# Properties

 Modulus $5054$ Structure $$C_{6}\times C_{342}$$ Order $2052$

Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(5054)

pari: g = idealstar(,5054,2)

## Character group

 sage: G.order()  pari: g.no Order = 2052 sage: H.invariants()  pari: g.cyc Structure = $$C_{6}\times C_{342}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{5054}(1445,\cdot)$, $\chi_{5054}(1807,\cdot)$

## First 32 of 2052 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 $$-1$$ $$1$$ $$3$$ $$5$$ $$9$$ $$11$$ $$13$$ $$15$$ $$17$$ $$23$$ $$25$$ $$27$$
$$\chi_{5054}(1,\cdot)$$ 5054.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{5054}(3,\cdot)$$ 5054.ck 342 no $$1$$ $$1$$ $$e\left(\frac{113}{171}\right)$$ $$e\left(\frac{43}{342}\right)$$ $$e\left(\frac{55}{171}\right)$$ $$e\left(\frac{7}{57}\right)$$ $$e\left(\frac{37}{171}\right)$$ $$e\left(\frac{269}{342}\right)$$ $$e\left(\frac{7}{342}\right)$$ $$e\left(\frac{115}{171}\right)$$ $$e\left(\frac{43}{171}\right)$$ $$e\left(\frac{56}{57}\right)$$
$$\chi_{5054}(5,\cdot)$$ 5054.ce 342 no $$-1$$ $$1$$ $$e\left(\frac{43}{342}\right)$$ $$e\left(\frac{187}{342}\right)$$ $$e\left(\frac{43}{171}\right)$$ $$e\left(\frac{10}{19}\right)$$ $$e\left(\frac{233}{342}\right)$$ $$e\left(\frac{115}{171}\right)$$ $$e\left(\frac{49}{342}\right)$$ $$e\left(\frac{121}{171}\right)$$ $$e\left(\frac{16}{171}\right)$$ $$e\left(\frac{43}{114}\right)$$
$$\chi_{5054}(9,\cdot)$$ 5054.cb 171 no $$1$$ $$1$$ $$e\left(\frac{55}{171}\right)$$ $$e\left(\frac{43}{171}\right)$$ $$e\left(\frac{110}{171}\right)$$ $$e\left(\frac{14}{57}\right)$$ $$e\left(\frac{74}{171}\right)$$ $$e\left(\frac{98}{171}\right)$$ $$e\left(\frac{7}{171}\right)$$ $$e\left(\frac{59}{171}\right)$$ $$e\left(\frac{86}{171}\right)$$ $$e\left(\frac{55}{57}\right)$$
$$\chi_{5054}(11,\cdot)$$ 5054.bl 57 no $$1$$ $$1$$ $$e\left(\frac{7}{57}\right)$$ $$e\left(\frac{10}{19}\right)$$ $$e\left(\frac{14}{57}\right)$$ $$e\left(\frac{5}{57}\right)$$ $$e\left(\frac{7}{57}\right)$$ $$e\left(\frac{37}{57}\right)$$ $$e\left(\frac{4}{57}\right)$$ $$e\left(\frac{50}{57}\right)$$ $$e\left(\frac{1}{19}\right)$$ $$e\left(\frac{7}{19}\right)$$
$$\chi_{5054}(13,\cdot)$$ 5054.cl 342 no $$1$$ $$1$$ $$e\left(\frac{37}{171}\right)$$ $$e\left(\frac{233}{342}\right)$$ $$e\left(\frac{74}{171}\right)$$ $$e\left(\frac{7}{57}\right)$$ $$e\left(\frac{170}{171}\right)$$ $$e\left(\frac{307}{342}\right)$$ $$e\left(\frac{311}{342}\right)$$ $$e\left(\frac{77}{171}\right)$$ $$e\left(\frac{62}{171}\right)$$ $$e\left(\frac{37}{57}\right)$$
$$\chi_{5054}(15,\cdot)$$ 5054.ch 342 no $$-1$$ $$1$$ $$e\left(\frac{269}{342}\right)$$ $$e\left(\frac{115}{171}\right)$$ $$e\left(\frac{98}{171}\right)$$ $$e\left(\frac{37}{57}\right)$$ $$e\left(\frac{307}{342}\right)$$ $$e\left(\frac{157}{342}\right)$$ $$e\left(\frac{28}{171}\right)$$ $$e\left(\frac{65}{171}\right)$$ $$e\left(\frac{59}{171}\right)$$ $$e\left(\frac{41}{114}\right)$$
$$\chi_{5054}(17,\cdot)$$ 5054.cj 342 no $$-1$$ $$1$$ $$e\left(\frac{7}{342}\right)$$ $$e\left(\frac{49}{342}\right)$$ $$e\left(\frac{7}{171}\right)$$ $$e\left(\frac{4}{57}\right)$$ $$e\left(\frac{311}{342}\right)$$ $$e\left(\frac{28}{171}\right)$$ $$e\left(\frac{175}{342}\right)$$ $$e\left(\frac{139}{171}\right)$$ $$e\left(\frac{49}{171}\right)$$ $$e\left(\frac{7}{114}\right)$$
$$\chi_{5054}(23,\cdot)$$ 5054.cb 171 no $$1$$ $$1$$ $$e\left(\frac{115}{171}\right)$$ $$e\left(\frac{121}{171}\right)$$ $$e\left(\frac{59}{171}\right)$$ $$e\left(\frac{50}{57}\right)$$ $$e\left(\frac{77}{171}\right)$$ $$e\left(\frac{65}{171}\right)$$ $$e\left(\frac{139}{171}\right)$$ $$e\left(\frac{170}{171}\right)$$ $$e\left(\frac{71}{171}\right)$$ $$e\left(\frac{1}{57}\right)$$
$$\chi_{5054}(25,\cdot)$$ 5054.ca 171 no $$1$$ $$1$$ $$e\left(\frac{43}{171}\right)$$ $$e\left(\frac{16}{171}\right)$$ $$e\left(\frac{86}{171}\right)$$ $$e\left(\frac{1}{19}\right)$$ $$e\left(\frac{62}{171}\right)$$ $$e\left(\frac{59}{171}\right)$$ $$e\left(\frac{49}{171}\right)$$ $$e\left(\frac{71}{171}\right)$$ $$e\left(\frac{32}{171}\right)$$ $$e\left(\frac{43}{57}\right)$$
$$\chi_{5054}(27,\cdot)$$ 5054.bv 114 no $$1$$ $$1$$ $$e\left(\frac{56}{57}\right)$$ $$e\left(\frac{43}{114}\right)$$ $$e\left(\frac{55}{57}\right)$$ $$e\left(\frac{7}{19}\right)$$ $$e\left(\frac{37}{57}\right)$$ $$e\left(\frac{41}{114}\right)$$ $$e\left(\frac{7}{114}\right)$$ $$e\left(\frac{1}{57}\right)$$ $$e\left(\frac{43}{57}\right)$$ $$e\left(\frac{18}{19}\right)$$
$$\chi_{5054}(29,\cdot)$$ 5054.ch 342 no $$-1$$ $$1$$ $$e\left(\frac{311}{342}\right)$$ $$e\left(\frac{91}{171}\right)$$ $$e\left(\frac{140}{171}\right)$$ $$e\left(\frac{4}{57}\right)$$ $$e\left(\frac{121}{342}\right)$$ $$e\left(\frac{151}{342}\right)$$ $$e\left(\frac{40}{171}\right)$$ $$e\left(\frac{44}{171}\right)$$ $$e\left(\frac{11}{171}\right)$$ $$e\left(\frac{83}{114}\right)$$
$$\chi_{5054}(31,\cdot)$$ 5054.bo 114 no $$1$$ $$1$$ $$e\left(\frac{6}{19}\right)$$ $$e\left(\frac{43}{114}\right)$$ $$e\left(\frac{12}{19}\right)$$ $$e\left(\frac{2}{57}\right)$$ $$e\left(\frac{56}{57}\right)$$ $$e\left(\frac{79}{114}\right)$$ $$e\left(\frac{15}{38}\right)$$ $$e\left(\frac{13}{19}\right)$$ $$e\left(\frac{43}{57}\right)$$ $$e\left(\frac{18}{19}\right)$$
$$\chi_{5054}(33,\cdot)$$ 5054.cf 342 no $$1$$ $$1$$ $$e\left(\frac{134}{171}\right)$$ $$e\left(\frac{223}{342}\right)$$ $$e\left(\frac{97}{171}\right)$$ $$e\left(\frac{4}{19}\right)$$ $$e\left(\frac{58}{171}\right)$$ $$e\left(\frac{149}{342}\right)$$ $$e\left(\frac{31}{342}\right)$$ $$e\left(\frac{94}{171}\right)$$ $$e\left(\frac{52}{171}\right)$$ $$e\left(\frac{20}{57}\right)$$
$$\chi_{5054}(37,\cdot)$$ 5054.bt 114 no $$-1$$ $$1$$ $$e\left(\frac{71}{114}\right)$$ $$e\left(\frac{11}{57}\right)$$ $$e\left(\frac{14}{57}\right)$$ $$e\left(\frac{43}{57}\right)$$ $$e\left(\frac{11}{38}\right)$$ $$e\left(\frac{31}{38}\right)$$ $$e\left(\frac{4}{57}\right)$$ $$e\left(\frac{50}{57}\right)$$ $$e\left(\frac{22}{57}\right)$$ $$e\left(\frac{33}{38}\right)$$
$$\chi_{5054}(39,\cdot)$$ 5054.bn 57 no $$1$$ $$1$$ $$e\left(\frac{50}{57}\right)$$ $$e\left(\frac{46}{57}\right)$$ $$e\left(\frac{43}{57}\right)$$ $$e\left(\frac{14}{57}\right)$$ $$e\left(\frac{4}{19}\right)$$ $$e\left(\frac{13}{19}\right)$$ $$e\left(\frac{53}{57}\right)$$ $$e\left(\frac{7}{57}\right)$$ $$e\left(\frac{35}{57}\right)$$ $$e\left(\frac{12}{19}\right)$$
$$\chi_{5054}(41,\cdot)$$ 5054.cl 342 no $$1$$ $$1$$ $$e\left(\frac{125}{171}\right)$$ $$e\left(\frac{325}{342}\right)$$ $$e\left(\frac{79}{171}\right)$$ $$e\left(\frac{56}{57}\right)$$ $$e\left(\frac{163}{171}\right)$$ $$e\left(\frac{233}{342}\right)$$ $$e\left(\frac{265}{342}\right)$$ $$e\left(\frac{103}{171}\right)$$ $$e\left(\frac{154}{171}\right)$$ $$e\left(\frac{11}{57}\right)$$
$$\chi_{5054}(43,\cdot)$$ 5054.cc 171 no $$1$$ $$1$$ $$e\left(\frac{23}{171}\right)$$ $$e\left(\frac{47}{171}\right)$$ $$e\left(\frac{46}{171}\right)$$ $$e\left(\frac{29}{57}\right)$$ $$e\left(\frac{4}{171}\right)$$ $$e\left(\frac{70}{171}\right)$$ $$e\left(\frac{62}{171}\right)$$ $$e\left(\frac{34}{171}\right)$$ $$e\left(\frac{94}{171}\right)$$ $$e\left(\frac{23}{57}\right)$$
$$\chi_{5054}(45,\cdot)$$ 5054.by 114 no $$-1$$ $$1$$ $$e\left(\frac{17}{38}\right)$$ $$e\left(\frac{91}{114}\right)$$ $$e\left(\frac{17}{19}\right)$$ $$e\left(\frac{44}{57}\right)$$ $$e\left(\frac{13}{114}\right)$$ $$e\left(\frac{14}{57}\right)$$ $$e\left(\frac{7}{38}\right)$$ $$e\left(\frac{1}{19}\right)$$ $$e\left(\frac{34}{57}\right)$$ $$e\left(\frac{13}{38}\right)$$
$$\chi_{5054}(47,\cdot)$$ 5054.cj 342 no $$-1$$ $$1$$ $$e\left(\frac{137}{342}\right)$$ $$e\left(\frac{275}{342}\right)$$ $$e\left(\frac{137}{171}\right)$$ $$e\left(\frac{5}{57}\right)$$ $$e\left(\frac{175}{342}\right)$$ $$e\left(\frac{35}{171}\right)$$ $$e\left(\frac{5}{342}\right)$$ $$e\left(\frac{131}{171}\right)$$ $$e\left(\frac{104}{171}\right)$$ $$e\left(\frac{23}{114}\right)$$
$$\chi_{5054}(51,\cdot)$$ 5054.ci 342 no $$-1$$ $$1$$ $$e\left(\frac{233}{342}\right)$$ $$e\left(\frac{46}{171}\right)$$ $$e\left(\frac{62}{171}\right)$$ $$e\left(\frac{11}{57}\right)$$ $$e\left(\frac{43}{342}\right)$$ $$e\left(\frac{325}{342}\right)$$ $$e\left(\frac{91}{171}\right)$$ $$e\left(\frac{83}{171}\right)$$ $$e\left(\frac{92}{171}\right)$$ $$e\left(\frac{5}{114}\right)$$
$$\chi_{5054}(53,\cdot)$$ 5054.cd 342 no $$-1$$ $$1$$ $$e\left(\frac{137}{342}\right)$$ $$e\left(\frac{109}{171}\right)$$ $$e\left(\frac{137}{171}\right)$$ $$e\left(\frac{8}{19}\right)$$ $$e\left(\frac{289}{342}\right)$$ $$e\left(\frac{13}{342}\right)$$ $$e\left(\frac{88}{171}\right)$$ $$e\left(\frac{131}{171}\right)$$ $$e\left(\frac{47}{171}\right)$$ $$e\left(\frac{23}{114}\right)$$
$$\chi_{5054}(55,\cdot)$$ 5054.cg 342 no $$-1$$ $$1$$ $$e\left(\frac{85}{342}\right)$$ $$e\left(\frac{25}{342}\right)$$ $$e\left(\frac{85}{171}\right)$$ $$e\left(\frac{35}{57}\right)$$ $$e\left(\frac{275}{342}\right)$$ $$e\left(\frac{55}{171}\right)$$ $$e\left(\frac{73}{342}\right)$$ $$e\left(\frac{100}{171}\right)$$ $$e\left(\frac{25}{171}\right)$$ $$e\left(\frac{85}{114}\right)$$
$$\chi_{5054}(59,\cdot)$$ 5054.ck 342 no $$1$$ $$1$$ $$e\left(\frac{125}{171}\right)$$ $$e\left(\frac{211}{342}\right)$$ $$e\left(\frac{79}{171}\right)$$ $$e\left(\frac{37}{57}\right)$$ $$e\left(\frac{106}{171}\right)$$ $$e\left(\frac{119}{342}\right)$$ $$e\left(\frac{265}{342}\right)$$ $$e\left(\frac{103}{171}\right)$$ $$e\left(\frac{40}{171}\right)$$ $$e\left(\frac{11}{57}\right)$$
$$\chi_{5054}(61,\cdot)$$ 5054.cj 342 no $$-1$$ $$1$$ $$e\left(\frac{77}{342}\right)$$ $$e\left(\frac{197}{342}\right)$$ $$e\left(\frac{77}{171}\right)$$ $$e\left(\frac{44}{57}\right)$$ $$e\left(\frac{1}{342}\right)$$ $$e\left(\frac{137}{171}\right)$$ $$e\left(\frac{215}{342}\right)$$ $$e\left(\frac{161}{171}\right)$$ $$e\left(\frac{26}{171}\right)$$ $$e\left(\frac{77}{114}\right)$$
$$\chi_{5054}(65,\cdot)$$ 5054.bz 114 no $$-1$$ $$1$$ $$e\left(\frac{13}{38}\right)$$ $$e\left(\frac{13}{57}\right)$$ $$e\left(\frac{13}{19}\right)$$ $$e\left(\frac{37}{57}\right)$$ $$e\left(\frac{77}{114}\right)$$ $$e\left(\frac{65}{114}\right)$$ $$e\left(\frac{1}{19}\right)$$ $$e\left(\frac{3}{19}\right)$$ $$e\left(\frac{26}{57}\right)$$ $$e\left(\frac{1}{38}\right)$$
$$\chi_{5054}(67,\cdot)$$ 5054.cd 342 no $$-1$$ $$1$$ $$e\left(\frac{341}{342}\right)$$ $$e\left(\frac{139}{171}\right)$$ $$e\left(\frac{170}{171}\right)$$ $$e\left(\frac{17}{19}\right)$$ $$e\left(\frac{265}{342}\right)$$ $$e\left(\frac{277}{342}\right)$$ $$e\left(\frac{73}{171}\right)$$ $$e\left(\frac{29}{171}\right)$$ $$e\left(\frac{107}{171}\right)$$ $$e\left(\frac{113}{114}\right)$$
$$\chi_{5054}(69,\cdot)$$ 5054.m 6 no $$1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$
$$\chi_{5054}(71,\cdot)$$ 5054.ch 342 no $$-1$$ $$1$$ $$e\left(\frac{37}{342}\right)$$ $$e\left(\frac{101}{171}\right)$$ $$e\left(\frac{37}{171}\right)$$ $$e\left(\frac{32}{57}\right)$$ $$e\left(\frac{341}{342}\right)$$ $$e\left(\frac{239}{342}\right)$$ $$e\left(\frac{35}{171}\right)$$ $$e\left(\frac{124}{171}\right)$$ $$e\left(\frac{31}{171}\right)$$ $$e\left(\frac{37}{114}\right)$$
$$\chi_{5054}(73,\cdot)$$ 5054.cj 342 no $$-1$$ $$1$$ $$e\left(\frac{235}{342}\right)$$ $$e\left(\frac{277}{342}\right)$$ $$e\left(\frac{64}{171}\right)$$ $$e\left(\frac{4}{57}\right)$$ $$e\left(\frac{83}{342}\right)$$ $$e\left(\frac{85}{171}\right)$$ $$e\left(\frac{61}{342}\right)$$ $$e\left(\frac{25}{171}\right)$$ $$e\left(\frac{106}{171}\right)$$ $$e\left(\frac{7}{114}\right)$$
$$\chi_{5054}(75,\cdot)$$ 5054.bw 114 no $$1$$ $$1$$ $$e\left(\frac{52}{57}\right)$$ $$e\left(\frac{25}{114}\right)$$ $$e\left(\frac{47}{57}\right)$$ $$e\left(\frac{10}{57}\right)$$ $$e\left(\frac{11}{19}\right)$$ $$e\left(\frac{5}{38}\right)$$ $$e\left(\frac{35}{114}\right)$$ $$e\left(\frac{5}{57}\right)$$ $$e\left(\frac{25}{57}\right)$$ $$e\left(\frac{14}{19}\right)$$
$$\chi_{5054}(79,\cdot)$$ 5054.cd 342 no $$-1$$ $$1$$ $$e\left(\frac{103}{342}\right)$$ $$e\left(\frac{47}{171}\right)$$ $$e\left(\frac{103}{171}\right)$$ $$e\left(\frac{16}{19}\right)$$ $$e\left(\frac{65}{342}\right)$$ $$e\left(\frac{197}{342}\right)$$ $$e\left(\frac{5}{171}\right)$$ $$e\left(\frac{91}{171}\right)$$ $$e\left(\frac{94}{171}\right)$$ $$e\left(\frac{103}{114}\right)$$