# Properties

 Modulus 804 Structure $$C_{66}\times C_{2}\times C_{2}$$ Order 264

Show commands for: SageMath / Pari/GP

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

sage: H = DirichletGroup_conrey(804)

pari: g = idealstar(,804,2)

## Character group

 sage: G.order()  pari: g.no Order = 264 sage: H.invariants()  pari: g.cyc Structure = $$C_{66}\times C_{2}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{804}(337,\cdot)$, $\chi_{804}(269,\cdot)$, $\chi_{804}(403,\cdot)$

## First 32 of 264 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
$$\chi_{804}(1,\cdot)$$ 804.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{804}(5,\cdot)$$ 804.s 22 no $$1$$ $$1$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$-1$$ $$e\left(\frac{15}{22}\right)$$
$$\chi_{804}(7,\cdot)$$ 804.bf 66 no $$1$$ $$1$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{41}{66}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{65}{66}\right)$$ $$e\left(\frac{17}{66}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{29}{33}\right)$$
$$\chi_{804}(11,\cdot)$$ 804.bb 66 yes $$-1$$ $$1$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{49}{66}\right)$$ $$e\left(\frac{65}{66}\right)$$ $$e\left(\frac{47}{66}\right)$$ $$e\left(\frac{29}{66}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{17}{33}\right)$$
$$\chi_{804}(13,\cdot)$$ 804.bc 66 no $$-1$$ $$1$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{41}{66}\right)$$ $$e\left(\frac{65}{66}\right)$$ $$e\left(\frac{31}{66}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{35}{66}\right)$$
$$\chi_{804}(17,\cdot)$$ 804.be 66 no $$-1$$ $$1$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{47}{66}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{37}{66}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{43}{66}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{19}{33}\right)$$
$$\chi_{804}(19,\cdot)$$ 804.z 66 no $$-1$$ $$1$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{65}{66}\right)$$ $$e\left(\frac{29}{66}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{1}{66}\right)$$ $$e\left(\frac{49}{66}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{41}{66}\right)$$
$$\chi_{804}(23,\cdot)$$ 804.bd 66 yes $$1$$ $$1$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{17}{66}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{43}{66}\right)$$ $$e\left(\frac{49}{66}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{29}{66}\right)$$
$$\chi_{804}(25,\cdot)$$ 804.q 11 no $$1$$ $$1$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$1$$ $$e\left(\frac{4}{11}\right)$$
$$\chi_{804}(29,\cdot)$$ 804.k 6 no $$-1$$ $$1$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{804}(31,\cdot)$$ 804.bf 66 no $$1$$ $$1$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{35}{66}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{41}{66}\right)$$ $$e\left(\frac{29}{66}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{32}{33}\right)$$
$$\chi_{804}(35,\cdot)$$ 804.bd 66 yes $$1$$ $$1$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{49}{66}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{23}{66}\right)$$ $$e\left(\frac{17}{66}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{37}{66}\right)$$
$$\chi_{804}(37,\cdot)$$ 804.i 3 no $$1$$ $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{804}(41,\cdot)$$ 804.ba 66 no $$1$$ $$1$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{31}{66}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{17}{66}\right)$$ $$e\left(\frac{59}{66}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{65}{66}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{49}{66}\right)$$
$$\chi_{804}(43,\cdot)$$ 804.u 22 no $$1$$ $$1$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$1$$ $$e\left(\frac{10}{11}\right)$$
$$\chi_{804}(47,\cdot)$$ 804.bd 66 yes $$1$$ $$1$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{61}{66}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{65}{66}\right)$$ $$e\left(\frac{5}{66}\right)$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{7}{66}\right)$$
$$\chi_{804}(49,\cdot)$$ 804.y 33 no $$1$$ $$1$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{25}{33}\right)$$
$$\chi_{804}(53,\cdot)$$ 804.s 22 no $$1$$ $$1$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$-1$$ $$e\left(\frac{13}{22}\right)$$
$$\chi_{804}(55,\cdot)$$ 804.z 66 no $$-1$$ $$1$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{19}{66}\right)$$ $$e\left(\frac{43}{66}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{47}{66}\right)$$ $$e\left(\frac{59}{66}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{13}{66}\right)$$
$$\chi_{804}(59,\cdot)$$ 804.w 22 yes $$1$$ $$1$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$-1$$ $$e\left(\frac{3}{22}\right)$$
$$\chi_{804}(61,\cdot)$$ 804.bc 66 no $$-1$$ $$1$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{29}{66}\right)$$ $$e\left(\frac{17}{66}\right)$$ $$e\left(\frac{1}{66}\right)$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{65}{66}\right)$$
$$\chi_{804}(65,\cdot)$$ 804.be 66 no $$-1$$ $$1$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{59}{66}\right)$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{31}{66}\right)$$ $$e\left(\frac{5}{33}\right)$$ $$e\left(\frac{61}{66}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{7}{33}\right)$$
$$\chi_{804}(71,\cdot)$$ 804.bd 66 yes $$1$$ $$1$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{13}{66}\right)$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{29}{66}\right)$$ $$e\left(\frac{53}{66}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{61}{66}\right)$$
$$\chi_{804}(73,\cdot)$$ 804.y 33 no $$1$$ $$1$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{16}{33}\right)$$
$$\chi_{804}(77,\cdot)$$ 804.be 66 no $$-1$$ $$1$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{53}{66}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{1}{66}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{19}{66}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{13}{33}\right)$$
$$\chi_{804}(79,\cdot)$$ 804.bf 66 no $$1$$ $$1$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{5}{33}\right)$$ $$e\left(\frac{53}{66}\right)$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{47}{66}\right)$$ $$e\left(\frac{59}{66}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{23}{33}\right)$$
$$\chi_{804}(83,\cdot)$$ 804.bd 66 yes $$1$$ $$1$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{59}{66}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{5}{33}\right)$$ $$e\left(\frac{25}{66}\right)$$ $$e\left(\frac{7}{66}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{23}{66}\right)$$
$$\chi_{804}(85,\cdot)$$ 804.bc 66 no $$-1$$ $$1$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{35}{66}\right)$$ $$e\left(\frac{41}{66}\right)$$ $$e\left(\frac{49}{66}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{17}{66}\right)$$
$$\chi_{804}(89,\cdot)$$ 804.v 22 no $$-1$$ $$1$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$-1$$ $$e\left(\frac{8}{11}\right)$$
$$\chi_{804}(91,\cdot)$$ 804.t 22 no $$-1$$ $$1$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$1$$ $$e\left(\frac{9}{22}\right)$$
$$\chi_{804}(95,\cdot)$$ 804.bb 66 yes $$-1$$ $$1$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{23}{66}\right)$$ $$e\left(\frac{13}{66}\right)$$ $$e\left(\frac{49}{66}\right)$$ $$e\left(\frac{19}{66}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{10}{33}\right)$$
$$\chi_{804}(97,\cdot)$$ 804.m 6 no $$-1$$ $$1$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$