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Properties

Modulus 45984598
Structure C2×C990C_{2}\times C_{990}
Order 19801980

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Show commands: PariGP / SageMath

sage: H = DirichletGroup(4598)
 
pari: g = idealstar(,4598,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 1980
sage: H.invariants()
 
pari: g.cyc
 
Structure = C2×C990C_{2}\times C_{990}
sage: H.gens()
 
pari: g.gen
 
Generators = χ4598(3269,⋅)\chi_{4598}(3269,\cdot), χ4598(3631,⋅)\chi_{4598}(3631,\cdot)

First 32 of 1980 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 2121 2323 2525
χ4598(1,⋅)\chi_{4598}(1,\cdot) 4598.a 1 no 11 11 11 11 11 11 11 11 11 11 11 11
χ4598(3,⋅)\chi_{4598}(3,\cdot) 4598.bg 90 no −1-1 11 e(7190)e\left(\frac{71}{90}\right) e(3445)e\left(\frac{34}{45}\right) e(1415)e\left(\frac{14}{15}\right) e(2645)e\left(\frac{26}{45}\right) e(3790)e\left(\frac{37}{90}\right) e(4990)e\left(\frac{49}{90}\right) e(1945)e\left(\frac{19}{45}\right) e(1318)e\left(\frac{13}{18}\right) e(49)e\left(\frac{4}{9}\right) e(2345)e\left(\frac{23}{45}\right)
χ4598(5,⋅)\chi_{4598}(5,\cdot) 4598.bs 495 no 11 11 e(3445)e\left(\frac{34}{45}\right) e(2495)e\left(\frac{2}{495}\right) e(7165)e\left(\frac{7}{165}\right) e(2345)e\left(\frac{23}{45}\right) e(193495)e\left(\frac{193}{495}\right) e(376495)e\left(\frac{376}{495}\right) e(422495)e\left(\frac{422}{495}\right) e(7999)e\left(\frac{79}{99}\right) e(8699)e\left(\frac{86}{99}\right) e(4495)e\left(\frac{4}{495}\right)
χ4598(7,⋅)\chi_{4598}(7,\cdot) 4598.br 330 no −1-1 11 e(1415)e\left(\frac{14}{15}\right) e(7165)e\left(\frac{7}{165}\right) e(49110)e\left(\frac{49}{110}\right) e(1315)e\left(\frac{13}{15}\right) e(31330)e\left(\frac{31}{330}\right) e(161165)e\left(\frac{161}{165}\right) e(149330)e\left(\frac{149}{330}\right) e(2566)e\left(\frac{25}{66}\right) e(433)e\left(\frac{4}{33}\right) e(14165)e\left(\frac{14}{165}\right)
χ4598(9,⋅)\chi_{4598}(9,\cdot) 4598.z 45 no 11 11 e(2645)e\left(\frac{26}{45}\right) e(2345)e\left(\frac{23}{45}\right) e(1315)e\left(\frac{13}{15}\right) e(745)e\left(\frac{7}{45}\right) e(3745)e\left(\frac{37}{45}\right) e(445)e\left(\frac{4}{45}\right) e(3845)e\left(\frac{38}{45}\right) e(49)e\left(\frac{4}{9}\right) e(89)e\left(\frac{8}{9}\right) e(145)e\left(\frac{1}{45}\right)
χ4598(13,⋅)\chi_{4598}(13,\cdot) 4598.bu 990 no 11 11 e(3790)e\left(\frac{37}{90}\right) e(193495)e\left(\frac{193}{495}\right) e(31330)e\left(\frac{31}{330}\right) e(3745)e\left(\frac{37}{45}\right) e(62495)e\left(\frac{62}{495}\right) e(793990)e\left(\frac{793}{990}\right) e(761990)e\left(\frac{761}{990}\right) e(5099)e\left(\frac{50}{99}\right) e(8299)e\left(\frac{82}{99}\right) e(386495)e\left(\frac{386}{495}\right)
χ4598(15,⋅)\chi_{4598}(15,\cdot) 4598.bt 990 no −1-1 11 e(4990)e\left(\frac{49}{90}\right) e(376495)e\left(\frac{376}{495}\right) e(161165)e\left(\frac{161}{165}\right) e(445)e\left(\frac{4}{45}\right) e(793990)e\left(\frac{793}{990}\right) e(301990)e\left(\frac{301}{990}\right) e(136495)e\left(\frac{136}{495}\right) e(103198)e\left(\frac{103}{198}\right) e(3199)e\left(\frac{31}{99}\right) e(257495)e\left(\frac{257}{495}\right)
χ4598(17,⋅)\chi_{4598}(17,\cdot) 4598.bv 990 no −1-1 11 e(1945)e\left(\frac{19}{45}\right) e(422495)e\left(\frac{422}{495}\right) e(149330)e\left(\frac{149}{330}\right) e(3845)e\left(\frac{38}{45}\right) e(761990)e\left(\frac{761}{990}\right) e(136495)e\left(\frac{136}{495}\right) e(379990)e\left(\frac{379}{990}\right) e(173198)e\left(\frac{173}{198}\right) e(2999)e\left(\frac{29}{99}\right) e(349495)e\left(\frac{349}{495}\right)
χ4598(21,⋅)\chi_{4598}(21,\cdot) 4598.bn 198 no 11 11 e(1318)e\left(\frac{13}{18}\right) e(7999)e\left(\frac{79}{99}\right) e(2566)e\left(\frac{25}{66}\right) e(49)e\left(\frac{4}{9}\right) e(5099)e\left(\frac{50}{99}\right) e(103198)e\left(\frac{103}{198}\right) e(173198)e\left(\frac{173}{198}\right) e(1099)e\left(\frac{10}{99}\right) e(5699)e\left(\frac{56}{99}\right) e(5999)e\left(\frac{59}{99}\right)
χ4598(23,⋅)\chi_{4598}(23,\cdot) 4598.bh 99 no 11 11 e(49)e\left(\frac{4}{9}\right) e(8699)e\left(\frac{86}{99}\right) e(433)e\left(\frac{4}{33}\right) e(89)e\left(\frac{8}{9}\right) e(8299)e\left(\frac{82}{99}\right) e(3199)e\left(\frac{31}{99}\right) e(2999)e\left(\frac{29}{99}\right) e(5699)e\left(\frac{56}{99}\right) e(7699)e\left(\frac{76}{99}\right) e(7399)e\left(\frac{73}{99}\right)
χ4598(25,⋅)\chi_{4598}(25,\cdot) 4598.bs 495 no 11 11 e(2345)e\left(\frac{23}{45}\right) e(4495)e\left(\frac{4}{495}\right) e(14165)e\left(\frac{14}{165}\right) e(145)e\left(\frac{1}{45}\right) e(386495)e\left(\frac{386}{495}\right) e(257495)e\left(\frac{257}{495}\right) e(349495)e\left(\frac{349}{495}\right) e(5999)e\left(\frac{59}{99}\right) e(7399)e\left(\frac{73}{99}\right) e(8495)e\left(\frac{8}{495}\right)
χ4598(27,⋅)\chi_{4598}(27,\cdot) 4598.v 30 no −1-1 11 e(1130)e\left(\frac{11}{30}\right) e(415)e\left(\frac{4}{15}\right) e(45)e\left(\frac{4}{5}\right) e(1115)e\left(\frac{11}{15}\right) e(730)e\left(\frac{7}{30}\right) e(1930)e\left(\frac{19}{30}\right) e(415)e\left(\frac{4}{15}\right) e(16)e\left(\frac{1}{6}\right) e(13)e\left(\frac{1}{3}\right) e(815)e\left(\frac{8}{15}\right)
χ4598(29,⋅)\chi_{4598}(29,\cdot) 4598.bu 990 no 11 11 e(7990)e\left(\frac{79}{90}\right) e(271495)e\left(\frac{271}{495}\right) e(247330)e\left(\frac{247}{330}\right) e(3445)e\left(\frac{34}{45}\right) e(164495)e\left(\frac{164}{495}\right) e(421990)e\left(\frac{421}{990}\right) e(17990)e\left(\frac{17}{990}\right) e(6299)e\left(\frac{62}{99}\right) e(7099)e\left(\frac{70}{99}\right) e(47495)e\left(\frac{47}{495}\right)
χ4598(31,⋅)\chi_{4598}(31,\cdot) 4598.bq 330 no −1-1 11 e(1930)e\left(\frac{19}{30}\right) e(31165)e\left(\frac{31}{165}\right) e(2655)e\left(\frac{26}{55}\right) e(415)e\left(\frac{4}{15}\right) e(43330)e\left(\frac{43}{330}\right) e(271330)e\left(\frac{271}{330}\right) e(106165)e\left(\frac{106}{165}\right) e(766)e\left(\frac{7}{66}\right) e(1333)e\left(\frac{13}{33}\right) e(62165)e\left(\frac{62}{165}\right)
χ4598(35,⋅)\chi_{4598}(35,\cdot) 4598.bv 990 no −1-1 11 e(3145)e\left(\frac{31}{45}\right) e(23495)e\left(\frac{23}{495}\right) e(161330)e\left(\frac{161}{330}\right) e(1745)e\left(\frac{17}{45}\right) e(479990)e\left(\frac{479}{990}\right) e(364495)e\left(\frac{364}{495}\right) e(301990)e\left(\frac{301}{990}\right) e(35198)e\left(\frac{35}{198}\right) e(9899)e\left(\frac{98}{99}\right) e(46495)e\left(\frac{46}{495}\right)
χ4598(37,⋅)\chi_{4598}(37,\cdot) 4598.bk 110 no −1-1 11 e(110)e\left(\frac{1}{10}\right) e(1455)e\left(\frac{14}{55}\right) e(3755)e\left(\frac{37}{55}\right) e(15)e\left(\frac{1}{5}\right) e(7110)e\left(\frac{7}{110}\right) e(39110)e\left(\frac{39}{110}\right) e(3955)e\left(\frac{39}{55}\right) e(1722)e\left(\frac{17}{22}\right) e(811)e\left(\frac{8}{11}\right) e(2855)e\left(\frac{28}{55}\right)
χ4598(39,⋅)\chi_{4598}(39,\cdot) 4598.bi 110 no −1-1 11 e(15)e\left(\frac{1}{5}\right) e(855)e\left(\frac{8}{55}\right) e(3110)e\left(\frac{3}{110}\right) e(25)e\left(\frac{2}{5}\right) e(59110)e\left(\frac{59}{110}\right) e(1955)e\left(\frac{19}{55}\right) e(21110)e\left(\frac{21}{110}\right) e(522)e\left(\frac{5}{22}\right) e(311)e\left(\frac{3}{11}\right) e(1655)e\left(\frac{16}{55}\right)
χ4598(41,⋅)\chi_{4598}(41,\cdot) 4598.bu 990 no 11 11 e(7190)e\left(\frac{71}{90}\right) e(14495)e\left(\frac{14}{495}\right) e(263330)e\left(\frac{263}{330}\right) e(2645)e\left(\frac{26}{45}\right) e(361495)e\left(\frac{361}{495}\right) e(809990)e\left(\frac{809}{990}\right) e(463990)e\left(\frac{463}{990}\right) e(5899)e\left(\frac{58}{99}\right) e(899)e\left(\frac{8}{99}\right) e(28495)e\left(\frac{28}{495}\right)
χ4598(43,⋅)\chi_{4598}(43,\cdot) 4598.bm 198 no −1-1 11 e(59)e\left(\frac{5}{9}\right) e(499)e\left(\frac{4}{99}\right) e(6166)e\left(\frac{61}{66}\right) e(19)e\left(\frac{1}{9}\right) e(79198)e\left(\frac{79}{198}\right) e(5999)e\left(\frac{59}{99}\right) e(5198)e\left(\frac{5}{198}\right) e(95198)e\left(\frac{95}{198}\right) e(6899)e\left(\frac{68}{99}\right) e(899)e\left(\frac{8}{99}\right)
χ4598(45,⋅)\chi_{4598}(45,\cdot) 4598.y 33 no 11 11 e(13)e\left(\frac{1}{3}\right) e(1733)e\left(\frac{17}{33}\right) e(1011)e\left(\frac{10}{11}\right) e(23)e\left(\frac{2}{3}\right) e(733)e\left(\frac{7}{33}\right) e(2833)e\left(\frac{28}{33}\right) e(2333)e\left(\frac{23}{33}\right) e(833)e\left(\frac{8}{33}\right) e(2533)e\left(\frac{25}{33}\right) e(133)e\left(\frac{1}{33}\right)
χ4598(47,⋅)\chi_{4598}(47,\cdot) 4598.bs 495 no 11 11 e(845)e\left(\frac{8}{45}\right) e(19495)e\left(\frac{19}{495}\right) e(149165)e\left(\frac{149}{165}\right) e(1645)e\left(\frac{16}{45}\right) e(101495)e\left(\frac{101}{495}\right) e(107495)e\left(\frac{107}{495}\right) e(49495)e\left(\frac{49}{495}\right) e(899)e\left(\frac{8}{99}\right) e(2599)e\left(\frac{25}{99}\right) e(38495)e\left(\frac{38}{495}\right)
χ4598(49,⋅)\chi_{4598}(49,\cdot) 4598.bl 165 no 11 11 e(1315)e\left(\frac{13}{15}\right) e(14165)e\left(\frac{14}{165}\right) e(4955)e\left(\frac{49}{55}\right) e(1115)e\left(\frac{11}{15}\right) e(31165)e\left(\frac{31}{165}\right) e(157165)e\left(\frac{157}{165}\right) e(149165)e\left(\frac{149}{165}\right) e(2533)e\left(\frac{25}{33}\right) e(833)e\left(\frac{8}{33}\right) e(28165)e\left(\frac{28}{165}\right)
χ4598(51,⋅)\chi_{4598}(51,\cdot) 4598.bu 990 no 11 11 e(1990)e\left(\frac{19}{90}\right) e(301495)e\left(\frac{301}{495}\right) e(127330)e\left(\frac{127}{330}\right) e(1945)e\left(\frac{19}{45}\right) e(89495)e\left(\frac{89}{495}\right) e(811990)e\left(\frac{811}{990}\right) e(797990)e\left(\frac{797}{990}\right) e(5999)e\left(\frac{59}{99}\right) e(7399)e\left(\frac{73}{99}\right) e(107495)e\left(\frac{107}{495}\right)
χ4598(53,⋅)\chi_{4598}(53,\cdot) 4598.bt 990 no −1-1 11 e(6790)e\left(\frac{67}{90}\right) e(43495)e\left(\frac{43}{495}\right) e(68165)e\left(\frac{68}{165}\right) e(2245)e\left(\frac{22}{45}\right) e(379990)e\left(\frac{379}{990}\right) e(823990)e\left(\frac{823}{990}\right) e(163495)e\left(\frac{163}{495}\right) e(31198)e\left(\frac{31}{198}\right) e(6799)e\left(\frac{67}{99}\right) e(86495)e\left(\frac{86}{495}\right)
χ4598(59,⋅)\chi_{4598}(59,\cdot) 4598.bt 990 no −1-1 11 e(2990)e\left(\frac{29}{90}\right) e(206495)e\left(\frac{206}{495}\right) e(61165)e\left(\frac{61}{165}\right) e(2945)e\left(\frac{29}{45}\right) e(653990)e\left(\frac{653}{990}\right) e(731990)e\left(\frac{731}{990}\right) e(401495)e\left(\frac{401}{495}\right) e(137198)e\left(\frac{137}{198}\right) e(4799)e\left(\frac{47}{99}\right) e(412495)e\left(\frac{412}{495}\right)
χ4598(61,⋅)\chi_{4598}(61,\cdot) 4598.bv 990 no −1-1 11 e(2945)e\left(\frac{29}{45}\right) e(52495)e\left(\frac{52}{495}\right) e(199330)e\left(\frac{199}{330}\right) e(1345)e\left(\frac{13}{45}\right) e(631990)e\left(\frac{631}{990}\right) e(371495)e\left(\frac{371}{495}\right) e(659990)e\left(\frac{659}{990}\right) e(49198)e\left(\frac{49}{198}\right) e(5899)e\left(\frac{58}{99}\right) e(104495)e\left(\frac{104}{495}\right)
χ4598(63,⋅)\chi_{4598}(63,\cdot) 4598.bv 990 no −1-1 11 e(2345)e\left(\frac{23}{45}\right) e(274495)e\left(\frac{274}{495}\right) e(103330)e\left(\frac{103}{330}\right) e(145)e\left(\frac{1}{45}\right) e(907990)e\left(\frac{907}{990}\right) e(32495)e\left(\frac{32}{495}\right) e(293990)e\left(\frac{293}{990}\right) e(163198)e\left(\frac{163}{198}\right) e(199)e\left(\frac{1}{99}\right) e(53495)e\left(\frac{53}{495}\right)
χ4598(65,⋅)\chi_{4598}(65,\cdot) 4598.bd 66 no 11 11 e(16)e\left(\frac{1}{6}\right) e(1333)e\left(\frac{13}{33}\right) e(322)e\left(\frac{3}{22}\right) e(13)e\left(\frac{1}{3}\right) e(1733)e\left(\frac{17}{33}\right) e(3766)e\left(\frac{37}{66}\right) e(4166)e\left(\frac{41}{66}\right) e(1033)e\left(\frac{10}{33}\right) e(2333)e\left(\frac{23}{33}\right) e(2633)e\left(\frac{26}{33}\right)
χ4598(67,⋅)\chi_{4598}(67,\cdot) 4598.bo 198 no −1-1 11 e(518)e\left(\frac{5}{18}\right) e(3899)e\left(\frac{38}{99}\right) e(133)e\left(\frac{1}{33}\right) e(59)e\left(\frac{5}{9}\right) e(107198)e\left(\frac{107}{198}\right) e(131198)e\left(\frac{131}{198}\right) e(9899)e\left(\frac{98}{99}\right) e(61198)e\left(\frac{61}{198}\right) e(5299)e\left(\frac{52}{99}\right) e(7699)e\left(\frac{76}{99}\right)
χ4598(69,⋅)\chi_{4598}(69,\cdot) 4598.bq 330 no −1-1 11 e(730)e\left(\frac{7}{30}\right) e(103165)e\left(\frac{103}{165}\right) e(355)e\left(\frac{3}{55}\right) e(715)e\left(\frac{7}{15}\right) e(79330)e\left(\frac{79}{330}\right) e(283330)e\left(\frac{283}{330}\right) e(118165)e\left(\frac{118}{165}\right) e(1966)e\left(\frac{19}{66}\right) e(733)e\left(\frac{7}{33}\right) e(41165)e\left(\frac{41}{165}\right)
χ4598(71,⋅)\chi_{4598}(71,\cdot) 4598.bt 990 no −1-1 11 e(2390)e\left(\frac{23}{90}\right) e(227495)e\left(\frac{227}{495}\right) e(52165)e\left(\frac{52}{165}\right) e(2345)e\left(\frac{23}{45}\right) e(251990)e\left(\frac{251}{990}\right) e(707990)e\left(\frac{707}{990}\right) e(377495)e\left(\frac{377}{495}\right) e(113198)e\left(\frac{113}{198}\right) e(5999)e\left(\frac{59}{99}\right) e(454495)e\left(\frac{454}{495}\right)
χ4598(73,⋅)\chi_{4598}(73,\cdot) 4598.bv 990 no −1-1 11 e(2245)e\left(\frac{22}{45}\right) e(221495)e\left(\frac{221}{495}\right) e(227330)e\left(\frac{227}{330}\right) e(4445)e\left(\frac{44}{45}\right) e(83990)e\left(\frac{83}{990}\right) e(463495)e\left(\frac{463}{495}\right) e(697990)e\left(\frac{697}{990}\right) e(35198)e\left(\frac{35}{198}\right) e(9899)e\left(\frac{98}{99}\right) e(442495)e\left(\frac{442}{495}\right)
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