# Properties

 Modulus 1021 Structure $$C_{1020}$$ Order 1020

Show commands for: Pari/GP / SageMath

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed

sage: H = DirichletGroup_conrey(1021)

pari: g = idealstar(,1021,2)

## Character group

 sage: G.order()  pari: g.no Order = 1020 sage: H.invariants()  pari: g.cyc Structure = $$C_{1020}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{1021}(10,\cdot)$

## First 32 of 1020 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.

orbit label order primitive -1 1 2 3 4 5 6 7 8 9 10 11
$$\chi_{1021}(1,\cdot)$$ 1021.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{1021}(2,\cdot)$$ 1021.v 340 yes $$-1$$ $$1$$ $$e\left(\frac{243}{340}\right)$$ $$e\left(\frac{5}{34}\right)$$ $$e\left(\frac{73}{170}\right)$$ $$e\left(\frac{52}{85}\right)$$ $$e\left(\frac{293}{340}\right)$$ $$e\left(\frac{113}{340}\right)$$ $$e\left(\frac{49}{340}\right)$$ $$e\left(\frac{5}{17}\right)$$ $$e\left(\frac{111}{340}\right)$$ $$e\left(\frac{19}{85}\right)$$
$$\chi_{1021}(3,\cdot)$$ 1021.m 34 yes $$1$$ $$1$$ $$e\left(\frac{5}{34}\right)$$ $$e\left(\frac{8}{17}\right)$$ $$e\left(\frac{5}{17}\right)$$ $$e\left(\frac{2}{17}\right)$$ $$e\left(\frac{21}{34}\right)$$ $$e\left(\frac{11}{34}\right)$$ $$e\left(\frac{15}{34}\right)$$ $$e\left(\frac{16}{17}\right)$$ $$e\left(\frac{9}{34}\right)$$ $$e\left(\frac{4}{17}\right)$$
$$\chi_{1021}(4,\cdot)$$ 1021.s 170 yes $$1$$ $$1$$ $$e\left(\frac{73}{170}\right)$$ $$e\left(\frac{5}{17}\right)$$ $$e\left(\frac{73}{85}\right)$$ $$e\left(\frac{19}{85}\right)$$ $$e\left(\frac{123}{170}\right)$$ $$e\left(\frac{113}{170}\right)$$ $$e\left(\frac{49}{170}\right)$$ $$e\left(\frac{10}{17}\right)$$ $$e\left(\frac{111}{170}\right)$$ $$e\left(\frac{38}{85}\right)$$
$$\chi_{1021}(5,\cdot)$$ 1021.u 255 yes $$1$$ $$1$$ $$e\left(\frac{52}{85}\right)$$ $$e\left(\frac{2}{17}\right)$$ $$e\left(\frac{19}{85}\right)$$ $$e\left(\frac{16}{255}\right)$$ $$e\left(\frac{62}{85}\right)$$ $$e\left(\frac{77}{85}\right)$$ $$e\left(\frac{71}{85}\right)$$ $$e\left(\frac{4}{17}\right)$$ $$e\left(\frac{172}{255}\right)$$ $$e\left(\frac{202}{255}\right)$$
$$\chi_{1021}(6,\cdot)$$ 1021.v 340 yes $$-1$$ $$1$$ $$e\left(\frac{293}{340}\right)$$ $$e\left(\frac{21}{34}\right)$$ $$e\left(\frac{123}{170}\right)$$ $$e\left(\frac{62}{85}\right)$$ $$e\left(\frac{163}{340}\right)$$ $$e\left(\frac{223}{340}\right)$$ $$e\left(\frac{199}{340}\right)$$ $$e\left(\frac{4}{17}\right)$$ $$e\left(\frac{201}{340}\right)$$ $$e\left(\frac{39}{85}\right)$$
$$\chi_{1021}(7,\cdot)$$ 1021.v 340 yes $$-1$$ $$1$$ $$e\left(\frac{113}{340}\right)$$ $$e\left(\frac{11}{34}\right)$$ $$e\left(\frac{113}{170}\right)$$ $$e\left(\frac{77}{85}\right)$$ $$e\left(\frac{223}{340}\right)$$ $$e\left(\frac{303}{340}\right)$$ $$e\left(\frac{339}{340}\right)$$ $$e\left(\frac{11}{17}\right)$$ $$e\left(\frac{81}{340}\right)$$ $$e\left(\frac{69}{85}\right)$$
$$\chi_{1021}(8,\cdot)$$ 1021.v 340 yes $$-1$$ $$1$$ $$e\left(\frac{49}{340}\right)$$ $$e\left(\frac{15}{34}\right)$$ $$e\left(\frac{49}{170}\right)$$ $$e\left(\frac{71}{85}\right)$$ $$e\left(\frac{199}{340}\right)$$ $$e\left(\frac{339}{340}\right)$$ $$e\left(\frac{147}{340}\right)$$ $$e\left(\frac{15}{17}\right)$$ $$e\left(\frac{333}{340}\right)$$ $$e\left(\frac{57}{85}\right)$$
$$\chi_{1021}(9,\cdot)$$ 1021.j 17 yes $$1$$ $$1$$ $$e\left(\frac{5}{17}\right)$$ $$e\left(\frac{16}{17}\right)$$ $$e\left(\frac{10}{17}\right)$$ $$e\left(\frac{4}{17}\right)$$ $$e\left(\frac{4}{17}\right)$$ $$e\left(\frac{11}{17}\right)$$ $$e\left(\frac{15}{17}\right)$$ $$e\left(\frac{15}{17}\right)$$ $$e\left(\frac{9}{17}\right)$$ $$e\left(\frac{8}{17}\right)$$
$$\chi_{1021}(10,\cdot)$$ 1021.x 1020 yes $$-1$$ $$1$$ $$e\left(\frac{111}{340}\right)$$ $$e\left(\frac{9}{34}\right)$$ $$e\left(\frac{111}{170}\right)$$ $$e\left(\frac{172}{255}\right)$$ $$e\left(\frac{201}{340}\right)$$ $$e\left(\frac{81}{340}\right)$$ $$e\left(\frac{333}{340}\right)$$ $$e\left(\frac{9}{17}\right)$$ $$e\left(\frac{1}{1020}\right)$$ $$e\left(\frac{4}{255}\right)$$
$$\chi_{1021}(11,\cdot)$$ 1021.u 255 yes $$1$$ $$1$$ $$e\left(\frac{19}{85}\right)$$ $$e\left(\frac{4}{17}\right)$$ $$e\left(\frac{38}{85}\right)$$ $$e\left(\frac{202}{255}\right)$$ $$e\left(\frac{39}{85}\right)$$ $$e\left(\frac{69}{85}\right)$$ $$e\left(\frac{57}{85}\right)$$ $$e\left(\frac{8}{17}\right)$$ $$e\left(\frac{4}{255}\right)$$ $$e\left(\frac{64}{255}\right)$$
$$\chi_{1021}(12,\cdot)$$ 1021.q 85 yes $$1$$ $$1$$ $$e\left(\frac{49}{85}\right)$$ $$e\left(\frac{13}{17}\right)$$ $$e\left(\frac{13}{85}\right)$$ $$e\left(\frac{29}{85}\right)$$ $$e\left(\frac{29}{85}\right)$$ $$e\left(\frac{84}{85}\right)$$ $$e\left(\frac{62}{85}\right)$$ $$e\left(\frac{9}{17}\right)$$ $$e\left(\frac{78}{85}\right)$$ $$e\left(\frac{58}{85}\right)$$
$$\chi_{1021}(13,\cdot)$$ 1021.p 68 yes $$-1$$ $$1$$ $$e\left(\frac{67}{68}\right)$$ $$e\left(\frac{29}{34}\right)$$ $$e\left(\frac{33}{34}\right)$$ $$e\left(\frac{10}{17}\right)$$ $$e\left(\frac{57}{68}\right)$$ $$e\left(\frac{25}{68}\right)$$ $$e\left(\frac{65}{68}\right)$$ $$e\left(\frac{12}{17}\right)$$ $$e\left(\frac{39}{68}\right)$$ $$e\left(\frac{3}{17}\right)$$
$$\chi_{1021}(14,\cdot)$$ 1021.q 85 yes $$1$$ $$1$$ $$e\left(\frac{4}{85}\right)$$ $$e\left(\frac{8}{17}\right)$$ $$e\left(\frac{8}{85}\right)$$ $$e\left(\frac{44}{85}\right)$$ $$e\left(\frac{44}{85}\right)$$ $$e\left(\frac{19}{85}\right)$$ $$e\left(\frac{12}{85}\right)$$ $$e\left(\frac{16}{17}\right)$$ $$e\left(\frac{48}{85}\right)$$ $$e\left(\frac{3}{85}\right)$$
$$\chi_{1021}(15,\cdot)$$ 1021.w 510 yes $$1$$ $$1$$ $$e\left(\frac{129}{170}\right)$$ $$e\left(\frac{10}{17}\right)$$ $$e\left(\frac{44}{85}\right)$$ $$e\left(\frac{46}{255}\right)$$ $$e\left(\frac{59}{170}\right)$$ $$e\left(\frac{39}{170}\right)$$ $$e\left(\frac{47}{170}\right)$$ $$e\left(\frac{3}{17}\right)$$ $$e\left(\frac{479}{510}\right)$$ $$e\left(\frac{7}{255}\right)$$
$$\chi_{1021}(16,\cdot)$$ 1021.q 85 yes $$1$$ $$1$$ $$e\left(\frac{73}{85}\right)$$ $$e\left(\frac{10}{17}\right)$$ $$e\left(\frac{61}{85}\right)$$ $$e\left(\frac{38}{85}\right)$$ $$e\left(\frac{38}{85}\right)$$ $$e\left(\frac{28}{85}\right)$$ $$e\left(\frac{49}{85}\right)$$ $$e\left(\frac{3}{17}\right)$$ $$e\left(\frac{26}{85}\right)$$ $$e\left(\frac{76}{85}\right)$$
$$\chi_{1021}(17,\cdot)$$ 1021.w 510 yes $$1$$ $$1$$ $$e\left(\frac{53}{170}\right)$$ $$e\left(\frac{2}{17}\right)$$ $$e\left(\frac{53}{85}\right)$$ $$e\left(\frac{152}{255}\right)$$ $$e\left(\frac{73}{170}\right)$$ $$e\left(\frac{103}{170}\right)$$ $$e\left(\frac{159}{170}\right)$$ $$e\left(\frac{4}{17}\right)$$ $$e\left(\frac{463}{510}\right)$$ $$e\left(\frac{134}{255}\right)$$
$$\chi_{1021}(18,\cdot)$$ 1021.v 340 yes $$-1$$ $$1$$ $$e\left(\frac{3}{340}\right)$$ $$e\left(\frac{3}{34}\right)$$ $$e\left(\frac{3}{170}\right)$$ $$e\left(\frac{72}{85}\right)$$ $$e\left(\frac{33}{340}\right)$$ $$e\left(\frac{333}{340}\right)$$ $$e\left(\frac{9}{340}\right)$$ $$e\left(\frac{3}{17}\right)$$ $$e\left(\frac{291}{340}\right)$$ $$e\left(\frac{59}{85}\right)$$
$$\chi_{1021}(19,\cdot)$$ 1021.t 204 yes $$-1$$ $$1$$ $$e\left(\frac{31}{68}\right)$$ $$e\left(\frac{19}{34}\right)$$ $$e\left(\frac{31}{34}\right)$$ $$e\left(\frac{5}{51}\right)$$ $$e\left(\frac{1}{68}\right)$$ $$e\left(\frac{41}{68}\right)$$ $$e\left(\frac{25}{68}\right)$$ $$e\left(\frac{2}{17}\right)$$ $$e\left(\frac{113}{204}\right)$$ $$e\left(\frac{44}{51}\right)$$
$$\chi_{1021}(20,\cdot)$$ 1021.w 510 yes $$1$$ $$1$$ $$e\left(\frac{7}{170}\right)$$ $$e\left(\frac{7}{17}\right)$$ $$e\left(\frac{7}{85}\right)$$ $$e\left(\frac{73}{255}\right)$$ $$e\left(\frac{77}{170}\right)$$ $$e\left(\frac{97}{170}\right)$$ $$e\left(\frac{21}{170}\right)$$ $$e\left(\frac{14}{17}\right)$$ $$e\left(\frac{167}{510}\right)$$ $$e\left(\frac{61}{255}\right)$$
$$\chi_{1021}(21,\cdot)$$ 1021.v 340 yes $$-1$$ $$1$$ $$e\left(\frac{163}{340}\right)$$ $$e\left(\frac{27}{34}\right)$$ $$e\left(\frac{163}{170}\right)$$ $$e\left(\frac{2}{85}\right)$$ $$e\left(\frac{93}{340}\right)$$ $$e\left(\frac{73}{340}\right)$$ $$e\left(\frac{149}{340}\right)$$ $$e\left(\frac{10}{17}\right)$$ $$e\left(\frac{171}{340}\right)$$ $$e\left(\frac{4}{85}\right)$$
$$\chi_{1021}(22,\cdot)$$ 1021.x 1020 yes $$-1$$ $$1$$ $$e\left(\frac{319}{340}\right)$$ $$e\left(\frac{13}{34}\right)$$ $$e\left(\frac{149}{170}\right)$$ $$e\left(\frac{103}{255}\right)$$ $$e\left(\frac{109}{340}\right)$$ $$e\left(\frac{49}{340}\right)$$ $$e\left(\frac{277}{340}\right)$$ $$e\left(\frac{13}{17}\right)$$ $$e\left(\frac{349}{1020}\right)$$ $$e\left(\frac{121}{255}\right)$$
$$\chi_{1021}(23,\cdot)$$ 1021.u 255 yes $$1$$ $$1$$ $$e\left(\frac{12}{85}\right)$$ $$e\left(\frac{7}{17}\right)$$ $$e\left(\frac{24}{85}\right)$$ $$e\left(\frac{56}{255}\right)$$ $$e\left(\frac{47}{85}\right)$$ $$e\left(\frac{57}{85}\right)$$ $$e\left(\frac{36}{85}\right)$$ $$e\left(\frac{14}{17}\right)$$ $$e\left(\frac{92}{255}\right)$$ $$e\left(\frac{197}{255}\right)$$
$$\chi_{1021}(24,\cdot)$$ 1021.v 340 yes $$-1$$ $$1$$ $$e\left(\frac{99}{340}\right)$$ $$e\left(\frac{31}{34}\right)$$ $$e\left(\frac{99}{170}\right)$$ $$e\left(\frac{81}{85}\right)$$ $$e\left(\frac{69}{340}\right)$$ $$e\left(\frac{109}{340}\right)$$ $$e\left(\frac{297}{340}\right)$$ $$e\left(\frac{14}{17}\right)$$ $$e\left(\frac{83}{340}\right)$$ $$e\left(\frac{77}{85}\right)$$
$$\chi_{1021}(25,\cdot)$$ 1021.u 255 yes $$1$$ $$1$$ $$e\left(\frac{19}{85}\right)$$ $$e\left(\frac{4}{17}\right)$$ $$e\left(\frac{38}{85}\right)$$ $$e\left(\frac{32}{255}\right)$$ $$e\left(\frac{39}{85}\right)$$ $$e\left(\frac{69}{85}\right)$$ $$e\left(\frac{57}{85}\right)$$ $$e\left(\frac{8}{17}\right)$$ $$e\left(\frac{89}{255}\right)$$ $$e\left(\frac{149}{255}\right)$$
$$\chi_{1021}(26,\cdot)$$ 1021.g 10 yes $$1$$ $$1$$ $$e\left(\frac{7}{10}\right)$$ $$1$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$1$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$
$$\chi_{1021}(27,\cdot)$$ 1021.m 34 yes $$1$$ $$1$$ $$e\left(\frac{15}{34}\right)$$ $$e\left(\frac{7}{17}\right)$$ $$e\left(\frac{15}{17}\right)$$ $$e\left(\frac{6}{17}\right)$$ $$e\left(\frac{29}{34}\right)$$ $$e\left(\frac{33}{34}\right)$$ $$e\left(\frac{11}{34}\right)$$ $$e\left(\frac{14}{17}\right)$$ $$e\left(\frac{27}{34}\right)$$ $$e\left(\frac{12}{17}\right)$$
$$\chi_{1021}(28,\cdot)$$ 1021.v 340 yes $$-1$$ $$1$$ $$e\left(\frac{259}{340}\right)$$ $$e\left(\frac{21}{34}\right)$$ $$e\left(\frac{89}{170}\right)$$ $$e\left(\frac{11}{85}\right)$$ $$e\left(\frac{129}{340}\right)$$ $$e\left(\frac{189}{340}\right)$$ $$e\left(\frac{97}{340}\right)$$ $$e\left(\frac{4}{17}\right)$$ $$e\left(\frac{303}{340}\right)$$ $$e\left(\frac{22}{85}\right)$$
$$\chi_{1021}(29,\cdot)$$ 1021.w 510 yes $$1$$ $$1$$ $$e\left(\frac{71}{170}\right)$$ $$e\left(\frac{3}{17}\right)$$ $$e\left(\frac{71}{85}\right)$$ $$e\left(\frac{194}{255}\right)$$ $$e\left(\frac{101}{170}\right)$$ $$e\left(\frac{61}{170}\right)$$ $$e\left(\frac{43}{170}\right)$$ $$e\left(\frac{6}{17}\right)$$ $$e\left(\frac{91}{510}\right)$$ $$e\left(\frac{218}{255}\right)$$
$$\chi_{1021}(30,\cdot)$$ 1021.x 1020 yes $$-1$$ $$1$$ $$e\left(\frac{161}{340}\right)$$ $$e\left(\frac{25}{34}\right)$$ $$e\left(\frac{161}{170}\right)$$ $$e\left(\frac{202}{255}\right)$$ $$e\left(\frac{71}{340}\right)$$ $$e\left(\frac{191}{340}\right)$$ $$e\left(\frac{143}{340}\right)$$ $$e\left(\frac{8}{17}\right)$$ $$e\left(\frac{271}{1020}\right)$$ $$e\left(\frac{64}{255}\right)$$
$$\chi_{1021}(31,\cdot)$$ 1021.x 1020 yes $$-1$$ $$1$$ $$e\left(\frac{117}{340}\right)$$ $$e\left(\frac{15}{34}\right)$$ $$e\left(\frac{117}{170}\right)$$ $$e\left(\frac{179}{255}\right)$$ $$e\left(\frac{267}{340}\right)$$ $$e\left(\frac{67}{340}\right)$$ $$e\left(\frac{11}{340}\right)$$ $$e\left(\frac{15}{17}\right)$$ $$e\left(\frac{47}{1020}\right)$$ $$e\left(\frac{188}{255}\right)$$
$$\chi_{1021}(32,\cdot)$$ 1021.p 68 yes $$-1$$ $$1$$ $$e\left(\frac{39}{68}\right)$$ $$e\left(\frac{25}{34}\right)$$ $$e\left(\frac{5}{34}\right)$$ $$e\left(\frac{1}{17}\right)$$ $$e\left(\frac{21}{68}\right)$$ $$e\left(\frac{45}{68}\right)$$ $$e\left(\frac{49}{68}\right)$$ $$e\left(\frac{8}{17}\right)$$ $$e\left(\frac{43}{68}\right)$$ $$e\left(\frac{2}{17}\right)$$