↑

Properties

Modulus 243675243675
Structure C2×C18×C3420C_{2}\times C_{18}\times C_{3420}
Order 123120123120

Learn more

Show commands: PariGP / SageMath

sage: H = DirichletGroup(243675)
 
pari: g = idealstar(,243675,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 123120
sage: H.invariants()
 
pari: g.cyc
 
Structure = C2×C18×C3420C_{2}\times C_{18}\times C_{3420}
sage: H.gens()
 
pari: g.gen
 
Generators = χ243675(36101,⋅)\chi_{243675}(36101,\cdot), χ243675(77977,⋅)\chi_{243675}(77977,\cdot), χ243675(129601,⋅)\chi_{243675}(129601,\cdot)

First 32 of 123120 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 22 44 77 88 1111 1313 1414 1616 1717 2222
χ243675(1,⋅)\chi_{243675}(1,\cdot) 243675.a 1 no 11 11 11 11 11 11 11 11 11 11 11 11
χ243675(2,⋅)\chi_{243675}(2,\cdot) 243675.beq 3420 yes −1-1 11 e(3713420)e\left(\frac{371}{3420}\right) e(3711710)e\left(\frac{371}{1710}\right) e(395684)e\left(\frac{395}{684}\right) e(3711140)e\left(\frac{371}{1140}\right) e(14031710)e\left(\frac{1403}{1710}\right) e(12193420)e\left(\frac{1219}{3420}\right) e(391570)e\left(\frac{391}{570}\right) e(371855)e\left(\frac{371}{855}\right) e(4933420)e\left(\frac{493}{3420}\right) e(353380)e\left(\frac{353}{380}\right)
χ243675(4,⋅)\chi_{243675}(4,\cdot) 243675.bbx 1710 yes 11 11 e(3711710)e\left(\frac{371}{1710}\right) e(371855)e\left(\frac{371}{855}\right) e(53342)e\left(\frac{53}{342}\right) e(371570)e\left(\frac{371}{570}\right) e(548855)e\left(\frac{548}{855}\right) e(12191710)e\left(\frac{1219}{1710}\right) e(106285)e\left(\frac{106}{285}\right) e(742855)e\left(\frac{742}{855}\right) e(4931710)e\left(\frac{493}{1710}\right) e(163190)e\left(\frac{163}{190}\right)
χ243675(7,⋅)\chi_{243675}(7,\cdot) 243675.yj 684 no −1-1 11 e(395684)e\left(\frac{395}{684}\right) e(53342)e\left(\frac{53}{342}\right) e(179684)e\left(\frac{179}{684}\right) e(167228)e\left(\frac{167}{228}\right) e(50171)e\left(\frac{50}{171}\right) e(109684)e\left(\frac{109}{684}\right) e(287342)e\left(\frac{287}{342}\right) e(53171)e\left(\frac{53}{171}\right) e(161228)e\left(\frac{161}{228}\right) e(595684)e\left(\frac{595}{684}\right)
χ243675(8,⋅)\chi_{243675}(8,\cdot) 243675.bac 1140 no −1-1 11 e(3711140)e\left(\frac{371}{1140}\right) e(371570)e\left(\frac{371}{570}\right) e(167228)e\left(\frac{167}{228}\right) e(371380)e\left(\frac{371}{380}\right) e(263570)e\left(\frac{263}{570}\right) e(791140)e\left(\frac{79}{1140}\right) e(11190)e\left(\frac{11}{190}\right) e(86285)e\left(\frac{86}{285}\right) e(4931140)e\left(\frac{493}{1140}\right) e(299380)e\left(\frac{299}{380}\right)
χ243675(11,⋅)\chi_{243675}(11,\cdot) 243675.bcc 1710 yes −1-1 11 e(14031710)e\left(\frac{1403}{1710}\right) e(548855)e\left(\frac{548}{855}\right) e(50171)e\left(\frac{50}{171}\right) e(263570)e\left(\frac{263}{570}\right) e(10431710)e\left(\frac{1043}{1710}\right) e(86855)e\left(\frac{86}{855}\right) e(1931710)e\left(\frac{193}{1710}\right) e(241855)e\left(\frac{241}{855}\right) e(121190)e\left(\frac{121}{190}\right) e(368855)e\left(\frac{368}{855}\right)
χ243675(13,⋅)\chi_{243675}(13,\cdot) 243675.bev 3420 yes 11 11 e(12193420)e\left(\frac{1219}{3420}\right) e(12191710)e\left(\frac{1219}{1710}\right) e(109684)e\left(\frac{109}{684}\right) e(791140)e\left(\frac{79}{1140}\right) e(86855)e\left(\frac{86}{855}\right) e(3413420)e\left(\frac{341}{3420}\right) e(4995)e\left(\frac{49}{95}\right) e(364855)e\left(\frac{364}{855}\right) e(14573420)e\left(\frac{1457}{3420}\right) e(5211140)e\left(\frac{521}{1140}\right)
χ243675(14,⋅)\chi_{243675}(14,\cdot) 243675.bdj 1710 yes 11 11 e(391570)e\left(\frac{391}{570}\right) e(106285)e\left(\frac{106}{285}\right) e(287342)e\left(\frac{287}{342}\right) e(11190)e\left(\frac{11}{190}\right) e(1931710)e\left(\frac{193}{1710}\right) e(4995)e\left(\frac{49}{95}\right) e(449855)e\left(\frac{449}{855}\right) e(212285)e\left(\frac{212}{285}\right) e(727855)e\left(\frac{727}{855}\right) e(683855)e\left(\frac{683}{855}\right)
χ243675(16,⋅)\chi_{243675}(16,\cdot) 243675.zk 855 yes 11 11 e(371855)e\left(\frac{371}{855}\right) e(742855)e\left(\frac{742}{855}\right) e(53171)e\left(\frac{53}{171}\right) e(86285)e\left(\frac{86}{285}\right) e(241855)e\left(\frac{241}{855}\right) e(364855)e\left(\frac{364}{855}\right) e(212285)e\left(\frac{212}{285}\right) e(629855)e\left(\frac{629}{855}\right) e(493855)e\left(\frac{493}{855}\right) e(6895)e\left(\frac{68}{95}\right)
χ243675(17,⋅)\chi_{243675}(17,\cdot) 243675.bdt 3420 no 11 11 e(4933420)e\left(\frac{493}{3420}\right) e(4931710)e\left(\frac{493}{1710}\right) e(161228)e\left(\frac{161}{228}\right) e(4931140)e\left(\frac{493}{1140}\right) e(121190)e\left(\frac{121}{190}\right) e(14573420)e\left(\frac{1457}{3420}\right) e(727855)e\left(\frac{727}{855}\right) e(493855)e\left(\frac{493}{855}\right) e(10093420)e\left(\frac{1009}{3420}\right) e(26713420)e\left(\frac{2671}{3420}\right)
χ243675(22,⋅)\chi_{243675}(22,\cdot) 243675.bdq 3420 yes 11 11 e(353380)e\left(\frac{353}{380}\right) e(163190)e\left(\frac{163}{190}\right) e(595684)e\left(\frac{595}{684}\right) e(299380)e\left(\frac{299}{380}\right) e(368855)e\left(\frac{368}{855}\right) e(5211140)e\left(\frac{521}{1140}\right) e(683855)e\left(\frac{683}{855}\right) e(6895)e\left(\frac{68}{95}\right) e(26713420)e\left(\frac{2671}{3420}\right) e(12293420)e\left(\frac{1229}{3420}\right)
χ243675(23,⋅)\chi_{243675}(23,\cdot) 243675.beb 3420 yes 11 11 e(20113420)e\left(\frac{2011}{3420}\right) e(3011710)e\left(\frac{301}{1710}\right) e(385684)e\left(\frac{385}{684}\right) e(8711140)e\left(\frac{871}{1140}\right) e(4931710)e\left(\frac{493}{1710}\right) e(26993420)e\left(\frac{2699}{3420}\right) e(43285)e\left(\frac{43}{285}\right) e(301855)e\left(\frac{301}{855}\right) e(27233420)e\left(\frac{2723}{3420}\right) e(333380)e\left(\frac{333}{380}\right)
χ243675(26,⋅)\chi_{243675}(26,\cdot) 243675.or 114 no −1-1 11 e(53114)e\left(\frac{53}{114}\right) e(5357)e\left(\frac{53}{57}\right) e(1419)e\left(\frac{14}{19}\right) e(1538)e\left(\frac{15}{38}\right) e(3538)e\left(\frac{35}{38}\right) e(2657)e\left(\frac{26}{57}\right) e(23114)e\left(\frac{23}{114}\right) e(4957)e\left(\frac{49}{57}\right) e(65114)e\left(\frac{65}{114}\right) e(2257)e\left(\frac{22}{57}\right)
χ243675(28,⋅)\chi_{243675}(28,\cdot) 243675.rq 180 no −1-1 11 e(143180)e\left(\frac{143}{180}\right) e(5390)e\left(\frac{53}{90}\right) e(512)e\left(\frac{5}{12}\right) e(2360)e\left(\frac{23}{60}\right) e(1415)e\left(\frac{14}{15}\right) e(157180)e\left(\frac{157}{180}\right) e(1990)e\left(\frac{19}{90}\right) e(845)e\left(\frac{8}{45}\right) e(179180)e\left(\frac{179}{180}\right) e(131180)e\left(\frac{131}{180}\right)
χ243675(29,⋅)\chi_{243675}(29,\cdot) 243675.baj 1710 yes 11 11 e(39190)e\left(\frac{39}{190}\right) e(3995)e\left(\frac{39}{95}\right) e(289342)e\left(\frac{289}{342}\right) e(117190)e\left(\frac{117}{190}\right) e(6711710)e\left(\frac{671}{1710}\right) e(199285)e\left(\frac{199}{285}\right) e(43855)e\left(\frac{43}{855}\right) e(7895)e\left(\frac{78}{95}\right) e(314855)e\left(\frac{314}{855}\right) e(511855)e\left(\frac{511}{855}\right)
χ243675(31,⋅)\chi_{243675}(31,\cdot) 243675.bcl 1710 yes −1-1 11 e(6791710)e\left(\frac{679}{1710}\right) e(679855)e\left(\frac{679}{855}\right) e(115171)e\left(\frac{115}{171}\right) e(109570)e\left(\frac{109}{570}\right) e(182855)e\left(\frac{182}{855}\right) e(16611710)e\left(\frac{1661}{1710}\right) e(1191710)e\left(\frac{119}{1710}\right) e(503855)e\left(\frac{503}{855}\right) e(995)e\left(\frac{9}{95}\right) e(10431710)e\left(\frac{1043}{1710}\right)
χ243675(32,⋅)\chi_{243675}(32,\cdot) 243675.yb 684 no −1-1 11 e(371684)e\left(\frac{371}{684}\right) e(29342)e\left(\frac{29}{342}\right) e(607684)e\left(\frac{607}{684}\right) e(143228)e\left(\frac{143}{228}\right) e(35342)e\left(\frac{35}{342}\right) e(535684)e\left(\frac{535}{684}\right) e(49114)e\left(\frac{49}{114}\right) e(29171)e\left(\frac{29}{171}\right) e(493684)e\left(\frac{493}{684}\right) e(4976)e\left(\frac{49}{76}\right)
χ243675(34,⋅)\chi_{243675}(34,\cdot) 243675.bdl 1710 yes −1-1 11 e(2495)e\left(\frac{24}{95}\right) e(4895)e\left(\frac{48}{95}\right) e(97342)e\left(\frac{97}{342}\right) e(7295)e\left(\frac{72}{95}\right) e(391855)e\left(\frac{391}{855}\right) e(223285)e\left(\frac{223}{285}\right) e(9171710)e\left(\frac{917}{1710}\right) e(195)e\left(\frac{1}{95}\right) e(7511710)e\left(\frac{751}{1710}\right) e(607855)e\left(\frac{607}{855}\right)
χ243675(37,⋅)\chi_{243675}(37,\cdot) 243675.zz 1140 no 11 11 e(10431140)e\left(\frac{1043}{1140}\right) e(473570)e\left(\frac{473}{570}\right) e(73228)e\left(\frac{73}{228}\right) e(283380)e\left(\frac{283}{380}\right) e(272285)e\left(\frac{272}{285}\right) e(5771140)e\left(\frac{577}{1140}\right) e(67285)e\left(\frac{67}{285}\right) e(188285)e\left(\frac{188}{285}\right) e(223380)e\left(\frac{223}{380}\right) e(9911140)e\left(\frac{991}{1140}\right)
χ243675(41,⋅)\chi_{243675}(41,\cdot) 243675.baq 1710 yes 11 11 e(97285)e\left(\frac{97}{285}\right) e(194285)e\left(\frac{194}{285}\right) e(85171)e\left(\frac{85}{171}\right) e(295)e\left(\frac{2}{95}\right) e(7871710)e\left(\frac{787}{1710}\right) e(461570)e\left(\frac{461}{570}\right) e(716855)e\left(\frac{716}{855}\right) e(103285)e\left(\frac{103}{285}\right) e(711710)e\left(\frac{71}{1710}\right) e(13691710)e\left(\frac{1369}{1710}\right)
χ243675(43,⋅)\chi_{243675}(43,\cdot) 243675.yv 684 no −1-1 11 e(85684)e\left(\frac{85}{684}\right) e(85342)e\left(\frac{85}{342}\right) e(77684)e\left(\frac{77}{684}\right) e(85228)e\left(\frac{85}{228}\right) e(68171)e\left(\frac{68}{171}\right) e(35684)e\left(\frac{35}{684}\right) e(938)e\left(\frac{9}{38}\right) e(85171)e\left(\frac{85}{171}\right) e(305684)e\left(\frac{305}{684}\right) e(119228)e\left(\frac{119}{228}\right)
χ243675(44,⋅)\chi_{243675}(44,\cdot) 243675.bda 1710 no −1-1 11 e(32855)e\left(\frac{32}{855}\right) e(64855)e\left(\frac{64}{855}\right) e(1738)e\left(\frac{17}{38}\right) e(32285)e\left(\frac{32}{285}\right) e(143570)e\left(\frac{143}{570}\right) e(13911710)e\left(\frac{1391}{1710}\right) e(8291710)e\left(\frac{829}{1710}\right) e(128855)e\left(\frac{128}{855}\right) e(791855)e\left(\frac{791}{855}\right) e(4931710)e\left(\frac{493}{1710}\right)
χ243675(46,⋅)\chi_{243675}(46,\cdot) 243675.xb 570 no −1-1 11 e(397570)e\left(\frac{397}{570}\right) e(112285)e\left(\frac{112}{285}\right) e(857)e\left(\frac{8}{57}\right) e(17190)e\left(\frac{17}{190}\right) e(31285)e\left(\frac{31}{285}\right) e(83570)e\left(\frac{83}{570}\right) e(159190)e\left(\frac{159}{190}\right) e(224285)e\left(\frac{224}{285}\right) e(268285)e\left(\frac{268}{285}\right) e(153190)e\left(\frac{153}{190}\right)
χ243675(47,⋅)\chi_{243675}(47,\cdot) 243675.bff 3420 yes 11 11 e(3591140)e\left(\frac{359}{1140}\right) e(359570)e\left(\frac{359}{570}\right) e(599684)e\left(\frac{599}{684}\right) e(359380)e\left(\frac{359}{380}\right) e(7011710)e\left(\frac{701}{1710}\right) e(3111140)e\left(\frac{311}{1140}\right) e(163855)e\left(\frac{163}{855}\right) e(74285)e\left(\frac{74}{285}\right) e(2213420)e\left(\frac{221}{3420}\right) e(24793420)e\left(\frac{2479}{3420}\right)
χ243675(49,⋅)\chi_{243675}(49,\cdot) 243675.ud 342 no 11 11 e(53342)e\left(\frac{53}{342}\right) e(53171)e\left(\frac{53}{171}\right) e(179342)e\left(\frac{179}{342}\right) e(53114)e\left(\frac{53}{114}\right) e(100171)e\left(\frac{100}{171}\right) e(109342)e\left(\frac{109}{342}\right) e(116171)e\left(\frac{116}{171}\right) e(106171)e\left(\frac{106}{171}\right) e(47114)e\left(\frac{47}{114}\right) e(253342)e\left(\frac{253}{342}\right)
χ243675(52,⋅)\chi_{243675}(52,\cdot) 243675.bec 3420 yes 11 11 e(19613420)e\left(\frac{1961}{3420}\right) e(2511710)e\left(\frac{251}{1710}\right) e(215684)e\left(\frac{215}{684}\right) e(8211140)e\left(\frac{821}{1140}\right) e(634855)e\left(\frac{634}{855}\right) e(27793420)e\left(\frac{2779}{3420}\right) e(253285)e\left(\frac{253}{285}\right) e(251855)e\left(\frac{251}{855}\right) e(24433420)e\left(\frac{2443}{3420}\right) e(3591140)e\left(\frac{359}{1140}\right)
χ243675(53,⋅)\chi_{243675}(53,\cdot) 243675.bey 3420 no −1-1 11 e(3173420)e\left(\frac{317}{3420}\right) e(3171710)e\left(\frac{317}{1710}\right) e(35228)e\left(\frac{35}{228}\right) e(3171140)e\left(\frac{317}{1140}\right) e(487570)e\left(\frac{487}{570}\right) e(16933420)e\left(\frac{1693}{3420}\right) e(4211710)e\left(\frac{421}{1710}\right) e(317855)e\left(\frac{317}{855}\right) e(30713420)e\left(\frac{3071}{3420}\right) e(32393420)e\left(\frac{3239}{3420}\right)
χ243675(56,⋅)\chi_{243675}(56,\cdot) 243675.bbn 1710 yes 11 11 e(772855)e\left(\frac{772}{855}\right) e(689855)e\left(\frac{689}{855}\right) e(170171)e\left(\frac{170}{171}\right) e(202285)e\left(\frac{202}{285}\right) e(12891710)e\left(\frac{1289}{1710}\right) e(3911710)e\left(\frac{391}{1710}\right) e(767855)e\left(\frac{767}{855}\right) e(523855)e\left(\frac{523}{855}\right) e(79570)e\left(\frac{79}{570}\right) e(11231710)e\left(\frac{1123}{1710}\right)
χ243675(58,⋅)\chi_{243675}(58,\cdot) 243675.beg 3420 yes −1-1 11 e(10733420)e\left(\frac{1073}{3420}\right) e(10731710)e\left(\frac{1073}{1710}\right) e(289684)e\left(\frac{289}{684}\right) e(10731140)e\left(\frac{1073}{1140}\right) e(182855)e\left(\frac{182}{855}\right) e(1873420)e\left(\frac{187}{3420}\right) e(12591710)e\left(\frac{1259}{1710}\right) e(218855)e\left(\frac{218}{855}\right) e(5831140)e\left(\frac{583}{1140}\right) e(18013420)e\left(\frac{1801}{3420}\right)
χ243675(59,⋅)\chi_{243675}(59,\cdot) 243675.bdj 1710 yes 11 11 e(289570)e\left(\frac{289}{570}\right) e(4285)e\left(\frac{4}{285}\right) e(113342)e\left(\frac{113}{342}\right) e(99190)e\left(\frac{99}{190}\right) e(13571710)e\left(\frac{1357}{1710}\right) e(6195)e\left(\frac{61}{95}\right) e(716855)e\left(\frac{716}{855}\right) e(8285)e\left(\frac{8}{285}\right) e(748855)e\left(\frac{748}{855}\right) e(257855)e\left(\frac{257}{855}\right)
χ243675(61,⋅)\chi_{243675}(61,\cdot) 243675.zr 855 yes 11 11 e(9195)e\left(\frac{91}{95}\right) e(8795)e\left(\frac{87}{95}\right) e(98171)e\left(\frac{98}{171}\right) e(8395)e\left(\frac{83}{95}\right) e(679855)e\left(\frac{679}{855}\right) e(232285)e\left(\frac{232}{285}\right) e(454855)e\left(\frac{454}{855}\right) e(7995)e\left(\frac{79}{95}\right) e(452855)e\left(\frac{452}{855}\right) e(643855)e\left(\frac{643}{855}\right)
χ243675(62,⋅)\chi_{243675}(62,\cdot) 243675.qn 180 no 11 11 e(91180)e\left(\frac{91}{180}\right) e(190)e\left(\frac{1}{90}\right) ii e(3160)e\left(\frac{31}{60}\right) e(130)e\left(\frac{1}{30}\right) e(59180)e\left(\frac{59}{180}\right) e(3445)e\left(\frac{34}{45}\right) e(145)e\left(\frac{1}{45}\right) e(43180)e\left(\frac{43}{180}\right) e(97180)e\left(\frac{97}{180}\right)
Click here to search among the remaining 123088 characters.