# Properties

 Modulus $145$ Structure $$C_{28}\times C_{4}$$ Order $112$

Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(145)

pari: g = idealstar(,145,2)

## Character group

 sage: G.order()  pari: g.no Order = 112 sage: H.invariants()  pari: g.cyc Structure = $$C_{28}\times C_{4}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{145}(117,\cdot)$, $\chi_{145}(31,\cdot)$

## First 32 of 112 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 $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$6$$ $$7$$ $$8$$ $$9$$ $$11$$ $$12$$ $$13$$
$$\chi_{145}(1,\cdot)$$ 145.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{145}(2,\cdot)$$ 145.o 28 yes $$1$$ $$1$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{19}{28}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{25}{28}\right)$$ $$-1$$ $$e\left(\frac{11}{28}\right)$$
$$\chi_{145}(3,\cdot)$$ 145.t 28 yes $$1$$ $$1$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{25}{28}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{13}{28}\right)$$ $$1$$ $$e\left(\frac{13}{28}\right)$$
$$\chi_{145}(4,\cdot)$$ 145.l 14 yes $$1$$ $$1$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$1$$ $$e\left(\frac{11}{14}\right)$$
$$\chi_{145}(6,\cdot)$$ 145.m 14 no $$1$$ $$1$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$-1$$ $$e\left(\frac{6}{7}\right)$$
$$\chi_{145}(7,\cdot)$$ 145.p 28 yes $$-1$$ $$1$$ $$e\left(\frac{19}{28}\right)$$ $$e\left(\frac{25}{28}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$e\left(\frac{1}{28}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$i$$ $$e\left(\frac{13}{28}\right)$$
$$\chi_{145}(8,\cdot)$$ 145.o 28 yes $$1$$ $$1$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{1}{28}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{19}{28}\right)$$ $$-1$$ $$e\left(\frac{5}{28}\right)$$
$$\chi_{145}(9,\cdot)$$ 145.l 14 yes $$1$$ $$1$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$1$$ $$e\left(\frac{13}{14}\right)$$
$$\chi_{145}(11,\cdot)$$ 145.r 28 no $$-1$$ $$1$$ $$e\left(\frac{25}{28}\right)$$ $$e\left(\frac{13}{28}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{19}{28}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$i$$ $$e\left(\frac{1}{14}\right)$$
$$\chi_{145}(12,\cdot)$$ 145.e 4 yes $$1$$ $$1$$ $$-1$$ $$1$$ $$1$$ $$-1$$ $$i$$ $$-1$$ $$1$$ $$i$$ $$1$$ $$i$$
$$\chi_{145}(13,\cdot)$$ 145.q 28 yes $$-1$$ $$1$$ $$e\left(\frac{11}{28}\right)$$ $$e\left(\frac{13}{28}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{13}{28}\right)$$ $$e\left(\frac{5}{28}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$i$$ $$e\left(\frac{23}{28}\right)$$
$$\chi_{145}(14,\cdot)$$ 145.s 28 yes $$-1$$ $$1$$ $$e\left(\frac{27}{28}\right)$$ $$e\left(\frac{23}{28}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{25}{28}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{17}{28}\right)$$ $$-i$$ $$e\left(\frac{6}{7}\right)$$
$$\chi_{145}(16,\cdot)$$ 145.k 7 no $$1$$ $$1$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$1$$ $$e\left(\frac{4}{7}\right)$$
$$\chi_{145}(17,\cdot)$$ 145.j 4 yes $$1$$ $$1$$ $$1$$ $$-1$$ $$1$$ $$-1$$ $$i$$ $$1$$ $$1$$ $$-i$$ $$-1$$ $$i$$
$$\chi_{145}(18,\cdot)$$ 145.o 28 yes $$1$$ $$1$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{13}{28}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{23}{28}\right)$$ $$-1$$ $$e\left(\frac{9}{28}\right)$$
$$\chi_{145}(19,\cdot)$$ 145.s 28 yes $$-1$$ $$1$$ $$e\left(\frac{23}{28}\right)$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{13}{28}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{1}{28}\right)$$ $$-i$$ $$e\left(\frac{2}{7}\right)$$
$$\chi_{145}(21,\cdot)$$ 145.r 28 no $$-1$$ $$1$$ $$e\left(\frac{17}{28}\right)$$ $$e\left(\frac{1}{28}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{23}{28}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{5}{28}\right)$$ $$i$$ $$e\left(\frac{13}{14}\right)$$
$$\chi_{145}(22,\cdot)$$ 145.q 28 yes $$-1$$ $$1$$ $$e\left(\frac{5}{28}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$e\left(\frac{15}{28}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$-i$$ $$e\left(\frac{13}{28}\right)$$
$$\chi_{145}(23,\cdot)$$ 145.p 28 yes $$-1$$ $$1$$ $$e\left(\frac{13}{28}\right)$$ $$e\left(\frac{23}{28}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$-i$$ $$e\left(\frac{3}{28}\right)$$
$$\chi_{145}(24,\cdot)$$ 145.n 14 yes $$1$$ $$1$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$-1$$ $$e\left(\frac{9}{14}\right)$$
$$\chi_{145}(26,\cdot)$$ 145.r 28 no $$-1$$ $$1$$ $$e\left(\frac{19}{28}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{1}{28}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{27}{28}\right)$$ $$-i$$ $$e\left(\frac{3}{14}\right)$$
$$\chi_{145}(27,\cdot)$$ 145.t 28 yes $$1$$ $$1$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{19}{28}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$1$$ $$e\left(\frac{11}{28}\right)$$
$$\chi_{145}(28,\cdot)$$ 145.h 4 yes $$-1$$ $$1$$ $$i$$ $$-i$$ $$-1$$ $$1$$ $$-i$$ $$-i$$ $$-1$$ $$-1$$ $$i$$ $$i$$
$$\chi_{145}(31,\cdot)$$ 145.r 28 no $$-1$$ $$1$$ $$e\left(\frac{1}{28}\right)$$ $$e\left(\frac{5}{28}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{25}{28}\right)$$ $$i$$ $$e\left(\frac{9}{14}\right)$$
$$\chi_{145}(32,\cdot)$$ 145.o 28 yes $$1$$ $$1$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{13}{28}\right)$$ $$-1$$ $$e\left(\frac{27}{28}\right)$$
$$\chi_{145}(33,\cdot)$$ 145.q 28 yes $$-1$$ $$1$$ $$e\left(\frac{23}{28}\right)$$ $$e\left(\frac{17}{28}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{17}{28}\right)$$ $$e\left(\frac{13}{28}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$i$$ $$e\left(\frac{15}{28}\right)$$
$$\chi_{145}(34,\cdot)$$ 145.l 14 yes $$1$$ $$1$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$1$$ $$e\left(\frac{9}{14}\right)$$
$$\chi_{145}(36,\cdot)$$ 145.k 7 no $$1$$ $$1$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$1$$ $$e\left(\frac{5}{7}\right)$$
$$\chi_{145}(37,\cdot)$$ 145.t 28 yes $$1$$ $$1$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{15}{28}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{19}{28}\right)$$ $$1$$ $$e\left(\frac{19}{28}\right)$$
$$\chi_{145}(38,\cdot)$$ 145.q 28 yes $$-1$$ $$1$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{1}{28}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{1}{28}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$i$$ $$e\left(\frac{19}{28}\right)$$
$$\chi_{145}(39,\cdot)$$ 145.s 28 yes $$-1$$ $$1$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{17}{28}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{27}{28}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{15}{28}\right)$$ $$i$$ $$e\left(\frac{2}{7}\right)$$
$$\chi_{145}(41,\cdot)$$ 145.g 4 no $$-1$$ $$1$$ $$i$$ $$i$$ $$-1$$ $$-1$$ $$1$$ $$-i$$ $$-1$$ $$i$$ $$-i$$ $$-1$$