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Properties

Modulus 8560085600
Structure C2×C2×C4×C2120C_{2}\times C_{2}\times C_{4}\times C_{2120}
Order 3392033920

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Show commands: PariGP / SageMath

sage: H = DirichletGroup(85600)
 
pari: g = idealstar(,85600,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 33920
sage: H.invariants()
 
pari: g.cyc
 
Structure = C2×C2×C4×C2120C_{2}\times C_{2}\times C_{4}\times C_{2120}
sage: H.gens()
 
pari: g.gen
 
Generators = χ85600(26751,⋅)\chi_{85600}(26751,\cdot), χ85600(32101,⋅)\chi_{85600}(32101,\cdot), χ85600(82177,⋅)\chi_{85600}(82177,\cdot), χ85600(16801,⋅)\chi_{85600}(16801,\cdot)

First 32 of 33920 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 1717 1919 2121 2323 2727
χ85600(1,⋅)\chi_{85600}(1,\cdot) 85600.a 1 no 11 11 11 11 11 11 11 11 11 11 11 11
χ85600(3,⋅)\chi_{85600}(3,\cdot) 85600.ic 2120 yes 11 11 e(6392120)e\left(\frac{639}{2120}\right) e(2153)e\left(\frac{21}{53}\right) e(6391060)e\left(\frac{639}{1060}\right) e(10672120)e\left(\frac{1067}{2120}\right) e(11032120)e\left(\frac{1103}{2120}\right) e(2131060)e\left(\frac{213}{1060}\right) e(19812120)e\left(\frac{1981}{2120}\right) e(14792120)e\left(\frac{1479}{2120}\right) e(144265)e\left(\frac{144}{265}\right) e(19172120)e\left(\frac{1917}{2120}\right)
χ85600(7,⋅)\chi_{85600}(7,\cdot) 85600.fa 212 no −1-1 11 e(2153)e\left(\frac{21}{53}\right) e(147212)e\left(\frac{147}{212}\right) e(4253)e\left(\frac{42}{53}\right) e(143212)e\left(\frac{143}{212}\right) e(19106)e\left(\frac{19}{106}\right) e(3212)e\left(\frac{3}{212}\right) e(83212)e\left(\frac{83}{212}\right) e(19212)e\left(\frac{19}{212}\right) e(191212)e\left(\frac{191}{212}\right) e(1053)e\left(\frac{10}{53}\right)
χ85600(9,⋅)\chi_{85600}(9,\cdot) 85600.hh 1060 no 11 11 e(6391060)e\left(\frac{639}{1060}\right) e(4253)e\left(\frac{42}{53}\right) e(109530)e\left(\frac{109}{530}\right) e(71060)e\left(\frac{7}{1060}\right) e(431060)e\left(\frac{43}{1060}\right) e(213530)e\left(\frac{213}{530}\right) e(9211060)e\left(\frac{921}{1060}\right) e(4191060)e\left(\frac{419}{1060}\right) e(23265)e\left(\frac{23}{265}\right) e(8571060)e\left(\frac{857}{1060}\right)
χ85600(11,⋅)\chi_{85600}(11,\cdot) 85600.if 2120 yes −1-1 11 e(10672120)e\left(\frac{1067}{2120}\right) e(143212)e\left(\frac{143}{212}\right) e(71060)e\left(\frac{7}{1060}\right) e(21012120)e\left(\frac{2101}{2120}\right) e(10192120)e\left(\frac{1019}{2120}\right) e(487530)e\left(\frac{487}{530}\right) e(9832120)e\left(\frac{983}{2120}\right) e(3772120)e\left(\frac{377}{2120}\right) e(9731060)e\left(\frac{973}{1060}\right) e(10812120)e\left(\frac{1081}{2120}\right)
χ85600(13,⋅)\chi_{85600}(13,\cdot) 85600.in 2120 yes −1-1 11 e(11032120)e\left(\frac{1103}{2120}\right) e(19106)e\left(\frac{19}{106}\right) e(431060)e\left(\frac{43}{1060}\right) e(10192120)e\left(\frac{1019}{2120}\right) e(512120)e\left(\frac{51}{2120}\right) e(7211060)e\left(\frac{721}{1060}\right) e(11172120)e\left(\frac{1117}{2120}\right) e(14832120)e\left(\frac{1483}{2120}\right) e(471530)e\left(\frac{471}{530}\right) e(11892120)e\left(\frac{1189}{2120}\right)
χ85600(17,⋅)\chi_{85600}(17,\cdot) 85600.hn 1060 no 11 11 e(2131060)e\left(\frac{213}{1060}\right) e(3212)e\left(\frac{3}{212}\right) e(213530)e\left(\frac{213}{530}\right) e(487530)e\left(\frac{487}{530}\right) e(7211060)e\left(\frac{721}{1060}\right) e(4071060)e\left(\frac{407}{1060}\right) e(143265)e\left(\frac{143}{265}\right) e(57265)e\left(\frac{57}{265}\right) e(1191060)e\left(\frac{119}{1060}\right) e(6391060)e\left(\frac{639}{1060}\right)
χ85600(19,⋅)\chi_{85600}(19,\cdot) 85600.ii 2120 yes −1-1 11 e(19812120)e\left(\frac{1981}{2120}\right) e(83212)e\left(\frac{83}{212}\right) e(9211060)e\left(\frac{921}{1060}\right) e(9832120)e\left(\frac{983}{2120}\right) e(11172120)e\left(\frac{1117}{2120}\right) e(143265)e\left(\frac{143}{265}\right) e(4692120)e\left(\frac{469}{2120}\right) e(6912120)e\left(\frac{691}{2120}\right) e(2891060)e\left(\frac{289}{1060}\right) e(17032120)e\left(\frac{1703}{2120}\right)
χ85600(21,⋅)\chi_{85600}(21,\cdot) 85600.ij 2120 yes −1-1 11 e(14792120)e\left(\frac{1479}{2120}\right) e(19212)e\left(\frac{19}{212}\right) e(4191060)e\left(\frac{419}{1060}\right) e(3772120)e\left(\frac{377}{2120}\right) e(14832120)e\left(\frac{1483}{2120}\right) e(57265)e\left(\frac{57}{265}\right) e(6912120)e\left(\frac{691}{2120}\right) e(16692120)e\left(\frac{1669}{2120}\right) e(4711060)e\left(\frac{471}{1060}\right) e(1972120)e\left(\frac{197}{2120}\right)
χ85600(23,⋅)\chi_{85600}(23,\cdot) 85600.hw 1060 no 11 11 e(144265)e\left(\frac{144}{265}\right) e(191212)e\left(\frac{191}{212}\right) e(23265)e\left(\frac{23}{265}\right) e(9731060)e\left(\frac{973}{1060}\right) e(471530)e\left(\frac{471}{530}\right) e(1191060)e\left(\frac{119}{1060}\right) e(2891060)e\left(\frac{289}{1060}\right) e(4711060)e\left(\frac{471}{1060}\right) e(3331060)e\left(\frac{333}{1060}\right) e(167265)e\left(\frac{167}{265}\right)
χ85600(27,⋅)\chi_{85600}(27,\cdot) 85600.ic 2120 yes 11 11 e(19172120)e\left(\frac{1917}{2120}\right) e(1053)e\left(\frac{10}{53}\right) e(8571060)e\left(\frac{857}{1060}\right) e(10812120)e\left(\frac{1081}{2120}\right) e(11892120)e\left(\frac{1189}{2120}\right) e(6391060)e\left(\frac{639}{1060}\right) e(17032120)e\left(\frac{1703}{2120}\right) e(1972120)e\left(\frac{197}{2120}\right) e(167265)e\left(\frac{167}{265}\right) e(15112120)e\left(\frac{1511}{2120}\right)
χ85600(29,⋅)\chi_{85600}(29,\cdot) 85600.ik 2120 yes 11 11 e(20292120)e\left(\frac{2029}{2120}\right) e(49212)e\left(\frac{49}{212}\right) e(9691060)e\left(\frac{969}{1060}\right) e(2472120)e\left(\frac{247}{2120}\right) e(15932120)e\left(\frac{1593}{2120}\right) e(147265)e\left(\frac{147}{265}\right) e(20612120)e\left(\frac{2061}{2120}\right) e(3992120)e\left(\frac{399}{2120}\right) e(711060)e\left(\frac{71}{1060}\right) e(18472120)e\left(\frac{1847}{2120}\right)
χ85600(31,⋅)\chi_{85600}(31,\cdot) 85600.go 530 no 11 11 e(69530)e\left(\frac{69}{530}\right) e(2453)e\left(\frac{24}{53}\right) e(69265)e\left(\frac{69}{265}\right) e(267530)e\left(\frac{267}{530}\right) e(44265)e\left(\frac{44}{265}\right) e(311530)e\left(\frac{311}{530}\right) e(301530)e\left(\frac{301}{530}\right) e(309530)e\left(\frac{309}{530}\right) e(367530)e\left(\frac{367}{530}\right) e(207530)e\left(\frac{207}{530}\right)
χ85600(33,⋅)\chi_{85600}(33,\cdot) 85600.hq 1060 no −1-1 11 e(8531060)e\left(\frac{853}{1060}\right) e(15212)e\left(\frac{15}{212}\right) e(323530)e\left(\frac{323}{530}\right) e(131265)e\left(\frac{131}{265}\right) e(11060)e\left(\frac{1}{1060}\right) e(1271060)e\left(\frac{127}{1060}\right) e(211530)e\left(\frac{211}{530}\right) e(232265)e\left(\frac{232}{265}\right) e(4891060)e\left(\frac{489}{1060}\right) e(4391060)e\left(\frac{439}{1060}\right)
χ85600(37,⋅)\chi_{85600}(37,\cdot) 85600.in 2120 yes −1-1 11 e(13132120)e\left(\frac{1313}{2120}\right) e(97106)e\left(\frac{97}{106}\right) e(2531060)e\left(\frac{253}{1060}\right) e(15092120)e\left(\frac{1509}{2120}\right) e(9412120)e\left(\frac{941}{2120}\right) e(7911060)e\left(\frac{791}{1060}\right) e(19872120)e\left(\frac{1987}{2120}\right) e(11332120)e\left(\frac{1133}{2120}\right) e(491530)e\left(\frac{491}{530}\right) e(18192120)e\left(\frac{1819}{2120}\right)
χ85600(39,⋅)\chi_{85600}(39,\cdot) 85600.hs 1060 no −1-1 11 e(8711060)e\left(\frac{871}{1060}\right) e(61106)e\left(\frac{61}{106}\right) e(341530)e\left(\frac{341}{530}\right) e(10431060)e\left(\frac{1043}{1060}\right) e(5771060)e\left(\frac{577}{1060}\right) e(467530)e\left(\frac{467}{530}\right) e(4891060)e\left(\frac{489}{1060}\right) e(4211060)e\left(\frac{421}{1060}\right) e(229530)e\left(\frac{229}{530}\right) e(4931060)e\left(\frac{493}{1060}\right)
χ85600(41,⋅)\chi_{85600}(41,\cdot) 85600.hu 1060 no 11 11 e(691060)e\left(\frac{69}{1060}\right) e(77106)e\left(\frac{77}{106}\right) e(69530)e\left(\frac{69}{530}\right) e(2671060)e\left(\frac{267}{1060}\right) e(3531060)e\left(\frac{353}{1060}\right) e(144265)e\left(\frac{144}{265}\right) e(3011060)e\left(\frac{301}{1060}\right) e(8391060)e\left(\frac{839}{1060}\right) e(51530)e\left(\frac{51}{530}\right) e(2071060)e\left(\frac{207}{1060}\right)
χ85600(43,⋅)\chi_{85600}(43,\cdot) 85600.fz 424 no −1-1 11 e(249424)e\left(\frac{249}{424}\right) e(2353)e\left(\frac{23}{53}\right) e(37212)e\left(\frac{37}{212}\right) e(369424)e\left(\frac{369}{424}\right) e(177424)e\left(\frac{177}{424}\right) e(83212)e\left(\frac{83}{212}\right) e(335424)e\left(\frac{335}{424}\right) e(9424)e\left(\frac{9}{424}\right) e(1106)e\left(\frac{1}{106}\right) e(323424)e\left(\frac{323}{424}\right)
χ85600(47,⋅)\chi_{85600}(47,\cdot) 85600.hp 1060 no 11 11 e(5671060)e\left(\frac{567}{1060}\right) e(111212)e\left(\frac{111}{212}\right) e(37530)e\left(\frac{37}{530}\right) e(79265)e\left(\frac{79}{265}\right) e(3891060)e\left(\frac{389}{1060}\right) e(1131060)e\left(\frac{113}{1060}\right) e(459530)e\left(\frac{459}{530}\right) e(31530)e\left(\frac{31}{530}\right) e(4811060)e\left(\frac{481}{1060}\right) e(6411060)e\left(\frac{641}{1060}\right)
χ85600(49,⋅)\chi_{85600}(49,\cdot) 85600.eo 106 no 11 11 e(4253)e\left(\frac{42}{53}\right) e(41106)e\left(\frac{41}{106}\right) e(3153)e\left(\frac{31}{53}\right) e(37106)e\left(\frac{37}{106}\right) e(1953)e\left(\frac{19}{53}\right) e(3106)e\left(\frac{3}{106}\right) e(83106)e\left(\frac{83}{106}\right) e(19106)e\left(\frac{19}{106}\right) e(85106)e\left(\frac{85}{106}\right) e(2053)e\left(\frac{20}{53}\right)
χ85600(51,⋅)\chi_{85600}(51,\cdot) 85600.gb 424 no 11 11 e(213424)e\left(\frac{213}{424}\right) e(87212)e\left(\frac{87}{212}\right) e(1212)e\left(\frac{1}{212}\right) e(179424)e\left(\frac{179}{424}\right) e(85424)e\left(\frac{85}{424}\right) e(3153)e\left(\frac{31}{53}\right) e(201424)e\left(\frac{201}{424}\right) e(387424)e\left(\frac{387}{424}\right) e(139212)e\left(\frac{139}{212}\right) e(215424)e\left(\frac{215}{424}\right)
χ85600(53,⋅)\chi_{85600}(53,\cdot) 85600.id 2120 yes −1-1 11 e(14092120)e\left(\frac{1409}{2120}\right) e(553)e\left(\frac{5}{53}\right) e(3491060)e\left(\frac{349}{1060}\right) e(10972120)e\left(\frac{1097}{2120}\right) e(18932120)e\left(\frac{1893}{2120}\right) e(2931060)e\left(\frac{293}{1060}\right) e(19912120)e\left(\frac{1991}{2120}\right) e(16092120)e\left(\frac{1609}{2120}\right) e(4265)e\left(\frac{4}{265}\right) e(21072120)e\left(\frac{2107}{2120}\right)
χ85600(57,⋅)\chi_{85600}(57,\cdot) 85600.fu 212 no −1-1 11 e(25106)e\left(\frac{25}{106}\right) e(167212)e\left(\frac{167}{212}\right) e(2553)e\left(\frac{25}{53}\right) e(205212)e\left(\frac{205}{212}\right) e(5106)e\left(\frac{5}{106}\right) e(157212)e\left(\frac{157}{212}\right) e(33212)e\left(\frac{33}{212}\right) e(5212)e\left(\frac{5}{212}\right) e(173212)e\left(\frac{173}{212}\right) e(75106)e\left(\frac{75}{106}\right)
χ85600(59,⋅)\chi_{85600}(59,\cdot) 85600.ig 2120 yes 11 11 e(13632120)e\left(\frac{1363}{2120}\right) e(163212)e\left(\frac{163}{212}\right) e(3031060)e\left(\frac{303}{1060}\right) e(14492120)e\left(\frac{1449}{2120}\right) e(20112120)e\left(\frac{2011}{2120}\right) e(183530)e\left(\frac{183}{530}\right) e(9072120)e\left(\frac{907}{2120}\right) e(8732120)e\left(\frac{873}{2120}\right) e(2471060)e\left(\frac{247}{1060}\right) e(19692120)e\left(\frac{1969}{2120}\right)
χ85600(61,⋅)\chi_{85600}(61,\cdot) 85600.ih 2120 yes 11 11 e(6972120)e\left(\frac{697}{2120}\right) e(171212)e\left(\frac{171}{212}\right) e(6971060)e\left(\frac{697}{1060}\right) e(15912120)e\left(\frac{1591}{2120}\right) e(3092120)e\left(\frac{309}{2120}\right) e(337530)e\left(\frac{337}{530}\right) e(8132120)e\left(\frac{813}{2120}\right) e(2872120)e\left(\frac{287}{2120}\right) e(9531060)e\left(\frac{953}{1060}\right) e(20912120)e\left(\frac{2091}{2120}\right)
χ85600(63,⋅)\chi_{85600}(63,\cdot) 85600.hk 1060 no −1-1 11 e(10591060)e\left(\frac{1059}{1060}\right) e(103212)e\left(\frac{103}{212}\right) e(529530)e\left(\frac{529}{530}\right) e(361530)e\left(\frac{361}{530}\right) e(2331060)e\left(\frac{233}{1060}\right) e(4411060)e\left(\frac{441}{1060}\right) e(69265)e\left(\frac{69}{265}\right) e(257530)e\left(\frac{257}{530}\right) e(10471060)e\left(\frac{1047}{1060}\right) e(10571060)e\left(\frac{1057}{1060}\right)
χ85600(67,⋅)\chi_{85600}(67,\cdot) 85600.ib 2120 yes −1-1 11 e(4112120)e\left(\frac{411}{2120}\right) e(1553)e\left(\frac{15}{53}\right) e(4111060)e\left(\frac{411}{1060}\right) e(3232120)e\left(\frac{323}{2120}\right) e(12272120)e\left(\frac{1227}{2120}\right) e(1371060)e\left(\frac{137}{1060}\right) e(13092120)e\left(\frac{1309}{2120}\right) e(10112120)e\left(\frac{1011}{2120}\right) e(77530)e\left(\frac{77}{530}\right) e(12332120)e\left(\frac{1233}{2120}\right)
χ85600(69,⋅)\chi_{85600}(69,\cdot) 85600.ik 2120 yes 11 11 e(17912120)e\left(\frac{1791}{2120}\right) e(63212)e\left(\frac{63}{212}\right) e(7311060)e\left(\frac{731}{1060}\right) e(8932120)e\left(\frac{893}{2120}\right) e(8672120)e\left(\frac{867}{2120}\right) e(83265)e\left(\frac{83}{265}\right) e(4392120)e\left(\frac{439}{2120}\right) e(3012120)e\left(\frac{301}{2120}\right) e(9091060)e\left(\frac{909}{1060}\right) e(11332120)e\left(\frac{1133}{2120}\right)
χ85600(71,⋅)\chi_{85600}(71,\cdot) 85600.ht 1060 no 11 11 e(2371060)e\left(\frac{237}{1060}\right) e(11106)e\left(\frac{11}{106}\right) e(237530)e\left(\frac{237}{530}\right) e(8711060)e\left(\frac{871}{1060}\right) e(9591060)e\left(\frac{959}{1060}\right) e(79530)e\left(\frac{79}{530}\right) e(5731060)e\left(\frac{573}{1060}\right) e(3471060)e\left(\frac{347}{1060}\right) e(174265)e\left(\frac{174}{265}\right) e(7111060)e\left(\frac{711}{1060}\right)
χ85600(73,⋅)\chi_{85600}(73,\cdot) 85600.hc 1060 no 11 11 e(483530)e\left(\frac{483}{530}\right) e(195212)e\left(\frac{195}{212}\right) e(218265)e\left(\frac{218}{265}\right) e(8231060)e\left(\frac{823}{1060}\right) e(351530)e\left(\frac{351}{530}\right) e(9091060)e\left(\frac{909}{1060}\right) e(2391060)e\left(\frac{239}{1060}\right) e(8811060)e\left(\frac{881}{1060}\right) e(1031060)e\left(\frac{103}{1060}\right) e(389530)e\left(\frac{389}{530}\right)
χ85600(77,⋅)\chi_{85600}(77,\cdot) 85600.io 2120 yes 11 11 e(19072120)e\left(\frac{1907}{2120}\right) e(39106)e\left(\frac{39}{106}\right) e(8471060)e\left(\frac{847}{1060}\right) e(14112120)e\left(\frac{1411}{2120}\right) e(13992120)e\left(\frac{1399}{2120}\right) e(9891060)e\left(\frac{989}{1060}\right) e(18132120)e\left(\frac{1813}{2120}\right) e(5672120)e\left(\frac{567}{2120}\right) e(217265)e\left(\frac{217}{265}\right) e(14812120)e\left(\frac{1481}{2120}\right)
χ85600(79,⋅)\chi_{85600}(79,\cdot) 85600.gq 530 no −1-1 11 e(221530)e\left(\frac{221}{530}\right) e(4053)e\left(\frac{40}{53}\right) e(221265)e\left(\frac{221}{265}\right) e(249265)e\left(\frac{249}{265}\right) e(91265)e\left(\frac{91}{265}\right) e(59530)e\left(\frac{59}{530}\right) e(242265)e\left(\frac{242}{265}\right) e(91530)e\left(\frac{91}{530}\right) e(244265)e\left(\frac{244}{265}\right) e(133530)e\left(\frac{133}{530}\right)
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