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Properties

Modulus 11251125
Structure C2×C300C_{2}\times C_{300}
Order 600600

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Show commands: PariGP / SageMath

sage: H = DirichletGroup(1125)
 
pari: g = idealstar(,1125,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 600
sage: H.invariants()
 
pari: g.cyc
 
Structure = C2×C300C_{2}\times C_{300}
sage: H.gens()
 
pari: g.gen
 
Generators = χ1125(1001,⋅)\chi_{1125}(1001,\cdot), χ1125(127,⋅)\chi_{1125}(127,\cdot)

First 32 of 600 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 1919
χ1125(1,⋅)\chi_{1125}(1,\cdot) 1125.a 1 no 11 11 11 11 11 11 11 11 11 11 11 11
χ1125(2,⋅)\chi_{1125}(2,\cdot) 1125.bj 300 yes 11 11 e(53300)e\left(\frac{53}{300}\right) e(53150)e\left(\frac{53}{150}\right) e(3160)e\left(\frac{31}{60}\right) e(53100)e\left(\frac{53}{100}\right) e(139150)e\left(\frac{139}{150}\right) e(217300)e\left(\frac{217}{300}\right) e(5275)e\left(\frac{52}{75}\right) e(5375)e\left(\frac{53}{75}\right) e(23100)e\left(\frac{23}{100}\right) e(950)e\left(\frac{9}{50}\right)
χ1125(4,⋅)\chi_{1125}(4,\cdot) 1125.bf 150 yes 11 11 e(53150)e\left(\frac{53}{150}\right) e(5375)e\left(\frac{53}{75}\right) e(130)e\left(\frac{1}{30}\right) e(350)e\left(\frac{3}{50}\right) e(6475)e\left(\frac{64}{75}\right) e(67150)e\left(\frac{67}{150}\right) e(2975)e\left(\frac{29}{75}\right) e(3175)e\left(\frac{31}{75}\right) e(2350)e\left(\frac{23}{50}\right) e(925)e\left(\frac{9}{25}\right)
χ1125(7,⋅)\chi_{1125}(7,\cdot) 1125.bb 60 no −1-1 11 e(3160)e\left(\frac{31}{60}\right) e(130)e\left(\frac{1}{30}\right) e(1112)e\left(\frac{11}{12}\right) e(1120)e\left(\frac{11}{20}\right) e(415)e\left(\frac{4}{15}\right) e(2960)e\left(\frac{29}{60}\right) e(1330)e\left(\frac{13}{30}\right) e(115)e\left(\frac{1}{15}\right) e(120)e\left(\frac{1}{20}\right) e(310)e\left(\frac{3}{10}\right)
χ1125(8,⋅)\chi_{1125}(8,\cdot) 1125.be 100 no 11 11 e(53100)e\left(\frac{53}{100}\right) e(350)e\left(\frac{3}{50}\right) e(1120)e\left(\frac{11}{20}\right) e(59100)e\left(\frac{59}{100}\right) e(3950)e\left(\frac{39}{50}\right) e(17100)e\left(\frac{17}{100}\right) e(225)e\left(\frac{2}{25}\right) e(325)e\left(\frac{3}{25}\right) e(69100)e\left(\frac{69}{100}\right) e(2750)e\left(\frac{27}{50}\right)
χ1125(11,⋅)\chi_{1125}(11,\cdot) 1125.bh 150 yes −1-1 11 e(139150)e\left(\frac{139}{150}\right) e(6475)e\left(\frac{64}{75}\right) e(415)e\left(\frac{4}{15}\right) e(3950)e\left(\frac{39}{50}\right) e(139150)e\left(\frac{139}{150}\right) e(7375)e\left(\frac{73}{75}\right) e(29150)e\left(\frac{29}{150}\right) e(5375)e\left(\frac{53}{75}\right) e(4950)e\left(\frac{49}{50}\right) e(1725)e\left(\frac{17}{25}\right)
χ1125(13,⋅)\chi_{1125}(13,\cdot) 1125.bi 300 yes −1-1 11 e(217300)e\left(\frac{217}{300}\right) e(67150)e\left(\frac{67}{150}\right) e(2960)e\left(\frac{29}{60}\right) e(17100)e\left(\frac{17}{100}\right) e(7375)e\left(\frac{73}{75}\right) e(263300)e\left(\frac{263}{300}\right) e(31150)e\left(\frac{31}{150}\right) e(6775)e\left(\frac{67}{75}\right) e(47100)e\left(\frac{47}{100}\right) e(150)e\left(\frac{1}{50}\right)
χ1125(14,⋅)\chi_{1125}(14,\cdot) 1125.bg 150 yes −1-1 11 e(5275)e\left(\frac{52}{75}\right) e(2975)e\left(\frac{29}{75}\right) e(1330)e\left(\frac{13}{30}\right) e(225)e\left(\frac{2}{25}\right) e(29150)e\left(\frac{29}{150}\right) e(31150)e\left(\frac{31}{150}\right) e(19150)e\left(\frac{19}{150}\right) e(5875)e\left(\frac{58}{75}\right) e(725)e\left(\frac{7}{25}\right) e(1225)e\left(\frac{12}{25}\right)
χ1125(16,⋅)\chi_{1125}(16,\cdot) 1125.bc 75 yes 11 11 e(5375)e\left(\frac{53}{75}\right) e(3175)e\left(\frac{31}{75}\right) e(115)e\left(\frac{1}{15}\right) e(325)e\left(\frac{3}{25}\right) e(5375)e\left(\frac{53}{75}\right) e(6775)e\left(\frac{67}{75}\right) e(5875)e\left(\frac{58}{75}\right) e(6275)e\left(\frac{62}{75}\right) e(2325)e\left(\frac{23}{25}\right) e(1825)e\left(\frac{18}{25}\right)
χ1125(17,⋅)\chi_{1125}(17,\cdot) 1125.be 100 no 11 11 e(23100)e\left(\frac{23}{100}\right) e(2350)e\left(\frac{23}{50}\right) e(120)e\left(\frac{1}{20}\right) e(69100)e\left(\frac{69}{100}\right) e(4950)e\left(\frac{49}{50}\right) e(47100)e\left(\frac{47}{100}\right) e(725)e\left(\frac{7}{25}\right) e(2325)e\left(\frac{23}{25}\right) e(79100)e\left(\frac{79}{100}\right) e(750)e\left(\frac{7}{50}\right)
χ1125(19,⋅)\chi_{1125}(19,\cdot) 1125.y 50 no 11 11 e(950)e\left(\frac{9}{50}\right) e(925)e\left(\frac{9}{25}\right) e(310)e\left(\frac{3}{10}\right) e(2750)e\left(\frac{27}{50}\right) e(1725)e\left(\frac{17}{25}\right) e(150)e\left(\frac{1}{50}\right) e(1225)e\left(\frac{12}{25}\right) e(1825)e\left(\frac{18}{25}\right) e(750)e\left(\frac{7}{50}\right) e(625)e\left(\frac{6}{25}\right)
χ1125(22,⋅)\chi_{1125}(22,\cdot) 1125.bi 300 yes −1-1 11 e(31300)e\left(\frac{31}{300}\right) e(31150)e\left(\frac{31}{150}\right) e(4760)e\left(\frac{47}{60}\right) e(31100)e\left(\frac{31}{100}\right) e(6475)e\left(\frac{64}{75}\right) e(209300)e\left(\frac{209}{300}\right) e(133150)e\left(\frac{133}{150}\right) e(3175)e\left(\frac{31}{75}\right) e(21100)e\left(\frac{21}{100}\right) e(4350)e\left(\frac{43}{50}\right)
χ1125(23,⋅)\chi_{1125}(23,\cdot) 1125.bj 300 yes 11 11 e(43300)e\left(\frac{43}{300}\right) e(43150)e\left(\frac{43}{150}\right) e(4160)e\left(\frac{41}{60}\right) e(43100)e\left(\frac{43}{100}\right) e(59150)e\left(\frac{59}{150}\right) e(227300)e\left(\frac{227}{300}\right) e(6275)e\left(\frac{62}{75}\right) e(4375)e\left(\frac{43}{75}\right) e(13100)e\left(\frac{13}{100}\right) e(2950)e\left(\frac{29}{50}\right)
χ1125(26,⋅)\chi_{1125}(26,\cdot) 1125.n 10 no −1-1 11 e(910)e\left(\frac{9}{10}\right) e(45)e\left(\frac{4}{5}\right) 11 e(710)e\left(\frac{7}{10}\right) e(910)e\left(\frac{9}{10}\right) e(35)e\left(\frac{3}{5}\right) e(910)e\left(\frac{9}{10}\right) e(35)e\left(\frac{3}{5}\right) e(710)e\left(\frac{7}{10}\right) e(15)e\left(\frac{1}{5}\right)
χ1125(28,⋅)\chi_{1125}(28,\cdot) 1125.bd 100 no −1-1 11 e(87100)e\left(\frac{87}{100}\right) e(3750)e\left(\frac{37}{50}\right) e(1920)e\left(\frac{19}{20}\right) e(61100)e\left(\frac{61}{100}\right) e(325)e\left(\frac{3}{25}\right) e(93100)e\left(\frac{93}{100}\right) e(4150)e\left(\frac{41}{50}\right) e(1225)e\left(\frac{12}{25}\right) e(51100)e\left(\frac{51}{100}\right) e(3350)e\left(\frac{33}{50}\right)
χ1125(29,⋅)\chi_{1125}(29,\cdot) 1125.bg 150 yes −1-1 11 e(5975)e\left(\frac{59}{75}\right) e(4375)e\left(\frac{43}{75}\right) e(1130)e\left(\frac{11}{30}\right) e(925)e\left(\frac{9}{25}\right) e(43150)e\left(\frac{43}{150}\right) e(77150)e\left(\frac{77}{150}\right) e(23150)e\left(\frac{23}{150}\right) e(1175)e\left(\frac{11}{75}\right) e(1925)e\left(\frac{19}{25}\right) e(425)e\left(\frac{4}{25}\right)
χ1125(31,⋅)\chi_{1125}(31,\cdot) 1125.bc 75 yes 11 11 e(6175)e\left(\frac{61}{75}\right) e(4775)e\left(\frac{47}{75}\right) e(215)e\left(\frac{2}{15}\right) e(1125)e\left(\frac{11}{25}\right) e(6175)e\left(\frac{61}{75}\right) e(2975)e\left(\frac{29}{75}\right) e(7175)e\left(\frac{71}{75}\right) e(1975)e\left(\frac{19}{75}\right) e(125)e\left(\frac{1}{25}\right) e(1625)e\left(\frac{16}{25}\right)
χ1125(32,⋅)\chi_{1125}(32,\cdot) 1125.ba 60 no 11 11 e(5360)e\left(\frac{53}{60}\right) e(2330)e\left(\frac{23}{30}\right) e(712)e\left(\frac{7}{12}\right) e(1320)e\left(\frac{13}{20}\right) e(1930)e\left(\frac{19}{30}\right) e(3760)e\left(\frac{37}{60}\right) e(715)e\left(\frac{7}{15}\right) e(815)e\left(\frac{8}{15}\right) e(320)e\left(\frac{3}{20}\right) e(910)e\left(\frac{9}{10}\right)
χ1125(34,⋅)\chi_{1125}(34,\cdot) 1125.bf 150 yes 11 11 e(61150)e\left(\frac{61}{150}\right) e(6175)e\left(\frac{61}{75}\right) e(1730)e\left(\frac{17}{30}\right) e(1150)e\left(\frac{11}{50}\right) e(6875)e\left(\frac{68}{75}\right) e(29150)e\left(\frac{29}{150}\right) e(7375)e\left(\frac{73}{75}\right) e(4775)e\left(\frac{47}{75}\right) e(150)e\left(\frac{1}{50}\right) e(825)e\left(\frac{8}{25}\right)
χ1125(37,⋅)\chi_{1125}(37,\cdot) 1125.bd 100 no −1-1 11 e(29100)e\left(\frac{29}{100}\right) e(2950)e\left(\frac{29}{50}\right) e(1320)e\left(\frac{13}{20}\right) e(87100)e\left(\frac{87}{100}\right) e(125)e\left(\frac{1}{25}\right) e(31100)e\left(\frac{31}{100}\right) e(4750)e\left(\frac{47}{50}\right) e(425)e\left(\frac{4}{25}\right) e(17100)e\left(\frac{17}{100}\right) e(1150)e\left(\frac{11}{50}\right)
χ1125(38,⋅)\chi_{1125}(38,\cdot) 1125.bj 300 yes 11 11 e(107300)e\left(\frac{107}{300}\right) e(107150)e\left(\frac{107}{150}\right) e(4960)e\left(\frac{49}{60}\right) e(7100)e\left(\frac{7}{100}\right) e(91150)e\left(\frac{91}{150}\right) e(223300)e\left(\frac{223}{300}\right) e(1375)e\left(\frac{13}{75}\right) e(3275)e\left(\frac{32}{75}\right) e(37100)e\left(\frac{37}{100}\right) e(2150)e\left(\frac{21}{50}\right)
χ1125(41,⋅)\chi_{1125}(41,\cdot) 1125.bh 150 yes −1-1 11 e(41150)e\left(\frac{41}{150}\right) e(4175)e\left(\frac{41}{75}\right) e(1115)e\left(\frac{11}{15}\right) e(4150)e\left(\frac{41}{50}\right) e(41150)e\left(\frac{41}{150}\right) e(6275)e\left(\frac{62}{75}\right) e(1150)e\left(\frac{1}{150}\right) e(775)e\left(\frac{7}{75}\right) e(3150)e\left(\frac{31}{50}\right) e(2325)e\left(\frac{23}{25}\right)
χ1125(43,⋅)\chi_{1125}(43,\cdot) 1125.bb 60 no −1-1 11 e(3760)e\left(\frac{37}{60}\right) e(730)e\left(\frac{7}{30}\right) e(512)e\left(\frac{5}{12}\right) e(1720)e\left(\frac{17}{20}\right) e(1315)e\left(\frac{13}{15}\right) e(2360)e\left(\frac{23}{60}\right) e(130)e\left(\frac{1}{30}\right) e(715)e\left(\frac{7}{15}\right) e(720)e\left(\frac{7}{20}\right) e(110)e\left(\frac{1}{10}\right)
χ1125(44,⋅)\chi_{1125}(44,\cdot) 1125.z 50 no −1-1 11 e(725)e\left(\frac{7}{25}\right) e(1425)e\left(\frac{14}{25}\right) e(310)e\left(\frac{3}{10}\right) e(2125)e\left(\frac{21}{25}\right) e(3950)e\left(\frac{39}{50}\right) e(2150)e\left(\frac{21}{50}\right) e(2950)e\left(\frac{29}{50}\right) e(325)e\left(\frac{3}{25}\right) e(1125)e\left(\frac{11}{25}\right) e(125)e\left(\frac{1}{25}\right)
χ1125(46,⋅)\chi_{1125}(46,\cdot) 1125.t 25 no 11 11 e(825)e\left(\frac{8}{25}\right) e(1625)e\left(\frac{16}{25}\right) e(15)e\left(\frac{1}{5}\right) e(2425)e\left(\frac{24}{25}\right) e(825)e\left(\frac{8}{25}\right) e(1225)e\left(\frac{12}{25}\right) e(1325)e\left(\frac{13}{25}\right) e(725)e\left(\frac{7}{25}\right) e(925)e\left(\frac{9}{25}\right) e(1925)e\left(\frac{19}{25}\right)
χ1125(47,⋅)\chi_{1125}(47,\cdot) 1125.bj 300 yes 11 11 e(41300)e\left(\frac{41}{300}\right) e(41150)e\left(\frac{41}{150}\right) e(760)e\left(\frac{7}{60}\right) e(41100)e\left(\frac{41}{100}\right) e(133150)e\left(\frac{133}{150}\right) e(49300)e\left(\frac{49}{300}\right) e(1975)e\left(\frac{19}{75}\right) e(4175)e\left(\frac{41}{75}\right) e(31100)e\left(\frac{31}{100}\right) e(2350)e\left(\frac{23}{50}\right)
χ1125(49,⋅)\chi_{1125}(49,\cdot) 1125.v 30 no 11 11 e(130)e\left(\frac{1}{30}\right) e(115)e\left(\frac{1}{15}\right) e(56)e\left(\frac{5}{6}\right) e(110)e\left(\frac{1}{10}\right) e(815)e\left(\frac{8}{15}\right) e(2930)e\left(\frac{29}{30}\right) e(1315)e\left(\frac{13}{15}\right) e(215)e\left(\frac{2}{15}\right) e(110)e\left(\frac{1}{10}\right) e(35)e\left(\frac{3}{5}\right)
χ1125(52,⋅)\chi_{1125}(52,\cdot) 1125.bi 300 yes −1-1 11 e(23300)e\left(\frac{23}{300}\right) e(23150)e\left(\frac{23}{150}\right) e(3160)e\left(\frac{31}{60}\right) e(23100)e\left(\frac{23}{100}\right) e(6275)e\left(\frac{62}{75}\right) e(97300)e\left(\frac{97}{300}\right) e(89150)e\left(\frac{89}{150}\right) e(2375)e\left(\frac{23}{75}\right) e(93100)e\left(\frac{93}{100}\right) e(1950)e\left(\frac{19}{50}\right)
χ1125(53,⋅)\chi_{1125}(53,\cdot) 1125.be 100 no 11 11 e(17100)e\left(\frac{17}{100}\right) e(1750)e\left(\frac{17}{50}\right) e(1920)e\left(\frac{19}{20}\right) e(51100)e\left(\frac{51}{100}\right) e(2150)e\left(\frac{21}{50}\right) e(13100)e\left(\frac{13}{100}\right) e(325)e\left(\frac{3}{25}\right) e(1725)e\left(\frac{17}{25}\right) e(41100)e\left(\frac{41}{100}\right) e(350)e\left(\frac{3}{50}\right)
χ1125(56,⋅)\chi_{1125}(56,\cdot) 1125.bh 150 yes −1-1 11 e(7150)e\left(\frac{7}{150}\right) e(775)e\left(\frac{7}{75}\right) e(715)e\left(\frac{7}{15}\right) e(750)e\left(\frac{7}{50}\right) e(7150)e\left(\frac{7}{150}\right) e(4975)e\left(\frac{49}{75}\right) e(77150)e\left(\frac{77}{150}\right) e(1475)e\left(\frac{14}{75}\right) e(3750)e\left(\frac{37}{50}\right) e(2125)e\left(\frac{21}{25}\right)
χ1125(58,⋅)\chi_{1125}(58,\cdot) 1125.bi 300 yes −1-1 11 e(289300)e\left(\frac{289}{300}\right) e(139150)e\left(\frac{139}{150}\right) e(5360)e\left(\frac{53}{60}\right) e(89100)e\left(\frac{89}{100}\right) e(1675)e\left(\frac{16}{75}\right) e(71300)e\left(\frac{71}{300}\right) e(127150)e\left(\frac{127}{150}\right) e(6475)e\left(\frac{64}{75}\right) e(99100)e\left(\frac{99}{100}\right) e(1750)e\left(\frac{17}{50}\right)
χ1125(59,⋅)\chi_{1125}(59,\cdot) 1125.bg 150 yes −1-1 11 e(1375)e\left(\frac{13}{75}\right) e(2675)e\left(\frac{26}{75}\right) e(730)e\left(\frac{7}{30}\right) e(1325)e\left(\frac{13}{25}\right) e(101150)e\left(\frac{101}{150}\right) e(139150)e\left(\frac{139}{150}\right) e(61150)e\left(\frac{61}{150}\right) e(5275)e\left(\frac{52}{75}\right) e(825)e\left(\frac{8}{25}\right) e(325)e\left(\frac{3}{25}\right)
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