# Properties

 Modulus $1048$ Structure $$C_{130}\times C_{2}\times C_{2}$$ Order $520$

Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(1048)

pari: g = idealstar(,1048,2)

## Character group

 sage: G.order()  pari: g.no Order = 520 sage: H.invariants()  pari: g.cyc Structure = $$C_{130}\times C_{2}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{1048}(263,\cdot)$, $\chi_{1048}(525,\cdot)$, $\chi_{1048}(657,\cdot)$

## First 32 of 520 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 $$-1$$ $$1$$ $$3$$ $$5$$ $$7$$ $$9$$ $$11$$ $$13$$ $$15$$ $$17$$ $$19$$ $$21$$
$$\chi_{1048}(1,\cdot)$$ 1048.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{1048}(3,\cdot)$$ 1048.be 130 yes $$-1$$ $$1$$ $$e\left(\frac{57}{65}\right)$$ $$e\left(\frac{127}{130}\right)$$ $$e\left(\frac{87}{130}\right)$$ $$e\left(\frac{49}{65}\right)$$ $$e\left(\frac{1}{65}\right)$$ $$e\left(\frac{61}{130}\right)$$ $$e\left(\frac{111}{130}\right)$$ $$e\left(\frac{53}{65}\right)$$ $$e\left(\frac{5}{13}\right)$$ $$e\left(\frac{71}{130}\right)$$
$$\chi_{1048}(5,\cdot)$$ 1048.ba 130 yes $$1$$ $$1$$ $$e\left(\frac{127}{130}\right)$$ $$e\left(\frac{101}{130}\right)$$ $$e\left(\frac{63}{65}\right)$$ $$e\left(\frac{62}{65}\right)$$ $$e\left(\frac{41}{130}\right)$$ $$e\left(\frac{113}{130}\right)$$ $$e\left(\frac{49}{65}\right)$$ $$e\left(\frac{14}{65}\right)$$ $$e\left(\frac{23}{26}\right)$$ $$e\left(\frac{123}{130}\right)$$
$$\chi_{1048}(7,\cdot)$$ 1048.bc 130 no $$-1$$ $$1$$ $$e\left(\frac{87}{130}\right)$$ $$e\left(\frac{63}{65}\right)$$ $$e\left(\frac{51}{130}\right)$$ $$e\left(\frac{22}{65}\right)$$ $$e\left(\frac{111}{130}\right)$$ $$e\left(\frac{19}{65}\right)$$ $$e\left(\frac{83}{130}\right)$$ $$e\left(\frac{49}{65}\right)$$ $$e\left(\frac{9}{26}\right)$$ $$e\left(\frac{4}{65}\right)$$
$$\chi_{1048}(9,\cdot)$$ 1048.y 65 no $$1$$ $$1$$ $$e\left(\frac{49}{65}\right)$$ $$e\left(\frac{62}{65}\right)$$ $$e\left(\frac{22}{65}\right)$$ $$e\left(\frac{33}{65}\right)$$ $$e\left(\frac{2}{65}\right)$$ $$e\left(\frac{61}{65}\right)$$ $$e\left(\frac{46}{65}\right)$$ $$e\left(\frac{41}{65}\right)$$ $$e\left(\frac{10}{13}\right)$$ $$e\left(\frac{6}{65}\right)$$
$$\chi_{1048}(11,\cdot)$$ 1048.be 130 yes $$-1$$ $$1$$ $$e\left(\frac{1}{65}\right)$$ $$e\left(\frac{41}{130}\right)$$ $$e\left(\frac{111}{130}\right)$$ $$e\left(\frac{2}{65}\right)$$ $$e\left(\frac{8}{65}\right)$$ $$e\left(\frac{33}{130}\right)$$ $$e\left(\frac{43}{130}\right)$$ $$e\left(\frac{34}{65}\right)$$ $$e\left(\frac{1}{13}\right)$$ $$e\left(\frac{113}{130}\right)$$
$$\chi_{1048}(13,\cdot)$$ 1048.ba 130 yes $$1$$ $$1$$ $$e\left(\frac{61}{130}\right)$$ $$e\left(\frac{113}{130}\right)$$ $$e\left(\frac{19}{65}\right)$$ $$e\left(\frac{61}{65}\right)$$ $$e\left(\frac{33}{130}\right)$$ $$e\left(\frac{129}{130}\right)$$ $$e\left(\frac{22}{65}\right)$$ $$e\left(\frac{62}{65}\right)$$ $$e\left(\frac{9}{26}\right)$$ $$e\left(\frac{99}{130}\right)$$
$$\chi_{1048}(15,\cdot)$$ 1048.bc 130 no $$-1$$ $$1$$ $$e\left(\frac{111}{130}\right)$$ $$e\left(\frac{49}{65}\right)$$ $$e\left(\frac{83}{130}\right)$$ $$e\left(\frac{46}{65}\right)$$ $$e\left(\frac{43}{130}\right)$$ $$e\left(\frac{22}{65}\right)$$ $$e\left(\frac{79}{130}\right)$$ $$e\left(\frac{2}{65}\right)$$ $$e\left(\frac{7}{26}\right)$$ $$e\left(\frac{32}{65}\right)$$
$$\chi_{1048}(17,\cdot)$$ 1048.bf 130 no $$-1$$ $$1$$ $$e\left(\frac{53}{65}\right)$$ $$e\left(\frac{14}{65}\right)$$ $$e\left(\frac{49}{65}\right)$$ $$e\left(\frac{41}{65}\right)$$ $$e\left(\frac{34}{65}\right)$$ $$e\left(\frac{62}{65}\right)$$ $$e\left(\frac{2}{65}\right)$$ $$e\left(\frac{29}{130}\right)$$ $$e\left(\frac{15}{26}\right)$$ $$e\left(\frac{37}{65}\right)$$
$$\chi_{1048}(19,\cdot)$$ 1048.t 26 yes $$1$$ $$1$$ $$e\left(\frac{5}{13}\right)$$ $$e\left(\frac{23}{26}\right)$$ $$e\left(\frac{9}{26}\right)$$ $$e\left(\frac{10}{13}\right)$$ $$e\left(\frac{1}{13}\right)$$ $$e\left(\frac{9}{26}\right)$$ $$e\left(\frac{7}{26}\right)$$ $$e\left(\frac{15}{26}\right)$$ $$e\left(\frac{11}{26}\right)$$ $$e\left(\frac{19}{26}\right)$$
$$\chi_{1048}(21,\cdot)$$ 1048.ba 130 yes $$1$$ $$1$$ $$e\left(\frac{71}{130}\right)$$ $$e\left(\frac{123}{130}\right)$$ $$e\left(\frac{4}{65}\right)$$ $$e\left(\frac{6}{65}\right)$$ $$e\left(\frac{113}{130}\right)$$ $$e\left(\frac{99}{130}\right)$$ $$e\left(\frac{32}{65}\right)$$ $$e\left(\frac{37}{65}\right)$$ $$e\left(\frac{19}{26}\right)$$ $$e\left(\frac{79}{130}\right)$$
$$\chi_{1048}(23,\cdot)$$ 1048.bb 130 no $$1$$ $$1$$ $$e\left(\frac{31}{130}\right)$$ $$e\left(\frac{9}{65}\right)$$ $$e\left(\frac{63}{130}\right)$$ $$e\left(\frac{31}{65}\right)$$ $$e\left(\frac{53}{130}\right)$$ $$e\left(\frac{12}{65}\right)$$ $$e\left(\frac{49}{130}\right)$$ $$e\left(\frac{79}{130}\right)$$ $$e\left(\frac{9}{13}\right)$$ $$e\left(\frac{47}{65}\right)$$
$$\chi_{1048}(25,\cdot)$$ 1048.y 65 no $$1$$ $$1$$ $$e\left(\frac{62}{65}\right)$$ $$e\left(\frac{36}{65}\right)$$ $$e\left(\frac{61}{65}\right)$$ $$e\left(\frac{59}{65}\right)$$ $$e\left(\frac{41}{65}\right)$$ $$e\left(\frac{48}{65}\right)$$ $$e\left(\frac{33}{65}\right)$$ $$e\left(\frac{28}{65}\right)$$ $$e\left(\frac{10}{13}\right)$$ $$e\left(\frac{58}{65}\right)$$
$$\chi_{1048}(27,\cdot)$$ 1048.be 130 yes $$-1$$ $$1$$ $$e\left(\frac{41}{65}\right)$$ $$e\left(\frac{121}{130}\right)$$ $$e\left(\frac{1}{130}\right)$$ $$e\left(\frac{17}{65}\right)$$ $$e\left(\frac{3}{65}\right)$$ $$e\left(\frac{53}{130}\right)$$ $$e\left(\frac{73}{130}\right)$$ $$e\left(\frac{29}{65}\right)$$ $$e\left(\frac{2}{13}\right)$$ $$e\left(\frac{83}{130}\right)$$
$$\chi_{1048}(29,\cdot)$$ 1048.z 130 yes $$-1$$ $$1$$ $$e\left(\frac{97}{130}\right)$$ $$e\left(\frac{71}{130}\right)$$ $$e\left(\frac{43}{65}\right)$$ $$e\left(\frac{32}{65}\right)$$ $$e\left(\frac{61}{130}\right)$$ $$e\left(\frac{73}{130}\right)$$ $$e\left(\frac{19}{65}\right)$$ $$e\left(\frac{113}{130}\right)$$ $$e\left(\frac{3}{13}\right)$$ $$e\left(\frac{53}{130}\right)$$
$$\chi_{1048}(31,\cdot)$$ 1048.bb 130 no $$1$$ $$1$$ $$e\left(\frac{73}{130}\right)$$ $$e\left(\frac{17}{65}\right)$$ $$e\left(\frac{119}{130}\right)$$ $$e\left(\frac{8}{65}\right)$$ $$e\left(\frac{129}{130}\right)$$ $$e\left(\frac{1}{65}\right)$$ $$e\left(\frac{107}{130}\right)$$ $$e\left(\frac{77}{130}\right)$$ $$e\left(\frac{4}{13}\right)$$ $$e\left(\frac{31}{65}\right)$$
$$\chi_{1048}(33,\cdot)$$ 1048.y 65 no $$1$$ $$1$$ $$e\left(\frac{58}{65}\right)$$ $$e\left(\frac{19}{65}\right)$$ $$e\left(\frac{34}{65}\right)$$ $$e\left(\frac{51}{65}\right)$$ $$e\left(\frac{9}{65}\right)$$ $$e\left(\frac{47}{65}\right)$$ $$e\left(\frac{12}{65}\right)$$ $$e\left(\frac{22}{65}\right)$$ $$e\left(\frac{6}{13}\right)$$ $$e\left(\frac{27}{65}\right)$$
$$\chi_{1048}(35,\cdot)$$ 1048.be 130 yes $$-1$$ $$1$$ $$e\left(\frac{42}{65}\right)$$ $$e\left(\frac{97}{130}\right)$$ $$e\left(\frac{47}{130}\right)$$ $$e\left(\frac{19}{65}\right)$$ $$e\left(\frac{11}{65}\right)$$ $$e\left(\frac{21}{130}\right)$$ $$e\left(\frac{51}{130}\right)$$ $$e\left(\frac{63}{65}\right)$$ $$e\left(\frac{3}{13}\right)$$ $$e\left(\frac{1}{130}\right)$$
$$\chi_{1048}(37,\cdot)$$ 1048.z 130 yes $$-1$$ $$1$$ $$e\left(\frac{27}{130}\right)$$ $$e\left(\frac{1}{130}\right)$$ $$e\left(\frac{18}{65}\right)$$ $$e\left(\frac{27}{65}\right)$$ $$e\left(\frac{21}{130}\right)$$ $$e\left(\frac{23}{130}\right)$$ $$e\left(\frac{14}{65}\right)$$ $$e\left(\frac{73}{130}\right)$$ $$e\left(\frac{7}{13}\right)$$ $$e\left(\frac{63}{130}\right)$$
$$\chi_{1048}(39,\cdot)$$ 1048.u 26 no $$-1$$ $$1$$ $$e\left(\frac{9}{26}\right)$$ $$e\left(\frac{11}{13}\right)$$ $$e\left(\frac{25}{26}\right)$$ $$e\left(\frac{9}{13}\right)$$ $$e\left(\frac{7}{26}\right)$$ $$e\left(\frac{6}{13}\right)$$ $$e\left(\frac{5}{26}\right)$$ $$e\left(\frac{10}{13}\right)$$ $$e\left(\frac{19}{26}\right)$$ $$e\left(\frac{4}{13}\right)$$
$$\chi_{1048}(41,\cdot)$$ 1048.y 65 no $$1$$ $$1$$ $$e\left(\frac{51}{65}\right)$$ $$e\left(\frac{38}{65}\right)$$ $$e\left(\frac{3}{65}\right)$$ $$e\left(\frac{37}{65}\right)$$ $$e\left(\frac{18}{65}\right)$$ $$e\left(\frac{29}{65}\right)$$ $$e\left(\frac{24}{65}\right)$$ $$e\left(\frac{44}{65}\right)$$ $$e\left(\frac{12}{13}\right)$$ $$e\left(\frac{54}{65}\right)$$
$$\chi_{1048}(43,\cdot)$$ 1048.be 130 yes $$-1$$ $$1$$ $$e\left(\frac{44}{65}\right)$$ $$e\left(\frac{49}{130}\right)$$ $$e\left(\frac{9}{130}\right)$$ $$e\left(\frac{23}{65}\right)$$ $$e\left(\frac{27}{65}\right)$$ $$e\left(\frac{87}{130}\right)$$ $$e\left(\frac{7}{130}\right)$$ $$e\left(\frac{1}{65}\right)$$ $$e\left(\frac{5}{13}\right)$$ $$e\left(\frac{97}{130}\right)$$
$$\chi_{1048}(45,\cdot)$$ 1048.w 26 yes $$1$$ $$1$$ $$e\left(\frac{19}{26}\right)$$ $$e\left(\frac{19}{26}\right)$$ $$e\left(\frac{4}{13}\right)$$ $$e\left(\frac{6}{13}\right)$$ $$e\left(\frac{9}{26}\right)$$ $$e\left(\frac{21}{26}\right)$$ $$e\left(\frac{6}{13}\right)$$ $$e\left(\frac{11}{13}\right)$$ $$e\left(\frac{17}{26}\right)$$ $$e\left(\frac{1}{26}\right)$$
$$\chi_{1048}(47,\cdot)$$ 1048.v 26 no $$1$$ $$1$$ $$e\left(\frac{17}{26}\right)$$ $$e\left(\frac{2}{13}\right)$$ $$e\left(\frac{1}{26}\right)$$ $$e\left(\frac{4}{13}\right)$$ $$e\left(\frac{19}{26}\right)$$ $$e\left(\frac{7}{13}\right)$$ $$e\left(\frac{21}{26}\right)$$ $$e\left(\frac{19}{26}\right)$$ $$e\left(\frac{10}{13}\right)$$ $$e\left(\frac{9}{13}\right)$$
$$\chi_{1048}(49,\cdot)$$ 1048.y 65 no $$1$$ $$1$$ $$e\left(\frac{22}{65}\right)$$ $$e\left(\frac{61}{65}\right)$$ $$e\left(\frac{51}{65}\right)$$ $$e\left(\frac{44}{65}\right)$$ $$e\left(\frac{46}{65}\right)$$ $$e\left(\frac{38}{65}\right)$$ $$e\left(\frac{18}{65}\right)$$ $$e\left(\frac{33}{65}\right)$$ $$e\left(\frac{9}{13}\right)$$ $$e\left(\frac{8}{65}\right)$$
$$\chi_{1048}(51,\cdot)$$ 1048.t 26 yes $$1$$ $$1$$ $$e\left(\frac{9}{13}\right)$$ $$e\left(\frac{5}{26}\right)$$ $$e\left(\frac{11}{26}\right)$$ $$e\left(\frac{5}{13}\right)$$ $$e\left(\frac{7}{13}\right)$$ $$e\left(\frac{11}{26}\right)$$ $$e\left(\frac{23}{26}\right)$$ $$e\left(\frac{1}{26}\right)$$ $$e\left(\frac{25}{26}\right)$$ $$e\left(\frac{3}{26}\right)$$
$$\chi_{1048}(53,\cdot)$$ 1048.o 10 yes $$1$$ $$1$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$-1$$ $$e\left(\frac{1}{10}\right)$$
$$\chi_{1048}(55,\cdot)$$ 1048.bc 130 no $$-1$$ $$1$$ $$e\left(\frac{129}{130}\right)$$ $$e\left(\frac{6}{65}\right)$$ $$e\left(\frac{107}{130}\right)$$ $$e\left(\frac{64}{65}\right)$$ $$e\left(\frac{57}{130}\right)$$ $$e\left(\frac{8}{65}\right)$$ $$e\left(\frac{11}{130}\right)$$ $$e\left(\frac{48}{65}\right)$$ $$e\left(\frac{25}{26}\right)$$ $$e\left(\frac{53}{65}\right)$$
$$\chi_{1048}(57,\cdot)$$ 1048.bf 130 no $$-1$$ $$1$$ $$e\left(\frac{17}{65}\right)$$ $$e\left(\frac{56}{65}\right)$$ $$e\left(\frac{1}{65}\right)$$ $$e\left(\frac{34}{65}\right)$$ $$e\left(\frac{6}{65}\right)$$ $$e\left(\frac{53}{65}\right)$$ $$e\left(\frac{8}{65}\right)$$ $$e\left(\frac{51}{130}\right)$$ $$e\left(\frac{21}{26}\right)$$ $$e\left(\frac{18}{65}\right)$$
$$\chi_{1048}(59,\cdot)$$ 1048.be 130 yes $$-1$$ $$1$$ $$e\left(\frac{27}{65}\right)$$ $$e\left(\frac{67}{130}\right)$$ $$e\left(\frac{7}{130}\right)$$ $$e\left(\frac{54}{65}\right)$$ $$e\left(\frac{21}{65}\right)$$ $$e\left(\frac{111}{130}\right)$$ $$e\left(\frac{121}{130}\right)$$ $$e\left(\frac{8}{65}\right)$$ $$e\left(\frac{1}{13}\right)$$ $$e\left(\frac{61}{130}\right)$$
$$\chi_{1048}(61,\cdot)$$ 1048.o 10 yes $$1$$ $$1$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$-1$$ $$e\left(\frac{3}{10}\right)$$
$$\chi_{1048}(63,\cdot)$$ 1048.u 26 no $$-1$$ $$1$$ $$e\left(\frac{11}{26}\right)$$ $$e\left(\frac{12}{13}\right)$$ $$e\left(\frac{19}{26}\right)$$ $$e\left(\frac{11}{13}\right)$$ $$e\left(\frac{23}{26}\right)$$ $$e\left(\frac{3}{13}\right)$$ $$e\left(\frac{9}{26}\right)$$ $$e\left(\frac{5}{13}\right)$$ $$e\left(\frac{3}{26}\right)$$ $$e\left(\frac{2}{13}\right)$$