# Properties

 Modulus 354 Structure $$C_{58}\times C_{2}$$ Order 116

Show commands for: SageMath / Pari/GP

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed

sage: H = DirichletGroup_conrey(354)

pari: g = idealstar(,354,2)

## Character group

 sage: G.order()  pari: g.no Order = 116 sage: H.invariants()  pari: g.cyc Structure = $$C_{58}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{354}(61,\cdot)$, $\chi_{354}(119,\cdot)$

## First 32 of 116 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.

orbit label order primitive -1 1 5 7 11 13 17 19 23 25 29 31
$$\chi_{354}(1,\cdot)$$ 354.a 1 No $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{354}(5,\cdot)$$ 354.h 58 No $$-1$$ $$1$$ $$e\left(\frac{7}{58}\right)$$ $$e\left(\frac{25}{29}\right)$$ $$e\left(\frac{5}{58}\right)$$ $$e\left(\frac{19}{29}\right)$$ $$e\left(\frac{37}{58}\right)$$ $$e\left(\frac{27}{29}\right)$$ $$e\left(\frac{3}{58}\right)$$ $$e\left(\frac{7}{29}\right)$$ $$e\left(\frac{23}{58}\right)$$ $$e\left(\frac{2}{29}\right)$$
$$\chi_{354}(7,\cdot)$$ 354.e 29 No $$1$$ $$1$$ $$e\left(\frac{25}{29}\right)$$ $$e\left(\frac{17}{29}\right)$$ $$e\left(\frac{22}{29}\right)$$ $$e\left(\frac{28}{29}\right)$$ $$e\left(\frac{12}{29}\right)$$ $$e\left(\frac{23}{29}\right)$$ $$e\left(\frac{19}{29}\right)$$ $$e\left(\frac{21}{29}\right)$$ $$e\left(\frac{20}{29}\right)$$ $$e\left(\frac{6}{29}\right)$$
$$\chi_{354}(11,\cdot)$$ 354.g 58 No $$1$$ $$1$$ $$e\left(\frac{5}{58}\right)$$ $$e\left(\frac{22}{29}\right)$$ $$e\left(\frac{8}{29}\right)$$ $$e\left(\frac{23}{58}\right)$$ $$e\left(\frac{43}{58}\right)$$ $$e\left(\frac{11}{29}\right)$$ $$e\left(\frac{28}{29}\right)$$ $$e\left(\frac{5}{29}\right)$$ $$e\left(\frac{33}{58}\right)$$ $$e\left(\frac{7}{58}\right)$$
$$\chi_{354}(13,\cdot)$$ 354.f 58 No $$-1$$ $$1$$ $$e\left(\frac{19}{29}\right)$$ $$e\left(\frac{28}{29}\right)$$ $$e\left(\frac{23}{58}\right)$$ $$e\left(\frac{53}{58}\right)$$ $$e\left(\frac{1}{29}\right)$$ $$e\left(\frac{14}{29}\right)$$ $$e\left(\frac{37}{58}\right)$$ $$e\left(\frac{9}{29}\right)$$ $$e\left(\frac{21}{29}\right)$$ $$e\left(\frac{1}{58}\right)$$
$$\chi_{354}(17,\cdot)$$ 354.h 58 No $$-1$$ $$1$$ $$e\left(\frac{37}{58}\right)$$ $$e\left(\frac{12}{29}\right)$$ $$e\left(\frac{43}{58}\right)$$ $$e\left(\frac{1}{29}\right)$$ $$e\left(\frac{5}{58}\right)$$ $$e\left(\frac{6}{29}\right)$$ $$e\left(\frac{49}{58}\right)$$ $$e\left(\frac{8}{29}\right)$$ $$e\left(\frac{47}{58}\right)$$ $$e\left(\frac{23}{29}\right)$$
$$\chi_{354}(19,\cdot)$$ 354.e 29 No $$1$$ $$1$$ $$e\left(\frac{27}{29}\right)$$ $$e\left(\frac{23}{29}\right)$$ $$e\left(\frac{11}{29}\right)$$ $$e\left(\frac{14}{29}\right)$$ $$e\left(\frac{6}{29}\right)$$ $$e\left(\frac{26}{29}\right)$$ $$e\left(\frac{24}{29}\right)$$ $$e\left(\frac{25}{29}\right)$$ $$e\left(\frac{10}{29}\right)$$ $$e\left(\frac{3}{29}\right)$$
$$\chi_{354}(23,\cdot)$$ 354.g 58 No $$1$$ $$1$$ $$e\left(\frac{3}{58}\right)$$ $$e\left(\frac{19}{29}\right)$$ $$e\left(\frac{28}{29}\right)$$ $$e\left(\frac{37}{58}\right)$$ $$e\left(\frac{49}{58}\right)$$ $$e\left(\frac{24}{29}\right)$$ $$e\left(\frac{11}{29}\right)$$ $$e\left(\frac{3}{29}\right)$$ $$e\left(\frac{43}{58}\right)$$ $$e\left(\frac{39}{58}\right)$$
$$\chi_{354}(25,\cdot)$$ 354.e 29 No $$1$$ $$1$$ $$e\left(\frac{7}{29}\right)$$ $$e\left(\frac{21}{29}\right)$$ $$e\left(\frac{5}{29}\right)$$ $$e\left(\frac{9}{29}\right)$$ $$e\left(\frac{8}{29}\right)$$ $$e\left(\frac{25}{29}\right)$$ $$e\left(\frac{3}{29}\right)$$ $$e\left(\frac{14}{29}\right)$$ $$e\left(\frac{23}{29}\right)$$ $$e\left(\frac{4}{29}\right)$$
$$\chi_{354}(29,\cdot)$$ 354.h 58 No $$-1$$ $$1$$ $$e\left(\frac{23}{58}\right)$$ $$e\left(\frac{20}{29}\right)$$ $$e\left(\frac{33}{58}\right)$$ $$e\left(\frac{21}{29}\right)$$ $$e\left(\frac{47}{58}\right)$$ $$e\left(\frac{10}{29}\right)$$ $$e\left(\frac{43}{58}\right)$$ $$e\left(\frac{23}{29}\right)$$ $$e\left(\frac{1}{58}\right)$$ $$e\left(\frac{19}{29}\right)$$
$$\chi_{354}(31,\cdot)$$ 354.f 58 No $$-1$$ $$1$$ $$e\left(\frac{2}{29}\right)$$ $$e\left(\frac{6}{29}\right)$$ $$e\left(\frac{7}{58}\right)$$ $$e\left(\frac{1}{58}\right)$$ $$e\left(\frac{23}{29}\right)$$ $$e\left(\frac{3}{29}\right)$$ $$e\left(\frac{39}{58}\right)$$ $$e\left(\frac{4}{29}\right)$$ $$e\left(\frac{19}{29}\right)$$ $$e\left(\frac{23}{58}\right)$$
$$\chi_{354}(35,\cdot)$$ 354.h 58 No $$-1$$ $$1$$ $$e\left(\frac{57}{58}\right)$$ $$e\left(\frac{13}{29}\right)$$ $$e\left(\frac{49}{58}\right)$$ $$e\left(\frac{18}{29}\right)$$ $$e\left(\frac{3}{58}\right)$$ $$e\left(\frac{21}{29}\right)$$ $$e\left(\frac{41}{58}\right)$$ $$e\left(\frac{28}{29}\right)$$ $$e\left(\frac{5}{58}\right)$$ $$e\left(\frac{8}{29}\right)$$
$$\chi_{354}(37,\cdot)$$ 354.f 58 No $$-1$$ $$1$$ $$e\left(\frac{20}{29}\right)$$ $$e\left(\frac{2}{29}\right)$$ $$e\left(\frac{41}{58}\right)$$ $$e\left(\frac{39}{58}\right)$$ $$e\left(\frac{27}{29}\right)$$ $$e\left(\frac{1}{29}\right)$$ $$e\left(\frac{13}{58}\right)$$ $$e\left(\frac{11}{29}\right)$$ $$e\left(\frac{16}{29}\right)$$ $$e\left(\frac{27}{58}\right)$$
$$\chi_{354}(41,\cdot)$$ 354.h 58 No $$-1$$ $$1$$ $$e\left(\frac{55}{58}\right)$$ $$e\left(\frac{10}{29}\right)$$ $$e\left(\frac{31}{58}\right)$$ $$e\left(\frac{25}{29}\right)$$ $$e\left(\frac{9}{58}\right)$$ $$e\left(\frac{5}{29}\right)$$ $$e\left(\frac{7}{58}\right)$$ $$e\left(\frac{26}{29}\right)$$ $$e\left(\frac{15}{58}\right)$$ $$e\left(\frac{24}{29}\right)$$
$$\chi_{354}(43,\cdot)$$ 354.f 58 No $$-1$$ $$1$$ $$e\left(\frac{12}{29}\right)$$ $$e\left(\frac{7}{29}\right)$$ $$e\left(\frac{13}{58}\right)$$ $$e\left(\frac{35}{58}\right)$$ $$e\left(\frac{22}{29}\right)$$ $$e\left(\frac{18}{29}\right)$$ $$e\left(\frac{31}{58}\right)$$ $$e\left(\frac{24}{29}\right)$$ $$e\left(\frac{27}{29}\right)$$ $$e\left(\frac{51}{58}\right)$$
$$\chi_{354}(47,\cdot)$$ 354.g 58 No $$1$$ $$1$$ $$e\left(\frac{51}{58}\right)$$ $$e\left(\frac{4}{29}\right)$$ $$e\left(\frac{12}{29}\right)$$ $$e\left(\frac{49}{58}\right)$$ $$e\left(\frac{21}{58}\right)$$ $$e\left(\frac{2}{29}\right)$$ $$e\left(\frac{13}{29}\right)$$ $$e\left(\frac{22}{29}\right)$$ $$e\left(\frac{35}{58}\right)$$ $$e\left(\frac{25}{58}\right)$$
$$\chi_{354}(49,\cdot)$$ 354.e 29 No $$1$$ $$1$$ $$e\left(\frac{21}{29}\right)$$ $$e\left(\frac{5}{29}\right)$$ $$e\left(\frac{15}{29}\right)$$ $$e\left(\frac{27}{29}\right)$$ $$e\left(\frac{24}{29}\right)$$ $$e\left(\frac{17}{29}\right)$$ $$e\left(\frac{9}{29}\right)$$ $$e\left(\frac{13}{29}\right)$$ $$e\left(\frac{11}{29}\right)$$ $$e\left(\frac{12}{29}\right)$$
$$\chi_{354}(53,\cdot)$$ 354.h 58 No $$-1$$ $$1$$ $$e\left(\frac{45}{58}\right)$$ $$e\left(\frac{24}{29}\right)$$ $$e\left(\frac{57}{58}\right)$$ $$e\left(\frac{2}{29}\right)$$ $$e\left(\frac{39}{58}\right)$$ $$e\left(\frac{12}{29}\right)$$ $$e\left(\frac{11}{58}\right)$$ $$e\left(\frac{16}{29}\right)$$ $$e\left(\frac{7}{58}\right)$$ $$e\left(\frac{17}{29}\right)$$
$$\chi_{354}(55,\cdot)$$ 354.f 58 No $$-1$$ $$1$$ $$e\left(\frac{6}{29}\right)$$ $$e\left(\frac{18}{29}\right)$$ $$e\left(\frac{21}{58}\right)$$ $$e\left(\frac{3}{58}\right)$$ $$e\left(\frac{11}{29}\right)$$ $$e\left(\frac{9}{29}\right)$$ $$e\left(\frac{1}{58}\right)$$ $$e\left(\frac{12}{29}\right)$$ $$e\left(\frac{28}{29}\right)$$ $$e\left(\frac{11}{58}\right)$$
$$\chi_{354}(61,\cdot)$$ 354.f 58 No $$-1$$ $$1$$ $$e\left(\frac{3}{29}\right)$$ $$e\left(\frac{9}{29}\right)$$ $$e\left(\frac{25}{58}\right)$$ $$e\left(\frac{45}{58}\right)$$ $$e\left(\frac{20}{29}\right)$$ $$e\left(\frac{19}{29}\right)$$ $$e\left(\frac{15}{58}\right)$$ $$e\left(\frac{6}{29}\right)$$ $$e\left(\frac{14}{29}\right)$$ $$e\left(\frac{49}{58}\right)$$
$$\chi_{354}(65,\cdot)$$ 354.g 58 No $$1$$ $$1$$ $$e\left(\frac{45}{58}\right)$$ $$e\left(\frac{24}{29}\right)$$ $$e\left(\frac{14}{29}\right)$$ $$e\left(\frac{33}{58}\right)$$ $$e\left(\frac{39}{58}\right)$$ $$e\left(\frac{12}{29}\right)$$ $$e\left(\frac{20}{29}\right)$$ $$e\left(\frac{16}{29}\right)$$ $$e\left(\frac{7}{58}\right)$$ $$e\left(\frac{5}{58}\right)$$
$$\chi_{354}(67,\cdot)$$ 354.f 58 No $$-1$$ $$1$$ $$e\left(\frac{9}{29}\right)$$ $$e\left(\frac{27}{29}\right)$$ $$e\left(\frac{17}{58}\right)$$ $$e\left(\frac{19}{58}\right)$$ $$e\left(\frac{2}{29}\right)$$ $$e\left(\frac{28}{29}\right)$$ $$e\left(\frac{45}{58}\right)$$ $$e\left(\frac{18}{29}\right)$$ $$e\left(\frac{13}{29}\right)$$ $$e\left(\frac{31}{58}\right)$$
$$\chi_{354}(71,\cdot)$$ 354.h 58 No $$-1$$ $$1$$ $$e\left(\frac{51}{58}\right)$$ $$e\left(\frac{4}{29}\right)$$ $$e\left(\frac{53}{58}\right)$$ $$e\left(\frac{10}{29}\right)$$ $$e\left(\frac{21}{58}\right)$$ $$e\left(\frac{2}{29}\right)$$ $$e\left(\frac{55}{58}\right)$$ $$e\left(\frac{22}{29}\right)$$ $$e\left(\frac{35}{58}\right)$$ $$e\left(\frac{27}{29}\right)$$
$$\chi_{354}(73,\cdot)$$ 354.f 58 No $$-1$$ $$1$$ $$e\left(\frac{28}{29}\right)$$ $$e\left(\frac{26}{29}\right)$$ $$e\left(\frac{11}{58}\right)$$ $$e\left(\frac{43}{58}\right)$$ $$e\left(\frac{3}{29}\right)$$ $$e\left(\frac{13}{29}\right)$$ $$e\left(\frac{53}{58}\right)$$ $$e\left(\frac{27}{29}\right)$$ $$e\left(\frac{5}{29}\right)$$ $$e\left(\frac{3}{58}\right)$$
$$\chi_{354}(77,\cdot)$$ 354.g 58 No $$1$$ $$1$$ $$e\left(\frac{55}{58}\right)$$ $$e\left(\frac{10}{29}\right)$$ $$e\left(\frac{1}{29}\right)$$ $$e\left(\frac{21}{58}\right)$$ $$e\left(\frac{9}{58}\right)$$ $$e\left(\frac{5}{29}\right)$$ $$e\left(\frac{18}{29}\right)$$ $$e\left(\frac{26}{29}\right)$$ $$e\left(\frac{15}{58}\right)$$ $$e\left(\frac{19}{58}\right)$$
$$\chi_{354}(79,\cdot)$$ 354.e 29 No $$1$$ $$1$$ $$e\left(\frac{24}{29}\right)$$ $$e\left(\frac{14}{29}\right)$$ $$e\left(\frac{13}{29}\right)$$ $$e\left(\frac{6}{29}\right)$$ $$e\left(\frac{15}{29}\right)$$ $$e\left(\frac{7}{29}\right)$$ $$e\left(\frac{2}{29}\right)$$ $$e\left(\frac{19}{29}\right)$$ $$e\left(\frac{25}{29}\right)$$ $$e\left(\frac{22}{29}\right)$$
$$\chi_{354}(83,\cdot)$$ 354.g 58 No $$1$$ $$1$$ $$e\left(\frac{57}{58}\right)$$ $$e\left(\frac{13}{29}\right)$$ $$e\left(\frac{10}{29}\right)$$ $$e\left(\frac{7}{58}\right)$$ $$e\left(\frac{3}{58}\right)$$ $$e\left(\frac{21}{29}\right)$$ $$e\left(\frac{6}{29}\right)$$ $$e\left(\frac{28}{29}\right)$$ $$e\left(\frac{5}{58}\right)$$ $$e\left(\frac{45}{58}\right)$$
$$\chi_{354}(85,\cdot)$$ 354.e 29 No $$1$$ $$1$$ $$e\left(\frac{22}{29}\right)$$ $$e\left(\frac{8}{29}\right)$$ $$e\left(\frac{24}{29}\right)$$ $$e\left(\frac{20}{29}\right)$$ $$e\left(\frac{21}{29}\right)$$ $$e\left(\frac{4}{29}\right)$$ $$e\left(\frac{26}{29}\right)$$ $$e\left(\frac{15}{29}\right)$$ $$e\left(\frac{6}{29}\right)$$ $$e\left(\frac{25}{29}\right)$$
$$\chi_{354}(89,\cdot)$$ 354.g 58 No $$1$$ $$1$$ $$e\left(\frac{23}{58}\right)$$ $$e\left(\frac{20}{29}\right)$$ $$e\left(\frac{2}{29}\right)$$ $$e\left(\frac{13}{58}\right)$$ $$e\left(\frac{47}{58}\right)$$ $$e\left(\frac{10}{29}\right)$$ $$e\left(\frac{7}{29}\right)$$ $$e\left(\frac{23}{29}\right)$$ $$e\left(\frac{1}{58}\right)$$ $$e\left(\frac{9}{58}\right)$$
$$\chi_{354}(91,\cdot)$$ 354.f 58 No $$-1$$ $$1$$ $$e\left(\frac{15}{29}\right)$$ $$e\left(\frac{16}{29}\right)$$ $$e\left(\frac{9}{58}\right)$$ $$e\left(\frac{51}{58}\right)$$ $$e\left(\frac{13}{29}\right)$$ $$e\left(\frac{8}{29}\right)$$ $$e\left(\frac{17}{58}\right)$$ $$e\left(\frac{1}{29}\right)$$ $$e\left(\frac{12}{29}\right)$$ $$e\left(\frac{13}{58}\right)$$
$$\chi_{354}(95,\cdot)$$ 354.h 58 No $$-1$$ $$1$$ $$e\left(\frac{3}{58}\right)$$ $$e\left(\frac{19}{29}\right)$$ $$e\left(\frac{27}{58}\right)$$ $$e\left(\frac{4}{29}\right)$$ $$e\left(\frac{49}{58}\right)$$ $$e\left(\frac{24}{29}\right)$$ $$e\left(\frac{51}{58}\right)$$ $$e\left(\frac{3}{29}\right)$$ $$e\left(\frac{43}{58}\right)$$ $$e\left(\frac{5}{29}\right)$$
$$\chi_{354}(97,\cdot)$$ 354.f 58 No $$-1$$ $$1$$ $$e\left(\frac{1}{29}\right)$$ $$e\left(\frac{3}{29}\right)$$ $$e\left(\frac{47}{58}\right)$$ $$e\left(\frac{15}{58}\right)$$ $$e\left(\frac{26}{29}\right)$$ $$e\left(\frac{16}{29}\right)$$ $$e\left(\frac{5}{58}\right)$$ $$e\left(\frac{2}{29}\right)$$ $$e\left(\frac{24}{29}\right)$$ $$e\left(\frac{55}{58}\right)$$