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Properties

Modulus 18151815
Structure C2×C2×C220C_{2}\times C_{2}\times C_{220}
Order 880880

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Show commands: PariGP / SageMath

sage: H = DirichletGroup(1815)
 
pari: g = idealstar(,1815,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 880
sage: H.invariants()
 
pari: g.cyc
 
Structure = C2×C2×C220C_{2}\times C_{2}\times C_{220}
sage: H.gens()
 
pari: g.gen
 
Generators = χ1815(1211,⋅)\chi_{1815}(1211,\cdot), χ1815(727,⋅)\chi_{1815}(727,\cdot), χ1815(1696,⋅)\chi_{1815}(1696,\cdot)

First 32 of 880 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 1313 1414 1616 1717 1919 2323
χ1815(1,⋅)\chi_{1815}(1,\cdot) 1815.a 1 no 11 11 11 11 11 11 11 11 11 11 11 11
χ1815(2,⋅)\chi_{1815}(2,\cdot) 1815.bv 220 yes −1-1 11 e(167220)e\left(\frac{167}{220}\right) e(57110)e\left(\frac{57}{110}\right) e(69220)e\left(\frac{69}{220}\right) e(61220)e\left(\frac{61}{220}\right) e(147220)e\left(\frac{147}{220}\right) e(455)e\left(\frac{4}{55}\right) e(255)e\left(\frac{2}{55}\right) e(43220)e\left(\frac{43}{220}\right) e(1455)e\left(\frac{14}{55}\right) e(3944)e\left(\frac{39}{44}\right)
χ1815(4,⋅)\chi_{1815}(4,\cdot) 1815.bm 110 no 11 11 e(57110)e\left(\frac{57}{110}\right) e(255)e\left(\frac{2}{55}\right) e(69110)e\left(\frac{69}{110}\right) e(61110)e\left(\frac{61}{110}\right) e(37110)e\left(\frac{37}{110}\right) e(855)e\left(\frac{8}{55}\right) e(455)e\left(\frac{4}{55}\right) e(43110)e\left(\frac{43}{110}\right) e(2855)e\left(\frac{28}{55}\right) e(1722)e\left(\frac{17}{22}\right)
χ1815(7,⋅)\chi_{1815}(7,\cdot) 1815.bt 220 no 11 11 e(69220)e\left(\frac{69}{220}\right) e(69110)e\left(\frac{69}{110}\right) e(153220)e\left(\frac{153}{220}\right) e(207220)e\left(\frac{207}{220}\right) e(39220)e\left(\frac{39}{220}\right) e(1110)e\left(\frac{1}{110}\right) e(1455)e\left(\frac{14}{55}\right) e(81220)e\left(\frac{81}{220}\right) e(4355)e\left(\frac{43}{55}\right) e(944)e\left(\frac{9}{44}\right)
χ1815(8,⋅)\chi_{1815}(8,\cdot) 1815.bv 220 yes −1-1 11 e(61220)e\left(\frac{61}{220}\right) e(61110)e\left(\frac{61}{110}\right) e(207220)e\left(\frac{207}{220}\right) e(183220)e\left(\frac{183}{220}\right) e(1220)e\left(\frac{1}{220}\right) e(1255)e\left(\frac{12}{55}\right) e(655)e\left(\frac{6}{55}\right) e(129220)e\left(\frac{129}{220}\right) e(4255)e\left(\frac{42}{55}\right) e(2944)e\left(\frac{29}{44}\right)
χ1815(13,⋅)\chi_{1815}(13,\cdot) 1815.bt 220 no 11 11 e(147220)e\left(\frac{147}{220}\right) e(37110)e\left(\frac{37}{110}\right) e(39220)e\left(\frac{39}{220}\right) e(1220)e\left(\frac{1}{220}\right) e(217220)e\left(\frac{217}{220}\right) e(93110)e\left(\frac{93}{110}\right) e(3755)e\left(\frac{37}{55}\right) e(163220)e\left(\frac{163}{220}\right) e(3955)e\left(\frac{39}{55}\right) e(2344)e\left(\frac{23}{44}\right)
χ1815(14,⋅)\chi_{1815}(14,\cdot) 1815.bq 110 yes −1-1 11 e(455)e\left(\frac{4}{55}\right) e(855)e\left(\frac{8}{55}\right) e(1110)e\left(\frac{1}{110}\right) e(1255)e\left(\frac{12}{55}\right) e(93110)e\left(\frac{93}{110}\right) e(9110)e\left(\frac{9}{110}\right) e(1655)e\left(\frac{16}{55}\right) e(3155)e\left(\frac{31}{55}\right) e(255)e\left(\frac{2}{55}\right) e(111)e\left(\frac{1}{11}\right)
χ1815(16,⋅)\chi_{1815}(16,\cdot) 1815.bk 55 no 11 11 e(255)e\left(\frac{2}{55}\right) e(455)e\left(\frac{4}{55}\right) e(1455)e\left(\frac{14}{55}\right) e(655)e\left(\frac{6}{55}\right) e(3755)e\left(\frac{37}{55}\right) e(1655)e\left(\frac{16}{55}\right) e(855)e\left(\frac{8}{55}\right) e(4355)e\left(\frac{43}{55}\right) e(155)e\left(\frac{1}{55}\right) e(611)e\left(\frac{6}{11}\right)
χ1815(17,⋅)\chi_{1815}(17,\cdot) 1815.bv 220 yes −1-1 11 e(43220)e\left(\frac{43}{220}\right) e(43110)e\left(\frac{43}{110}\right) e(81220)e\left(\frac{81}{220}\right) e(129220)e\left(\frac{129}{220}\right) e(163220)e\left(\frac{163}{220}\right) e(3155)e\left(\frac{31}{55}\right) e(4355)e\left(\frac{43}{55}\right) e(127220)e\left(\frac{127}{220}\right) e(2655)e\left(\frac{26}{55}\right) e(1944)e\left(\frac{19}{44}\right)
χ1815(19,⋅)\chi_{1815}(19,\cdot) 1815.br 110 no −1-1 11 e(1455)e\left(\frac{14}{55}\right) e(2855)e\left(\frac{28}{55}\right) e(4355)e\left(\frac{43}{55}\right) e(4255)e\left(\frac{42}{55}\right) e(3955)e\left(\frac{39}{55}\right) e(255)e\left(\frac{2}{55}\right) e(155)e\left(\frac{1}{55}\right) e(2655)e\left(\frac{26}{55}\right) e(69110)e\left(\frac{69}{110}\right) e(722)e\left(\frac{7}{22}\right)
χ1815(23,⋅)\chi_{1815}(23,\cdot) 1815.bh 44 yes 11 11 e(3944)e\left(\frac{39}{44}\right) e(1722)e\left(\frac{17}{22}\right) e(944)e\left(\frac{9}{44}\right) e(2944)e\left(\frac{29}{44}\right) e(2344)e\left(\frac{23}{44}\right) e(111)e\left(\frac{1}{11}\right) e(611)e\left(\frac{6}{11}\right) e(1944)e\left(\frac{19}{44}\right) e(722)e\left(\frac{7}{22}\right) e(1344)e\left(\frac{13}{44}\right)
χ1815(26,⋅)\chi_{1815}(26,\cdot) 1815.bo 110 no −1-1 11 e(47110)e\left(\frac{47}{110}\right) e(4755)e\left(\frac{47}{55}\right) e(2755)e\left(\frac{27}{55}\right) e(31110)e\left(\frac{31}{110}\right) e(3655)e\left(\frac{36}{55}\right) e(101110)e\left(\frac{101}{110}\right) e(3955)e\left(\frac{39}{55}\right) e(103110)e\left(\frac{103}{110}\right) e(5355)e\left(\frac{53}{55}\right) e(922)e\left(\frac{9}{22}\right)
χ1815(28,⋅)\chi_{1815}(28,\cdot) 1815.bt 220 no 11 11 e(183220)e\left(\frac{183}{220}\right) e(73110)e\left(\frac{73}{110}\right) e(71220)e\left(\frac{71}{220}\right) e(109220)e\left(\frac{109}{220}\right) e(113220)e\left(\frac{113}{220}\right) e(17110)e\left(\frac{17}{110}\right) e(1855)e\left(\frac{18}{55}\right) e(167220)e\left(\frac{167}{220}\right) e(1655)e\left(\frac{16}{55}\right) e(4344)e\left(\frac{43}{44}\right)
χ1815(29,⋅)\chi_{1815}(29,\cdot) 1815.bn 110 yes 11 11 e(17110)e\left(\frac{17}{110}\right) e(1755)e\left(\frac{17}{55}\right) e(3255)e\left(\frac{32}{55}\right) e(51110)e\left(\frac{51}{110}\right) e(655)e\left(\frac{6}{55}\right) e(81110)e\left(\frac{81}{110}\right) e(3455)e\left(\frac{34}{55}\right) e(63110)e\left(\frac{63}{110}\right) e(91110)e\left(\frac{91}{110}\right) e(911)e\left(\frac{9}{11}\right)
χ1815(31,⋅)\chi_{1815}(31,\cdot) 1815.bk 55 no 11 11 e(4355)e\left(\frac{43}{55}\right) e(3155)e\left(\frac{31}{55}\right) e(2655)e\left(\frac{26}{55}\right) e(1955)e\left(\frac{19}{55}\right) e(5355)e\left(\frac{53}{55}\right) e(1455)e\left(\frac{14}{55}\right) e(755)e\left(\frac{7}{55}\right) e(1755)e\left(\frac{17}{55}\right) e(4955)e\left(\frac{49}{55}\right) e(811)e\left(\frac{8}{11}\right)
χ1815(32,⋅)\chi_{1815}(32,\cdot) 1815.bg 44 yes −1-1 11 e(3544)e\left(\frac{35}{44}\right) e(1322)e\left(\frac{13}{22}\right) e(2544)e\left(\frac{25}{44}\right) e(1744)e\left(\frac{17}{44}\right) e(1544)e\left(\frac{15}{44}\right) e(411)e\left(\frac{4}{11}\right) e(211)e\left(\frac{2}{11}\right) e(4344)e\left(\frac{43}{44}\right) e(311)e\left(\frac{3}{11}\right) e(1944)e\left(\frac{19}{44}\right)
χ1815(34,⋅)\chi_{1815}(34,\cdot) 1815.be 22 no 11 11 e(2122)e\left(\frac{21}{22}\right) e(1011)e\left(\frac{10}{11}\right) e(1522)e\left(\frac{15}{22}\right) e(1922)e\left(\frac{19}{22}\right) e(922)e\left(\frac{9}{22}\right) e(711)e\left(\frac{7}{11}\right) e(911)e\left(\frac{9}{11}\right) e(1722)e\left(\frac{17}{22}\right) e(811)e\left(\frac{8}{11}\right) e(722)e\left(\frac{7}{22}\right)
χ1815(37,⋅)\chi_{1815}(37,\cdot) 1815.bs 220 no −1-1 11 e(139220)e\left(\frac{139}{220}\right) e(29110)e\left(\frac{29}{110}\right) e(203220)e\left(\frac{203}{220}\right) e(197220)e\left(\frac{197}{220}\right) e(69220)e\left(\frac{69}{220}\right) e(61110)e\left(\frac{61}{110}\right) e(2955)e\left(\frac{29}{55}\right) e(211220)e\left(\frac{211}{220}\right) e(21110)e\left(\frac{21}{110}\right) e(2144)e\left(\frac{21}{44}\right)
χ1815(38,⋅)\chi_{1815}(38,\cdot) 1815.bu 220 yes 11 11 e(3220)e\left(\frac{3}{220}\right) e(3110)e\left(\frac{3}{110}\right) e(21220)e\left(\frac{21}{220}\right) e(9220)e\left(\frac{9}{220}\right) e(83220)e\left(\frac{83}{220}\right) e(655)e\left(\frac{6}{55}\right) e(355)e\left(\frac{3}{55}\right) e(147220)e\left(\frac{147}{220}\right) e(97110)e\left(\frac{97}{110}\right) e(944)e\left(\frac{9}{44}\right)
χ1815(41,⋅)\chi_{1815}(41,\cdot) 1815.bp 110 no 11 11 e(3955)e\left(\frac{39}{55}\right) e(2355)e\left(\frac{23}{55}\right) e(51110)e\left(\frac{51}{110}\right) e(755)e\left(\frac{7}{55}\right) e(13110)e\left(\frac{13}{110}\right) e(19110)e\left(\frac{19}{110}\right) e(4655)e\left(\frac{46}{55}\right) e(4155)e\left(\frac{41}{55}\right) e(39110)e\left(\frac{39}{110}\right) e(322)e\left(\frac{3}{22}\right)
χ1815(43,⋅)\chi_{1815}(43,\cdot) 1815.bi 44 no 11 11 e(4344)e\left(\frac{43}{44}\right) e(2122)e\left(\frac{21}{22}\right) e(1544)e\left(\frac{15}{44}\right) e(4144)e\left(\frac{41}{44}\right) e(944)e\left(\frac{9}{44}\right) e(722)e\left(\frac{7}{22}\right) e(1011)e\left(\frac{10}{11}\right) e(3944)e\left(\frac{39}{44}\right) e(411)e\left(\frac{4}{11}\right) e(744)e\left(\frac{7}{44}\right)
χ1815(46,⋅)\chi_{1815}(46,\cdot) 1815.bl 110 no −1-1 11 e(71110)e\left(\frac{71}{110}\right) e(1655)e\left(\frac{16}{55}\right) e(57110)e\left(\frac{57}{110}\right) e(103110)e\left(\frac{103}{110}\right) e(21110)e\left(\frac{21}{110}\right) e(955)e\left(\frac{9}{55}\right) e(3255)e\left(\frac{32}{55}\right) e(69110)e\left(\frac{69}{110}\right) e(63110)e\left(\frac{63}{110}\right) e(211)e\left(\frac{2}{11}\right)
χ1815(47,⋅)\chi_{1815}(47,\cdot) 1815.bu 220 yes 11 11 e(141220)e\left(\frac{141}{220}\right) e(31110)e\left(\frac{31}{110}\right) e(107220)e\left(\frac{107}{220}\right) e(203220)e\left(\frac{203}{220}\right) e(161220)e\left(\frac{161}{220}\right) e(755)e\left(\frac{7}{55}\right) e(3155)e\left(\frac{31}{55}\right) e(89220)e\left(\frac{89}{220}\right) e(49110)e\left(\frac{49}{110}\right) e(2744)e\left(\frac{27}{44}\right)
χ1815(49,⋅)\chi_{1815}(49,\cdot) 1815.bm 110 no 11 11 e(69110)e\left(\frac{69}{110}\right) e(1455)e\left(\frac{14}{55}\right) e(43110)e\left(\frac{43}{110}\right) e(97110)e\left(\frac{97}{110}\right) e(39110)e\left(\frac{39}{110}\right) e(155)e\left(\frac{1}{55}\right) e(2855)e\left(\frac{28}{55}\right) e(81110)e\left(\frac{81}{110}\right) e(3155)e\left(\frac{31}{55}\right) e(922)e\left(\frac{9}{22}\right)
χ1815(52,⋅)\chi_{1815}(52,\cdot) 1815.bt 220 no 11 11 e(41220)e\left(\frac{41}{220}\right) e(41110)e\left(\frac{41}{110}\right) e(177220)e\left(\frac{177}{220}\right) e(123220)e\left(\frac{123}{220}\right) e(71220)e\left(\frac{71}{220}\right) e(109110)e\left(\frac{109}{110}\right) e(4155)e\left(\frac{41}{55}\right) e(29220)e\left(\frac{29}{220}\right) e(1255)e\left(\frac{12}{55}\right) e(1344)e\left(\frac{13}{44}\right)
χ1815(53,⋅)\chi_{1815}(53,\cdot) 1815.bu 220 yes 11 11 e(47220)e\left(\frac{47}{220}\right) e(47110)e\left(\frac{47}{110}\right) e(109220)e\left(\frac{109}{220}\right) e(141220)e\left(\frac{141}{220}\right) e(127220)e\left(\frac{127}{220}\right) e(3955)e\left(\frac{39}{55}\right) e(4755)e\left(\frac{47}{55}\right) e(103220)e\left(\frac{103}{220}\right) e(53110)e\left(\frac{53}{110}\right) e(944)e\left(\frac{9}{44}\right)
χ1815(56,⋅)\chi_{1815}(56,\cdot) 1815.bc 22 no −1-1 11 e(1322)e\left(\frac{13}{22}\right) e(211)e\left(\frac{2}{11}\right) e(711)e\left(\frac{7}{11}\right) e(1722)e\left(\frac{17}{22}\right) e(211)e\left(\frac{2}{11}\right) e(522)e\left(\frac{5}{22}\right) e(411)e\left(\frac{4}{11}\right) e(2122)e\left(\frac{21}{22}\right) e(611)e\left(\frac{6}{11}\right) e(1922)e\left(\frac{19}{22}\right)
χ1815(58,⋅)\chi_{1815}(58,\cdot) 1815.bs 220 no −1-1 11 e(201220)e\left(\frac{201}{220}\right) e(91110)e\left(\frac{91}{110}\right) e(197220)e\left(\frac{197}{220}\right) e(163220)e\left(\frac{163}{220}\right) e(171220)e\left(\frac{171}{220}\right) e(89110)e\left(\frac{89}{110}\right) e(3655)e\left(\frac{36}{55}\right) e(169220)e\left(\frac{169}{220}\right) e(9110)e\left(\frac{9}{110}\right) e(3144)e\left(\frac{31}{44}\right)
χ1815(59,⋅)\chi_{1815}(59,\cdot) 1815.bq 110 yes −1-1 11 e(1655)e\left(\frac{16}{55}\right) e(3255)e\left(\frac{32}{55}\right) e(59110)e\left(\frac{59}{110}\right) e(4855)e\left(\frac{48}{55}\right) e(97110)e\left(\frac{97}{110}\right) e(91110)e\left(\frac{91}{110}\right) e(955)e\left(\frac{9}{55}\right) e(1455)e\left(\frac{14}{55}\right) e(855)e\left(\frac{8}{55}\right) e(411)e\left(\frac{4}{11}\right)
χ1815(61,⋅)\chi_{1815}(61,\cdot) 1815.bl 110 no −1-1 11 e(109110)e\left(\frac{109}{110}\right) e(5455)e\left(\frac{54}{55}\right) e(103110)e\left(\frac{103}{110}\right) e(107110)e\left(\frac{107}{110}\right) e(9110)e\left(\frac{9}{110}\right) e(5155)e\left(\frac{51}{55}\right) e(5355)e\left(\frac{53}{55}\right) e(61110)e\left(\frac{61}{110}\right) e(27110)e\left(\frac{27}{110}\right) e(411)e\left(\frac{4}{11}\right)
χ1815(62,⋅)\chi_{1815}(62,\cdot) 1815.bv 220 yes −1-1 11 e(119220)e\left(\frac{119}{220}\right) e(9110)e\left(\frac{9}{110}\right) e(173220)e\left(\frac{173}{220}\right) e(137220)e\left(\frac{137}{220}\right) e(139220)e\left(\frac{139}{220}\right) e(1855)e\left(\frac{18}{55}\right) e(955)e\left(\frac{9}{55}\right) e(111220)e\left(\frac{111}{220}\right) e(855)e\left(\frac{8}{55}\right) e(2744)e\left(\frac{27}{44}\right)
χ1815(64,⋅)\chi_{1815}(64,\cdot) 1815.bm 110 no 11 11 e(61110)e\left(\frac{61}{110}\right) e(655)e\left(\frac{6}{55}\right) e(97110)e\left(\frac{97}{110}\right) e(73110)e\left(\frac{73}{110}\right) e(1110)e\left(\frac{1}{110}\right) e(2455)e\left(\frac{24}{55}\right) e(1255)e\left(\frac{12}{55}\right) e(19110)e\left(\frac{19}{110}\right) e(2955)e\left(\frac{29}{55}\right) e(722)e\left(\frac{7}{22}\right)
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