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Properties

Modulus 4620846208
Structure C2×C2×C5472C_{2}\times C_{2}\times C_{5472}
Order 2188821888

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Show commands: PariGP / SageMath

sage: H = DirichletGroup(46208)
 
pari: g = idealstar(,46208,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 21888
sage: H.invariants()
 
pari: g.cyc
 
Structure = C2×C2×C5472C_{2}\times C_{2}\times C_{5472}
sage: H.gens()
 
pari: g.gen
 
Generators = χ46208(28159,⋅)\chi_{46208}(28159,\cdot), χ46208(36101,⋅)\chi_{46208}(36101,\cdot), χ46208(14081,⋅)\chi_{46208}(14081,\cdot)

First 32 of 21888 characters

Each row describes a character. When available, the columns show the orbit label, order of the character, whether the character is primitive, and several values of the character.

Character Orbit Order Primitive −1-1 11 33 55 77 99 1111 1313 1515 1717 2121 2323
χ46208(1,⋅)\chi_{46208}(1,\cdot) 46208.a 1 no 11 11 11 11 11 11 11 11 11 11 11 11
χ46208(3,⋅)\chi_{46208}(3,\cdot) 46208.fm 5472 yes 11 11 e(15075472)e\left(\frac{1507}{5472}\right) e(21135472)e\left(\frac{2113}{5472}\right) e(367912)e\left(\frac{367}{912}\right) e(15072736)e\left(\frac{1507}{2736}\right) e(16871824)e\left(\frac{1687}{1824}\right) e(6715472)e\left(\frac{671}{5472}\right) e(9051368)e\left(\frac{905}{1368}\right) e(6551368)e\left(\frac{655}{1368}\right) e(37095472)e\left(\frac{3709}{5472}\right) e(4152736)e\left(\frac{415}{2736}\right)
χ46208(5,⋅)\chi_{46208}(5,\cdot) 46208.fl 5472 yes 11 11 e(21135472)e\left(\frac{2113}{5472}\right) e(22515472)e\left(\frac{2251}{5472}\right) e(61912)e\left(\frac{61}{912}\right) e(21132736)e\left(\frac{2113}{2736}\right) e(15491824)e\left(\frac{1549}{1824}\right) e(35575472)e\left(\frac{3557}{5472}\right) e(10911368)e\left(\frac{1091}{1368}\right) e(2531368)e\left(\frac{253}{1368}\right) e(24795472)e\left(\frac{2479}{5472}\right) e(13092736)e\left(\frac{1309}{2736}\right)
χ46208(7,⋅)\chi_{46208}(7,\cdot) 46208.eu 912 no −1-1 11 e(367912)e\left(\frac{367}{912}\right) e(61912)e\left(\frac{61}{912}\right) e(63152)e\left(\frac{63}{152}\right) e(367456)e\left(\frac{367}{456}\right) e(243304)e\left(\frac{243}{304}\right) e(899912)e\left(\frac{899}{912}\right) e(107228)e\left(\frac{107}{228}\right) e(199228)e\left(\frac{199}{228}\right) e(745912)e\left(\frac{745}{912}\right) e(415456)e\left(\frac{415}{456}\right)
χ46208(9,⋅)\chi_{46208}(9,\cdot) 46208.fh 2736 no 11 11 e(15072736)e\left(\frac{1507}{2736}\right) e(21132736)e\left(\frac{2113}{2736}\right) e(367456)e\left(\frac{367}{456}\right) e(1391368)e\left(\frac{139}{1368}\right) e(775912)e\left(\frac{775}{912}\right) e(6712736)e\left(\frac{671}{2736}\right) e(221684)e\left(\frac{221}{684}\right) e(655684)e\left(\frac{655}{684}\right) e(9732736)e\left(\frac{973}{2736}\right) e(4151368)e\left(\frac{415}{1368}\right)
χ46208(11,⋅)\chi_{46208}(11,\cdot) 46208.ff 1824 yes −1-1 11 e(16871824)e\left(\frac{1687}{1824}\right) e(15491824)e\left(\frac{1549}{1824}\right) e(243304)e\left(\frac{243}{304}\right) e(775912)e\left(\frac{775}{912}\right) e(427608)e\left(\frac{427}{608}\right) e(17631824)e\left(\frac{1763}{1824}\right) e(353456)e\left(\frac{353}{456}\right) e(355456)e\left(\frac{355}{456}\right) e(13211824)e\left(\frac{1321}{1824}\right) e(211912)e\left(\frac{211}{912}\right)
χ46208(13,⋅)\chi_{46208}(13,\cdot) 46208.fn 5472 yes −1-1 11 e(6715472)e\left(\frac{671}{5472}\right) e(35575472)e\left(\frac{3557}{5472}\right) e(899912)e\left(\frac{899}{912}\right) e(6712736)e\left(\frac{671}{2736}\right) e(17631824)e\left(\frac{1763}{1824}\right) e(28755472)e\left(\frac{2875}{5472}\right) e(10571368)e\left(\frac{1057}{1368}\right) e(7311368)e\left(\frac{731}{1368}\right) e(5935472)e\left(\frac{593}{5472}\right) e(352736)e\left(\frac{35}{2736}\right)
χ46208(15,⋅)\chi_{46208}(15,\cdot) 46208.fa 1368 no 11 11 e(9051368)e\left(\frac{905}{1368}\right) e(10911368)e\left(\frac{1091}{1368}\right) e(107228)e\left(\frac{107}{228}\right) e(221684)e\left(\frac{221}{684}\right) e(353456)e\left(\frac{353}{456}\right) e(10571368)e\left(\frac{1057}{1368}\right) e(157342)e\left(\frac{157}{342}\right) e(227342)e\left(\frac{227}{342}\right) e(1791368)e\left(\frac{179}{1368}\right) e(431684)e\left(\frac{431}{684}\right)
χ46208(17,⋅)\chi_{46208}(17,\cdot) 46208.fb 1368 no 11 11 e(6551368)e\left(\frac{655}{1368}\right) e(2531368)e\left(\frac{253}{1368}\right) e(199228)e\left(\frac{199}{228}\right) e(655684)e\left(\frac{655}{684}\right) e(355456)e\left(\frac{355}{456}\right) e(7311368)e\left(\frac{731}{1368}\right) e(227342)e\left(\frac{227}{342}\right) e(289342)e\left(\frac{289}{342}\right) e(4811368)e\left(\frac{481}{1368}\right) e(499684)e\left(\frac{499}{684}\right)
χ46208(21,⋅)\chi_{46208}(21,\cdot) 46208.fn 5472 yes −1-1 11 e(37095472)e\left(\frac{3709}{5472}\right) e(24795472)e\left(\frac{2479}{5472}\right) e(745912)e\left(\frac{745}{912}\right) e(9732736)e\left(\frac{973}{2736}\right) e(13211824)e\left(\frac{1321}{1824}\right) e(5935472)e\left(\frac{593}{5472}\right) e(1791368)e\left(\frac{179}{1368}\right) e(4811368)e\left(\frac{481}{1368}\right) e(27075472)e\left(\frac{2707}{5472}\right) e(1692736)e\left(\frac{169}{2736}\right)
χ46208(23,⋅)\chi_{46208}(23,\cdot) 46208.fj 2736 no −1-1 11 e(4152736)e\left(\frac{415}{2736}\right) e(13092736)e\left(\frac{1309}{2736}\right) e(415456)e\left(\frac{415}{456}\right) e(4151368)e\left(\frac{415}{1368}\right) e(211912)e\left(\frac{211}{912}\right) e(352736)e\left(\frac{35}{2736}\right) e(431684)e\left(\frac{431}{684}\right) e(499684)e\left(\frac{499}{684}\right) e(1692736)e\left(\frac{169}{2736}\right) e(13031368)e\left(\frac{1303}{1368}\right)
χ46208(25,⋅)\chi_{46208}(25,\cdot) 46208.fh 2736 no 11 11 e(21132736)e\left(\frac{2113}{2736}\right) e(22512736)e\left(\frac{2251}{2736}\right) e(61456)e\left(\frac{61}{456}\right) e(7451368)e\left(\frac{745}{1368}\right) e(637912)e\left(\frac{637}{912}\right) e(8212736)e\left(\frac{821}{2736}\right) e(407684)e\left(\frac{407}{684}\right) e(253684)e\left(\frac{253}{684}\right) e(24792736)e\left(\frac{2479}{2736}\right) e(13091368)e\left(\frac{1309}{1368}\right)
χ46208(27,⋅)\chi_{46208}(27,\cdot) 46208.fe 1824 yes 11 11 e(15071824)e\left(\frac{1507}{1824}\right) e(2891824)e\left(\frac{289}{1824}\right) e(63304)e\left(\frac{63}{304}\right) e(595912)e\left(\frac{595}{912}\right) e(471608)e\left(\frac{471}{608}\right) e(6711824)e\left(\frac{671}{1824}\right) e(449456)e\left(\frac{449}{456}\right) e(199456)e\left(\frac{199}{456}\right) e(611824)e\left(\frac{61}{1824}\right) e(415912)e\left(\frac{415}{912}\right)
χ46208(29,⋅)\chi_{46208}(29,\cdot) 46208.fn 5472 yes −1-1 11 e(24115472)e\left(\frac{2411}{5472}\right) e(20575472)e\left(\frac{2057}{5472}\right) e(815912)e\left(\frac{815}{912}\right) e(24112736)e\left(\frac{2411}{2736}\right) e(14391824)e\left(\frac{1439}{1824}\right) e(555472)e\left(\frac{55}{5472}\right) e(11171368)e\left(\frac{1117}{1368}\right) e(11751368)e\left(\frac{1175}{1368}\right) e(18295472)e\left(\frac{1829}{5472}\right) e(1912736)e\left(\frac{191}{2736}\right)
χ46208(31,⋅)\chi_{46208}(31,\cdot) 46208.dq 228 no 11 11 e(91228)e\left(\frac{91}{228}\right) e(181228)e\left(\frac{181}{228}\right) e(1719)e\left(\frac{17}{19}\right) e(91114)e\left(\frac{91}{114}\right) e(976)e\left(\frac{9}{76}\right) e(53228)e\left(\frac{53}{228}\right) e(1157)e\left(\frac{11}{57}\right) e(1357)e\left(\frac{13}{57}\right) e(67228)e\left(\frac{67}{228}\right) e(2057)e\left(\frac{20}{57}\right)
χ46208(33,⋅)\chi_{46208}(33,\cdot) 46208.eq 684 no −1-1 11 e(137684)e\left(\frac{137}{684}\right) e(161684)e\left(\frac{161}{684}\right) e(23114)e\left(\frac{23}{114}\right) e(137342)e\left(\frac{137}{342}\right) e(143228)e\left(\frac{143}{228}\right) e(61684)e\left(\frac{61}{684}\right) e(149342)e\left(\frac{149}{342}\right) e(44171)e\left(\frac{44}{171}\right) e(275684)e\left(\frac{275}{684}\right) e(131342)e\left(\frac{131}{342}\right)
χ46208(35,⋅)\chi_{46208}(35,\cdot) 46208.fk 5472 yes −1-1 11 e(43155472)e\left(\frac{4315}{5472}\right) e(26175472)e\left(\frac{2617}{5472}\right) e(439912)e\left(\frac{439}{912}\right) e(15792736)e\left(\frac{1579}{2736}\right) e(11831824)e\left(\frac{1183}{1824}\right) e(34795472)e\left(\frac{3479}{5472}\right) e(3651368)e\left(\frac{365}{1368}\right) e(791368)e\left(\frac{79}{1368}\right) e(14775472)e\left(\frac{1477}{5472}\right) e(10632736)e\left(\frac{1063}{2736}\right)
χ46208(37,⋅)\chi_{46208}(37,\cdot) 46208.eo 608 yes −1-1 11 e(385608)e\left(\frac{385}{608}\right) e(187608)e\left(\frac{187}{608}\right) e(167304)e\left(\frac{167}{304}\right) e(81304)e\left(\frac{81}{304}\right) e(503608)e\left(\frac{503}{608}\right) e(5608)e\left(\frac{5}{608}\right) e(143152)e\left(\frac{143}{152}\right) e(93152)e\left(\frac{93}{152}\right) e(111608)e\left(\frac{111}{608}\right) e(45304)e\left(\frac{45}{304}\right)
χ46208(39,⋅)\chi_{46208}(39,\cdot) 46208.dy 304 no −1-1 11 e(121304)e\left(\frac{121}{304}\right) e(11304)e\left(\frac{11}{304}\right) e(59152)e\left(\frac{59}{152}\right) e(121152)e\left(\frac{121}{152}\right) e(271304)e\left(\frac{271}{304}\right) e(197304)e\left(\frac{197}{304}\right) e(3376)e\left(\frac{33}{76}\right) e(176)e\left(\frac{1}{76}\right) e(239304)e\left(\frac{239}{304}\right) e(25152)e\left(\frac{25}{152}\right)
χ46208(41,⋅)\chi_{46208}(41,\cdot) 46208.fi 2736 no −1-1 11 e(1192736)e\left(\frac{119}{2736}\right) e(10612736)e\left(\frac{1061}{2736}\right) e(347456)e\left(\frac{347}{456}\right) e(1191368)e\left(\frac{119}{1368}\right) e(611912)e\left(\frac{611}{912}\right) e(14112736)e\left(\frac{1411}{2736}\right) e(295684)e\left(\frac{295}{684}\right) e(359684)e\left(\frac{359}{684}\right) e(22012736)e\left(\frac{2201}{2736}\right) e(9951368)e\left(\frac{995}{1368}\right)
χ46208(43,⋅)\chi_{46208}(43,\cdot) 46208.fk 5472 yes −1-1 11 e(19335472)e\left(\frac{1933}{5472}\right) e(9915472)e\left(\frac{991}{5472}\right) e(337912)e\left(\frac{337}{912}\right) e(19332736)e\left(\frac{1933}{2736}\right) e(731824)e\left(\frac{73}{1824}\right) e(33775472)e\left(\frac{3377}{5472}\right) e(7311368)e\left(\frac{731}{1368}\right) e(10091368)e\left(\frac{1009}{1368}\right) e(39555472)e\left(\frac{3955}{5472}\right) e(10572736)e\left(\frac{1057}{2736}\right)
χ46208(45,⋅)\chi_{46208}(45,\cdot) 46208.fd 1824 yes 11 11 e(17091824)e\left(\frac{1709}{1824}\right) e(3351824)e\left(\frac{335}{1824}\right) e(265304)e\left(\frac{265}{304}\right) e(797912)e\left(\frac{797}{912}\right) e(425608)e\left(\frac{425}{608}\right) e(16331824)e\left(\frac{1633}{1824}\right) e(55456)e\left(\frac{55}{456}\right) e(65456)e\left(\frac{65}{456}\right) e(14751824)e\left(\frac{1475}{1824}\right) e(713912)e\left(\frac{713}{912}\right)
χ46208(47,⋅)\chi_{46208}(47,\cdot) 46208.ez 1368 no −1-1 11 e(2631368)e\left(\frac{263}{1368}\right) e(171368)e\left(\frac{17}{1368}\right) e(149228)e\left(\frac{149}{228}\right) e(263684)e\left(\frac{263}{684}\right) e(59456)e\left(\frac{59}{456}\right) e(8711368)e\left(\frac{871}{1368}\right) e(35171)e\left(\frac{35}{171}\right) e(233342)e\left(\frac{233}{342}\right) e(11571368)e\left(\frac{1157}{1368}\right) e(581684)e\left(\frac{581}{684}\right)
χ46208(49,⋅)\chi_{46208}(49,\cdot) 46208.ej 456 no 11 11 e(367456)e\left(\frac{367}{456}\right) e(61456)e\left(\frac{61}{456}\right) e(6376)e\left(\frac{63}{76}\right) e(139228)e\left(\frac{139}{228}\right) e(91152)e\left(\frac{91}{152}\right) e(443456)e\left(\frac{443}{456}\right) e(107114)e\left(\frac{107}{114}\right) e(85114)e\left(\frac{85}{114}\right) e(289456)e\left(\frac{289}{456}\right) e(187228)e\left(\frac{187}{228}\right)
χ46208(51,⋅)\chi_{46208}(51,\cdot) 46208.fm 5472 yes 11 11 e(41275472)e\left(\frac{4127}{5472}\right) e(31255472)e\left(\frac{3125}{5472}\right) e(251912)e\left(\frac{251}{912}\right) e(13912736)e\left(\frac{1391}{2736}\right) e(12831824)e\left(\frac{1283}{1824}\right) e(35955472)e\left(\frac{3595}{5472}\right) e(4451368)e\left(\frac{445}{1368}\right) e(4431368)e\left(\frac{443}{1368}\right) e(1615472)e\left(\frac{161}{5472}\right) e(24112736)e\left(\frac{2411}{2736}\right)
χ46208(53,⋅)\chi_{46208}(53,\cdot) 46208.fn 5472 yes −1-1 11 e(11095472)e\left(\frac{1109}{5472}\right) e(25195472)e\left(\frac{2519}{5472}\right) e(881912)e\left(\frac{881}{912}\right) e(11092736)e\left(\frac{1109}{2736}\right) e(651824)e\left(\frac{65}{1824}\right) e(10335472)e\left(\frac{1033}{5472}\right) e(9071368)e\left(\frac{907}{1368}\right) e(3051368)e\left(\frac{305}{1368}\right) e(9235472)e\left(\frac{923}{5472}\right) e(16972736)e\left(\frac{1697}{2736}\right)
χ46208(55,⋅)\chi_{46208}(55,\cdot) 46208.fj 2736 no −1-1 11 e(8512736)e\left(\frac{851}{2736}\right) e(7132736)e\left(\frac{713}{2736}\right) e(395456)e\left(\frac{395}{456}\right) e(8511368)e\left(\frac{851}{1368}\right) e(503912)e\left(\frac{503}{912}\right) e(16872736)e\left(\frac{1687}{2736}\right) e(391684)e\left(\frac{391}{684}\right) e(659684)e\left(\frac{659}{684}\right) e(4852736)e\left(\frac{485}{2736}\right) e(9711368)e\left(\frac{971}{1368}\right)
χ46208(59,⋅)\chi_{46208}(59,\cdot) 46208.fm 5472 yes 11 11 e(36015472)e\left(\frac{3601}{5472}\right) e(17235472)e\left(\frac{1723}{5472}\right) e(181912)e\left(\frac{181}{912}\right) e(8652736)e\left(\frac{865}{2736}\right) e(11651824)e\left(\frac{1165}{1824}\right) e(4855472)e\left(\frac{485}{5472}\right) e(13311368)e\left(\frac{1331}{1368}\right) e(6611368)e\left(\frac{661}{1368}\right) e(46875472)e\left(\frac{4687}{5472}\right) e(5652736)e\left(\frac{565}{2736}\right)
χ46208(61,⋅)\chi_{46208}(61,\cdot) 46208.fl 5472 yes 11 11 e(9475472)e\left(\frac{947}{5472}\right) e(175472)e\left(\frac{17}{5472}\right) e(263912)e\left(\frac{263}{912}\right) e(9472736)e\left(\frac{947}{2736}\right) e(16551824)e\left(\frac{1655}{1824}\right) e(22395472)e\left(\frac{2239}{5472}\right) e(2411368)e\left(\frac{241}{1368}\right) e(5751368)e\left(\frac{575}{1368}\right) e(25255472)e\left(\frac{2525}{5472}\right) e(16072736)e\left(\frac{1607}{2736}\right)
χ46208(63,⋅)\chi_{46208}(63,\cdot) 46208.ee 342 no −1-1 11 e(163171)e\left(\frac{163}{171}\right) e(287342)e\left(\frac{287}{342}\right) e(25114)e\left(\frac{25}{114}\right) e(155171)e\left(\frac{155}{171}\right) e(3757)e\left(\frac{37}{57}\right) e(79342)e\left(\frac{79}{342}\right) e(271342)e\left(\frac{271}{342}\right) e(142171)e\left(\frac{142}{171}\right) e(59342)e\left(\frac{59}{342}\right) e(73342)e\left(\frac{73}{342}\right)
χ46208(65,⋅)\chi_{46208}(65,\cdot) 46208.dd 114 no −1-1 11 e(2957)e\left(\frac{29}{57}\right) e(7114)e\left(\frac{7}{114}\right) e(119)e\left(\frac{1}{19}\right) e(157)e\left(\frac{1}{57}\right) e(3138)e\left(\frac{31}{38}\right) e(1057)e\left(\frac{10}{57}\right) e(65114)e\left(\frac{65}{114}\right) e(4157)e\left(\frac{41}{57}\right) e(3257)e\left(\frac{32}{57}\right) e(2857)e\left(\frac{28}{57}\right)
χ46208(67,⋅)\chi_{46208}(67,\cdot) 46208.fm 5472 yes 11 11 e(33475472)e\left(\frac{3347}{5472}\right) e(4015472)e\left(\frac{401}{5472}\right) e(383912)e\left(\frac{383}{912}\right) e(6112736)e\left(\frac{611}{2736}\right) e(3591824)e\left(\frac{359}{1824}\right) e(37275472)e\left(\frac{3727}{5472}\right) e(9371368)e\left(\frac{937}{1368}\right) e(5271368)e\left(\frac{527}{1368}\right) e(1735472)e\left(\frac{173}{5472}\right) e(17752736)e\left(\frac{1775}{2736}\right)
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