Properties

Modulus 2890028900
Structure C2×C4×C1360C_{2}\times C_{4}\times C_{1360}
Order 1088010880

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Show commands: PariGP / SageMath

sage: H = DirichletGroup(28900)
 
pari: g = idealstar(,28900,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 10880
sage: H.invariants()
 
pari: g.cyc
 
Structure = C2×C4×C1360C_{2}\times C_{4}\times C_{1360}
sage: H.gens()
 
pari: g.gen
 
Generators = χ28900(14451,)\chi_{28900}(14451,\cdot), χ28900(24277,)\chi_{28900}(24277,\cdot), χ28900(23701,)\chi_{28900}(23701,\cdot)

First 32 of 10880 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 77 99 1111 1313 1919 2121 2323 2727 2929
χ28900(1,)\chi_{28900}(1,\cdot) 28900.a 1 no 11 11 11 11 11 11 11 11 11 11 11 11
χ28900(3,)\chi_{28900}(3,\cdot) 28900.fg 1360 yes 1-1 11 e(12971360)e\left(\frac{1297}{1360}\right) e(223272)e\left(\frac{223}{272}\right) e(617680)e\left(\frac{617}{680}\right) e(2511360)e\left(\frac{251}{1360}\right) e(63170)e\left(\frac{63}{170}\right) e(579680)e\left(\frac{579}{680}\right) e(263340)e\left(\frac{263}{340}\right) e(2311360)e\left(\frac{231}{1360}\right) e(11711360)e\left(\frac{1171}{1360}\right) e(2171360)e\left(\frac{217}{1360}\right)
χ28900(7,)\chi_{28900}(7,\cdot) 28900.el 272 no 1-1 11 e(223272)e\left(\frac{223}{272}\right) e(21272)e\left(\frac{21}{272}\right) e(87136)e\left(\frac{87}{136}\right) e(165272)e\left(\frac{165}{272}\right) e(1534)e\left(\frac{15}{34}\right) e(133136)e\left(\frac{133}{136}\right) e(6168)e\left(\frac{61}{68}\right) e(89272)e\left(\frac{89}{272}\right) e(125272)e\left(\frac{125}{272}\right) e(199272)e\left(\frac{199}{272}\right)
χ28900(9,)\chi_{28900}(9,\cdot) 28900.ff 680 no 11 11 e(617680)e\left(\frac{617}{680}\right) e(87136)e\left(\frac{87}{136}\right) e(277340)e\left(\frac{277}{340}\right) e(251680)e\left(\frac{251}{680}\right) e(6385)e\left(\frac{63}{85}\right) e(239340)e\left(\frac{239}{340}\right) e(93170)e\left(\frac{93}{170}\right) e(231680)e\left(\frac{231}{680}\right) e(491680)e\left(\frac{491}{680}\right) e(217680)e\left(\frac{217}{680}\right)
χ28900(11,)\chi_{28900}(11,\cdot) 28900.fj 1360 yes 11 11 e(2511360)e\left(\frac{251}{1360}\right) e(165272)e\left(\frac{165}{272}\right) e(251680)e\left(\frac{251}{680}\right) e(3331360)e\left(\frac{333}{1360}\right) e(263340)e\left(\frac{263}{340}\right) e(57680)e\left(\frac{57}{680}\right) e(269340)e\left(\frac{269}{340}\right) e(2131360)e\left(\frac{213}{1360}\right) e(7531360)e\left(\frac{753}{1360}\right) e(2311360)e\left(\frac{231}{1360}\right)
χ28900(13,)\chi_{28900}(13,\cdot) 28900.en 340 no 1-1 11 e(63170)e\left(\frac{63}{170}\right) e(1534)e\left(\frac{15}{34}\right) e(6385)e\left(\frac{63}{85}\right) e(263340)e\left(\frac{263}{340}\right) e(97340)e\left(\frac{97}{340}\right) e(1685)e\left(\frac{16}{85}\right) e(6985)e\left(\frac{69}{85}\right) e(1285)e\left(\frac{12}{85}\right) e(19170)e\left(\frac{19}{170}\right) e(331340)e\left(\frac{331}{340}\right)
χ28900(19,)\chi_{28900}(19,\cdot) 28900.fe 680 yes 1-1 11 e(579680)e\left(\frac{579}{680}\right) e(133136)e\left(\frac{133}{136}\right) e(239340)e\left(\frac{239}{340}\right) e(57680)e\left(\frac{57}{680}\right) e(1685)e\left(\frac{16}{85}\right) e(143340)e\left(\frac{143}{340}\right) e(141170)e\left(\frac{141}{170}\right) e(597680)e\left(\frac{597}{680}\right) e(377680)e\left(\frac{377}{680}\right) e(159680)e\left(\frac{159}{680}\right)
χ28900(21,)\chi_{28900}(21,\cdot) 28900.es 340 no 11 11 e(263340)e\left(\frac{263}{340}\right) e(6168)e\left(\frac{61}{68}\right) e(93170)e\left(\frac{93}{170}\right) e(269340)e\left(\frac{269}{340}\right) e(6985)e\left(\frac{69}{85}\right) e(141170)e\left(\frac{141}{170}\right) e(5785)e\left(\frac{57}{85}\right) e(169340)e\left(\frac{169}{340}\right) e(109340)e\left(\frac{109}{340}\right) e(303340)e\left(\frac{303}{340}\right)
χ28900(23,)\chi_{28900}(23,\cdot) 28900.fn 1360 yes 1-1 11 e(2311360)e\left(\frac{231}{1360}\right) e(89272)e\left(\frac{89}{272}\right) e(231680)e\left(\frac{231}{680}\right) e(2131360)e\left(\frac{213}{1360}\right) e(1285)e\left(\frac{12}{85}\right) e(597680)e\left(\frac{597}{680}\right) e(169340)e\left(\frac{169}{340}\right) e(5131360)e\left(\frac{513}{1360}\right) e(6931360)e\left(\frac{693}{1360}\right) e(7911360)e\left(\frac{791}{1360}\right)
χ28900(27,)\chi_{28900}(27,\cdot) 28900.fg 1360 yes 1-1 11 e(11711360)e\left(\frac{1171}{1360}\right) e(125272)e\left(\frac{125}{272}\right) e(491680)e\left(\frac{491}{680}\right) e(7531360)e\left(\frac{753}{1360}\right) e(19170)e\left(\frac{19}{170}\right) e(377680)e\left(\frac{377}{680}\right) e(109340)e\left(\frac{109}{340}\right) e(6931360)e\left(\frac{693}{1360}\right) e(7931360)e\left(\frac{793}{1360}\right) e(6511360)e\left(\frac{651}{1360}\right)
χ28900(29,)\chi_{28900}(29,\cdot) 28900.fl 1360 no 1-1 11 e(2171360)e\left(\frac{217}{1360}\right) e(199272)e\left(\frac{199}{272}\right) e(217680)e\left(\frac{217}{680}\right) e(2311360)e\left(\frac{231}{1360}\right) e(331340)e\left(\frac{331}{340}\right) e(159680)e\left(\frac{159}{680}\right) e(303340)e\left(\frac{303}{340}\right) e(7911360)e\left(\frac{791}{1360}\right) e(6511360)e\left(\frac{651}{1360}\right) e(8771360)e\left(\frac{877}{1360}\right)
χ28900(31,)\chi_{28900}(31,\cdot) 28900.fj 1360 yes 11 11 e(4531360)e\left(\frac{453}{1360}\right) e(171272)e\left(\frac{171}{272}\right) e(453680)e\left(\frac{453}{680}\right) e(8991360)e\left(\frac{899}{1360}\right) e(29340)e\left(\frac{29}{340}\right) e(111680)e\left(\frac{111}{680}\right) e(327340)e\left(\frac{327}{340}\right) e(3791360)e\left(\frac{379}{1360}\right) e(13591360)e\left(\frac{1359}{1360}\right) e(12731360)e\left(\frac{1273}{1360}\right)
χ28900(33,)\chi_{28900}(33,\cdot) 28900.eo 340 no 1-1 11 e(47340)e\left(\frac{47}{340}\right) e(2968)e\left(\frac{29}{68}\right) e(47170)e\left(\frac{47}{170}\right) e(73170)e\left(\frac{73}{170}\right) e(49340)e\left(\frac{49}{340}\right) e(159170)e\left(\frac{159}{170}\right) e(4885)e\left(\frac{48}{85}\right) e(111340)e\left(\frac{111}{340}\right) e(141340)e\left(\frac{141}{340}\right) e(2885)e\left(\frac{28}{85}\right)
χ28900(37,)\chi_{28900}(37,\cdot) 28900.fm 1360 no 11 11 e(8491360)e\left(\frac{849}{1360}\right) e(207272)e\left(\frac{207}{272}\right) e(169680)e\left(\frac{169}{680}\right) e(1471360)e\left(\frac{147}{1360}\right) e(4385)e\left(\frac{43}{85}\right) e(503680)e\left(\frac{503}{680}\right) e(131340)e\left(\frac{131}{340}\right) e(9671360)e\left(\frac{967}{1360}\right) e(11871360)e\left(\frac{1187}{1360}\right) e(2491360)e\left(\frac{249}{1360}\right)
χ28900(39,)\chi_{28900}(39,\cdot) 28900.fk 1360 yes 11 11 e(4411360)e\left(\frac{441}{1360}\right) e(71272)e\left(\frac{71}{272}\right) e(441680)e\left(\frac{441}{680}\right) e(13031360)e\left(\frac{1303}{1360}\right) e(223340)e\left(\frac{223}{340}\right) e(27680)e\left(\frac{27}{680}\right) e(199340)e\left(\frac{199}{340}\right) e(4231360)e\left(\frac{423}{1360}\right) e(13231360)e\left(\frac{1323}{1360}\right) e(1811360)e\left(\frac{181}{1360}\right)
χ28900(41,)\chi_{28900}(41,\cdot) 28900.fi 1360 no 1-1 11 e(391360)e\left(\frac{39}{1360}\right) e(121272)e\left(\frac{121}{272}\right) e(39680)e\left(\frac{39}{680}\right) e(8971360)e\left(\frac{897}{1360}\right) e(7340)e\left(\frac{7}{340}\right) e(273680)e\left(\frac{273}{680}\right) e(161340)e\left(\frac{161}{340}\right) e(5371360)e\left(\frac{537}{1360}\right) e(1171360)e\left(\frac{117}{1360}\right) e(13391360)e\left(\frac{1339}{1360}\right)
χ28900(43,)\chi_{28900}(43,\cdot) 28900.dr 136 no 11 11 e(79136)e\left(\frac{79}{136}\right) e(5136)e\left(\frac{5}{136}\right) e(1168)e\left(\frac{11}{68}\right) e(83136)e\left(\frac{83}{136}\right) e(768)e\left(\frac{7}{68}\right) e(4368)e\left(\frac{43}{68}\right) e(2134)e\left(\frac{21}{34}\right) e(5136)e\left(\frac{5}{136}\right) e(101136)e\left(\frac{101}{136}\right) e(49136)e\left(\frac{49}{136}\right)
χ28900(47,)\chi_{28900}(47,\cdot) 28900.em 340 yes 11 11 e(139170)e\left(\frac{139}{170}\right) e(2534)e\left(\frac{25}{34}\right) e(5485)e\left(\frac{54}{85}\right) e(189340)e\left(\frac{189}{340}\right) e(71340)e\left(\frac{71}{340}\right) e(161170)e\left(\frac{161}{170}\right) e(4785)e\left(\frac{47}{85}\right) e(7185)e\left(\frac{71}{85}\right) e(77170)e\left(\frac{77}{170}\right) e(223340)e\left(\frac{223}{340}\right)
χ28900(49,)\chi_{28900}(49,\cdot) 28900.dp 136 no 11 11 e(87136)e\left(\frac{87}{136}\right) e(21136)e\left(\frac{21}{136}\right) e(1968)e\left(\frac{19}{68}\right) e(29136)e\left(\frac{29}{136}\right) e(1517)e\left(\frac{15}{17}\right) e(6568)e\left(\frac{65}{68}\right) e(2734)e\left(\frac{27}{34}\right) e(89136)e\left(\frac{89}{136}\right) e(125136)e\left(\frac{125}{136}\right) e(63136)e\left(\frac{63}{136}\right)
χ28900(53,)\chi_{28900}(53,\cdot) 28900.fa 680 no 1-1 11 e(141680)e\left(\frac{141}{680}\right) e(19136)e\left(\frac{19}{136}\right) e(141340)e\left(\frac{141}{340}\right) e(13680)e\left(\frac{13}{680}\right) e(31340)e\left(\frac{31}{340}\right) e(307340)e\left(\frac{307}{340}\right) e(59170)e\left(\frac{59}{170}\right) e(503680)e\left(\frac{503}{680}\right) e(423680)e\left(\frac{423}{680}\right) e(251680)e\left(\frac{251}{680}\right)
χ28900(57,)\chi_{28900}(57,\cdot) 28900.ek 272 no 11 11 e(219272)e\left(\frac{219}{272}\right) e(217272)e\left(\frac{217}{272}\right) e(83136)e\left(\frac{83}{136}\right) e(73272)e\left(\frac{73}{272}\right) e(1934)e\left(\frac{19}{34}\right) e(37136)e\left(\frac{37}{136}\right) e(4168)e\left(\frac{41}{68}\right) e(13272)e\left(\frac{13}{272}\right) e(113272)e\left(\frac{113}{272}\right) e(107272)e\left(\frac{107}{272}\right)
χ28900(59,)\chi_{28900}(59,\cdot) 28900.fe 680 yes 1-1 11 e(177680)e\left(\frac{177}{680}\right) e(47136)e\left(\frac{47}{136}\right) e(177340)e\left(\frac{177}{340}\right) e(331680)e\left(\frac{331}{680}\right) e(7885)e\left(\frac{78}{85}\right) e(49340)e\left(\frac{49}{340}\right) e(103170)e\left(\frac{103}{170}\right) e(31680)e\left(\frac{31}{680}\right) e(531680)e\left(\frac{531}{680}\right) e(637680)e\left(\frac{637}{680}\right)
χ28900(61,)\chi_{28900}(61,\cdot) 28900.fi 1360 no 1-1 11 e(7511360)e\left(\frac{751}{1360}\right) e(161272)e\left(\frac{161}{272}\right) e(71680)e\left(\frac{71}{680}\right) e(9531360)e\left(\frac{953}{1360}\right) e(283340)e\left(\frac{283}{340}\right) e(497680)e\left(\frac{497}{680}\right) e(49340)e\left(\frac{49}{340}\right) e(1931360)e\left(\frac{193}{1360}\right) e(8931360)e\left(\frac{893}{1360}\right) e(8511360)e\left(\frac{851}{1360}\right)
χ28900(63,)\chi_{28900}(63,\cdot) 28900.fg 1360 yes 1-1 11 e(9891360)e\left(\frac{989}{1360}\right) e(195272)e\left(\frac{195}{272}\right) e(309680)e\left(\frac{309}{680}\right) e(13271360)e\left(\frac{1327}{1360}\right) e(31170)e\left(\frac{31}{170}\right) e(463680)e\left(\frac{463}{680}\right) e(151340)e\left(\frac{151}{340}\right) e(9071360)e\left(\frac{907}{1360}\right) e(2471360)e\left(\frac{247}{1360}\right) e(691360)e\left(\frac{69}{1360}\right)
χ28900(67,)\chi_{28900}(67,\cdot) 28900.ev 340 yes 11 11 e(247340)e\left(\frac{247}{340}\right) e(4168)e\left(\frac{41}{68}\right) e(77170)e\left(\frac{77}{170}\right) e(3985)e\left(\frac{39}{85}\right) e(319340)e\left(\frac{319}{340}\right) e(5785)e\left(\frac{57}{85}\right) e(2885)e\left(\frac{28}{85}\right) e(171340)e\left(\frac{171}{340}\right) e(61340)e\left(\frac{61}{340}\right) e(7385)e\left(\frac{73}{85}\right)
χ28900(69,)\chi_{28900}(69,\cdot) 28900.ea 170 no 11 11 e(21170)e\left(\frac{21}{170}\right) e(534)e\left(\frac{5}{34}\right) e(2185)e\left(\frac{21}{85}\right) e(2985)e\left(\frac{29}{85}\right) e(87170)e\left(\frac{87}{170}\right) e(6285)e\left(\frac{62}{85}\right) e(2385)e\left(\frac{23}{85}\right) e(93170)e\left(\frac{93}{170}\right) e(63170)e\left(\frac{63}{170}\right) e(6385)e\left(\frac{63}{85}\right)
χ28900(71,)\chi_{28900}(71,\cdot) 28900.fj 1360 yes 11 11 e(8771360)e\left(\frac{877}{1360}\right) e(259272)e\left(\frac{259}{272}\right) e(197680)e\left(\frac{197}{680}\right) e(11311360)e\left(\frac{1131}{1360}\right) e(201340)e\left(\frac{201}{340}\right) e(359680)e\left(\frac{359}{680}\right) e(203340)e\left(\frac{203}{340}\right) e(10911360)e\left(\frac{1091}{1360}\right) e(12711360)e\left(\frac{1271}{1360}\right) e(4171360)e\left(\frac{417}{1360}\right)
χ28900(73,)\chi_{28900}(73,\cdot) 28900.fh 1360 no 11 11 e(6211360)e\left(\frac{621}{1360}\right) e(211272)e\left(\frac{211}{272}\right) e(621680)e\left(\frac{621}{680}\right) e(10231360)e\left(\frac{1023}{1360}\right) e(59170)e\left(\frac{59}{170}\right) e(267680)e\left(\frac{267}{680}\right) e(79340)e\left(\frac{79}{340}\right) e(4431360)e\left(\frac{443}{1360}\right) e(5031360)e\left(\frac{503}{1360}\right) e(12611360)e\left(\frac{1261}{1360}\right)
χ28900(77,)\chi_{28900}(77,\cdot) 28900.fa 680 no 1-1 11 e(3680)e\left(\frac{3}{680}\right) e(93136)e\left(\frac{93}{136}\right) e(3340)e\left(\frac{3}{340}\right) e(579680)e\left(\frac{579}{680}\right) e(73340)e\left(\frac{73}{340}\right) e(21340)e\left(\frac{21}{340}\right) e(117170)e\left(\frac{117}{170}\right) e(329680)e\left(\frac{329}{680}\right) e(9680)e\left(\frac{9}{680}\right) e(613680)e\left(\frac{613}{680}\right)
χ28900(79,)\chi_{28900}(79,\cdot) 28900.fk 1360 yes 11 11 e(11071360)e\left(\frac{1107}{1360}\right) e(45272)e\left(\frac{45}{272}\right) e(427680)e\left(\frac{427}{680}\right) e(3011360)e\left(\frac{301}{1360}\right) e(81340)e\left(\frac{81}{340}\right) e(609680)e\left(\frac{609}{680}\right) e(333340)e\left(\frac{333}{340}\right) e(7011360)e\left(\frac{701}{1360}\right) e(6011360)e\left(\frac{601}{1360}\right) e(12871360)e\left(\frac{1287}{1360}\right)
χ28900(81,)\chi_{28900}(81,\cdot) 28900.es 340 no 11 11 e(277340)e\left(\frac{277}{340}\right) e(1968)e\left(\frac{19}{68}\right) e(107170)e\left(\frac{107}{170}\right) e(251340)e\left(\frac{251}{340}\right) e(4185)e\left(\frac{41}{85}\right) e(69170)e\left(\frac{69}{170}\right) e(885)e\left(\frac{8}{85}\right) e(231340)e\left(\frac{231}{340}\right) e(151340)e\left(\frac{151}{340}\right) e(217340)e\left(\frac{217}{340}\right)
χ28900(83,)\chi_{28900}(83,\cdot) 28900.fc 680 yes 11 11 e(669680)e\left(\frac{669}{680}\right) e(67136)e\left(\frac{67}{136}\right) e(329340)e\left(\frac{329}{340}\right) e(597680)e\left(\frac{597}{680}\right) e(299340)e\left(\frac{299}{340}\right) e(93340)e\left(\frac{93}{340}\right) e(81170)e\left(\frac{81}{170}\right) e(607680)e\left(\frac{607}{680}\right) e(647680)e\left(\frac{647}{680}\right) e(359680)e\left(\frac{359}{680}\right)
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