# Properties

 Modulus $705$ Structure $$C_{92}\times C_{2}\times C_{2}$$ Order $368$

Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(705)

pari: g = idealstar(,705,2)

## Character group

 sage: G.order()  pari: g.no Order = 368 sage: H.invariants()  pari: g.cyc Structure = $$C_{92}\times C_{2}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{705}(236,\cdot)$, $\chi_{705}(142,\cdot)$, $\chi_{705}(616,\cdot)$

## First 32 of 368 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 $$-1$$ $$1$$ $$2$$ $$4$$ $$7$$ $$8$$ $$11$$ $$13$$ $$14$$ $$16$$ $$17$$ $$19$$
$$\chi_{705}(1,\cdot)$$ 705.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{705}(2,\cdot)$$ 705.w 92 yes $$1$$ $$1$$ $$e\left(\frac{73}{92}\right)$$ $$e\left(\frac{27}{46}\right)$$ $$e\left(\frac{71}{92}\right)$$ $$e\left(\frac{35}{92}\right)$$ $$e\left(\frac{11}{46}\right)$$ $$e\left(\frac{5}{92}\right)$$ $$e\left(\frac{13}{23}\right)$$ $$e\left(\frac{4}{23}\right)$$ $$e\left(\frac{1}{92}\right)$$ $$e\left(\frac{5}{46}\right)$$
$$\chi_{705}(4,\cdot)$$ 705.s 46 no $$1$$ $$1$$ $$e\left(\frac{27}{46}\right)$$ $$e\left(\frac{4}{23}\right)$$ $$e\left(\frac{25}{46}\right)$$ $$e\left(\frac{35}{46}\right)$$ $$e\left(\frac{11}{23}\right)$$ $$e\left(\frac{5}{46}\right)$$ $$e\left(\frac{3}{23}\right)$$ $$e\left(\frac{8}{23}\right)$$ $$e\left(\frac{1}{46}\right)$$ $$e\left(\frac{5}{23}\right)$$
$$\chi_{705}(7,\cdot)$$ 705.v 92 no $$-1$$ $$1$$ $$e\left(\frac{71}{92}\right)$$ $$e\left(\frac{25}{46}\right)$$ $$e\left(\frac{47}{92}\right)$$ $$e\left(\frac{29}{92}\right)$$ $$e\left(\frac{20}{23}\right)$$ $$e\left(\frac{37}{92}\right)$$ $$e\left(\frac{13}{46}\right)$$ $$e\left(\frac{2}{23}\right)$$ $$e\left(\frac{35}{92}\right)$$ $$e\left(\frac{37}{46}\right)$$
$$\chi_{705}(8,\cdot)$$ 705.w 92 yes $$1$$ $$1$$ $$e\left(\frac{35}{92}\right)$$ $$e\left(\frac{35}{46}\right)$$ $$e\left(\frac{29}{92}\right)$$ $$e\left(\frac{13}{92}\right)$$ $$e\left(\frac{33}{46}\right)$$ $$e\left(\frac{15}{92}\right)$$ $$e\left(\frac{16}{23}\right)$$ $$e\left(\frac{12}{23}\right)$$ $$e\left(\frac{3}{92}\right)$$ $$e\left(\frac{15}{46}\right)$$
$$\chi_{705}(11,\cdot)$$ 705.q 46 no $$1$$ $$1$$ $$e\left(\frac{11}{46}\right)$$ $$e\left(\frac{11}{23}\right)$$ $$e\left(\frac{20}{23}\right)$$ $$e\left(\frac{33}{46}\right)$$ $$e\left(\frac{13}{23}\right)$$ $$e\left(\frac{31}{46}\right)$$ $$e\left(\frac{5}{46}\right)$$ $$e\left(\frac{22}{23}\right)$$ $$e\left(\frac{43}{46}\right)$$ $$e\left(\frac{39}{46}\right)$$
$$\chi_{705}(13,\cdot)$$ 705.x 92 no $$1$$ $$1$$ $$e\left(\frac{5}{92}\right)$$ $$e\left(\frac{5}{46}\right)$$ $$e\left(\frac{37}{92}\right)$$ $$e\left(\frac{15}{92}\right)$$ $$e\left(\frac{31}{46}\right)$$ $$e\left(\frac{81}{92}\right)$$ $$e\left(\frac{21}{46}\right)$$ $$e\left(\frac{5}{23}\right)$$ $$e\left(\frac{53}{92}\right)$$ $$e\left(\frac{6}{23}\right)$$
$$\chi_{705}(14,\cdot)$$ 705.p 46 yes $$-1$$ $$1$$ $$e\left(\frac{13}{23}\right)$$ $$e\left(\frac{3}{23}\right)$$ $$e\left(\frac{13}{46}\right)$$ $$e\left(\frac{16}{23}\right)$$ $$e\left(\frac{5}{46}\right)$$ $$e\left(\frac{21}{46}\right)$$ $$e\left(\frac{39}{46}\right)$$ $$e\left(\frac{6}{23}\right)$$ $$e\left(\frac{9}{23}\right)$$ $$e\left(\frac{21}{23}\right)$$
$$\chi_{705}(16,\cdot)$$ 705.m 23 no $$1$$ $$1$$ $$e\left(\frac{4}{23}\right)$$ $$e\left(\frac{8}{23}\right)$$ $$e\left(\frac{2}{23}\right)$$ $$e\left(\frac{12}{23}\right)$$ $$e\left(\frac{22}{23}\right)$$ $$e\left(\frac{5}{23}\right)$$ $$e\left(\frac{6}{23}\right)$$ $$e\left(\frac{16}{23}\right)$$ $$e\left(\frac{1}{23}\right)$$ $$e\left(\frac{10}{23}\right)$$
$$\chi_{705}(17,\cdot)$$ 705.w 92 yes $$1$$ $$1$$ $$e\left(\frac{1}{92}\right)$$ $$e\left(\frac{1}{46}\right)$$ $$e\left(\frac{35}{92}\right)$$ $$e\left(\frac{3}{92}\right)$$ $$e\left(\frac{43}{46}\right)$$ $$e\left(\frac{53}{92}\right)$$ $$e\left(\frac{9}{23}\right)$$ $$e\left(\frac{1}{23}\right)$$ $$e\left(\frac{29}{92}\right)$$ $$e\left(\frac{7}{46}\right)$$
$$\chi_{705}(19,\cdot)$$ 705.t 46 no $$-1$$ $$1$$ $$e\left(\frac{5}{46}\right)$$ $$e\left(\frac{5}{23}\right)$$ $$e\left(\frac{37}{46}\right)$$ $$e\left(\frac{15}{46}\right)$$ $$e\left(\frac{39}{46}\right)$$ $$e\left(\frac{6}{23}\right)$$ $$e\left(\frac{21}{23}\right)$$ $$e\left(\frac{10}{23}\right)$$ $$e\left(\frac{7}{46}\right)$$ $$e\left(\frac{1}{46}\right)$$
$$\chi_{705}(22,\cdot)$$ 705.x 92 no $$1$$ $$1$$ $$e\left(\frac{3}{92}\right)$$ $$e\left(\frac{3}{46}\right)$$ $$e\left(\frac{59}{92}\right)$$ $$e\left(\frac{9}{92}\right)$$ $$e\left(\frac{37}{46}\right)$$ $$e\left(\frac{67}{92}\right)$$ $$e\left(\frac{31}{46}\right)$$ $$e\left(\frac{3}{23}\right)$$ $$e\left(\frac{87}{92}\right)$$ $$e\left(\frac{22}{23}\right)$$
$$\chi_{705}(23,\cdot)$$ 705.u 92 yes $$-1$$ $$1$$ $$e\left(\frac{19}{92}\right)$$ $$e\left(\frac{19}{46}\right)$$ $$e\left(\frac{21}{92}\right)$$ $$e\left(\frac{57}{92}\right)$$ $$e\left(\frac{6}{23}\right)$$ $$e\left(\frac{41}{92}\right)$$ $$e\left(\frac{10}{23}\right)$$ $$e\left(\frac{19}{23}\right)$$ $$e\left(\frac{91}{92}\right)$$ $$e\left(\frac{9}{23}\right)$$
$$\chi_{705}(26,\cdot)$$ 705.q 46 no $$1$$ $$1$$ $$e\left(\frac{39}{46}\right)$$ $$e\left(\frac{16}{23}\right)$$ $$e\left(\frac{4}{23}\right)$$ $$e\left(\frac{25}{46}\right)$$ $$e\left(\frac{21}{23}\right)$$ $$e\left(\frac{43}{46}\right)$$ $$e\left(\frac{1}{46}\right)$$ $$e\left(\frac{9}{23}\right)$$ $$e\left(\frac{27}{46}\right)$$ $$e\left(\frac{17}{46}\right)$$
$$\chi_{705}(28,\cdot)$$ 705.v 92 no $$-1$$ $$1$$ $$e\left(\frac{33}{92}\right)$$ $$e\left(\frac{33}{46}\right)$$ $$e\left(\frac{5}{92}\right)$$ $$e\left(\frac{7}{92}\right)$$ $$e\left(\frac{8}{23}\right)$$ $$e\left(\frac{47}{92}\right)$$ $$e\left(\frac{19}{46}\right)$$ $$e\left(\frac{10}{23}\right)$$ $$e\left(\frac{37}{92}\right)$$ $$e\left(\frac{1}{46}\right)$$
$$\chi_{705}(29,\cdot)$$ 705.o 46 yes $$1$$ $$1$$ $$e\left(\frac{16}{23}\right)$$ $$e\left(\frac{9}{23}\right)$$ $$e\left(\frac{39}{46}\right)$$ $$e\left(\frac{2}{23}\right)$$ $$e\left(\frac{19}{23}\right)$$ $$e\left(\frac{20}{23}\right)$$ $$e\left(\frac{25}{46}\right)$$ $$e\left(\frac{18}{23}\right)$$ $$e\left(\frac{4}{23}\right)$$ $$e\left(\frac{11}{46}\right)$$
$$\chi_{705}(31,\cdot)$$ 705.n 46 no $$-1$$ $$1$$ $$e\left(\frac{4}{23}\right)$$ $$e\left(\frac{8}{23}\right)$$ $$e\left(\frac{2}{23}\right)$$ $$e\left(\frac{12}{23}\right)$$ $$e\left(\frac{21}{46}\right)$$ $$e\left(\frac{33}{46}\right)$$ $$e\left(\frac{6}{23}\right)$$ $$e\left(\frac{16}{23}\right)$$ $$e\left(\frac{1}{23}\right)$$ $$e\left(\frac{43}{46}\right)$$
$$\chi_{705}(32,\cdot)$$ 705.w 92 yes $$1$$ $$1$$ $$e\left(\frac{89}{92}\right)$$ $$e\left(\frac{43}{46}\right)$$ $$e\left(\frac{79}{92}\right)$$ $$e\left(\frac{83}{92}\right)$$ $$e\left(\frac{9}{46}\right)$$ $$e\left(\frac{25}{92}\right)$$ $$e\left(\frac{19}{23}\right)$$ $$e\left(\frac{20}{23}\right)$$ $$e\left(\frac{5}{92}\right)$$ $$e\left(\frac{25}{46}\right)$$
$$\chi_{705}(34,\cdot)$$ 705.s 46 no $$1$$ $$1$$ $$e\left(\frac{37}{46}\right)$$ $$e\left(\frac{14}{23}\right)$$ $$e\left(\frac{7}{46}\right)$$ $$e\left(\frac{19}{46}\right)$$ $$e\left(\frac{4}{23}\right)$$ $$e\left(\frac{29}{46}\right)$$ $$e\left(\frac{22}{23}\right)$$ $$e\left(\frac{5}{23}\right)$$ $$e\left(\frac{15}{46}\right)$$ $$e\left(\frac{6}{23}\right)$$
$$\chi_{705}(37,\cdot)$$ 705.v 92 no $$-1$$ $$1$$ $$e\left(\frac{63}{92}\right)$$ $$e\left(\frac{17}{46}\right)$$ $$e\left(\frac{43}{92}\right)$$ $$e\left(\frac{5}{92}\right)$$ $$e\left(\frac{9}{23}\right)$$ $$e\left(\frac{73}{92}\right)$$ $$e\left(\frac{7}{46}\right)$$ $$e\left(\frac{17}{23}\right)$$ $$e\left(\frac{79}{92}\right)$$ $$e\left(\frac{27}{46}\right)$$
$$\chi_{705}(38,\cdot)$$ 705.u 92 yes $$-1$$ $$1$$ $$e\left(\frac{83}{92}\right)$$ $$e\left(\frac{37}{46}\right)$$ $$e\left(\frac{53}{92}\right)$$ $$e\left(\frac{65}{92}\right)$$ $$e\left(\frac{2}{23}\right)$$ $$e\left(\frac{29}{92}\right)$$ $$e\left(\frac{11}{23}\right)$$ $$e\left(\frac{14}{23}\right)$$ $$e\left(\frac{15}{92}\right)$$ $$e\left(\frac{3}{23}\right)$$
$$\chi_{705}(41,\cdot)$$ 705.q 46 no $$1$$ $$1$$ $$e\left(\frac{17}{46}\right)$$ $$e\left(\frac{17}{23}\right)$$ $$e\left(\frac{10}{23}\right)$$ $$e\left(\frac{5}{46}\right)$$ $$e\left(\frac{18}{23}\right)$$ $$e\left(\frac{27}{46}\right)$$ $$e\left(\frac{37}{46}\right)$$ $$e\left(\frac{11}{23}\right)$$ $$e\left(\frac{33}{46}\right)$$ $$e\left(\frac{31}{46}\right)$$
$$\chi_{705}(43,\cdot)$$ 705.x 92 no $$1$$ $$1$$ $$e\left(\frac{77}{92}\right)$$ $$e\left(\frac{31}{46}\right)$$ $$e\left(\frac{73}{92}\right)$$ $$e\left(\frac{47}{92}\right)$$ $$e\left(\frac{45}{46}\right)$$ $$e\left(\frac{33}{92}\right)$$ $$e\left(\frac{29}{46}\right)$$ $$e\left(\frac{8}{23}\right)$$ $$e\left(\frac{25}{92}\right)$$ $$e\left(\frac{5}{23}\right)$$
$$\chi_{705}(44,\cdot)$$ 705.o 46 yes $$1$$ $$1$$ $$e\left(\frac{19}{23}\right)$$ $$e\left(\frac{15}{23}\right)$$ $$e\left(\frac{19}{46}\right)$$ $$e\left(\frac{11}{23}\right)$$ $$e\left(\frac{1}{23}\right)$$ $$e\left(\frac{18}{23}\right)$$ $$e\left(\frac{11}{46}\right)$$ $$e\left(\frac{7}{23}\right)$$ $$e\left(\frac{22}{23}\right)$$ $$e\left(\frac{3}{46}\right)$$
$$\chi_{705}(46,\cdot)$$ 705.h 2 no $$-1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$-1$$ $$-1$$ $$1$$ $$1$$ $$1$$ $$-1$$
$$\chi_{705}(49,\cdot)$$ 705.s 46 no $$1$$ $$1$$ $$e\left(\frac{25}{46}\right)$$ $$e\left(\frac{2}{23}\right)$$ $$e\left(\frac{1}{46}\right)$$ $$e\left(\frac{29}{46}\right)$$ $$e\left(\frac{17}{23}\right)$$ $$e\left(\frac{37}{46}\right)$$ $$e\left(\frac{13}{23}\right)$$ $$e\left(\frac{4}{23}\right)$$ $$e\left(\frac{35}{46}\right)$$ $$e\left(\frac{14}{23}\right)$$
$$\chi_{705}(52,\cdot)$$ 705.x 92 no $$1$$ $$1$$ $$e\left(\frac{59}{92}\right)$$ $$e\left(\frac{13}{46}\right)$$ $$e\left(\frac{87}{92}\right)$$ $$e\left(\frac{85}{92}\right)$$ $$e\left(\frac{7}{46}\right)$$ $$e\left(\frac{91}{92}\right)$$ $$e\left(\frac{27}{46}\right)$$ $$e\left(\frac{13}{23}\right)$$ $$e\left(\frac{55}{92}\right)$$ $$e\left(\frac{11}{23}\right)$$
$$\chi_{705}(53,\cdot)$$ 705.w 92 yes $$1$$ $$1$$ $$e\left(\frac{11}{92}\right)$$ $$e\left(\frac{11}{46}\right)$$ $$e\left(\frac{17}{92}\right)$$ $$e\left(\frac{33}{92}\right)$$ $$e\left(\frac{13}{46}\right)$$ $$e\left(\frac{31}{92}\right)$$ $$e\left(\frac{7}{23}\right)$$ $$e\left(\frac{11}{23}\right)$$ $$e\left(\frac{43}{92}\right)$$ $$e\left(\frac{31}{46}\right)$$
$$\chi_{705}(56,\cdot)$$ 705.r 46 no $$-1$$ $$1$$ $$e\left(\frac{7}{46}\right)$$ $$e\left(\frac{7}{23}\right)$$ $$e\left(\frac{19}{23}\right)$$ $$e\left(\frac{21}{46}\right)$$ $$e\left(\frac{27}{46}\right)$$ $$e\left(\frac{13}{23}\right)$$ $$e\left(\frac{45}{46}\right)$$ $$e\left(\frac{14}{23}\right)$$ $$e\left(\frac{19}{46}\right)$$ $$e\left(\frac{3}{23}\right)$$
$$\chi_{705}(58,\cdot)$$ 705.x 92 no $$1$$ $$1$$ $$e\left(\frac{45}{92}\right)$$ $$e\left(\frac{45}{46}\right)$$ $$e\left(\frac{57}{92}\right)$$ $$e\left(\frac{43}{92}\right)$$ $$e\left(\frac{3}{46}\right)$$ $$e\left(\frac{85}{92}\right)$$ $$e\left(\frac{5}{46}\right)$$ $$e\left(\frac{22}{23}\right)$$ $$e\left(\frac{17}{92}\right)$$ $$e\left(\frac{8}{23}\right)$$
$$\chi_{705}(59,\cdot)$$ 705.p 46 yes $$-1$$ $$1$$ $$e\left(\frac{21}{23}\right)$$ $$e\left(\frac{19}{23}\right)$$ $$e\left(\frac{21}{46}\right)$$ $$e\left(\frac{17}{23}\right)$$ $$e\left(\frac{1}{46}\right)$$ $$e\left(\frac{41}{46}\right)$$ $$e\left(\frac{17}{46}\right)$$ $$e\left(\frac{15}{23}\right)$$ $$e\left(\frac{11}{23}\right)$$ $$e\left(\frac{18}{23}\right)$$
$$\chi_{705}(61,\cdot)$$ 705.m 23 no $$1$$ $$1$$ $$e\left(\frac{13}{23}\right)$$ $$e\left(\frac{3}{23}\right)$$ $$e\left(\frac{18}{23}\right)$$ $$e\left(\frac{16}{23}\right)$$ $$e\left(\frac{14}{23}\right)$$ $$e\left(\frac{22}{23}\right)$$ $$e\left(\frac{8}{23}\right)$$ $$e\left(\frac{6}{23}\right)$$ $$e\left(\frac{9}{23}\right)$$ $$e\left(\frac{21}{23}\right)$$