# Properties

 Modulus $8379$ Structure $$C_{6}\times C_{6}\times C_{126}$$ Order $4536$

Show commands: PariGP / SageMath

sage: H = DirichletGroup(8379)

pari: g = idealstar(,8379,2)

## Character group

 sage: G.order()  pari: g.no Order = 4536 sage: H.invariants()  pari: g.cyc Structure = $$C_{6}\times C_{6}\times C_{126}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{8379}(6518,\cdot)$, $\chi_{8379}(7696,\cdot)$, $\chi_{8379}(2206,\cdot)$

## First 32 of 4536 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 $$-1$$ $$1$$ $$2$$ $$4$$ $$5$$ $$8$$ $$10$$ $$11$$ $$13$$ $$16$$ $$17$$ $$20$$
$$\chi_{8379}(1,\cdot)$$ 8379.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{8379}(2,\cdot)$$ 8379.nk 126 yes $$1$$ $$1$$ $$e\left(\frac{20}{63}\right)$$ $$e\left(\frac{40}{63}\right)$$ $$e\left(\frac{85}{126}\right)$$ $$e\left(\frac{20}{21}\right)$$ $$e\left(\frac{125}{126}\right)$$ $$e\left(\frac{25}{42}\right)$$ $$e\left(\frac{5}{126}\right)$$ $$e\left(\frac{17}{63}\right)$$ $$e\left(\frac{67}{126}\right)$$ $$e\left(\frac{13}{42}\right)$$
$$\chi_{8379}(4,\cdot)$$ 8379.lq 63 yes $$1$$ $$1$$ $$e\left(\frac{40}{63}\right)$$ $$e\left(\frac{17}{63}\right)$$ $$e\left(\frac{22}{63}\right)$$ $$e\left(\frac{19}{21}\right)$$ $$e\left(\frac{62}{63}\right)$$ $$e\left(\frac{4}{21}\right)$$ $$e\left(\frac{5}{63}\right)$$ $$e\left(\frac{34}{63}\right)$$ $$e\left(\frac{4}{63}\right)$$ $$e\left(\frac{13}{21}\right)$$
$$\chi_{8379}(5,\cdot)$$ 8379.mg 126 yes $$1$$ $$1$$ $$e\left(\frac{85}{126}\right)$$ $$e\left(\frac{22}{63}\right)$$ $$e\left(\frac{26}{63}\right)$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{11}{126}\right)$$ $$e\left(\frac{5}{42}\right)$$ $$e\left(\frac{113}{126}\right)$$ $$e\left(\frac{44}{63}\right)$$ $$e\left(\frac{41}{63}\right)$$ $$e\left(\frac{16}{21}\right)$$
$$\chi_{8379}(8,\cdot)$$ 8379.kb 42 no $$1$$ $$1$$ $$e\left(\frac{20}{21}\right)$$ $$e\left(\frac{19}{21}\right)$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{41}{42}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{5}{42}\right)$$ $$e\left(\frac{17}{21}\right)$$ $$e\left(\frac{25}{42}\right)$$ $$e\left(\frac{13}{14}\right)$$
$$\chi_{8379}(10,\cdot)$$ 8379.ly 126 no $$1$$ $$1$$ $$e\left(\frac{125}{126}\right)$$ $$e\left(\frac{62}{63}\right)$$ $$e\left(\frac{11}{126}\right)$$ $$e\left(\frac{41}{42}\right)$$ $$e\left(\frac{5}{63}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{59}{63}\right)$$ $$e\left(\frac{61}{63}\right)$$ $$e\left(\frac{23}{126}\right)$$ $$e\left(\frac{1}{14}\right)$$
$$\chi_{8379}(11,\cdot)$$ 8379.iq 42 yes $$-1$$ $$1$$ $$e\left(\frac{25}{42}\right)$$ $$e\left(\frac{4}{21}\right)$$ $$e\left(\frac{5}{42}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{11}{42}\right)$$ $$e\left(\frac{2}{21}\right)$$ $$e\left(\frac{8}{21}\right)$$ $$e\left(\frac{41}{42}\right)$$ $$e\left(\frac{13}{42}\right)$$
$$\chi_{8379}(13,\cdot)$$ 8379.mo 126 yes $$1$$ $$1$$ $$e\left(\frac{5}{126}\right)$$ $$e\left(\frac{5}{63}\right)$$ $$e\left(\frac{113}{126}\right)$$ $$e\left(\frac{5}{42}\right)$$ $$e\left(\frac{59}{63}\right)$$ $$e\left(\frac{2}{21}\right)$$ $$e\left(\frac{62}{63}\right)$$ $$e\left(\frac{10}{63}\right)$$ $$e\left(\frac{53}{126}\right)$$ $$e\left(\frac{41}{42}\right)$$
$$\chi_{8379}(16,\cdot)$$ 8379.lq 63 yes $$1$$ $$1$$ $$e\left(\frac{17}{63}\right)$$ $$e\left(\frac{34}{63}\right)$$ $$e\left(\frac{44}{63}\right)$$ $$e\left(\frac{17}{21}\right)$$ $$e\left(\frac{61}{63}\right)$$ $$e\left(\frac{8}{21}\right)$$ $$e\left(\frac{10}{63}\right)$$ $$e\left(\frac{5}{63}\right)$$ $$e\left(\frac{8}{63}\right)$$ $$e\left(\frac{5}{21}\right)$$
$$\chi_{8379}(17,\cdot)$$ 8379.lz 126 no $$1$$ $$1$$ $$e\left(\frac{67}{126}\right)$$ $$e\left(\frac{4}{63}\right)$$ $$e\left(\frac{41}{63}\right)$$ $$e\left(\frac{25}{42}\right)$$ $$e\left(\frac{23}{126}\right)$$ $$e\left(\frac{41}{42}\right)$$ $$e\left(\frac{53}{126}\right)$$ $$e\left(\frac{8}{63}\right)$$ $$e\left(\frac{59}{63}\right)$$ $$e\left(\frac{5}{7}\right)$$
$$\chi_{8379}(20,\cdot)$$ 8379.ji 42 no $$1$$ $$1$$ $$e\left(\frac{13}{42}\right)$$ $$e\left(\frac{13}{21}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{13}{42}\right)$$ $$e\left(\frac{41}{42}\right)$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{8}{21}\right)$$
$$\chi_{8379}(22,\cdot)$$ 8379.lw 126 yes $$-1$$ $$1$$ $$e\left(\frac{115}{126}\right)$$ $$e\left(\frac{52}{63}\right)$$ $$e\left(\frac{50}{63}\right)$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{89}{126}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{17}{126}\right)$$ $$e\left(\frac{41}{63}\right)$$ $$e\left(\frac{32}{63}\right)$$ $$e\left(\frac{13}{21}\right)$$
$$\chi_{8379}(23,\cdot)$$ 8379.my 126 yes $$-1$$ $$1$$ $$e\left(\frac{59}{126}\right)$$ $$e\left(\frac{59}{63}\right)$$ $$e\left(\frac{23}{126}\right)$$ $$e\left(\frac{17}{42}\right)$$ $$e\left(\frac{41}{63}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{5}{63}\right)$$ $$e\left(\frac{55}{63}\right)$$ $$e\left(\frac{29}{126}\right)$$ $$e\left(\frac{5}{42}\right)$$
$$\chi_{8379}(25,\cdot)$$ 8379.lp 63 yes $$1$$ $$1$$ $$e\left(\frac{22}{63}\right)$$ $$e\left(\frac{44}{63}\right)$$ $$e\left(\frac{52}{63}\right)$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{11}{63}\right)$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{50}{63}\right)$$ $$e\left(\frac{25}{63}\right)$$ $$e\left(\frac{19}{63}\right)$$ $$e\left(\frac{11}{21}\right)$$
$$\chi_{8379}(26,\cdot)$$ 8379.ku 42 no $$1$$ $$1$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{29}{42}\right)$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{20}{21}\right)$$ $$e\left(\frac{2}{7}\right)$$
$$\chi_{8379}(29,\cdot)$$ 8379.nz 126 yes $$1$$ $$1$$ $$e\left(\frac{16}{63}\right)$$ $$e\left(\frac{32}{63}\right)$$ $$e\left(\frac{47}{126}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{79}{126}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{25}{126}\right)$$ $$e\left(\frac{1}{63}\right)$$ $$e\left(\frac{83}{126}\right)$$ $$e\left(\frac{37}{42}\right)$$
$$\chi_{8379}(31,\cdot)$$ 8379.bi 6 no $$1$$ $$1$$ $$-1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{8379}(32,\cdot)$$ 8379.nk 126 yes $$1$$ $$1$$ $$e\left(\frac{37}{63}\right)$$ $$e\left(\frac{11}{63}\right)$$ $$e\left(\frac{47}{126}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{121}{126}\right)$$ $$e\left(\frac{41}{42}\right)$$ $$e\left(\frac{25}{126}\right)$$ $$e\left(\frac{22}{63}\right)$$ $$e\left(\frac{83}{126}\right)$$ $$e\left(\frac{23}{42}\right)$$
$$\chi_{8379}(34,\cdot)$$ 8379.lv 126 yes $$1$$ $$1$$ $$e\left(\frac{107}{126}\right)$$ $$e\left(\frac{44}{63}\right)$$ $$e\left(\frac{41}{126}\right)$$ $$e\left(\frac{23}{42}\right)$$ $$e\left(\frac{11}{63}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{29}{63}\right)$$ $$e\left(\frac{25}{63}\right)$$ $$e\left(\frac{59}{126}\right)$$ $$e\left(\frac{1}{42}\right)$$
$$\chi_{8379}(37,\cdot)$$ 8379.jf 42 no $$-1$$ $$1$$ $$e\left(\frac{13}{42}\right)$$ $$e\left(\frac{13}{21}\right)$$ $$e\left(\frac{2}{21}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{17}{42}\right)$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{5}{7}\right)$$
$$\chi_{8379}(40,\cdot)$$ 8379.mp 126 yes $$1$$ $$1$$ $$e\left(\frac{79}{126}\right)$$ $$e\left(\frac{16}{63}\right)$$ $$e\left(\frac{55}{126}\right)$$ $$e\left(\frac{37}{42}\right)$$ $$e\left(\frac{4}{63}\right)$$ $$e\left(\frac{19}{21}\right)$$ $$e\left(\frac{1}{63}\right)$$ $$e\left(\frac{32}{63}\right)$$ $$e\left(\frac{31}{126}\right)$$ $$e\left(\frac{29}{42}\right)$$
$$\chi_{8379}(41,\cdot)$$ 8379.oc 126 yes $$-1$$ $$1$$ $$e\left(\frac{53}{63}\right)$$ $$e\left(\frac{43}{63}\right)$$ $$e\left(\frac{5}{63}\right)$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{58}{63}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{4}{63}\right)$$ $$e\left(\frac{23}{63}\right)$$ $$e\left(\frac{41}{63}\right)$$ $$e\left(\frac{16}{21}\right)$$
$$\chi_{8379}(43,\cdot)$$ 8379.lr 63 yes $$1$$ $$1$$ $$e\left(\frac{17}{63}\right)$$ $$e\left(\frac{34}{63}\right)$$ $$e\left(\frac{44}{63}\right)$$ $$e\left(\frac{17}{21}\right)$$ $$e\left(\frac{61}{63}\right)$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{31}{63}\right)$$ $$e\left(\frac{5}{63}\right)$$ $$e\left(\frac{29}{63}\right)$$ $$e\left(\frac{5}{21}\right)$$
$$\chi_{8379}(44,\cdot)$$ 8379.mk 126 no $$-1$$ $$1$$ $$e\left(\frac{29}{126}\right)$$ $$e\left(\frac{29}{63}\right)$$ $$e\left(\frac{59}{126}\right)$$ $$e\left(\frac{29}{42}\right)$$ $$e\left(\frac{44}{63}\right)$$ $$e\left(\frac{19}{42}\right)$$ $$e\left(\frac{11}{63}\right)$$ $$e\left(\frac{58}{63}\right)$$ $$e\left(\frac{5}{126}\right)$$ $$e\left(\frac{13}{14}\right)$$
$$\chi_{8379}(46,\cdot)$$ 8379.kv 42 no $$-1$$ $$1$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{20}{21}\right)$$ $$e\left(\frac{5}{42}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{3}{7}\right)$$
$$\chi_{8379}(47,\cdot)$$ 8379.mi 126 yes $$1$$ $$1$$ $$e\left(\frac{89}{126}\right)$$ $$e\left(\frac{26}{63}\right)$$ $$e\left(\frac{25}{63}\right)$$ $$e\left(\frac{5}{42}\right)$$ $$e\left(\frac{13}{126}\right)$$ $$e\left(\frac{11}{42}\right)$$ $$e\left(\frac{61}{126}\right)$$ $$e\left(\frac{52}{63}\right)$$ $$e\left(\frac{58}{63}\right)$$ $$e\left(\frac{17}{21}\right)$$
$$\chi_{8379}(50,\cdot)$$ 8379.bp 6 no $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{8379}(52,\cdot)$$ 8379.lu 126 yes $$1$$ $$1$$ $$e\left(\frac{85}{126}\right)$$ $$e\left(\frac{22}{63}\right)$$ $$e\left(\frac{31}{126}\right)$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{58}{63}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{4}{63}\right)$$ $$e\left(\frac{44}{63}\right)$$ $$e\left(\frac{61}{126}\right)$$ $$e\left(\frac{25}{42}\right)$$
$$\chi_{8379}(53,\cdot)$$ 8379.od 126 no $$1$$ $$1$$ $$e\left(\frac{19}{63}\right)$$ $$e\left(\frac{38}{63}\right)$$ $$e\left(\frac{23}{126}\right)$$ $$e\left(\frac{19}{21}\right)$$ $$e\left(\frac{61}{126}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{115}{126}\right)$$ $$e\left(\frac{13}{63}\right)$$ $$e\left(\frac{71}{126}\right)$$ $$e\left(\frac{11}{14}\right)$$
$$\chi_{8379}(55,\cdot)$$ 8379.nx 126 no $$-1$$ $$1$$ $$e\left(\frac{17}{63}\right)$$ $$e\left(\frac{34}{63}\right)$$ $$e\left(\frac{67}{126}\right)$$ $$e\left(\frac{17}{21}\right)$$ $$e\left(\frac{101}{126}\right)$$ $$e\left(\frac{8}{21}\right)$$ $$e\left(\frac{125}{126}\right)$$ $$e\left(\frac{5}{63}\right)$$ $$e\left(\frac{79}{126}\right)$$ $$e\left(\frac{1}{14}\right)$$
$$\chi_{8379}(58,\cdot)$$ 8379.hn 21 no $$1$$ $$1$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{13}{21}\right)$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{4}{21}\right)$$ $$e\left(\frac{4}{21}\right)$$
$$\chi_{8379}(59,\cdot)$$ 8379.no 126 yes $$-1$$ $$1$$ $$e\left(\frac{59}{63}\right)$$ $$e\left(\frac{55}{63}\right)$$ $$e\left(\frac{2}{63}\right)$$ $$e\left(\frac{17}{21}\right)$$ $$e\left(\frac{61}{63}\right)$$ $$e\left(\frac{37}{42}\right)$$ $$e\left(\frac{10}{63}\right)$$ $$e\left(\frac{47}{63}\right)$$ $$e\left(\frac{50}{63}\right)$$ $$e\left(\frac{19}{21}\right)$$