Properties

 Modulus $102$ Structure $$C_{2}\times C_{16}$$ Order $32$

Show commands: PariGP / SageMath

sage: H = DirichletGroup(102)

pari: g = idealstar(,102,2)

Character group

 sage: G.order()  pari: g.no Order = 32 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{16}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{102}(35,\cdot)$, $\chi_{102}(37,\cdot)$

First 32 of 32 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 $$-1$$ $$1$$ $$5$$ $$7$$ $$11$$ $$13$$ $$19$$ $$23$$ $$25$$ $$29$$ $$31$$ $$35$$
$$\chi_{102}(1,\cdot)$$ 102.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{102}(5,\cdot)$$ 102.i 16 no $$1$$ $$1$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$i$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$-1$$
$$\chi_{102}(7,\cdot)$$ 102.j 16 no $$-1$$ $$1$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$-i$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$1$$
$$\chi_{102}(11,\cdot)$$ 102.i 16 no $$1$$ $$1$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$-i$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$-1$$
$$\chi_{102}(13,\cdot)$$ 102.f 4 no $$1$$ $$1$$ $$i$$ $$-i$$ $$-i$$ $$1$$ $$-1$$ $$-i$$ $$-1$$ $$i$$ $$i$$ $$1$$
$$\chi_{102}(19,\cdot)$$ 102.h 8 no $$1$$ $$1$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$-1$$ $$i$$ $$e\left(\frac{1}{8}\right)$$ $$-i$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$1$$
$$\chi_{102}(23,\cdot)$$ 102.i 16 no $$1$$ $$1$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$-i$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$-1$$
$$\chi_{102}(25,\cdot)$$ 102.h 8 no $$1$$ $$1$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$-1$$ $$-i$$ $$e\left(\frac{3}{8}\right)$$ $$i$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$1$$
$$\chi_{102}(29,\cdot)$$ 102.i 16 no $$1$$ $$1$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$i$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$-1$$
$$\chi_{102}(31,\cdot)$$ 102.j 16 no $$-1$$ $$1$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$i$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$1$$
$$\chi_{102}(35,\cdot)$$ 102.c 2 no $$-1$$ $$1$$ $$-1$$ $$1$$ $$-1$$ $$1$$ $$1$$ $$-1$$ $$1$$ $$-1$$ $$1$$ $$-1$$
$$\chi_{102}(37,\cdot)$$ 102.j 16 no $$-1$$ $$1$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$i$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$1$$
$$\chi_{102}(41,\cdot)$$ 102.i 16 no $$1$$ $$1$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$-i$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$-1$$
$$\chi_{102}(43,\cdot)$$ 102.h 8 no $$1$$ $$1$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$-1$$ $$-i$$ $$e\left(\frac{7}{8}\right)$$ $$i$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$1$$
$$\chi_{102}(47,\cdot)$$ 102.e 4 no $$-1$$ $$1$$ $$-i$$ $$-i$$ $$i$$ $$1$$ $$-1$$ $$i$$ $$-1$$ $$-i$$ $$i$$ $$-1$$
$$\chi_{102}(49,\cdot)$$ 102.h 8 no $$1$$ $$1$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$-1$$ $$i$$ $$e\left(\frac{5}{8}\right)$$ $$-i$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$1$$
$$\chi_{102}(53,\cdot)$$ 102.g 8 no $$-1$$ $$1$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$-1$$ $$i$$ $$e\left(\frac{5}{8}\right)$$ $$-i$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$-1$$
$$\chi_{102}(55,\cdot)$$ 102.f 4 no $$1$$ $$1$$ $$-i$$ $$i$$ $$i$$ $$1$$ $$-1$$ $$i$$ $$-1$$ $$-i$$ $$-i$$ $$1$$
$$\chi_{102}(59,\cdot)$$ 102.g 8 no $$-1$$ $$1$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$-1$$ $$-i$$ $$e\left(\frac{7}{8}\right)$$ $$i$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$-1$$
$$\chi_{102}(61,\cdot)$$ 102.j 16 no $$-1$$ $$1$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$-i$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$1$$
$$\chi_{102}(65,\cdot)$$ 102.i 16 no $$1$$ $$1$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$i$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$-1$$
$$\chi_{102}(67,\cdot)$$ 102.b 2 no $$1$$ $$1$$ $$-1$$ $$-1$$ $$-1$$ $$1$$ $$1$$ $$-1$$ $$1$$ $$-1$$ $$-1$$ $$1$$
$$\chi_{102}(71,\cdot)$$ 102.i 16 no $$1$$ $$1$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$i$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$-1$$
$$\chi_{102}(73,\cdot)$$ 102.j 16 no $$-1$$ $$1$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$i$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$1$$
$$\chi_{102}(77,\cdot)$$ 102.g 8 no $$-1$$ $$1$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$-1$$ $$-i$$ $$e\left(\frac{3}{8}\right)$$ $$i$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$-1$$
$$\chi_{102}(79,\cdot)$$ 102.j 16 no $$-1$$ $$1$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$-i$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$1$$
$$\chi_{102}(83,\cdot)$$ 102.g 8 no $$-1$$ $$1$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$-1$$ $$i$$ $$e\left(\frac{1}{8}\right)$$ $$-i$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$-1$$
$$\chi_{102}(89,\cdot)$$ 102.e 4 no $$-1$$ $$1$$ $$i$$ $$i$$ $$-i$$ $$1$$ $$-1$$ $$-i$$ $$-1$$ $$i$$ $$-i$$ $$-1$$
$$\chi_{102}(91,\cdot)$$ 102.j 16 no $$-1$$ $$1$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$-i$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$1$$
$$\chi_{102}(95,\cdot)$$ 102.i 16 no $$1$$ $$1$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$-i$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$-1$$
$$\chi_{102}(97,\cdot)$$ 102.j 16 no $$-1$$ $$1$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$i$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$1$$
$$\chi_{102}(101,\cdot)$$ 102.d 2 no $$-1$$ $$1$$ $$1$$ $$-1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$-1$$ $$-1$$