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Properties

Modulus 43344334
Structure C2×C980C_{2}\times C_{980}
Order 19601960

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Show commands: PariGP / SageMath

sage: H = DirichletGroup(4334)
 
pari: g = idealstar(,4334,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 1960
sage: H.invariants()
 
pari: g.cyc
 
Structure = C2×C980C_{2}\times C_{980}
sage: H.gens()
 
pari: g.gen
 
Generators = χ4334(1971,⋅)\chi_{4334}(1971,\cdot), χ4334(199,⋅)\chi_{4334}(199,\cdot)

First 32 of 1960 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 1313 1515 1717 1919 2121 2323
χ4334(1,⋅)\chi_{4334}(1,\cdot) 4334.a 1 no 11 11 11 11 11 11 11 11 11 11 11 11
χ4334(3,⋅)\chi_{4334}(3,\cdot) 4334.bi 980 no −1-1 11 e(537980)e\left(\frac{537}{980}\right) e(381980)e\left(\frac{381}{980}\right) e(209490)e\left(\frac{209}{490}\right) e(47490)e\left(\frac{47}{490}\right) e(869980)e\left(\frac{869}{980}\right) e(459490)e\left(\frac{459}{490}\right) e(31980)e\left(\frac{31}{980}\right) e(4370)e\left(\frac{43}{70}\right) e(191196)e\left(\frac{191}{196}\right) e(4049)e\left(\frac{40}{49}\right)
χ4334(5,⋅)\chi_{4334}(5,\cdot) 4334.bi 980 no −1-1 11 e(381980)e\left(\frac{381}{980}\right) e(13980)e\left(\frac{13}{980}\right) e(47490)e\left(\frac{47}{490}\right) e(381490)e\left(\frac{381}{490}\right) e(737980)e\left(\frac{737}{980}\right) e(197490)e\left(\frac{197}{490}\right) e(783980)e\left(\frac{783}{980}\right) e(970)e\left(\frac{9}{70}\right) e(95196)e\left(\frac{95}{196}\right) e(2449)e\left(\frac{24}{49}\right)
χ4334(7,⋅)\chi_{4334}(7,\cdot) 4334.bf 490 no −1-1 11 e(209490)e\left(\frac{209}{490}\right) e(47490)e\left(\frac{47}{490}\right) e(321490)e\left(\frac{321}{490}\right) e(209245)e\left(\frac{209}{245}\right) e(79245)e\left(\frac{79}{245}\right) e(128245)e\left(\frac{128}{245}\right) e(181245)e\left(\frac{181}{245}\right) e(5770)e\left(\frac{57}{70}\right) e(449)e\left(\frac{4}{49}\right) e(1949)e\left(\frac{19}{49}\right)
χ4334(9,⋅)\chi_{4334}(9,\cdot) 4334.bh 490 no 11 11 e(47490)e\left(\frac{47}{490}\right) e(381490)e\left(\frac{381}{490}\right) e(209245)e\left(\frac{209}{245}\right) e(47245)e\left(\frac{47}{245}\right) e(379490)e\left(\frac{379}{490}\right) e(214245)e\left(\frac{214}{245}\right) e(31490)e\left(\frac{31}{490}\right) e(835)e\left(\frac{8}{35}\right) e(9398)e\left(\frac{93}{98}\right) e(3149)e\left(\frac{31}{49}\right)
χ4334(13,⋅)\chi_{4334}(13,\cdot) 4334.bj 980 no 11 11 e(869980)e\left(\frac{869}{980}\right) e(737980)e\left(\frac{737}{980}\right) e(79245)e\left(\frac{79}{245}\right) e(379490)e\left(\frac{379}{490}\right) e(283980)e\left(\frac{283}{980}\right) e(313490)e\left(\frac{313}{490}\right) e(177980)e\left(\frac{177}{980}\right) e(3335)e\left(\frac{33}{35}\right) e(41196)e\left(\frac{41}{196}\right) e(1549)e\left(\frac{15}{49}\right)
χ4334(15,⋅)\chi_{4334}(15,\cdot) 4334.bh 490 no 11 11 e(459490)e\left(\frac{459}{490}\right) e(197490)e\left(\frac{197}{490}\right) e(128245)e\left(\frac{128}{245}\right) e(214245)e\left(\frac{214}{245}\right) e(313490)e\left(\frac{313}{490}\right) e(83245)e\left(\frac{83}{245}\right) e(407490)e\left(\frac{407}{490}\right) e(2635)e\left(\frac{26}{35}\right) e(4598)e\left(\frac{45}{98}\right) e(1549)e\left(\frac{15}{49}\right)
χ4334(17,⋅)\chi_{4334}(17,\cdot) 4334.bj 980 no 11 11 e(31980)e\left(\frac{31}{980}\right) e(783980)e\left(\frac{783}{980}\right) e(181245)e\left(\frac{181}{245}\right) e(31490)e\left(\frac{31}{490}\right) e(177980)e\left(\frac{177}{980}\right) e(407490)e\left(\frac{407}{490}\right) e(83980)e\left(\frac{83}{980}\right) e(2235)e\left(\frac{22}{35}\right) e(151196)e\left(\frac{151}{196}\right) e(1749)e\left(\frac{17}{49}\right)
χ4334(19,⋅)\chi_{4334}(19,\cdot) 4334.u 70 no −1-1 11 e(4370)e\left(\frac{43}{70}\right) e(970)e\left(\frac{9}{70}\right) e(5770)e\left(\frac{57}{70}\right) e(835)e\left(\frac{8}{35}\right) e(3335)e\left(\frac{33}{35}\right) e(2635)e\left(\frac{26}{35}\right) e(2235)e\left(\frac{22}{35}\right) e(910)e\left(\frac{9}{10}\right) e(37)e\left(\frac{3}{7}\right) e(27)e\left(\frac{2}{7}\right)
χ4334(21,⋅)\chi_{4334}(21,\cdot) 4334.bc 196 no 11 11 e(191196)e\left(\frac{191}{196}\right) e(95196)e\left(\frac{95}{196}\right) e(449)e\left(\frac{4}{49}\right) e(9398)e\left(\frac{93}{98}\right) e(41196)e\left(\frac{41}{196}\right) e(4598)e\left(\frac{45}{98}\right) e(151196)e\left(\frac{151}{196}\right) e(37)e\left(\frac{3}{7}\right) e(11196)e\left(\frac{11}{196}\right) e(1049)e\left(\frac{10}{49}\right)
χ4334(23,⋅)\chi_{4334}(23,\cdot) 4334.t 49 no 11 11 e(4049)e\left(\frac{40}{49}\right) e(2449)e\left(\frac{24}{49}\right) e(1949)e\left(\frac{19}{49}\right) e(3149)e\left(\frac{31}{49}\right) e(1549)e\left(\frac{15}{49}\right) e(1549)e\left(\frac{15}{49}\right) e(1749)e\left(\frac{17}{49}\right) e(27)e\left(\frac{2}{7}\right) e(1049)e\left(\frac{10}{49}\right) e(2349)e\left(\frac{23}{49}\right)
χ4334(25,⋅)\chi_{4334}(25,\cdot) 4334.bh 490 no 11 11 e(381490)e\left(\frac{381}{490}\right) e(13490)e\left(\frac{13}{490}\right) e(47245)e\left(\frac{47}{245}\right) e(136245)e\left(\frac{136}{245}\right) e(247490)e\left(\frac{247}{490}\right) e(197245)e\left(\frac{197}{245}\right) e(293490)e\left(\frac{293}{490}\right) e(935)e\left(\frac{9}{35}\right) e(9598)e\left(\frac{95}{98}\right) e(4849)e\left(\frac{48}{49}\right)
χ4334(27,⋅)\chi_{4334}(27,\cdot) 4334.bi 980 no −1-1 11 e(631980)e\left(\frac{631}{980}\right) e(163980)e\left(\frac{163}{980}\right) e(137490)e\left(\frac{137}{490}\right) e(141490)e\left(\frac{141}{490}\right) e(647980)e\left(\frac{647}{980}\right) e(397490)e\left(\frac{397}{490}\right) e(93980)e\left(\frac{93}{980}\right) e(5970)e\left(\frac{59}{70}\right) e(181196)e\left(\frac{181}{196}\right) e(2249)e\left(\frac{22}{49}\right)
χ4334(29,⋅)\chi_{4334}(29,\cdot) 4334.bg 490 no −1-1 11 e(207245)e\left(\frac{207}{245}\right) e(36245)e\left(\frac{36}{245}\right) e(351490)e\left(\frac{351}{490}\right) e(169245)e\left(\frac{169}{245}\right) e(143490)e\left(\frac{143}{490}\right) e(243245)e\left(\frac{243}{245}\right) e(247490)e\left(\frac{247}{490}\right) e(2770)e\left(\frac{27}{70}\right) e(5598)e\left(\frac{55}{98}\right) e(249)e\left(\frac{2}{49}\right)
χ4334(31,⋅)\chi_{4334}(31,\cdot) 4334.bi 980 no −1-1 11 e(9980)e\left(\frac{9}{980}\right) e(417980)e\left(\frac{417}{980}\right) e(113490)e\left(\frac{113}{490}\right) e(9490)e\left(\frac{9}{490}\right) e(573980)e\left(\frac{573}{980}\right) e(213490)e\left(\frac{213}{490}\right) e(767980)e\left(\frac{767}{980}\right) e(4170)e\left(\frac{41}{70}\right) e(47196)e\left(\frac{47}{196}\right) e(1649)e\left(\frac{16}{49}\right)
χ4334(35,⋅)\chi_{4334}(35,\cdot) 4334.bj 980 no 11 11 e(799980)e\left(\frac{799}{980}\right) e(107980)e\left(\frac{107}{980}\right) e(184245)e\left(\frac{184}{245}\right) e(309490)e\left(\frac{309}{490}\right) e(73980)e\left(\frac{73}{980}\right) e(453490)e\left(\frac{453}{490}\right) e(527980)e\left(\frac{527}{980}\right) e(3335)e\left(\frac{33}{35}\right) e(111196)e\left(\frac{111}{196}\right) e(4349)e\left(\frac{43}{49}\right)
χ4334(37,⋅)\chi_{4334}(37,\cdot) 4334.be 245 no 11 11 e(222245)e\left(\frac{222}{245}\right) e(241245)e\left(\frac{241}{245}\right) e(103245)e\left(\frac{103}{245}\right) e(199245)e\left(\frac{199}{245}\right) e(169245)e\left(\frac{169}{245}\right) e(218245)e\left(\frac{218}{245}\right) e(136245)e\left(\frac{136}{245}\right) e(1635)e\left(\frac{16}{35}\right) e(1649)e\left(\frac{16}{49}\right) e(2749)e\left(\frac{27}{49}\right)
χ4334(39,⋅)\chi_{4334}(39,\cdot) 4334.bf 490 no −1-1 11 e(213490)e\left(\frac{213}{490}\right) e(69490)e\left(\frac{69}{490}\right) e(367490)e\left(\frac{367}{490}\right) e(213245)e\left(\frac{213}{245}\right) e(43245)e\left(\frac{43}{245}\right) e(141245)e\left(\frac{141}{245}\right) e(52245)e\left(\frac{52}{245}\right) e(3970)e\left(\frac{39}{70}\right) e(949)e\left(\frac{9}{49}\right) e(649)e\left(\frac{6}{49}\right)
χ4334(41,⋅)\chi_{4334}(41,\cdot) 4334.bf 490 no −1-1 11 e(481490)e\left(\frac{481}{490}\right) e(73490)e\left(\frac{73}{490}\right) e(19490)e\left(\frac{19}{490}\right) e(236245)e\left(\frac{236}{245}\right) e(81245)e\left(\frac{81}{245}\right) e(32245)e\left(\frac{32}{245}\right) e(229245)e\left(\frac{229}{245}\right) e(2370)e\left(\frac{23}{70}\right) e(149)e\left(\frac{1}{49}\right) e(1749)e\left(\frac{17}{49}\right)
χ4334(43,⋅)\chi_{4334}(43,\cdot) 4334.z 98 no −1-1 11 e(398)e\left(\frac{3}{98}\right) e(4198)e\left(\frac{41}{98}\right) e(5998)e\left(\frac{59}{98}\right) e(349)e\left(\frac{3}{49}\right) e(2249)e\left(\frac{22}{49}\right) e(2249)e\left(\frac{22}{49}\right) e(3849)e\left(\frac{38}{49}\right) e(1114)e\left(\frac{11}{14}\right) e(3149)e\left(\frac{31}{49}\right) e(3749)e\left(\frac{37}{49}\right)
χ4334(45,⋅)\chi_{4334}(45,\cdot) 4334.bd 196 no −1-1 11 e(95196)e\left(\frac{95}{196}\right) e(155196)e\left(\frac{155}{196}\right) e(9398)e\left(\frac{93}{98}\right) e(9598)e\left(\frac{95}{98}\right) e(103196)e\left(\frac{103}{196}\right) e(2798)e\left(\frac{27}{98}\right) e(169196)e\left(\frac{169}{196}\right) e(514)e\left(\frac{5}{14}\right) e(85196)e\left(\frac{85}{196}\right) e(649)e\left(\frac{6}{49}\right)
χ4334(47,⋅)\chi_{4334}(47,\cdot) 4334.bh 490 no 11 11 e(171490)e\left(\frac{171}{490}\right) e(83490)e\left(\frac{83}{490}\right) e(187245)e\left(\frac{187}{245}\right) e(171245)e\left(\frac{171}{245}\right) e(107490)e\left(\frac{107}{490}\right) e(127245)e\left(\frac{127}{245}\right) e(363490)e\left(\frac{363}{490}\right) e(935)e\left(\frac{9}{35}\right) e(1198)e\left(\frac{11}{98}\right) e(2049)e\left(\frac{20}{49}\right)
χ4334(49,⋅)\chi_{4334}(49,\cdot) 4334.be 245 no 11 11 e(209245)e\left(\frac{209}{245}\right) e(47245)e\left(\frac{47}{245}\right) e(76245)e\left(\frac{76}{245}\right) e(173245)e\left(\frac{173}{245}\right) e(158245)e\left(\frac{158}{245}\right) e(11245)e\left(\frac{11}{245}\right) e(117245)e\left(\frac{117}{245}\right) e(2235)e\left(\frac{22}{35}\right) e(849)e\left(\frac{8}{49}\right) e(3849)e\left(\frac{38}{49}\right)
χ4334(51,⋅)\chi_{4334}(51,\cdot) 4334.bg 490 no −1-1 11 e(142245)e\left(\frac{142}{245}\right) e(46245)e\left(\frac{46}{245}\right) e(81490)e\left(\frac{81}{490}\right) e(39245)e\left(\frac{39}{245}\right) e(33490)e\left(\frac{33}{490}\right) e(188245)e\left(\frac{188}{245}\right) e(57490)e\left(\frac{57}{490}\right) e(1770)e\left(\frac{17}{70}\right) e(7398)e\left(\frac{73}{98}\right) e(849)e\left(\frac{8}{49}\right)
χ4334(53,⋅)\chi_{4334}(53,\cdot) 4334.be 245 no 11 11 e(71245)e\left(\frac{71}{245}\right) e(23245)e\left(\frac{23}{245}\right) e(204245)e\left(\frac{204}{245}\right) e(142245)e\left(\frac{142}{245}\right) e(192245)e\left(\frac{192}{245}\right) e(94245)e\left(\frac{94}{245}\right) e(198245)e\left(\frac{198}{245}\right) e(1335)e\left(\frac{13}{35}\right) e(649)e\left(\frac{6}{49}\right) e(449)e\left(\frac{4}{49}\right)
χ4334(57,⋅)\chi_{4334}(57,\cdot) 4334.bj 980 no 11 11 e(159980)e\left(\frac{159}{980}\right) e(507980)e\left(\frac{507}{980}\right) e(59245)e\left(\frac{59}{245}\right) e(159490)e\left(\frac{159}{490}\right) e(813980)e\left(\frac{813}{980}\right) e(333490)e\left(\frac{333}{490}\right) e(647980)e\left(\frac{647}{980}\right) e(1835)e\left(\frac{18}{35}\right) e(79196)e\left(\frac{79}{196}\right) e(549)e\left(\frac{5}{49}\right)
χ4334(59,⋅)\chi_{4334}(59,\cdot) 4334.be 245 no 11 11 e(242245)e\left(\frac{242}{245}\right) e(106245)e\left(\frac{106}{245}\right) e(88245)e\left(\frac{88}{245}\right) e(239245)e\left(\frac{239}{245}\right) e(54245)e\left(\frac{54}{245}\right) e(103245)e\left(\frac{103}{245}\right) e(71245)e\left(\frac{71}{245}\right) e(3135)e\left(\frac{31}{35}\right) e(1749)e\left(\frac{17}{49}\right) e(4449)e\left(\frac{44}{49}\right)
χ4334(61,⋅)\chi_{4334}(61,\cdot) 4334.bg 490 no −1-1 11 e(74245)e\left(\frac{74}{245}\right) e(162245)e\left(\frac{162}{245}\right) e(477490)e\left(\frac{477}{490}\right) e(148245)e\left(\frac{148}{245}\right) e(31490)e\left(\frac{31}{490}\right) e(236245)e\left(\frac{236}{245}\right) e(9490)e\left(\frac{9}{490}\right) e(6970)e\left(\frac{69}{70}\right) e(2798)e\left(\frac{27}{98}\right) e(949)e\left(\frac{9}{49}\right)
χ4334(63,⋅)\chi_{4334}(63,\cdot) 4334.bg 490 no −1-1 11 e(128245)e\left(\frac{128}{245}\right) e(214245)e\left(\frac{214}{245}\right) e(249490)e\left(\frac{249}{490}\right) e(11245)e\left(\frac{11}{245}\right) e(47490)e\left(\frac{47}{490}\right) e(97245)e\left(\frac{97}{245}\right) e(393490)e\left(\frac{393}{490}\right) e(370)e\left(\frac{3}{70}\right) e(398)e\left(\frac{3}{98}\right) e(149)e\left(\frac{1}{49}\right)
χ4334(65,⋅)\chi_{4334}(65,\cdot) 4334.z 98 no −1-1 11 e(2798)e\left(\frac{27}{98}\right) e(7598)e\left(\frac{75}{98}\right) e(4198)e\left(\frac{41}{98}\right) e(2749)e\left(\frac{27}{49}\right) e(249)e\left(\frac{2}{49}\right) e(249)e\left(\frac{2}{49}\right) e(4849)e\left(\frac{48}{49}\right) e(114)e\left(\frac{1}{14}\right) e(3449)e\left(\frac{34}{49}\right) e(3949)e\left(\frac{39}{49}\right)
χ4334(67,⋅)\chi_{4334}(67,\cdot) 4334.bd 196 no −1-1 11 e(137196)e\left(\frac{137}{196}\right) e(141196)e\left(\frac{141}{196}\right) e(6598)e\left(\frac{65}{98}\right) e(3998)e\left(\frac{39}{98}\right) e(33196)e\left(\frac{33}{196}\right) e(4198)e\left(\frac{41}{98}\right) e(155196)e\left(\frac{155}{196}\right) e(514)e\left(\frac{5}{14}\right) e(71196)e\left(\frac{71}{196}\right) e(2049)e\left(\frac{20}{49}\right)
χ4334(69,⋅)\chi_{4334}(69,\cdot) 4334.ba 140 no −1-1 11 e(51140)e\left(\frac{51}{140}\right) e(123140)e\left(\frac{123}{140}\right) e(5770)e\left(\frac{57}{70}\right) e(5170)e\left(\frac{51}{70}\right) e(27140)e\left(\frac{27}{140}\right) e(1770)e\left(\frac{17}{70}\right) e(53140)e\left(\frac{53}{140}\right) e(910)e\left(\frac{9}{10}\right) e(528)e\left(\frac{5}{28}\right) e(27)e\left(\frac{2}{7}\right)
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