# Properties

 Modulus $7581$ Structure $$C_{342}\times C_{6}\times C_{2}$$ Order $4104$

Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(7581)

pari: g = idealstar(,7581,2)

## Character group

 sage: G.order()  pari: g.no Order = 4104 sage: H.invariants()  pari: g.cyc Structure = $$C_{342}\times C_{6}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{7581}(2528,\cdot)$, $\chi_{7581}(6499,\cdot)$, $\chi_{7581}(1807,\cdot)$

## First 32 of 4104 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 $$-1$$ $$1$$ $$2$$ $$4$$ $$5$$ $$8$$ $$10$$ $$11$$ $$13$$ $$16$$ $$17$$ $$20$$
$$\chi_{7581}(1,\cdot)$$ 7581.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{7581}(2,\cdot)$$ 7581.ex 342 yes $$1$$ $$1$$ $$e\left(\frac{29}{171}\right)$$ $$e\left(\frac{58}{171}\right)$$ $$e\left(\frac{289}{342}\right)$$ $$e\left(\frac{29}{57}\right)$$ $$e\left(\frac{5}{342}\right)$$ $$e\left(\frac{5}{38}\right)$$ $$e\left(\frac{329}{342}\right)$$ $$e\left(\frac{116}{171}\right)$$ $$e\left(\frac{169}{342}\right)$$ $$e\left(\frac{7}{38}\right)$$
$$\chi_{7581}(4,\cdot)$$ 7581.ea 171 no $$1$$ $$1$$ $$e\left(\frac{58}{171}\right)$$ $$e\left(\frac{116}{171}\right)$$ $$e\left(\frac{118}{171}\right)$$ $$e\left(\frac{1}{57}\right)$$ $$e\left(\frac{5}{171}\right)$$ $$e\left(\frac{5}{19}\right)$$ $$e\left(\frac{158}{171}\right)$$ $$e\left(\frac{61}{171}\right)$$ $$e\left(\frac{169}{171}\right)$$ $$e\left(\frac{7}{19}\right)$$
$$\chi_{7581}(5,\cdot)$$ 7581.en 342 yes $$1$$ $$1$$ $$e\left(\frac{289}{342}\right)$$ $$e\left(\frac{118}{171}\right)$$ $$e\left(\frac{8}{171}\right)$$ $$e\left(\frac{61}{114}\right)$$ $$e\left(\frac{305}{342}\right)$$ $$e\left(\frac{1}{38}\right)$$ $$e\left(\frac{233}{342}\right)$$ $$e\left(\frac{65}{171}\right)$$ $$e\left(\frac{110}{171}\right)$$ $$e\left(\frac{14}{19}\right)$$
$$\chi_{7581}(8,\cdot)$$ 7581.ds 114 no $$1$$ $$1$$ $$e\left(\frac{29}{57}\right)$$ $$e\left(\frac{1}{57}\right)$$ $$e\left(\frac{61}{114}\right)$$ $$e\left(\frac{10}{19}\right)$$ $$e\left(\frac{5}{114}\right)$$ $$e\left(\frac{15}{38}\right)$$ $$e\left(\frac{101}{114}\right)$$ $$e\left(\frac{2}{57}\right)$$ $$e\left(\frac{55}{114}\right)$$ $$e\left(\frac{21}{38}\right)$$
$$\chi_{7581}(10,\cdot)$$ 7581.ee 342 no $$1$$ $$1$$ $$e\left(\frac{5}{342}\right)$$ $$e\left(\frac{5}{171}\right)$$ $$e\left(\frac{305}{342}\right)$$ $$e\left(\frac{5}{114}\right)$$ $$e\left(\frac{155}{171}\right)$$ $$e\left(\frac{3}{19}\right)$$ $$e\left(\frac{110}{171}\right)$$ $$e\left(\frac{10}{171}\right)$$ $$e\left(\frac{47}{342}\right)$$ $$e\left(\frac{35}{38}\right)$$
$$\chi_{7581}(11,\cdot)$$ 7581.dy 114 yes $$-1$$ $$1$$ $$e\left(\frac{5}{38}\right)$$ $$e\left(\frac{5}{19}\right)$$ $$e\left(\frac{1}{38}\right)$$ $$e\left(\frac{15}{38}\right)$$ $$e\left(\frac{3}{19}\right)$$ $$e\left(\frac{67}{114}\right)$$ $$e\left(\frac{7}{57}\right)$$ $$e\left(\frac{10}{19}\right)$$ $$e\left(\frac{65}{114}\right)$$ $$e\left(\frac{11}{38}\right)$$
$$\chi_{7581}(13,\cdot)$$ 7581.em 342 no $$1$$ $$1$$ $$e\left(\frac{329}{342}\right)$$ $$e\left(\frac{158}{171}\right)$$ $$e\left(\frac{233}{342}\right)$$ $$e\left(\frac{101}{114}\right)$$ $$e\left(\frac{110}{171}\right)$$ $$e\left(\frac{7}{57}\right)$$ $$e\left(\frac{170}{171}\right)$$ $$e\left(\frac{145}{171}\right)$$ $$e\left(\frac{311}{342}\right)$$ $$e\left(\frac{23}{38}\right)$$
$$\chi_{7581}(16,\cdot)$$ 7581.ea 171 no $$1$$ $$1$$ $$e\left(\frac{116}{171}\right)$$ $$e\left(\frac{61}{171}\right)$$ $$e\left(\frac{65}{171}\right)$$ $$e\left(\frac{2}{57}\right)$$ $$e\left(\frac{10}{171}\right)$$ $$e\left(\frac{10}{19}\right)$$ $$e\left(\frac{145}{171}\right)$$ $$e\left(\frac{122}{171}\right)$$ $$e\left(\frac{167}{171}\right)$$ $$e\left(\frac{14}{19}\right)$$
$$\chi_{7581}(17,\cdot)$$ 7581.eg 342 yes $$1$$ $$1$$ $$e\left(\frac{169}{342}\right)$$ $$e\left(\frac{169}{171}\right)$$ $$e\left(\frac{110}{171}\right)$$ $$e\left(\frac{55}{114}\right)$$ $$e\left(\frac{47}{342}\right)$$ $$e\left(\frac{65}{114}\right)$$ $$e\left(\frac{311}{342}\right)$$ $$e\left(\frac{167}{171}\right)$$ $$e\left(\frac{2}{171}\right)$$ $$e\left(\frac{12}{19}\right)$$
$$\chi_{7581}(20,\cdot)$$ 7581.cr 38 yes $$1$$ $$1$$ $$e\left(\frac{7}{38}\right)$$ $$e\left(\frac{7}{19}\right)$$ $$e\left(\frac{14}{19}\right)$$ $$e\left(\frac{21}{38}\right)$$ $$e\left(\frac{35}{38}\right)$$ $$e\left(\frac{11}{38}\right)$$ $$e\left(\frac{23}{38}\right)$$ $$e\left(\frac{14}{19}\right)$$ $$e\left(\frac{12}{19}\right)$$ $$e\left(\frac{2}{19}\right)$$
$$\chi_{7581}(22,\cdot)$$ 7581.ej 342 no $$-1$$ $$1$$ $$e\left(\frac{103}{342}\right)$$ $$e\left(\frac{103}{171}\right)$$ $$e\left(\frac{149}{171}\right)$$ $$e\left(\frac{103}{114}\right)$$ $$e\left(\frac{59}{342}\right)$$ $$e\left(\frac{41}{57}\right)$$ $$e\left(\frac{29}{342}\right)$$ $$e\left(\frac{35}{171}\right)$$ $$e\left(\frac{11}{171}\right)$$ $$e\left(\frac{9}{19}\right)$$
$$\chi_{7581}(23,\cdot)$$ 7581.eh 342 yes $$-1$$ $$1$$ $$e\left(\frac{203}{342}\right)$$ $$e\left(\frac{32}{171}\right)$$ $$e\left(\frac{71}{342}\right)$$ $$e\left(\frac{89}{114}\right)$$ $$e\left(\frac{137}{171}\right)$$ $$e\left(\frac{43}{114}\right)$$ $$e\left(\frac{77}{171}\right)$$ $$e\left(\frac{64}{171}\right)$$ $$e\left(\frac{107}{342}\right)$$ $$e\left(\frac{15}{38}\right)$$
$$\chi_{7581}(25,\cdot)$$ 7581.ea 171 no $$1$$ $$1$$ $$e\left(\frac{118}{171}\right)$$ $$e\left(\frac{65}{171}\right)$$ $$e\left(\frac{16}{171}\right)$$ $$e\left(\frac{4}{57}\right)$$ $$e\left(\frac{134}{171}\right)$$ $$e\left(\frac{1}{19}\right)$$ $$e\left(\frac{62}{171}\right)$$ $$e\left(\frac{130}{171}\right)$$ $$e\left(\frac{49}{171}\right)$$ $$e\left(\frac{9}{19}\right)$$
$$\chi_{7581}(26,\cdot)$$ 7581.dw 114 yes $$1$$ $$1$$ $$e\left(\frac{5}{38}\right)$$ $$e\left(\frac{5}{19}\right)$$ $$e\left(\frac{10}{19}\right)$$ $$e\left(\frac{15}{38}\right)$$ $$e\left(\frac{25}{38}\right)$$ $$e\left(\frac{29}{114}\right)$$ $$e\left(\frac{109}{114}\right)$$ $$e\left(\frac{10}{19}\right)$$ $$e\left(\frac{23}{57}\right)$$ $$e\left(\frac{15}{19}\right)$$
$$\chi_{7581}(29,\cdot)$$ 7581.es 342 no $$1$$ $$1$$ $$e\left(\frac{94}{171}\right)$$ $$e\left(\frac{17}{171}\right)$$ $$e\left(\frac{11}{342}\right)$$ $$e\left(\frac{37}{57}\right)$$ $$e\left(\frac{199}{342}\right)$$ $$e\left(\frac{65}{114}\right)$$ $$e\left(\frac{121}{342}\right)$$ $$e\left(\frac{34}{171}\right)$$ $$e\left(\frac{251}{342}\right)$$ $$e\left(\frac{5}{38}\right)$$
$$\chi_{7581}(31,\cdot)$$ 7581.df 114 no $$1$$ $$1$$ $$e\left(\frac{25}{114}\right)$$ $$e\left(\frac{25}{57}\right)$$ $$e\left(\frac{43}{114}\right)$$ $$e\left(\frac{25}{38}\right)$$ $$e\left(\frac{34}{57}\right)$$ $$e\left(\frac{2}{57}\right)$$ $$e\left(\frac{56}{57}\right)$$ $$e\left(\frac{50}{57}\right)$$ $$e\left(\frac{15}{38}\right)$$ $$e\left(\frac{31}{38}\right)$$
$$\chi_{7581}(32,\cdot)$$ 7581.ex 342 yes $$1$$ $$1$$ $$e\left(\frac{145}{171}\right)$$ $$e\left(\frac{119}{171}\right)$$ $$e\left(\frac{77}{342}\right)$$ $$e\left(\frac{31}{57}\right)$$ $$e\left(\frac{25}{342}\right)$$ $$e\left(\frac{25}{38}\right)$$ $$e\left(\frac{277}{342}\right)$$ $$e\left(\frac{67}{171}\right)$$ $$e\left(\frac{161}{342}\right)$$ $$e\left(\frac{35}{38}\right)$$
$$\chi_{7581}(34,\cdot)$$ 7581.em 342 no $$1$$ $$1$$ $$e\left(\frac{227}{342}\right)$$ $$e\left(\frac{56}{171}\right)$$ $$e\left(\frac{167}{342}\right)$$ $$e\left(\frac{113}{114}\right)$$ $$e\left(\frac{26}{171}\right)$$ $$e\left(\frac{40}{57}\right)$$ $$e\left(\frac{149}{171}\right)$$ $$e\left(\frac{112}{171}\right)$$ $$e\left(\frac{173}{342}\right)$$ $$e\left(\frac{31}{38}\right)$$
$$\chi_{7581}(37,\cdot)$$ 7581.dl 114 no $$-1$$ $$1$$ $$e\left(\frac{91}{114}\right)$$ $$e\left(\frac{34}{57}\right)$$ $$e\left(\frac{11}{57}\right)$$ $$e\left(\frac{15}{38}\right)$$ $$e\left(\frac{113}{114}\right)$$ $$e\left(\frac{43}{57}\right)$$ $$e\left(\frac{11}{38}\right)$$ $$e\left(\frac{11}{57}\right)$$ $$e\left(\frac{4}{57}\right)$$ $$e\left(\frac{15}{19}\right)$$
$$\chi_{7581}(40,\cdot)$$ 7581.ee 342 no $$1$$ $$1$$ $$e\left(\frac{121}{342}\right)$$ $$e\left(\frac{121}{171}\right)$$ $$e\left(\frac{199}{342}\right)$$ $$e\left(\frac{7}{114}\right)$$ $$e\left(\frac{160}{171}\right)$$ $$e\left(\frac{8}{19}\right)$$ $$e\left(\frac{97}{171}\right)$$ $$e\left(\frac{71}{171}\right)$$ $$e\left(\frac{43}{342}\right)$$ $$e\left(\frac{11}{38}\right)$$
$$\chi_{7581}(41,\cdot)$$ 7581.er 342 yes $$-1$$ $$1$$ $$e\left(\frac{119}{171}\right)$$ $$e\left(\frac{67}{171}\right)$$ $$e\left(\frac{77}{171}\right)$$ $$e\left(\frac{5}{57}\right)$$ $$e\left(\frac{25}{171}\right)$$ $$e\left(\frac{55}{114}\right)$$ $$e\left(\frac{163}{171}\right)$$ $$e\left(\frac{134}{171}\right)$$ $$e\left(\frac{47}{171}\right)$$ $$e\left(\frac{16}{19}\right)$$
$$\chi_{7581}(43,\cdot)$$ 7581.ec 171 no $$1$$ $$1$$ $$e\left(\frac{26}{171}\right)$$ $$e\left(\frac{52}{171}\right)$$ $$e\left(\frac{47}{171}\right)$$ $$e\left(\frac{26}{57}\right)$$ $$e\left(\frac{73}{171}\right)$$ $$e\left(\frac{29}{57}\right)$$ $$e\left(\frac{4}{171}\right)$$ $$e\left(\frac{104}{171}\right)$$ $$e\left(\frac{62}{171}\right)$$ $$e\left(\frac{11}{19}\right)$$
$$\chi_{7581}(44,\cdot)$$ 7581.eh 342 yes $$-1$$ $$1$$ $$e\left(\frac{161}{342}\right)$$ $$e\left(\frac{161}{171}\right)$$ $$e\left(\frac{245}{342}\right)$$ $$e\left(\frac{47}{114}\right)$$ $$e\left(\frac{32}{171}\right)$$ $$e\left(\frac{97}{114}\right)$$ $$e\left(\frac{8}{171}\right)$$ $$e\left(\frac{151}{171}\right)$$ $$e\left(\frac{191}{342}\right)$$ $$e\left(\frac{25}{38}\right)$$
$$\chi_{7581}(46,\cdot)$$ 7581.dx 114 no $$-1$$ $$1$$ $$e\left(\frac{29}{38}\right)$$ $$e\left(\frac{10}{19}\right)$$ $$e\left(\frac{1}{19}\right)$$ $$e\left(\frac{11}{38}\right)$$ $$e\left(\frac{31}{38}\right)$$ $$e\left(\frac{29}{57}\right)$$ $$e\left(\frac{47}{114}\right)$$ $$e\left(\frac{1}{19}\right)$$ $$e\left(\frac{46}{57}\right)$$ $$e\left(\frac{11}{19}\right)$$
$$\chi_{7581}(47,\cdot)$$ 7581.eg 342 yes $$1$$ $$1$$ $$e\left(\frac{83}{342}\right)$$ $$e\left(\frac{83}{171}\right)$$ $$e\left(\frac{52}{171}\right)$$ $$e\left(\frac{83}{114}\right)$$ $$e\left(\frac{187}{342}\right)$$ $$e\left(\frac{67}{114}\right)$$ $$e\left(\frac{175}{342}\right)$$ $$e\left(\frac{166}{171}\right)$$ $$e\left(\frac{88}{171}\right)$$ $$e\left(\frac{15}{19}\right)$$
$$\chi_{7581}(50,\cdot)$$ 7581.ds 114 no $$1$$ $$1$$ $$e\left(\frac{49}{57}\right)$$ $$e\left(\frac{41}{57}\right)$$ $$e\left(\frac{107}{114}\right)$$ $$e\left(\frac{11}{19}\right)$$ $$e\left(\frac{91}{114}\right)$$ $$e\left(\frac{7}{38}\right)$$ $$e\left(\frac{37}{114}\right)$$ $$e\left(\frac{25}{57}\right)$$ $$e\left(\frac{89}{114}\right)$$ $$e\left(\frac{25}{38}\right)$$
$$\chi_{7581}(52,\cdot)$$ 7581.el 342 no $$1$$ $$1$$ $$e\left(\frac{103}{342}\right)$$ $$e\left(\frac{103}{171}\right)$$ $$e\left(\frac{127}{342}\right)$$ $$e\left(\frac{103}{114}\right)$$ $$e\left(\frac{115}{171}\right)$$ $$e\left(\frac{22}{57}\right)$$ $$e\left(\frac{157}{171}\right)$$ $$e\left(\frac{35}{171}\right)$$ $$e\left(\frac{307}{342}\right)$$ $$e\left(\frac{37}{38}\right)$$
$$\chi_{7581}(53,\cdot)$$ 7581.ex 342 yes $$1$$ $$1$$ $$e\left(\frac{13}{171}\right)$$ $$e\left(\frac{26}{171}\right)$$ $$e\left(\frac{47}{342}\right)$$ $$e\left(\frac{13}{57}\right)$$ $$e\left(\frac{73}{342}\right)$$ $$e\left(\frac{35}{38}\right)$$ $$e\left(\frac{289}{342}\right)$$ $$e\left(\frac{52}{171}\right)$$ $$e\left(\frac{5}{342}\right)$$ $$e\left(\frac{11}{38}\right)$$
$$\chi_{7581}(55,\cdot)$$ 7581.eu 342 no $$-1$$ $$1$$ $$e\left(\frac{167}{171}\right)$$ $$e\left(\frac{163}{171}\right)$$ $$e\left(\frac{25}{342}\right)$$ $$e\left(\frac{53}{57}\right)$$ $$e\left(\frac{17}{342}\right)$$ $$e\left(\frac{35}{57}\right)$$ $$e\left(\frac{275}{342}\right)$$ $$e\left(\frac{155}{171}\right)$$ $$e\left(\frac{73}{342}\right)$$ $$e\left(\frac{1}{38}\right)$$
$$\chi_{7581}(58,\cdot)$$ 7581.cw 57 no $$1$$ $$1$$ $$e\left(\frac{41}{57}\right)$$ $$e\left(\frac{25}{57}\right)$$ $$e\left(\frac{50}{57}\right)$$ $$e\left(\frac{3}{19}\right)$$ $$e\left(\frac{34}{57}\right)$$ $$e\left(\frac{40}{57}\right)$$ $$e\left(\frac{6}{19}\right)$$ $$e\left(\frac{50}{57}\right)$$ $$e\left(\frac{13}{57}\right)$$ $$e\left(\frac{6}{19}\right)$$
$$\chi_{7581}(59,\cdot)$$ 7581.eq 342 yes $$-1$$ $$1$$ $$e\left(\frac{62}{171}\right)$$ $$e\left(\frac{124}{171}\right)$$ $$e\left(\frac{20}{171}\right)$$ $$e\left(\frac{5}{57}\right)$$ $$e\left(\frac{82}{171}\right)$$ $$e\left(\frac{17}{114}\right)$$ $$e\left(\frac{106}{171}\right)$$ $$e\left(\frac{77}{171}\right)$$ $$e\left(\frac{47}{171}\right)$$ $$e\left(\frac{16}{19}\right)$$