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Properties

Modulus 253253
Structure C2×C110C_{2}\times C_{110}
Order 220220

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Show commands: PariGP / SageMath

sage: H = DirichletGroup(253)
 
pari: g = idealstar(,253,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 220
sage: H.invariants()
 
pari: g.cyc
 
Structure = C2×C110C_{2}\times C_{110}
sage: H.gens()
 
pari: g.gen
 
Generators = χ253(24,⋅)\chi_{253}(24,\cdot), χ253(166,⋅)\chi_{253}(166,\cdot)

First 32 of 220 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 33 44 55 66 77 88 99 1010 1212
χ253(1,⋅)\chi_{253}(1,\cdot) 253.a 1 no 11 11 11 11 11 11 11 11 11 11 11 11
χ253(2,⋅)\chi_{253}(2,\cdot) 253.o 110 yes −1-1 11 e(31110)e\left(\frac{31}{110}\right) e(1455)e\left(\frac{14}{55}\right) e(3155)e\left(\frac{31}{55}\right) e(2755)e\left(\frac{27}{55}\right) e(59110)e\left(\frac{59}{110}\right) e(47110)e\left(\frac{47}{110}\right) e(93110)e\left(\frac{93}{110}\right) e(2855)e\left(\frac{28}{55}\right) e(1722)e\left(\frac{17}{22}\right) e(911)e\left(\frac{9}{11}\right)
χ253(3,⋅)\chi_{253}(3,\cdot) 253.m 55 yes 11 11 e(1455)e\left(\frac{14}{55}\right) e(255)e\left(\frac{2}{55}\right) e(2855)e\left(\frac{28}{55}\right) e(5155)e\left(\frac{51}{55}\right) e(1655)e\left(\frac{16}{55}\right) e(2355)e\left(\frac{23}{55}\right) e(4255)e\left(\frac{42}{55}\right) e(455)e\left(\frac{4}{55}\right) e(211)e\left(\frac{2}{11}\right) e(611)e\left(\frac{6}{11}\right)
χ253(4,⋅)\chi_{253}(4,\cdot) 253.m 55 yes 11 11 e(3155)e\left(\frac{31}{55}\right) e(2855)e\left(\frac{28}{55}\right) e(755)e\left(\frac{7}{55}\right) e(5455)e\left(\frac{54}{55}\right) e(455)e\left(\frac{4}{55}\right) e(4755)e\left(\frac{47}{55}\right) e(3855)e\left(\frac{38}{55}\right) e(155)e\left(\frac{1}{55}\right) e(611)e\left(\frac{6}{11}\right) e(711)e\left(\frac{7}{11}\right)
χ253(5,⋅)\chi_{253}(5,\cdot) 253.p 110 yes −1-1 11 e(2755)e\left(\frac{27}{55}\right) e(5155)e\left(\frac{51}{55}\right) e(5455)e\left(\frac{54}{55}\right) e(71110)e\left(\frac{71}{110}\right) e(2355)e\left(\frac{23}{55}\right) e(73110)e\left(\frac{73}{110}\right) e(2655)e\left(\frac{26}{55}\right) e(4755)e\left(\frac{47}{55}\right) e(322)e\left(\frac{3}{22}\right) e(1011)e\left(\frac{10}{11}\right)
χ253(6,⋅)\chi_{253}(6,\cdot) 253.o 110 yes −1-1 11 e(59110)e\left(\frac{59}{110}\right) e(1655)e\left(\frac{16}{55}\right) e(455)e\left(\frac{4}{55}\right) e(2355)e\left(\frac{23}{55}\right) e(91110)e\left(\frac{91}{110}\right) e(93110)e\left(\frac{93}{110}\right) e(67110)e\left(\frac{67}{110}\right) e(3255)e\left(\frac{32}{55}\right) e(2122)e\left(\frac{21}{22}\right) e(411)e\left(\frac{4}{11}\right)
χ253(7,⋅)\chi_{253}(7,\cdot) 253.n 110 yes 11 11 e(47110)e\left(\frac{47}{110}\right) e(2355)e\left(\frac{23}{55}\right) e(4755)e\left(\frac{47}{55}\right) e(73110)e\left(\frac{73}{110}\right) e(93110)e\left(\frac{93}{110}\right) e(1755)e\left(\frac{17}{55}\right) e(31110)e\left(\frac{31}{110}\right) e(4655)e\left(\frac{46}{55}\right) e(111)e\left(\frac{1}{11}\right) e(311)e\left(\frac{3}{11}\right)
χ253(8,⋅)\chi_{253}(8,\cdot) 253.o 110 yes −1-1 11 e(93110)e\left(\frac{93}{110}\right) e(4255)e\left(\frac{42}{55}\right) e(3855)e\left(\frac{38}{55}\right) e(2655)e\left(\frac{26}{55}\right) e(67110)e\left(\frac{67}{110}\right) e(31110)e\left(\frac{31}{110}\right) e(59110)e\left(\frac{59}{110}\right) e(2955)e\left(\frac{29}{55}\right) e(722)e\left(\frac{7}{22}\right) e(511)e\left(\frac{5}{11}\right)
χ253(9,⋅)\chi_{253}(9,\cdot) 253.m 55 yes 11 11 e(2855)e\left(\frac{28}{55}\right) e(455)e\left(\frac{4}{55}\right) e(155)e\left(\frac{1}{55}\right) e(4755)e\left(\frac{47}{55}\right) e(3255)e\left(\frac{32}{55}\right) e(4655)e\left(\frac{46}{55}\right) e(2955)e\left(\frac{29}{55}\right) e(855)e\left(\frac{8}{55}\right) e(411)e\left(\frac{4}{11}\right) e(111)e\left(\frac{1}{11}\right)
χ253(10,⋅)\chi_{253}(10,\cdot) 253.l 22 yes 11 11 e(1722)e\left(\frac{17}{22}\right) e(211)e\left(\frac{2}{11}\right) e(611)e\left(\frac{6}{11}\right) e(322)e\left(\frac{3}{22}\right) e(2122)e\left(\frac{21}{22}\right) e(111)e\left(\frac{1}{11}\right) e(722)e\left(\frac{7}{22}\right) e(411)e\left(\frac{4}{11}\right) e(1011)e\left(\frac{10}{11}\right) e(811)e\left(\frac{8}{11}\right)
χ253(12,⋅)\chi_{253}(12,\cdot) 253.i 11 no 11 11 e(911)e\left(\frac{9}{11}\right) e(611)e\left(\frac{6}{11}\right) e(711)e\left(\frac{7}{11}\right) e(1011)e\left(\frac{10}{11}\right) e(411)e\left(\frac{4}{11}\right) e(311)e\left(\frac{3}{11}\right) e(511)e\left(\frac{5}{11}\right) e(111)e\left(\frac{1}{11}\right) e(811)e\left(\frac{8}{11}\right) e(211)e\left(\frac{2}{11}\right)
χ253(13,⋅)\chi_{253}(13,\cdot) 253.o 110 yes −1-1 11 e(41110)e\left(\frac{41}{110}\right) e(5455)e\left(\frac{54}{55}\right) e(4155)e\left(\frac{41}{55}\right) e(255)e\left(\frac{2}{55}\right) e(39110)e\left(\frac{39}{110}\right) e(87110)e\left(\frac{87}{110}\right) e(13110)e\left(\frac{13}{110}\right) e(5355)e\left(\frac{53}{55}\right) e(922)e\left(\frac{9}{22}\right) e(811)e\left(\frac{8}{11}\right)
χ253(14,⋅)\chi_{253}(14,\cdot) 253.p 110 yes −1-1 11 e(3955)e\left(\frac{39}{55}\right) e(3755)e\left(\frac{37}{55}\right) e(2355)e\left(\frac{23}{55}\right) e(17110)e\left(\frac{17}{110}\right) e(2155)e\left(\frac{21}{55}\right) e(81110)e\left(\frac{81}{110}\right) e(755)e\left(\frac{7}{55}\right) e(1955)e\left(\frac{19}{55}\right) e(1922)e\left(\frac{19}{22}\right) e(111)e\left(\frac{1}{11}\right)
χ253(15,⋅)\chi_{253}(15,\cdot) 253.p 110 yes −1-1 11 e(4155)e\left(\frac{41}{55}\right) e(5355)e\left(\frac{53}{55}\right) e(2755)e\left(\frac{27}{55}\right) e(63110)e\left(\frac{63}{110}\right) e(3955)e\left(\frac{39}{55}\right) e(9110)e\left(\frac{9}{110}\right) e(1355)e\left(\frac{13}{55}\right) e(5155)e\left(\frac{51}{55}\right) e(722)e\left(\frac{7}{22}\right) e(511)e\left(\frac{5}{11}\right)
χ253(16,⋅)\chi_{253}(16,\cdot) 253.m 55 yes 11 11 e(755)e\left(\frac{7}{55}\right) e(155)e\left(\frac{1}{55}\right) e(1455)e\left(\frac{14}{55}\right) e(5355)e\left(\frac{53}{55}\right) e(855)e\left(\frac{8}{55}\right) e(3955)e\left(\frac{39}{55}\right) e(2155)e\left(\frac{21}{55}\right) e(255)e\left(\frac{2}{55}\right) e(111)e\left(\frac{1}{11}\right) e(311)e\left(\frac{3}{11}\right)
χ253(17,⋅)\chi_{253}(17,\cdot) 253.n 110 yes 11 11 e(59110)e\left(\frac{59}{110}\right) e(1655)e\left(\frac{16}{55}\right) e(455)e\left(\frac{4}{55}\right) e(101110)e\left(\frac{101}{110}\right) e(91110)e\left(\frac{91}{110}\right) e(1955)e\left(\frac{19}{55}\right) e(67110)e\left(\frac{67}{110}\right) e(3255)e\left(\frac{32}{55}\right) e(511)e\left(\frac{5}{11}\right) e(411)e\left(\frac{4}{11}\right)
χ253(18,⋅)\chi_{253}(18,\cdot) 253.o 110 yes −1-1 11 e(87110)e\left(\frac{87}{110}\right) e(1855)e\left(\frac{18}{55}\right) e(3255)e\left(\frac{32}{55}\right) e(1955)e\left(\frac{19}{55}\right) e(13110)e\left(\frac{13}{110}\right) e(29110)e\left(\frac{29}{110}\right) e(41110)e\left(\frac{41}{110}\right) e(3655)e\left(\frac{36}{55}\right) e(322)e\left(\frac{3}{22}\right) e(1011)e\left(\frac{10}{11}\right)
χ253(19,⋅)\chi_{253}(19,\cdot) 253.n 110 yes 11 11 e(73110)e\left(\frac{73}{110}\right) e(1755)e\left(\frac{17}{55}\right) e(1855)e\left(\frac{18}{55}\right) e(97110)e\left(\frac{97}{110}\right) e(107110)e\left(\frac{107}{110}\right) e(355)e\left(\frac{3}{55}\right) e(109110)e\left(\frac{109}{110}\right) e(3455)e\left(\frac{34}{55}\right) e(611)e\left(\frac{6}{11}\right) e(711)e\left(\frac{7}{11}\right)
χ253(20,⋅)\chi_{253}(20,\cdot) 253.p 110 yes −1-1 11 e(355)e\left(\frac{3}{55}\right) e(2455)e\left(\frac{24}{55}\right) e(655)e\left(\frac{6}{55}\right) e(69110)e\left(\frac{69}{110}\right) e(2755)e\left(\frac{27}{55}\right) e(57110)e\left(\frac{57}{110}\right) e(955)e\left(\frac{9}{55}\right) e(4855)e\left(\frac{48}{55}\right) e(1522)e\left(\frac{15}{22}\right) e(611)e\left(\frac{6}{11}\right)
χ253(21,⋅)\chi_{253}(21,\cdot) 253.l 22 yes 11 11 e(1522)e\left(\frac{15}{22}\right) e(511)e\left(\frac{5}{11}\right) e(411)e\left(\frac{4}{11}\right) e(1322)e\left(\frac{13}{22}\right) e(322)e\left(\frac{3}{22}\right) e(811)e\left(\frac{8}{11}\right) e(122)e\left(\frac{1}{22}\right) e(1011)e\left(\frac{10}{11}\right) e(311)e\left(\frac{3}{11}\right) e(911)e\left(\frac{9}{11}\right)
χ253(24,⋅)\chi_{253}(24,\cdot) 253.g 10 no −1-1 11 e(110)e\left(\frac{1}{10}\right) e(45)e\left(\frac{4}{5}\right) e(15)e\left(\frac{1}{5}\right) e(25)e\left(\frac{2}{5}\right) e(910)e\left(\frac{9}{10}\right) e(710)e\left(\frac{7}{10}\right) e(310)e\left(\frac{3}{10}\right) e(35)e\left(\frac{3}{5}\right) −1-1 11
χ253(25,⋅)\chi_{253}(25,\cdot) 253.m 55 yes 11 11 e(5455)e\left(\frac{54}{55}\right) e(4755)e\left(\frac{47}{55}\right) e(5355)e\left(\frac{53}{55}\right) e(1655)e\left(\frac{16}{55}\right) e(4655)e\left(\frac{46}{55}\right) e(1855)e\left(\frac{18}{55}\right) e(5255)e\left(\frac{52}{55}\right) e(3955)e\left(\frac{39}{55}\right) e(311)e\left(\frac{3}{11}\right) e(911)e\left(\frac{9}{11}\right)
χ253(26,⋅)\chi_{253}(26,\cdot) 253.m 55 yes 11 11 e(3655)e\left(\frac{36}{55}\right) e(1355)e\left(\frac{13}{55}\right) e(1755)e\left(\frac{17}{55}\right) e(2955)e\left(\frac{29}{55}\right) e(4955)e\left(\frac{49}{55}\right) e(1255)e\left(\frac{12}{55}\right) e(5355)e\left(\frac{53}{55}\right) e(2655)e\left(\frac{26}{55}\right) e(211)e\left(\frac{2}{11}\right) e(611)e\left(\frac{6}{11}\right)
χ253(27,⋅)\chi_{253}(27,\cdot) 253.m 55 yes 11 11 e(4255)e\left(\frac{42}{55}\right) e(655)e\left(\frac{6}{55}\right) e(2955)e\left(\frac{29}{55}\right) e(4355)e\left(\frac{43}{55}\right) e(4855)e\left(\frac{48}{55}\right) e(1455)e\left(\frac{14}{55}\right) e(1655)e\left(\frac{16}{55}\right) e(1255)e\left(\frac{12}{55}\right) e(611)e\left(\frac{6}{11}\right) e(711)e\left(\frac{7}{11}\right)
χ253(28,⋅)\chi_{253}(28,\cdot) 253.n 110 yes 11 11 e(109110)e\left(\frac{109}{110}\right) e(5155)e\left(\frac{51}{55}\right) e(5455)e\left(\frac{54}{55}\right) e(71110)e\left(\frac{71}{110}\right) e(101110)e\left(\frac{101}{110}\right) e(955)e\left(\frac{9}{55}\right) e(107110)e\left(\frac{107}{110}\right) e(4755)e\left(\frac{47}{55}\right) e(711)e\left(\frac{7}{11}\right) e(1011)e\left(\frac{10}{11}\right)
χ253(29,⋅)\chi_{253}(29,\cdot) 253.o 110 yes −1-1 11 e(37110)e\left(\frac{37}{110}\right) e(3855)e\left(\frac{38}{55}\right) e(3755)e\left(\frac{37}{55}\right) e(3455)e\left(\frac{34}{55}\right) e(3110)e\left(\frac{3}{110}\right) e(49110)e\left(\frac{49}{110}\right) e(1110)e\left(\frac{1}{110}\right) e(2155)e\left(\frac{21}{55}\right) e(2122)e\left(\frac{21}{22}\right) e(411)e\left(\frac{4}{11}\right)
χ253(30,⋅)\chi_{253}(30,\cdot) 253.n 110 yes 11 11 e(3110)e\left(\frac{3}{110}\right) e(1255)e\left(\frac{12}{55}\right) e(355)e\left(\frac{3}{55}\right) e(7110)e\left(\frac{7}{110}\right) e(27110)e\left(\frac{27}{110}\right) e(2855)e\left(\frac{28}{55}\right) e(9110)e\left(\frac{9}{110}\right) e(2455)e\left(\frac{24}{55}\right) e(111)e\left(\frac{1}{11}\right) e(311)e\left(\frac{3}{11}\right)
χ253(31,⋅)\chi_{253}(31,\cdot) 253.m 55 yes 11 11 e(855)e\left(\frac{8}{55}\right) e(955)e\left(\frac{9}{55}\right) e(1655)e\left(\frac{16}{55}\right) e(3755)e\left(\frac{37}{55}\right) e(1755)e\left(\frac{17}{55}\right) e(2155)e\left(\frac{21}{55}\right) e(2455)e\left(\frac{24}{55}\right) e(1855)e\left(\frac{18}{55}\right) e(911)e\left(\frac{9}{11}\right) e(511)e\left(\frac{5}{11}\right)
χ253(32,⋅)\chi_{253}(32,\cdot) 253.k 22 yes −1-1 11 e(922)e\left(\frac{9}{22}\right) e(311)e\left(\frac{3}{11}\right) e(911)e\left(\frac{9}{11}\right) e(511)e\left(\frac{5}{11}\right) e(1522)e\left(\frac{15}{22}\right) e(322)e\left(\frac{3}{22}\right) e(522)e\left(\frac{5}{22}\right) e(611)e\left(\frac{6}{11}\right) e(1922)e\left(\frac{19}{22}\right) e(111)e\left(\frac{1}{11}\right)
χ253(34,⋅)\chi_{253}(34,\cdot) 253.j 22 no −1-1 11 e(911)e\left(\frac{9}{11}\right) e(611)e\left(\frac{6}{11}\right) e(711)e\left(\frac{7}{11}\right) e(922)e\left(\frac{9}{22}\right) e(411)e\left(\frac{4}{11}\right) e(1722)e\left(\frac{17}{22}\right) e(511)e\left(\frac{5}{11}\right) e(111)e\left(\frac{1}{11}\right) e(522)e\left(\frac{5}{22}\right) e(211)e\left(\frac{2}{11}\right)
χ253(35,⋅)\chi_{253}(35,\cdot) 253.o 110 yes −1-1 11 e(101110)e\left(\frac{101}{110}\right) e(1955)e\left(\frac{19}{55}\right) e(4655)e\left(\frac{46}{55}\right) e(1755)e\left(\frac{17}{55}\right) e(29110)e\left(\frac{29}{110}\right) e(107110)e\left(\frac{107}{110}\right) e(83110)e\left(\frac{83}{110}\right) e(3855)e\left(\frac{38}{55}\right) e(522)e\left(\frac{5}{22}\right) e(211)e\left(\frac{2}{11}\right)
χ253(36,⋅)\chi_{253}(36,\cdot) 253.m 55 yes 11 11 e(455)e\left(\frac{4}{55}\right) e(3255)e\left(\frac{32}{55}\right) e(855)e\left(\frac{8}{55}\right) e(4655)e\left(\frac{46}{55}\right) e(3655)e\left(\frac{36}{55}\right) e(3855)e\left(\frac{38}{55}\right) e(1255)e\left(\frac{12}{55}\right) e(955)e\left(\frac{9}{55}\right) e(1011)e\left(\frac{10}{11}\right) e(811)e\left(\frac{8}{11}\right)
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