# Properties

 Modulus $917415$ Structure $$C_{2}\times C_{2}\times C_{12}\times C_{36}\times C_{252}$$ Order $435456$

Show commands: PariGP / SageMath

sage: H = DirichletGroup(917415)

pari: g = idealstar(,917415,2)

## Character group

 sage: G.order()  pari: g.no Order = 435456 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{2}\times C_{12}\times C_{36}\times C_{252}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{917415}(101936,\cdot)$, $\chi_{917415}(366967,\cdot)$, $\chi_{917415}(772561,\cdot)$, $\chi_{917415}(221446,\cdot)$, $\chi_{917415}(371926,\cdot)$

## First 32 of 435456 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 $$-1$$ $$1$$ $$2$$ $$4$$ $$7$$ $$8$$ $$11$$ $$13$$ $$14$$ $$16$$ $$17$$ $$22$$
$$\chi_{917415}(1,\cdot)$$ 917415.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{917415}(2,\cdot)$$ 917415.uvf 252 yes $$-1$$ $$1$$ $$e\left(\frac{15}{28}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{143}{252}\right)$$ $$e\left(\frac{17}{28}\right)$$ $$e\left(\frac{47}{84}\right)$$ $$e\left(\frac{13}{42}\right)$$ $$e\left(\frac{13}{126}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$i$$ $$e\left(\frac{2}{21}\right)$$
$$\chi_{917415}(4,\cdot)$$ 917415.phi 126 yes $$1$$ $$1$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{17}{126}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{5}{42}\right)$$ $$e\left(\frac{13}{21}\right)$$ $$e\left(\frac{13}{63}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$-1$$ $$e\left(\frac{4}{21}\right)$$
$$\chi_{917415}(7,\cdot)$$ 917415.tiy 252 yes $$-1$$ $$1$$ $$e\left(\frac{143}{252}\right)$$ $$e\left(\frac{17}{126}\right)$$ $$e\left(\frac{127}{252}\right)$$ $$e\left(\frac{59}{84}\right)$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{61}{252}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{17}{63}\right)$$ $$e\left(\frac{29}{36}\right)$$ $$e\left(\frac{155}{252}\right)$$
$$\chi_{917415}(8,\cdot)$$ 917415.nbf 84 no $$-1$$ $$1$$ $$e\left(\frac{17}{28}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{59}{84}\right)$$ $$e\left(\frac{23}{28}\right)$$ $$e\left(\frac{19}{28}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{13}{42}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$-i$$ $$e\left(\frac{2}{7}\right)$$
$$\chi_{917415}(11,\cdot)$$ 917415.mtc 84 no $$1$$ $$1$$ $$e\left(\frac{47}{84}\right)$$ $$e\left(\frac{5}{42}\right)$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{19}{28}\right)$$ $$e\left(\frac{41}{84}\right)$$ $$e\left(\frac{19}{21}\right)$$ $$e\left(\frac{17}{28}\right)$$ $$e\left(\frac{5}{21}\right)$$ $$-i$$ $$e\left(\frac{1}{21}\right)$$
$$\chi_{917415}(13,\cdot)$$ 917415.pqs 252 yes $$-1$$ $$1$$ $$e\left(\frac{13}{42}\right)$$ $$e\left(\frac{13}{21}\right)$$ $$e\left(\frac{61}{252}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{19}{21}\right)$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{139}{252}\right)$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{3}{14}\right)$$
$$\chi_{917415}(14,\cdot)$$ 917415.upu 252 yes $$1$$ $$1$$ $$e\left(\frac{13}{126}\right)$$ $$e\left(\frac{13}{63}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{13}{42}\right)$$ $$e\left(\frac{17}{28}\right)$$ $$e\left(\frac{139}{252}\right)$$ $$e\left(\frac{11}{63}\right)$$ $$e\left(\frac{26}{63}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{179}{252}\right)$$
$$\chi_{917415}(16,\cdot)$$ 917415.lmo 63 no $$1$$ $$1$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{17}{63}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{26}{63}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$1$$ $$e\left(\frac{8}{21}\right)$$
$$\chi_{917415}(17,\cdot)$$ 917415.flq 36 no $$1$$ $$1$$ $$i$$ $$-1$$ $$e\left(\frac{29}{36}\right)$$ $$-i$$ $$-i$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$1$$
$$\chi_{917415}(22,\cdot)$$ 917415.ves 252 yes $$-1$$ $$1$$ $$e\left(\frac{2}{21}\right)$$ $$e\left(\frac{4}{21}\right)$$ $$e\left(\frac{155}{252}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{179}{252}\right)$$ $$e\left(\frac{8}{21}\right)$$ $$1$$ $$e\left(\frac{1}{7}\right)$$
$$\chi_{917415}(23,\cdot)$$ 917415.ugz 252 yes $$-1$$ $$1$$ $$e\left(\frac{52}{63}\right)$$ $$e\left(\frac{41}{63}\right)$$ $$e\left(\frac{55}{84}\right)$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{115}{126}\right)$$ $$e\left(\frac{121}{252}\right)$$ $$e\left(\frac{19}{63}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{22}{63}\right)$$
$$\chi_{917415}(26,\cdot)$$ 917415.mrn 84 no $$1$$ $$1$$ $$e\left(\frac{71}{84}\right)$$ $$e\left(\frac{29}{42}\right)$$ $$e\left(\frac{17}{21}\right)$$ $$e\left(\frac{15}{28}\right)$$ $$e\left(\frac{13}{28}\right)$$ $$e\left(\frac{23}{42}\right)$$ $$e\left(\frac{55}{84}\right)$$ $$e\left(\frac{8}{21}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{13}{42}\right)$$
$$\chi_{917415}(28,\cdot)$$ 917415.ijf 36 no $$-1$$ $$1$$ $$e\left(\frac{23}{36}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{23}{36}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{31}{36}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{11}{36}\right)$$ $$e\left(\frac{29}{36}\right)$$
$$\chi_{917415}(31,\cdot)$$ 917415.lzf 84 no $$-1$$ $$1$$ $$e\left(\frac{19}{42}\right)$$ $$e\left(\frac{19}{21}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{61}{84}\right)$$ $$e\left(\frac{19}{84}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{17}{21}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{28}\right)$$
$$\chi_{917415}(32,\cdot)$$ 917415.uvf 252 yes $$-1$$ $$1$$ $$e\left(\frac{19}{28}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{211}{252}\right)$$ $$e\left(\frac{1}{28}\right)$$ $$e\left(\frac{67}{84}\right)$$ $$e\left(\frac{23}{42}\right)$$ $$e\left(\frac{65}{126}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$i$$ $$e\left(\frac{10}{21}\right)$$
$$\chi_{917415}(34,\cdot)$$ 917415.phl 126 yes $$-1$$ $$1$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{47}{126}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{13}{42}\right)$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{10}{63}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{21}\right)$$
$$\chi_{917415}(41,\cdot)$$ 917415.hzj 36 no $$-1$$ $$1$$ $$e\left(\frac{31}{36}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{11}{36}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{13}{36}\right)$$ $$e\left(\frac{5}{18}\right)$$
$$\chi_{917415}(43,\cdot)$$ 917415.slq 252 yes $$-1$$ $$1$$ $$e\left(\frac{131}{252}\right)$$ $$e\left(\frac{5}{126}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{47}{84}\right)$$ $$e\left(\frac{37}{84}\right)$$ $$e\left(\frac{40}{63}\right)$$ $$e\left(\frac{53}{63}\right)$$ $$e\left(\frac{5}{63}\right)$$ $$e\left(\frac{23}{36}\right)$$ $$e\left(\frac{121}{126}\right)$$
$$\chi_{917415}(44,\cdot)$$ 917415.pzr 252 no $$1$$ $$1$$ $$e\left(\frac{53}{84}\right)$$ $$e\left(\frac{11}{42}\right)$$ $$e\left(\frac{23}{126}\right)$$ $$e\left(\frac{25}{28}\right)$$ $$e\left(\frac{17}{28}\right)$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{205}{252}\right)$$ $$e\left(\frac{11}{21}\right)$$ $$i$$ $$e\left(\frac{5}{21}\right)$$
$$\chi_{917415}(46,\cdot)$$ 917415.ieg 36 no $$1$$ $$1$$ $$e\left(\frac{13}{36}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{19}{36}\right)$$ $$e\left(\frac{4}{9}\right)$$
$$\chi_{917415}(47,\cdot)$$ 917415.txl 252 yes $$-1$$ $$1$$ $$e\left(\frac{58}{63}\right)$$ $$e\left(\frac{53}{63}\right)$$ $$e\left(\frac{53}{84}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{179}{252}\right)$$ $$e\left(\frac{139}{252}\right)$$ $$e\left(\frac{43}{63}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{61}{252}\right)$$
$$\chi_{917415}(49,\cdot)$$ 917415.oii 126 yes $$1$$ $$1$$ $$e\left(\frac{17}{126}\right)$$ $$e\left(\frac{17}{63}\right)$$ $$e\left(\frac{1}{126}\right)$$ $$e\left(\frac{17}{42}\right)$$ $$e\left(\frac{2}{21}\right)$$ $$e\left(\frac{61}{126}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{34}{63}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{29}{126}\right)$$
$$\chi_{917415}(52,\cdot)$$ 917415.uzz 252 yes $$-1$$ $$1$$ $$e\left(\frac{8}{21}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{95}{252}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{191}{252}\right)$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{17}{42}\right)$$
$$\chi_{917415}(53,\cdot)$$ 917415.rwa 252 no $$-1$$ $$1$$ $$e\left(\frac{65}{252}\right)$$ $$e\left(\frac{65}{126}\right)$$ $$e\left(\frac{101}{252}\right)$$ $$e\left(\frac{65}{84}\right)$$ $$e\left(\frac{13}{42}\right)$$ $$e\left(\frac{169}{252}\right)$$ $$e\left(\frac{83}{126}\right)$$ $$e\left(\frac{2}{63}\right)$$ $$e\left(\frac{5}{36}\right)$$ $$e\left(\frac{143}{252}\right)$$
$$\chi_{917415}(56,\cdot)$$ 917415.uep 252 no $$1$$ $$1$$ $$e\left(\frac{11}{63}\right)$$ $$e\left(\frac{22}{63}\right)$$ $$e\left(\frac{13}{63}\right)$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{61}{84}\right)$$ $$e\left(\frac{43}{252}\right)$$ $$e\left(\frac{8}{21}\right)$$ $$e\left(\frac{44}{63}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{227}{252}\right)$$
$$\chi_{917415}(59,\cdot)$$ 917415.fhu 36 no $$-1$$ $$1$$ $$i$$ $$-1$$ $$e\left(\frac{13}{18}\right)$$ $$-i$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{35}{36}\right)$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$
$$\chi_{917415}(61,\cdot)$$ 917415.vam 252 no $$1$$ $$1$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{16}{63}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{53}{84}\right)$$ $$e\left(\frac{27}{28}\right)$$ $$e\left(\frac{1}{63}\right)$$ $$e\left(\frac{1}{21}\right)$$ $$-1$$ $$e\left(\frac{11}{28}\right)$$
$$\chi_{917415}(62,\cdot)$$ 917415.psg 252 no $$1$$ $$1$$ $$e\left(\frac{83}{84}\right)$$ $$e\left(\frac{41}{42}\right)$$ $$e\left(\frac{83}{252}\right)$$ $$e\left(\frac{27}{28}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{15}{28}\right)$$ $$e\left(\frac{20}{63}\right)$$ $$e\left(\frac{20}{21}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{23}{84}\right)$$
$$\chi_{917415}(64,\cdot)$$ 917415.lld 42 no $$1$$ $$1$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{17}{42}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{13}{21}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$-1$$ $$e\left(\frac{4}{7}\right)$$
$$\chi_{917415}(67,\cdot)$$ 917415.psx 252 yes $$1$$ $$1$$ $$e\left(\frac{23}{84}\right)$$ $$e\left(\frac{23}{42}\right)$$ $$e\left(\frac{247}{252}\right)$$ $$e\left(\frac{23}{28}\right)$$ $$e\left(\frac{11}{42}\right)$$ $$e\left(\frac{71}{84}\right)$$ $$e\left(\frac{16}{63}\right)$$ $$e\left(\frac{2}{21}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{15}{28}\right)$$
$$\chi_{917415}(68,\cdot)$$ 917415.nbm 84 yes $$1$$ $$1$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{79}{84}\right)$$ $$e\left(\frac{27}{28}\right)$$ $$e\left(\frac{73}{84}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{11}{42}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{4}{21}\right)$$