# Properties

 Modulus $1520$ Structure $$C_{36}\times C_{4}\times C_{2}\times C_{2}$$ Order $576$

Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(1520)

pari: g = idealstar(,1520,2)

## Character group

 sage: G.order()  pari: g.no Order = 576 sage: H.invariants()  pari: g.cyc Structure = $$C_{36}\times C_{4}\times C_{2}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{1520}(191,\cdot)$, $\chi_{1520}(1141,\cdot)$, $\chi_{1520}(1217,\cdot)$, $\chi_{1520}(401,\cdot)$

## First 32 of 576 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 $$-1$$ $$1$$ $$3$$ $$7$$ $$9$$ $$11$$ $$13$$ $$17$$ $$21$$ $$23$$ $$27$$ $$29$$
$$\chi_{1520}(1,\cdot)$$ 1520.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{1520}(3,\cdot)$$ 1520.ef 36 yes $$-1$$ $$1$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{35}{36}\right)$$ $$e\left(\frac{17}{36}\right)$$ $$e\left(\frac{25}{36}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{36}\right)$$
$$\chi_{1520}(7,\cdot)$$ 1520.cu 12 no $$1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$-i$$ $$e\left(\frac{1}{6}\right)$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$i$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{1520}(9,\cdot)$$ 1520.dp 18 no $$1$$ $$1$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{18}\right)$$
$$\chi_{1520}(11,\cdot)$$ 1520.cv 12 no $$-1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$-i$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$-i$$ $$e\left(\frac{1}{12}\right)$$
$$\chi_{1520}(13,\cdot)$$ 1520.ed 36 yes $$1$$ $$1$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{19}{36}\right)$$ $$e\left(\frac{1}{36}\right)$$ $$e\left(\frac{11}{36}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{17}{36}\right)$$
$$\chi_{1520}(17,\cdot)$$ 1520.dw 36 no $$-1$$ $$1$$ $$e\left(\frac{35}{36}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{19}{36}\right)$$ $$e\left(\frac{29}{36}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{31}{36}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{17}{18}\right)$$
$$\chi_{1520}(21,\cdot)$$ 1520.eo 36 no $$-1$$ $$1$$ $$e\left(\frac{17}{36}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{36}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{11}{36}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{25}{36}\right)$$
$$\chi_{1520}(23,\cdot)$$ 1520.dz 36 no $$1$$ $$1$$ $$e\left(\frac{25}{36}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{11}{36}\right)$$ $$e\left(\frac{31}{36}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{35}{36}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{8}{9}\right)$$
$$\chi_{1520}(27,\cdot)$$ 1520.da 12 yes $$-1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$i$$ $$e\left(\frac{1}{3}\right)$$ $$-i$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$-1$$ $$e\left(\frac{1}{12}\right)$$
$$\chi_{1520}(29,\cdot)$$ 1520.du 36 yes $$-1$$ $$1$$ $$e\left(\frac{1}{36}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{17}{36}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{25}{36}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{11}{36}\right)$$
$$\chi_{1520}(31,\cdot)$$ 1520.bq 6 no $$1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$1$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{1520}(33,\cdot)$$ 1520.dy 36 no $$1$$ $$1$$ $$e\left(\frac{11}{36}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{36}\right)$$ $$e\left(\frac{23}{36}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{1}{36}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{9}\right)$$
$$\chi_{1520}(37,\cdot)$$ 1520.bn 4 yes $$1$$ $$1$$ $$1$$ $$-i$$ $$1$$ $$i$$ $$1$$ $$i$$ $$-i$$ $$i$$ $$1$$ $$-i$$
$$\chi_{1520}(39,\cdot)$$ 1520.i 2 no $$-1$$ $$1$$ $$-1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$-1$$ $$-1$$ $$1$$ $$-1$$ $$-1$$
$$\chi_{1520}(41,\cdot)$$ 1520.dh 18 no $$-1$$ $$1$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{9}\right)$$
$$\chi_{1520}(43,\cdot)$$ 1520.eh 36 yes $$1$$ $$1$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{23}{36}\right)$$ $$e\left(\frac{5}{36}\right)$$ $$e\left(\frac{1}{36}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{13}{36}\right)$$
$$\chi_{1520}(47,\cdot)$$ 1520.el 36 no $$1$$ $$1$$ $$e\left(\frac{1}{36}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{35}{36}\right)$$ $$e\left(\frac{25}{36}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{5}{36}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{18}\right)$$
$$\chi_{1520}(49,\cdot)$$ 1520.bz 6 no $$1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{1520}(51,\cdot)$$ 1520.dt 36 no $$1$$ $$1$$ $$e\left(\frac{13}{36}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{23}{36}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{1}{36}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{35}{36}\right)$$
$$\chi_{1520}(53,\cdot)$$ 1520.eg 36 yes $$1$$ $$1$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{31}{36}\right)$$ $$e\left(\frac{31}{36}\right)$$ $$e\left(\frac{35}{36}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{23}{36}\right)$$
$$\chi_{1520}(59,\cdot)$$ 1520.en 36 yes $$1$$ $$1$$ $$e\left(\frac{17}{36}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{19}{36}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{11}{36}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{25}{36}\right)$$
$$\chi_{1520}(61,\cdot)$$ 1520.em 36 no $$1$$ $$1$$ $$e\left(\frac{25}{36}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{29}{36}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{31}{36}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{5}{36}\right)$$
$$\chi_{1520}(63,\cdot)$$ 1520.el 36 no $$1$$ $$1$$ $$e\left(\frac{31}{36}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{36}\right)$$ $$e\left(\frac{19}{36}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{11}{36}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{13}{18}\right)$$
$$\chi_{1520}(67,\cdot)$$ 1520.ea 36 yes $$-1$$ $$1$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{25}{36}\right)$$ $$e\left(\frac{25}{36}\right)$$ $$e\left(\frac{23}{36}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{29}{36}\right)$$
$$\chi_{1520}(69,\cdot)$$ 1520.cx 12 yes $$-1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$i$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$i$$ $$e\left(\frac{11}{12}\right)$$
$$\chi_{1520}(71,\cdot)$$ 1520.dn 18 no $$1$$ $$1$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{9}\right)$$
$$\chi_{1520}(73,\cdot)$$ 1520.ei 36 no $$-1$$ $$1$$ $$e\left(\frac{23}{36}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{31}{36}\right)$$ $$e\left(\frac{35}{36}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{25}{36}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{7}{9}\right)$$
$$\chi_{1520}(77,\cdot)$$ 1520.bo 4 no $$-1$$ $$1$$ $$1$$ $$-i$$ $$1$$ $$-i$$ $$1$$ $$i$$ $$-i$$ $$i$$ $$1$$ $$-i$$
$$\chi_{1520}(79,\cdot)$$ 1520.dj 18 no $$1$$ $$1$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{18}\right)$$
$$\chi_{1520}(81,\cdot)$$ 1520.ce 9 no $$1$$ $$1$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{9}\right)$$
$$\chi_{1520}(83,\cdot)$$ 1520.ch 12 yes $$1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$-i$$ $$e\left(\frac{2}{3}\right)$$ $$i$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$1$$ $$e\left(\frac{5}{12}\right)$$