Global number field 46.0.3516370336176915030779886015601767871077707157889593350075735586626118367196692091787.1

• Label: 46.0.35163703361...1787.1
• Degree: $46$
• Signature: $[0, 23]$
• Discriminant: $-\,3^{23}\cdot 47^{44}$
• Root discriminant: $68.86$
• Ramified primes: $3, 47$
• Class number: Not computed
• Class group: Not computed
• Galois group: $C_{46}$ (as 46T1)

Normalized defining polynomial

\( x^{46} - x^{45} + 23 x^{44} - 20 x^{43} + 295 x^{42} - 232 x^{41} + 2591 x^{40} - 1841 x^{39} + 17196 x^{38} - 11094 x^{37} + 90115 x^{36} - 52612 x^{35} + 383674 x^{34} - 202420 x^{33} + 1347421 x^{32} - 638602 x^{31} + 3942124 x^{30} - 1670119 x^{29} + 9645429 x^{28} - 3619962 x^{27} + 19758077 x^{26} - 6515312 x^{25} + 33775844 x^{24} - 9654035 x^{23} + 47923922 x^{22} - 11732918 x^{21} + 55884245 x^{20} - 11469872 x^{19} + 52902122 x^{18} - 8963564 x^{17} + 39899588 x^{16} - 5363639 x^{15} + 23456774 x^{14} - 2477645 x^{13} + 10388534 x^{12} - 774410 x^{11} + 3336047 x^{10} - 192764 x^{9} + 724724 x^{8} - 17303 x^{7} + 98956 x^{6} - 3718 x^{5} + 7073 x^{4} + 220 x^{3} + 210 x^{2} - 12 x + 1 \)

Invariants

Degree:		$46$
Signature:		$[0, 23]$
Discriminant:		\(-3516370336176915030779886015601767871077707157889593350075735586626118367196692091787=-\,3^{23}\cdot 47^{44}\)
Root discriminant:		$68.86$
Ramified primes:		$3, 47$
This field is Galois and abelian over $\Q$.
Conductor:		\(141=3\cdot 47\)
Dirichlet character group:		$\lbrace$$\chi_{141}(128,·)$, $\chi_{141}(1,·)$, $\chi_{141}(2,·)$, $\chi_{141}(131,·)$, $\chi_{141}(4,·)$, $\chi_{141}(7,·)$, $\chi_{141}(8,·)$, $\chi_{141}(130,·)$, $\chi_{141}(14,·)$, $\chi_{141}(16,·)$, $\chi_{141}(17,·)$, $\chi_{141}(25,·)$, $\chi_{141}(28,·)$, $\chi_{141}(32,·)$, $\chi_{141}(34,·)$, $\chi_{141}(37,·)$, $\chi_{141}(49,·)$, $\chi_{141}(50,·)$, $\chi_{141}(53,·)$, $\chi_{141}(55,·)$, $\chi_{141}(56,·)$, $\chi_{141}(59,·)$, $\chi_{141}(61,·)$, $\chi_{141}(64,·)$, $\chi_{141}(65,·)$, $\chi_{141}(68,·)$, $\chi_{141}(71,·)$, $\chi_{141}(74,·)$, $\chi_{141}(79,·)$, $\chi_{141}(83,·)$, $\chi_{141}(89,·)$, $\chi_{141}(122,·)$, $\chi_{141}(95,·)$, $\chi_{141}(97,·)$, $\chi_{141}(98,·)$, $\chi_{141}(100,·)$, $\chi_{141}(101,·)$, $\chi_{141}(103,·)$, $\chi_{141}(106,·)$, $\chi_{141}(110,·)$, $\chi_{141}(112,·)$, $\chi_{141}(115,·)$, $\chi_{141}(118,·)$, $\chi_{141}(119,·)$, $\chi_{141}(121,·)$, $\chi_{141}(136,·)$$\rbrace$
This is a CM field.

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

$1$, $a$, $a^{2}$, $a^{3}$, $a^{4}$, $a^{5}$, $a^{6}$, $a^{7}$, $a^{8}$, $a^{9}$, $a^{10}$, $a^{11}$, $a^{12}$, $a^{13}$, $a^{14}$, $a^{15}$, $a^{16}$, $a^{17}$, $a^{18}$, $a^{19}$, $a^{20}$, $a^{21}$, $a^{22}$, $a^{23}$, $a^{24}$, $a^{25}$, $a^{26}$, $a^{27}$, $a^{28}$, $a^{29}$, $a^{30}$, $a^{31}$, $a^{32}$, $a^{33}$, $a^{34}$, $a^{35}$, $a^{36}$, $a^{37}$, $a^{38}$, $a^{39}$, $a^{40}$, $a^{41}$, $a^{42}$, $a^{43}$, $a^{44}$, $\frac{1}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{45} - \frac{5688131015910426403481681003023961196033725883904009410330053379474269821039647951045116435319360411105904547481919}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{44} - \frac{3054209967245349577954724568032167812960902655693669119119711411946345171127292636907828355200592682800082396166022}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{43} + \frac{4476247850477304080913140924629230813745253794559652562247084834192023792785642988014213516665234846802487706969847}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{42} + \frac{8711208502534771969418081056813292509279226387720917066480149084269759189740728620179100864365543141551047368586954}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{41} + \frac{628424215971165371957393292395187007161147322887100185111496210559379444386748612694478602750149052771239274025627}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{40} - \frac{4388279915796588219275447816893159193734132659867779405109549667515640624437992462187014354604208467273280371603014}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{39} + \frac{6489875875477694426650245251464174709279674231540610811191208123478020844653932258308405520580133698095092494812651}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{38} - \frac{6670085597515939905457337062655169700556449718502056049224935961970250608594918040515616921697096346935976924801620}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{37} + \frac{3464246680796801264295832374580206498432748373883371208563907661282610463563174038599978290999117599883910407307966}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{36} + \frac{3766448580664589198582578332611042257882255182116974808358897140305911072811731143494793453462903589185585749521489}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{35} - \frac{10570034285571127699071101461749301230635350089975967043021977039197329204216922236345356352439562335374552691717767}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{34} + \frac{7901935916163406380583850528044310761436064205552264813774262825415256813840704655240405981336405501306268364151841}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{33} - \frac{5148171628935247596966091595103411284510280250887025863995144708441779552984491392327411784365354850985897006644465}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{32} + \frac{12367684481251877942809789573090885747010692039931499837070167380620622156680191767349269845670931247685350406144781}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{31} - \frac{5165670302138197072937087576486088581216324461627257344681581588524662034542570492592123164836583986747522574183659}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{30} + \frac{5626425400161307063275318202300913487215192938718001992136003674471542512719712867323812218085894582423490643158609}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{29} + \frac{6645014158384829398994544836078608308494279206118183052206268237552884086015034941938289311462480843234084467179571}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{28} + \frac{4819802495231464079298366985566819395951343708560402142305719636248584666687763084948386029996311919959045136123677}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{27} - \frac{2350758899460435256209293062384267873124498013489344873194463426228002879097038717839134081400656189518953242183401}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{26} - \frac{12290688661072850157224857158239580982992963979527956382249595248992294839215261813223986192741163592033254101125769}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{25} - \frac{8674115524684609876939546757666880118464319309105625028795302182264838960563863478065283287026719229628904364563016}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{24} - \frac{6816162081699905869185752623925479759490159547807133765281243949074108282649869767227264817312016358319018377262122}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{23} + \frac{11629133140924162580183162639303784777856427871405540210363561952652357314900081710760538372777072862832651578687116}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{22} + \frac{4522408454104344749762589216614319956177324269700836195626495572366698283458662077044473907258368800509144853504194}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{21} + \frac{9348888956059297673814764078923111616964350847388229992425119736458660267142507444000101331776295052753644203368133}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{20} - \frac{4346861268371643311816292442481208718616834760771741162922669545722910867772948019275385952366566325071357694092330}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{19} + \frac{7380038390616402663536991637036272297377343077772013750363487553741989884258862333249702985780137026054599561949532}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{18} - \frac{4658496947404215085980155951103033736046176162642958089502850036826698965513348763195089624189540481112373868483344}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{17} - \frac{9642605459304074308325843604227787187185934587551490764856290323918722179992068241872148830569442952318904282670871}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{16} - \frac{12030710132680475237099995354850090789227065077583491674596808983759110434878724294429268434558379127178550121596419}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{15} + \frac{39259286402393082943771144697346194577031088451912035684403965007907119589193656669988732163633774837900182937191}{88476316263304991957748447273590176766265913472529363220219422001156496478892798965150701619700920494743092204937} a^{14} + \frac{7704968478148256349120327117470820771092439935297848972400797567099689538464630613713776223943611379179593919586385}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{13} - \frac{2133046531339114726182460085741542691730416500567159759354572320811421348444827928997194814749414184975344013321429}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{12} + \frac{4067389760118494919806247527848767173275668162235234045017174468920294797845492359328152743964008642372785344030955}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{11} - \frac{10672998828510174784041999189474642209223249271227050959374578980523256558033335872271968456120553389299704639248027}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{10} - \frac{8407856333458473654478337739470540319289675361553888565560569826784571616385820140523269816586323878438818459373638}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{9} - \frac{1406446119515758547687138651342501582497229267678235232199796049739444726281491256614032802601851140905475261247631}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{8} - \frac{7613026522287639003774334553943521691556632325591026543753747771117005991496354864174776117445110855570614801628480}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{7} + \frac{7547914970346674982455993927004607561296028432557019933976384666131291658390992673283900092941509839469678967406971}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{6} - \frac{11772650333501022050537931055518391046961353132451579807523628918110213983083861799351910910530298215321256038130655}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{5} - \frac{3647114217391861679113950067450651550597059300759151377007690103604333219038021571713384348676580326730265819353797}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{4} - \frac{6603179347924816636298102866672210689209563421841111615697271701442204414846887261272345119808310471411757280772123}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{3} - \frac{12087744026559249888922401396386570044165975448644108333985461422098114001677447933834825370303132537180578998087427}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{2} + \frac{5977272600465465159145598513208232959866880058279375255120998778165178840426820355153069480881945613774211836155667}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a + \frac{3040574339133240143200896024666498529324032587831916929591302761003527477658279915409543416798927584727995706585582}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171}$

Class group and class number

Not computed

Unit group

Rank:		$22$
Torsion generator:		\( -\frac{1883040814029630244679943272706235989005431219520364897048425778957039833013321309404711222732922045934066432002768}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{45} + \frac{1824628674831323044372084180800238627115401900077849444660438415494477173691195510005547987454369241598477555794731}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{44} - \frac{43220826734530982719479801308764784783671486669861996568244809674230234561977572964412781858052294154970339379314233}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{43} + \frac{36284655659585346544532888840227933895324435870383502646026466370483689198007539050073712871486705556054264030809864}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{42} - \frac{553623323290492382700115768027127086548932623787819793180960972219541767438431975852512315800000170051196352839885761}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{41} + \frac{418977002440622145206126784091865927930974753485709783806383917578444310033437105978090822491439280022429708052112609}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{40} - \frac{4856370542503996927057854410321712583564989420730689215088110123487243433987489389665947719072806278272422558028381616}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{39} + \frac{3307678836980921162506038348131977210313361206067511298534759419958988596131142128665695360738238891122222558631222008}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{38} - \frac{32193988989444813914180793491970864324996209952123785881806734573186843759493196920784775703540442766388133672983473156}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{37} + \frac{19824965302688000423766714288547248129588581541445714554033106713319937893856314238469585916451111064697538251748354193}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{36} - \frac{168517263460109400053064551949951542581222844427115504032109024664223885910882342271361240019703816215002815657102614182}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{35} + \frac{93436963384523123836376828116565080134680844358053803984889172914795524168151703497976882712991494301022259577429927493}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{34} - \frac{716655844387272373181628527765793020093598543191607239858687061320512352205048380549340355836118234351176444949155739345}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{33} + \frac{356989516436748512041743811492180155053119257242455810017821620325248861802860267325453299116757882256737466797883808709}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{32} - \frac{2513769599357696195648105804095226041616062379095866428621330096371739159361536293332778094784166620985354340531867381215}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{31} + \frac{1116972079121989183908375269797458675145018678878499278587312733110132051869489236876029996364512498227928710850506979161}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{30} - \frac{7345073796254131253710687146695454477163869061233221956063351075477630041348099450246128759910582157069973130065474210383}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{29} + \frac{2892891001699720480804670715686252122331097868616696671858048843295125586550230410295071309889557283819069925014439777289}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{28} - \frac{17946245257280705515934800716795854395957959590578852420909569622476859805380185980123663672058490244008844219231147413651}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{27} + \frac{6195711631260202492935180893628906573928683093898234837529110713187665653362925655025635693987869444594019614701916796252}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{26} - \frac{36704110073610631631824312197283047893833896878718459250471377041667425857211291818026960351736035109957138945351348074035}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{25} + \frac{10988585320474621016443197728400813085908168608981057716170007065576378310787078420440174004918543223346136477608683953489}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{24} - \frac{62630498526103804038350289405206389197328028476263506750067945621125776986742235164507776159255824234639809537681502581706}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{23} + \frac{15976207408534985708052360311756629601944529710981912350929577160599471441628904914609901275579551782056845019518664380197}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{22} - \frac{88676547076157417256084185734072729677531211575371824992471906153421865002624323085115013769991889364410030862924835529944}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{21} + \frac{18947630998890235968731522776324269047394093252190245327614085160486434638131465568931472100007721348582127910670044556820}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{20} - \frac{103136708990864783334320450772798457303477939351248638160199059304010512671236588503191848106304405041543556719487423195799}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{19} + \frac{17903278987550046184021632850168135128220881705746661448556550988097490606903537794701744497230656701385942180474126199243}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{18} - \frac{97319623885511350971251554558719755658809333414405540687614565510835546886663725693535476308802262427338323378899047084070}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{17} + \frac{13355210569731197370062865168444662502522859672101940565783050514635639209566960304553696071488847539607065745336669437522}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{16} - \frac{73089419295774556306202848358453562972686999468889369807080198049817860176633281516742798864235923387291552823004972839416}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{15} + \frac{26210609632548199858458605565558487980475845887179146246432923795840001714714727598314604388415415250538616417661970316}{88476316263304991957748447273590176766265913472529363220219422001156496478892798965150701619700920494743092204937} a^{14} - \frac{42731168216591129035481749089816150950771781103166839059674415559544164901830292309732966007264744389507539234618103285501}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{13} + \frac{3073214499655047431473366586507616235609658518039010484307677961231675956954522282433651821185146188206783122794231018965}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{12} - \frac{18771639502056197141605123114558786172762700481177715340860011057442115544429142031893623144699006854827379611687787286727}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{11} + \frac{741298601499673067953511786693166121430816104478687508664018843322695190475397422800293643875007141737405364729636521697}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{10} - \frac{5960454747109147346558707555033200693253603290374759043074401853257579268657677782017636968277676209470517930464888473125}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{9} + \frac{129190488941455819966973729144912511553444366326103490027297533988600394862435645845987100281435194939027427814980251975}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{8} - \frac{1269159016771499583099077507492866057655726055285256076329959322114803777418915699254388293863648603551619324378719081911}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{7} - \frac{20828841976164339615559271070374920107274245171953141099392291620891718278291253459043756029546640546206653957391906039}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{6} - \frac{168431941831548007344522111275240208844911210411774850368722641558307140091221491215152819520369032188885799591822864832}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{5} - \frac{437041170901170118807137404738207706805383457980754497759381304847034947090952703904878799692708451313199954232107583}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{4} - \frac{11097342029002773235834040199500738847717337357763267790242242206296581222584127883584349175721065702680480732292357949}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{3} - \frac{1188353763755349164461431746816254645805089367802707918896795522691768183317326642416463861589203078825604637362059523}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a^{2} - \frac{298624593793476125007335286253652634798157416138763753295095791870716335364148823366916470081655422176969098844811925}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} a + \frac{16645283599590884077989669197321707257842696195691150679332294834894721662993313463019095182776500723803702391065108}{25038797502515312724042810578426020024853253512725809791322096426327288503526662107137648558375360500012295093997171} \) (order $6$)
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

\(\Q(\sqrt{-3}) \), \(\Q(\zeta_{47})^+\)

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	$46$	$23^{2}$	$46$	$23^{2}$	$46$	$23^{2}$	$46$	$46$	$23^{2}$	$23^{2}$	$46$	$23^{2}$	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	Data not computed
47	Data not computed