# Properties

 Modulus $300$ Structure $$C_{2}\times C_{2}\times C_{20}$$ Order $80$

Show commands: PariGP / SageMath

sage: H = DirichletGroup(300)

pari: g = idealstar(,300,2)

## Character group

 sage: G.order()  pari: g.no Order = 80 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{2}\times C_{20}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{300}(151,\cdot)$, $\chi_{300}(101,\cdot)$, $\chi_{300}(277,\cdot)$

## First 32 of 80 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 $$-1$$ $$1$$ $$7$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$ $$29$$ $$31$$ $$37$$ $$41$$
$$\chi_{300}(1,\cdot)$$ 300.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{300}(7,\cdot)$$ 300.j 4 no $$1$$ $$1$$ $$-i$$ $$-1$$ $$-i$$ $$i$$ $$1$$ $$i$$ $$-1$$ $$-1$$ $$i$$ $$1$$
$$\chi_{300}(11,\cdot)$$ 300.n 10 yes $$1$$ $$1$$ $$-1$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$
$$\chi_{300}(13,\cdot)$$ 300.v 20 no $$-1$$ $$1$$ $$-i$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{4}{5}\right)$$
$$\chi_{300}(17,\cdot)$$ 300.x 20 no $$1$$ $$1$$ $$i$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$
$$\chi_{300}(19,\cdot)$$ 300.t 10 no $$-1$$ $$1$$ $$1$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$
$$\chi_{300}(23,\cdot)$$ 300.u 20 yes $$-1$$ $$1$$ $$i$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$
$$\chi_{300}(29,\cdot)$$ 300.q 10 no $$-1$$ $$1$$ $$-1$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$
$$\chi_{300}(31,\cdot)$$ 300.p 10 no $$-1$$ $$1$$ $$-1$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$
$$\chi_{300}(37,\cdot)$$ 300.v 20 no $$-1$$ $$1$$ $$i$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{4}{5}\right)$$
$$\chi_{300}(41,\cdot)$$ 300.s 10 no $$-1$$ $$1$$ $$1$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$
$$\chi_{300}(43,\cdot)$$ 300.j 4 no $$1$$ $$1$$ $$i$$ $$-1$$ $$i$$ $$-i$$ $$1$$ $$-i$$ $$-1$$ $$-1$$ $$-i$$ $$1$$
$$\chi_{300}(47,\cdot)$$ 300.u 20 yes $$-1$$ $$1$$ $$-i$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$
$$\chi_{300}(49,\cdot)$$ 300.d 2 no $$1$$ $$1$$ $$-1$$ $$1$$ $$-1$$ $$-1$$ $$1$$ $$-1$$ $$1$$ $$1$$ $$-1$$ $$1$$
$$\chi_{300}(53,\cdot)$$ 300.x 20 no $$1$$ $$1$$ $$-i$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$
$$\chi_{300}(59,\cdot)$$ 300.r 10 yes $$1$$ $$1$$ $$1$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$
$$\chi_{300}(61,\cdot)$$ 300.m 5 no $$1$$ $$1$$ $$1$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$
$$\chi_{300}(67,\cdot)$$ 300.w 20 no $$1$$ $$1$$ $$-i$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$
$$\chi_{300}(71,\cdot)$$ 300.n 10 yes $$1$$ $$1$$ $$-1$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$
$$\chi_{300}(73,\cdot)$$ 300.v 20 no $$-1$$ $$1$$ $$-i$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{1}{5}\right)$$
$$\chi_{300}(77,\cdot)$$ 300.x 20 no $$1$$ $$1$$ $$i$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$
$$\chi_{300}(79,\cdot)$$ 300.t 10 no $$-1$$ $$1$$ $$1$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$
$$\chi_{300}(83,\cdot)$$ 300.u 20 yes $$-1$$ $$1$$ $$i$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$
$$\chi_{300}(89,\cdot)$$ 300.q 10 no $$-1$$ $$1$$ $$-1$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$
$$\chi_{300}(91,\cdot)$$ 300.p 10 no $$-1$$ $$1$$ $$-1$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$
$$\chi_{300}(97,\cdot)$$ 300.v 20 no $$-1$$ $$1$$ $$i$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$
$$\chi_{300}(101,\cdot)$$ 300.g 2 no $$-1$$ $$1$$ $$1$$ $$-1$$ $$1$$ $$-1$$ $$1$$ $$-1$$ $$-1$$ $$1$$ $$1$$ $$-1$$
$$\chi_{300}(103,\cdot)$$ 300.w 20 no $$1$$ $$1$$ $$i$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$
$$\chi_{300}(107,\cdot)$$ 300.l 4 no $$-1$$ $$1$$ $$-i$$ $$1$$ $$-i$$ $$-i$$ $$1$$ $$-i$$ $$1$$ $$-1$$ $$i$$ $$-1$$
$$\chi_{300}(109,\cdot)$$ 300.o 10 no $$1$$ $$1$$ $$-1$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$
$$\chi_{300}(113,\cdot)$$ 300.x 20 no $$1$$ $$1$$ $$-i$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$
$$\chi_{300}(119,\cdot)$$ 300.r 10 yes $$1$$ $$1$$ $$1$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$