{r_1}\cdot (2\pi)^{r_2}\cdot R\cdot h}{w\cdot\sqrt{|D|}}\cr \approx\mathstrut &\frac{2^{46}\cdot(2\pi)^{0}\cdot 45504514750422600000000000000 \cdot 1}{2\cdot\sqrt{165269405800315006446654642733283089940652236420810887453559572571427563258244528313989}}\cr\approx \mathstrut & 0.124539770066175 \end{aligned}\] (assuming GRH)

Galois group

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

A cyclic group of order 46

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

Character table for $C_{46}$

Intermediate fields

\(\Q(\sqrt{141}) \), \(\Q(\zeta_{47})^+\)

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	$46$	R	$23^{2}$	$23^{2}$	$23^{2}$	$46$	$46$	$46$	$23^{2}$	$23^{2}$	$46$	$23^{2}$	$23^{2}$	$46$	R	$46$	$46$

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
\(3\)		Deg $46$	$2$	$23$	$23$
\(47\)		Deg $46$	$46$	$1$	$45$