↑

Properties

Modulus 4390443904
Structure C2×C2×C4704C_{2}\times C_{2}\times C_{4704}
Order 1881618816

Learn more

Show commands: PariGP / SageMath

sage: H = DirichletGroup(43904)
 
pari: g = idealstar(,43904,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 18816
sage: H.invariants()
 
pari: g.cyc
 
Structure = C2×C2×C4704C_{2}\times C_{2}\times C_{4704}
sage: H.gens()
 
pari: g.gen
 
Generators = χ43904(17151,⋅)\chi_{43904}(17151,\cdot), χ43904(9605,⋅)\chi_{43904}(9605,\cdot), χ43904(17153,⋅)\chi_{43904}(17153,\cdot)

First 32 of 18816 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 99 1111 1313 1515 1717 1919 2323 2525
χ43904(1,⋅)\chi_{43904}(1,\cdot) 43904.a 1 no 11 11 11 11 11 11 11 11 11 11 11 11
χ43904(3,⋅)\chi_{43904}(3,\cdot) 43904.fk 4704 yes 11 11 e(36914704)e\left(\frac{3691}{4704}\right) e(9054704)e\left(\frac{905}{4704}\right) e(13392352)e\left(\frac{1339}{2352}\right) e(8294704)e\left(\frac{829}{4704}\right) e(5891568)e\left(\frac{589}{1568}\right) e(383392)e\left(\frac{383}{392}\right) e(8351176)e\left(\frac{835}{1176}\right) e(4796)e\left(\frac{47}{96}\right) e(8712352)e\left(\frac{871}{2352}\right) e(9052352)e\left(\frac{905}{2352}\right)
χ43904(5,⋅)\chi_{43904}(5,\cdot) 43904.fl 4704 yes −1-1 11 e(9054704)e\left(\frac{905}{4704}\right) e(41954704)e\left(\frac{4195}{4704}\right) e(9052352)e\left(\frac{905}{2352}\right) e(8154704)e\left(\frac{815}{4704}\right) e(9111568)e\left(\frac{911}{1568}\right) e(33392)e\left(\frac{33}{392}\right) e(4011176)e\left(\frac{401}{1176}\right) e(8596)e\left(\frac{85}{96}\right) e(14452352)e\left(\frac{1445}{2352}\right) e(18432352)e\left(\frac{1843}{2352}\right)
χ43904(9,⋅)\chi_{43904}(9,\cdot) 43904.fh 2352 no 11 11 e(13392352)e\left(\frac{1339}{2352}\right) e(9052352)e\left(\frac{905}{2352}\right) e(1631176)e\left(\frac{163}{1176}\right) e(8292352)e\left(\frac{829}{2352}\right) e(589784)e\left(\frac{589}{784}\right) e(187196)e\left(\frac{187}{196}\right) e(247588)e\left(\frac{247}{588}\right) e(4748)e\left(\frac{47}{48}\right) e(8711176)e\left(\frac{871}{1176}\right) e(9051176)e\left(\frac{905}{1176}\right)
χ43904(11,⋅)\chi_{43904}(11,\cdot) 43904.fm 4704 yes −1-1 11 e(8294704)e\left(\frac{829}{4704}\right) e(8154704)e\left(\frac{815}{4704}\right) e(8292352)e\left(\frac{829}{2352}\right) e(20594704)e\left(\frac{2059}{4704}\right) e(7471568)e\left(\frac{747}{1568}\right) e(137392)e\left(\frac{137}{392}\right) e(731176)e\left(\frac{73}{1176}\right) e(8996)e\left(\frac{89}{96}\right) e(16812352)e\left(\frac{1681}{2352}\right) e(8152352)e\left(\frac{815}{2352}\right)
χ43904(13,⋅)\chi_{43904}(13,\cdot) 43904.ff 1568 yes −1-1 11 e(5891568)e\left(\frac{589}{1568}\right) e(9111568)e\left(\frac{911}{1568}\right) e(589784)e\left(\frac{589}{784}\right) e(7471568)e\left(\frac{747}{1568}\right) e(4811568)e\left(\frac{481}{1568}\right) e(375392)e\left(\frac{375}{392}\right) e(141392)e\left(\frac{141}{392}\right) e(932)e\left(\frac{9}{32}\right) e(425784)e\left(\frac{425}{784}\right) e(127784)e\left(\frac{127}{784}\right)
χ43904(15,⋅)\chi_{43904}(15,\cdot) 43904.ek 392 no −1-1 11 e(383392)e\left(\frac{383}{392}\right) e(33392)e\left(\frac{33}{392}\right) e(187196)e\left(\frac{187}{196}\right) e(137392)e\left(\frac{137}{392}\right) e(375392)e\left(\frac{375}{392}\right) e(349)e\left(\frac{3}{49}\right) e(598)e\left(\frac{5}{98}\right) e(38)e\left(\frac{3}{8}\right) e(193196)e\left(\frac{193}{196}\right) e(33196)e\left(\frac{33}{196}\right)
χ43904(17,⋅)\chi_{43904}(17,\cdot) 43904.ey 1176 no −1-1 11 e(8351176)e\left(\frac{835}{1176}\right) e(4011176)e\left(\frac{401}{1176}\right) e(247588)e\left(\frac{247}{588}\right) e(731176)e\left(\frac{73}{1176}\right) e(141392)e\left(\frac{141}{392}\right) e(598)e\left(\frac{5}{98}\right) e(92147)e\left(\frac{92}{147}\right) e(2324)e\left(\frac{23}{24}\right) e(115588)e\left(\frac{115}{588}\right) e(401588)e\left(\frac{401}{588}\right)
χ43904(19,⋅)\chi_{43904}(19,\cdot) 43904.cw 96 no 11 11 e(4796)e\left(\frac{47}{96}\right) e(8596)e\left(\frac{85}{96}\right) e(4748)e\left(\frac{47}{48}\right) e(8996)e\left(\frac{89}{96}\right) e(932)e\left(\frac{9}{32}\right) e(38)e\left(\frac{3}{8}\right) e(2324)e\left(\frac{23}{24}\right) e(1996)e\left(\frac{19}{96}\right) e(1148)e\left(\frac{11}{48}\right) e(3748)e\left(\frac{37}{48}\right)
χ43904(23,⋅)\chi_{43904}(23,\cdot) 43904.fj 2352 no −1-1 11 e(8712352)e\left(\frac{871}{2352}\right) e(14452352)e\left(\frac{1445}{2352}\right) e(8711176)e\left(\frac{871}{1176}\right) e(16812352)e\left(\frac{1681}{2352}\right) e(425784)e\left(\frac{425}{784}\right) e(193196)e\left(\frac{193}{196}\right) e(115588)e\left(\frac{115}{588}\right) e(1148)e\left(\frac{11}{48}\right) e(1271176)e\left(\frac{127}{1176}\right) e(2691176)e\left(\frac{269}{1176}\right)
χ43904(25,⋅)\chi_{43904}(25,\cdot) 43904.fh 2352 no 11 11 e(9052352)e\left(\frac{905}{2352}\right) e(18432352)e\left(\frac{1843}{2352}\right) e(9051176)e\left(\frac{905}{1176}\right) e(8152352)e\left(\frac{815}{2352}\right) e(127784)e\left(\frac{127}{784}\right) e(33196)e\left(\frac{33}{196}\right) e(401588)e\left(\frac{401}{588}\right) e(3748)e\left(\frac{37}{48}\right) e(2691176)e\left(\frac{269}{1176}\right) e(6671176)e\left(\frac{667}{1176}\right)
χ43904(27,⋅)\chi_{43904}(27,\cdot) 43904.fe 1568 yes 11 11 e(5551568)e\left(\frac{555}{1568}\right) e(9051568)e\left(\frac{905}{1568}\right) e(555784)e\left(\frac{555}{784}\right) e(8291568)e\left(\frac{829}{1568}\right) e(1991568)e\left(\frac{199}{1568}\right) e(365392)e\left(\frac{365}{392}\right) e(51392)e\left(\frac{51}{392}\right) e(1532)e\left(\frac{15}{32}\right) e(87784)e\left(\frac{87}{784}\right) e(121784)e\left(\frac{121}{784}\right)
χ43904(29,⋅)\chi_{43904}(29,\cdot) 43904.fd 1568 yes 11 11 e(4811568)e\left(\frac{481}{1568}\right) e(5231568)e\left(\frac{523}{1568}\right) e(481784)e\left(\frac{481}{784}\right) e(391568)e\left(\frac{39}{1568}\right) e(10611568)e\left(\frac{1061}{1568}\right) e(251392)e\left(\frac{251}{392}\right) e(5392)e\left(\frac{5}{392}\right) e(1332)e\left(\frac{13}{32}\right) e(781784)e\left(\frac{781}{784}\right) e(523784)e\left(\frac{523}{784}\right)
χ43904(31,⋅)\chi_{43904}(31,\cdot) 43904.ct 84 no 11 11 e(5984)e\left(\frac{59}{84}\right) e(3184)e\left(\frac{31}{84}\right) e(1742)e\left(\frac{17}{42}\right) e(7184)e\left(\frac{71}{84}\right) e(1928)e\left(\frac{19}{28}\right) e(114)e\left(\frac{1}{14}\right) e(1342)e\left(\frac{13}{42}\right) e(112)e\left(\frac{1}{12}\right) e(421)e\left(\frac{4}{21}\right) e(3142)e\left(\frac{31}{42}\right)
χ43904(33,⋅)\chi_{43904}(33,\cdot) 43904.en 588 no −1-1 11 e(565588)e\left(\frac{565}{588}\right) e(215588)e\left(\frac{215}{588}\right) e(271294)e\left(\frac{271}{294}\right) e(361588)e\left(\frac{361}{588}\right) e(167196)e\left(\frac{167}{196}\right) e(1649)e\left(\frac{16}{49}\right) e(227294)e\left(\frac{227}{294}\right) e(512)e\left(\frac{5}{12}\right) e(25294)e\left(\frac{25}{294}\right) e(215294)e\left(\frac{215}{294}\right)
χ43904(37,⋅)\chi_{43904}(37,\cdot) 43904.fn 4704 yes 11 11 e(28014704)e\left(\frac{2801}{4704}\right) e(3794704)e\left(\frac{379}{4704}\right) e(4492352)e\left(\frac{449}{2352}\right) e(35754704)e\left(\frac{3575}{4704}\right) e(7111568)e\left(\frac{711}{1568}\right) e(265392)e\left(\frac{265}{392}\right) e(1971176)e\left(\frac{197}{1176}\right) e(6196)e\left(\frac{61}{96}\right) e(5092352)e\left(\frac{509}{2352}\right) e(3792352)e\left(\frac{379}{2352}\right)
χ43904(39,⋅)\chi_{43904}(39,\cdot) 43904.fj 2352 no −1-1 11 e(3772352)e\left(\frac{377}{2352}\right) e(18192352)e\left(\frac{1819}{2352}\right) e(3771176)e\left(\frac{377}{1176}\right) e(15352352)e\left(\frac{1535}{2352}\right) e(535784)e\left(\frac{535}{784}\right) e(183196)e\left(\frac{183}{196}\right) e(41588)e\left(\frac{41}{588}\right) e(3748)e\left(\frac{37}{48}\right) e(10731176)e\left(\frac{1073}{1176}\right) e(6431176)e\left(\frac{643}{1176}\right)
χ43904(41,⋅)\chi_{43904}(41,\cdot) 43904.eu 784 no −1-1 11 e(341784)e\left(\frac{341}{784}\right) e(775784)e\left(\frac{775}{784}\right) e(341392)e\left(\frac{341}{392}\right) e(123784)e\left(\frac{123}{784}\right) e(361784)e\left(\frac{361}{784}\right) e(83196)e\left(\frac{83}{196}\right) e(159196)e\left(\frac{159}{196}\right) e(116)e\left(\frac{1}{16}\right) e(81392)e\left(\frac{81}{392}\right) e(383392)e\left(\frac{383}{392}\right)
χ43904(43,⋅)\chi_{43904}(43,\cdot) 43904.fc 1568 yes −1-1 11 e(3751568)e\left(\frac{375}{1568}\right) e(7811568)e\left(\frac{781}{1568}\right) e(375784)e\left(\frac{375}{784}\right) e(12171568)e\left(\frac{1217}{1568}\right) e(6431568)e\left(\frac{643}{1568}\right) e(289392)e\left(\frac{289}{392}\right) e(347392)e\left(\frac{347}{392}\right) e(1132)e\left(\frac{11}{32}\right) e(419784)e\left(\frac{419}{784}\right) e(781784)e\left(\frac{781}{784}\right)
χ43904(45,⋅)\chi_{43904}(45,\cdot) 43904.fl 4704 yes −1-1 11 e(35834704)e\left(\frac{3583}{4704}\right) e(13014704)e\left(\frac{1301}{4704}\right) e(12312352)e\left(\frac{1231}{2352}\right) e(24734704)e\left(\frac{2473}{4704}\right) e(5211568)e\left(\frac{521}{1568}\right) e(15392)e\left(\frac{15}{392}\right) e(8951176)e\left(\frac{895}{1176}\right) e(8396)e\left(\frac{83}{96}\right) e(8352352)e\left(\frac{835}{2352}\right) e(13012352)e\left(\frac{1301}{2352}\right)
χ43904(47,⋅)\chi_{43904}(47,\cdot) 43904.fb 1176 no 11 11 e(4191176)e\left(\frac{419}{1176}\right) e(6851176)e\left(\frac{685}{1176}\right) e(419588)e\left(\frac{419}{588}\right) e(5691176)e\left(\frac{569}{1176}\right) e(17392)e\left(\frac{17}{392}\right) e(4649)e\left(\frac{46}{49}\right) e(115147)e\left(\frac{115}{147}\right) e(724)e\left(\frac{7}{24}\right) e(401588)e\left(\frac{401}{588}\right) e(97588)e\left(\frac{97}{588}\right)
χ43904(51,⋅)\chi_{43904}(51,\cdot) 43904.fm 4704 yes −1-1 11 e(23274704)e\left(\frac{2327}{4704}\right) e(25094704)e\left(\frac{2509}{4704}\right) e(23272352)e\left(\frac{2327}{2352}\right) e(11214704)e\left(\frac{1121}{4704}\right) e(11531568)e\left(\frac{1153}{1568}\right) e(11392)e\left(\frac{11}{392}\right) e(3951176)e\left(\frac{395}{1176}\right) e(4396)e\left(\frac{43}{96}\right) e(13312352)e\left(\frac{1331}{2352}\right) e(1572352)e\left(\frac{157}{2352}\right)
χ43904(53,⋅)\chi_{43904}(53,\cdot) 43904.fn 4704 yes 11 11 e(23654704)e\left(\frac{2365}{4704}\right) e(6714704)e\left(\frac{671}{4704}\right) e(132352)e\left(\frac{13}{2352}\right) e(16754704)e\left(\frac{1675}{4704}\right) e(591568)e\left(\frac{59}{1568}\right) e(253392)e\left(\frac{253}{392}\right) e(2651176)e\left(\frac{265}{1176}\right) e(8996)e\left(\frac{89}{96}\right) e(18012352)e\left(\frac{1801}{2352}\right) e(6712352)e\left(\frac{671}{2352}\right)
χ43904(55,⋅)\chi_{43904}(55,\cdot) 43904.ew 784 no 11 11 e(289784)e\left(\frac{289}{784}\right) e(51784)e\left(\frac{51}{784}\right) e(289392)e\left(\frac{289}{392}\right) e(479784)e\left(\frac{479}{784}\right) e(45784)e\left(\frac{45}{784}\right) e(85196)e\left(\frac{85}{196}\right) e(79196)e\left(\frac{79}{196}\right) e(1316)e\left(\frac{13}{16}\right) e(129392)e\left(\frac{129}{392}\right) e(51392)e\left(\frac{51}{392}\right)
χ43904(57,⋅)\chi_{43904}(57,\cdot) 43904.ex 784 no 11 11 e(215784)e\left(\frac{215}{784}\right) e(61784)e\left(\frac{61}{784}\right) e(215392)e\left(\frac{215}{392}\right) e(81784)e\left(\frac{81}{784}\right) e(515784)e\left(\frac{515}{784}\right) e(69196)e\left(\frac{69}{196}\right) e(131196)e\left(\frac{131}{196}\right) e(1116)e\left(\frac{11}{16}\right) e(235392)e\left(\frac{235}{392}\right) e(61392)e\left(\frac{61}{392}\right)
χ43904(59,⋅)\chi_{43904}(59,\cdot) 43904.fk 4704 yes 11 11 e(6494704)e\left(\frac{649}{4704}\right) e(38274704)e\left(\frac{3827}{4704}\right) e(6492352)e\left(\frac{649}{2352}\right) e(40154704)e\left(\frac{4015}{4704}\right) e(8951568)e\left(\frac{895}{1568}\right) e(373392)e\left(\frac{373}{392}\right) e(11531176)e\left(\frac{1153}{1176}\right) e(5396)e\left(\frac{53}{96}\right) e(4452352)e\left(\frac{445}{2352}\right) e(14752352)e\left(\frac{1475}{2352}\right)
χ43904(61,⋅)\chi_{43904}(61,\cdot) 43904.fl 4704 yes −1-1 11 e(31794704)e\left(\frac{3179}{4704}\right) e(25214704)e\left(\frac{2521}{4704}\right) e(8272352)e\left(\frac{827}{2352}\right) e(25254704)e\left(\frac{2525}{4704}\right) e(13411568)e\left(\frac{1341}{1568}\right) e(83392)e\left(\frac{83}{392}\right) e(11631176)e\left(\frac{1163}{1176}\right) e(7996)e\left(\frac{79}{96}\right) e(472352)e\left(\frac{47}{2352}\right) e(1692352)e\left(\frac{169}{2352}\right)
χ43904(65,⋅)\chi_{43904}(65,\cdot) 43904.ec 294 no 11 11 e(167294)e\left(\frac{167}{294}\right) e(139294)e\left(\frac{139}{294}\right) e(20147)e\left(\frac{20}{147}\right) e(191294)e\left(\frac{191}{294}\right) e(8798)e\left(\frac{87}{98}\right) e(249)e\left(\frac{2}{49}\right) e(103147)e\left(\frac{103}{147}\right) e(16)e\left(\frac{1}{6}\right) e(23147)e\left(\frac{23}{147}\right) e(139147)e\left(\frac{139}{147}\right)
χ43904(67,⋅)\chi_{43904}(67,\cdot) 43904.es 672 no −1-1 11 e(445672)e\left(\frac{445}{672}\right) e(431672)e\left(\frac{431}{672}\right) e(109336)e\left(\frac{109}{336}\right) e(139672)e\left(\frac{139}{672}\right) e(107224)e\left(\frac{107}{224}\right) e(1756)e\left(\frac{17}{56}\right) e(25168)e\left(\frac{25}{168}\right) e(4796)e\left(\frac{47}{96}\right) e(97336)e\left(\frac{97}{336}\right) e(95336)e\left(\frac{95}{336}\right)
χ43904(69,⋅)\chi_{43904}(69,\cdot) 43904.ff 1568 yes −1-1 11 e(2431568)e\left(\frac{243}{1568}\right) e(12651568)e\left(\frac{1265}{1568}\right) e(243784)e\left(\frac{243}{784}\right) e(13971568)e\left(\frac{1397}{1568}\right) e(14391568)e\left(\frac{1439}{1568}\right) e(377392)e\left(\frac{377}{392}\right) e(355392)e\left(\frac{355}{392}\right) e(2332)e\left(\frac{23}{32}\right) e(375784)e\left(\frac{375}{784}\right) e(481784)e\left(\frac{481}{784}\right)
χ43904(71,⋅)\chi_{43904}(71,\cdot) 43904.ev 784 no −1-1 11 e(127784)e\left(\frac{127}{784}\right) e(253784)e\left(\frac{253}{784}\right) e(127392)e\left(\frac{127}{392}\right) e(201784)e\left(\frac{201}{784}\right) e(131784)e\left(\frac{131}{784}\right) e(95196)e\left(\frac{95}{196}\right) e(71196)e\left(\frac{71}{196}\right) e(316)e\left(\frac{3}{16}\right) e(271392)e\left(\frac{271}{392}\right) e(253392)e\left(\frac{253}{392}\right)
χ43904(73,⋅)\chi_{43904}(73,\cdot) 43904.fi 2352 no −1-1 11 e(7792352)e\left(\frac{779}{2352}\right) e(11292352)e\left(\frac{1129}{2352}\right) e(7791176)e\left(\frac{779}{1176}\right) e(7732352)e\left(\frac{773}{2352}\right) e(701784)e\left(\frac{701}{784}\right) e(159196)e\left(\frac{159}{196}\right) e(569588)e\left(\frac{569}{588}\right) e(3148)e\left(\frac{31}{48}\right) e(8151176)e\left(\frac{815}{1176}\right) e(11291176)e\left(\frac{1129}{1176}\right)
Click here to search among the remaining 18784 characters.