# Properties

 Modulus 4026 Structure $$C_{60}\times C_{10}\times C_{2}$$ Order 1200

Show commands for: SageMath / Pari/GP

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

sage: H = DirichletGroup_conrey(4026)

pari: g = idealstar(,4026,2)

## Character group

 sage: G.order()  pari: g.no Order = 1200 sage: H.invariants()  pari: g.cyc Structure = $$C_{60}\times C_{10}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{4026}(3235,\cdot)$, $\chi_{4026}(1465,\cdot)$, $\chi_{4026}(1343,\cdot)$

## First 32 of 1200 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 13 17 19 23 25 29 31 35
$$\chi_{4026}(1,\cdot)$$ 4026.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{4026}(5,\cdot)$$ 4026.fl 30 no $$-1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{14}{15}\right)$$
$$\chi_{4026}(7,\cdot)$$ 4026.fr 60 no $$1$$ $$1$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{41}{60}\right)$$
$$\chi_{4026}(13,\cdot)$$ 4026.ez 30 no $$-1$$ $$1$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$1$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{13}{30}\right)$$
$$\chi_{4026}(17,\cdot)$$ 4026.fo 60 no $$-1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{13}{60}\right)$$ $$e\left(\frac{37}{60}\right)$$ $$e\left(\frac{1}{60}\right)$$
$$\chi_{4026}(19,\cdot)$$ 4026.ev 30 no $$-1$$ $$1$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{1}{15}\right)$$
$$\chi_{4026}(23,\cdot)$$ 4026.dl 20 no $$1$$ $$1$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$1$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$-i$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{19}{20}\right)$$
$$\chi_{4026}(25,\cdot)$$ 4026.cu 15 no $$1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{13}{15}\right)$$
$$\chi_{4026}(29,\cdot)$$ 4026.ge 60 no $$-1$$ $$1$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{13}{60}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$-i$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{49}{60}\right)$$ $$e\left(\frac{37}{60}\right)$$ $$e\left(\frac{37}{60}\right)$$
$$\chi_{4026}(31,\cdot)$$ 4026.fw 60 no $$-1$$ $$1$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{37}{60}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{37}{60}\right)$$ $$e\left(\frac{37}{60}\right)$$ $$e\left(\frac{5}{12}\right)$$
$$\chi_{4026}(35,\cdot)$$ 4026.gd 60 no $$-1$$ $$1$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{37}{60}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{37}{60}\right)$$
$$\chi_{4026}(37,\cdot)$$ 4026.dn 20 no $$-1$$ $$1$$ $$e\left(\frac{1}{10}\right)$$ $$i$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$-1$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{7}{20}\right)$$
$$\chi_{4026}(41,\cdot)$$ 4026.bb 10 no $$1$$ $$1$$ $$-1$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$-1$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$1$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$
$$\chi_{4026}(43,\cdot)$$ 4026.fz 60 no $$1$$ $$1$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{37}{60}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{23}{60}\right)$$
$$\chi_{4026}(47,\cdot)$$ 4026.ep 30 no $$-1$$ $$1$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$-1$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{29}{30}\right)$$
$$\chi_{4026}(49,\cdot)$$ 4026.fj 30 no $$1$$ $$1$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{11}{30}\right)$$
$$\chi_{4026}(53,\cdot)$$ 4026.dw 20 no $$1$$ $$1$$ $$1$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$-i$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$1$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{3}{20}\right)$$
$$\chi_{4026}(59,\cdot)$$ 4026.fp 60 no $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{43}{60}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{23}{60}\right)$$
$$\chi_{4026}(65,\cdot)$$ 4026.es 30 no $$1$$ $$1$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{11}{30}\right)$$
$$\chi_{4026}(67,\cdot)$$ 4026.fq 60 no $$-1$$ $$1$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{43}{60}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{53}{60}\right)$$ $$e\left(\frac{17}{60}\right)$$
$$\chi_{4026}(71,\cdot)$$ 4026.gi 60 no $$1$$ $$1$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{43}{60}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{7}{60}\right)$$
$$\chi_{4026}(73,\cdot)$$ 4026.ey 30 no $$-1$$ $$1$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{4026}(79,\cdot)$$ 4026.gk 60 no $$1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{29}{60}\right)$$
$$\chi_{4026}(83,\cdot)$$ 4026.eg 30 no $$1$$ $$1$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{4026}(85,\cdot)$$ 4026.db 20 no $$1$$ $$1$$ $$-1$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$-i$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$1$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{19}{20}\right)$$
$$\chi_{4026}(89,\cdot)$$ 4026.dl 20 no $$1$$ $$1$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$1$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$i$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{17}{20}\right)$$
$$\chi_{4026}(91,\cdot)$$ 4026.gl 60 no $$-1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{7}{60}\right)$$
$$\chi_{4026}(95,\cdot)$$ 4026.ci 10 no $$1$$ $$1$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$1$$
$$\chi_{4026}(97,\cdot)$$ 4026.fb 30 no $$1$$ $$1$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{4026}(101,\cdot)$$ 4026.ge 60 no $$-1$$ $$1$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$i$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{11}{60}\right)$$
$$\chi_{4026}(103,\cdot)$$ 4026.cu 15 no $$1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{7}{15}\right)$$
$$\chi_{4026}(107,\cdot)$$ 4026.en 30 no $$1$$ $$1$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{13}{30}\right)$$