Properties

 Modulus 151 Structure $$C_{150}$$ Order 150

Show commands for: SageMath / Pari/GP

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
sage: H = DirichletGroup_conrey(151)
pari: g = idealstar(,151,2)

Character group

 sage: G.order() pari: g.no Order = 150 sage: H.invariants() pari: g.cyc Structure = $$C_{150}$$ sage: H.gens() pari: g.gen Generators = $\chi_{151}(6,\cdot)$

First 32 of 150 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 2 3 4 5 6 7 8 9 10 11
$$\chi_{151}(1,\cdot)$$ 151.a 1 No $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{151}(2,\cdot)$$ 151.g 15 Yes $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$1$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{13}{15}\right)$$
$$\chi_{151}(3,\cdot)$$ 151.j 50 Yes $$-1$$ $$1$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{37}{50}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{12}{25}\right)$$ $$e\left(\frac{27}{50}\right)$$ $$e\left(\frac{9}{50}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{12}{25}\right)$$ $$e\left(\frac{7}{25}\right)$$ $$e\left(\frac{19}{25}\right)$$
$$\chi_{151}(4,\cdot)$$ 151.g 15 Yes $$1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$1$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{11}{15}\right)$$
$$\chi_{151}(5,\cdot)$$ 151.k 75 Yes $$1$$ $$1$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{12}{25}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{47}{75}\right)$$ $$e\left(\frac{56}{75}\right)$$ $$e\left(\frac{2}{75}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{24}{25}\right)$$ $$e\left(\frac{67}{75}\right)$$ $$e\left(\frac{14}{75}\right)$$
$$\chi_{151}(6,\cdot)$$ 151.l 150 Yes $$-1$$ $$1$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{27}{50}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{56}{75}\right)$$ $$e\left(\frac{1}{150}\right)$$ $$e\left(\frac{67}{150}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{2}{25}\right)$$ $$e\left(\frac{16}{75}\right)$$ $$e\left(\frac{47}{75}\right)$$
$$\chi_{151}(7,\cdot)$$ 151.l 150 Yes $$-1$$ $$1$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{9}{50}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{2}{75}\right)$$ $$e\left(\frac{67}{150}\right)$$ $$e\left(\frac{139}{150}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{9}{25}\right)$$ $$e\left(\frac{22}{75}\right)$$ $$e\left(\frac{74}{75}\right)$$
$$\chi_{151}(8,\cdot)$$ 151.d 5 Yes $$1$$ $$1$$ $$1$$ $$e\left(\frac{2}{5}\right)$$ $$1$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$1$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$
$$\chi_{151}(9,\cdot)$$ 151.h 25 Yes $$1$$ $$1$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{12}{25}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{24}{25}\right)$$ $$e\left(\frac{2}{25}\right)$$ $$e\left(\frac{9}{25}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{24}{25}\right)$$ $$e\left(\frac{14}{25}\right)$$ $$e\left(\frac{13}{25}\right)$$
$$\chi_{151}(10,\cdot)$$ 151.k 75 Yes $$1$$ $$1$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{7}{25}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{67}{75}\right)$$ $$e\left(\frac{16}{75}\right)$$ $$e\left(\frac{22}{75}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{14}{25}\right)$$ $$e\left(\frac{62}{75}\right)$$ $$e\left(\frac{4}{75}\right)$$
$$\chi_{151}(11,\cdot)$$ 151.k 75 Yes $$1$$ $$1$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{19}{25}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{14}{75}\right)$$ $$e\left(\frac{47}{75}\right)$$ $$e\left(\frac{74}{75}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{13}{25}\right)$$ $$e\left(\frac{4}{75}\right)$$ $$e\left(\frac{68}{75}\right)$$
$$\chi_{151}(12,\cdot)$$ 151.l 150 Yes $$-1$$ $$1$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{17}{50}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{1}{75}\right)$$ $$e\left(\frac{71}{150}\right)$$ $$e\left(\frac{107}{150}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{17}{25}\right)$$ $$e\left(\frac{11}{75}\right)$$ $$e\left(\frac{37}{75}\right)$$
$$\chi_{151}(13,\cdot)$$ 151.l 150 Yes $$-1$$ $$1$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{7}{50}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{46}{75}\right)$$ $$e\left(\frac{41}{150}\right)$$ $$e\left(\frac{47}{150}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{7}{25}\right)$$ $$e\left(\frac{56}{75}\right)$$ $$e\left(\frac{52}{75}\right)$$
$$\chi_{151}(14,\cdot)$$ 151.l 150 Yes $$-1$$ $$1$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{49}{50}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{22}{75}\right)$$ $$e\left(\frac{137}{150}\right)$$ $$e\left(\frac{29}{150}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{24}{25}\right)$$ $$e\left(\frac{17}{75}\right)$$ $$e\left(\frac{64}{75}\right)$$
$$\chi_{151}(15,\cdot)$$ 151.l 150 Yes $$-1$$ $$1$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{11}{50}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{8}{75}\right)$$ $$e\left(\frac{43}{150}\right)$$ $$e\left(\frac{31}{150}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{11}{25}\right)$$ $$e\left(\frac{13}{75}\right)$$ $$e\left(\frac{71}{75}\right)$$
$$\chi_{151}(16,\cdot)$$ 151.g 15 Yes $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$1$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{7}{15}\right)$$
$$\chi_{151}(17,\cdot)$$ 151.k 75 Yes $$1$$ $$1$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{8}{25}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{23}{75}\right)$$ $$e\left(\frac{29}{75}\right)$$ $$e\left(\frac{68}{75}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{16}{25}\right)$$ $$e\left(\frac{28}{75}\right)$$ $$e\left(\frac{26}{75}\right)$$
$$\chi_{151}(18,\cdot)$$ 151.k 75 Yes $$1$$ $$1$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{7}{25}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{17}{75}\right)$$ $$e\left(\frac{41}{75}\right)$$ $$e\left(\frac{47}{75}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{14}{25}\right)$$ $$e\left(\frac{37}{75}\right)$$ $$e\left(\frac{29}{75}\right)$$
$$\chi_{151}(19,\cdot)$$ 151.d 5 Yes $$1$$ $$1$$ $$1$$ $$e\left(\frac{3}{5}\right)$$ $$1$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$1$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$
$$\chi_{151}(20,\cdot)$$ 151.h 25 Yes $$1$$ $$1$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{2}{25}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{4}{25}\right)$$ $$e\left(\frac{17}{25}\right)$$ $$e\left(\frac{14}{25}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{4}{25}\right)$$ $$e\left(\frac{19}{25}\right)$$ $$e\left(\frac{23}{25}\right)$$
$$\chi_{151}(21,\cdot)$$ 151.k 75 Yes $$1$$ $$1$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{23}{25}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{38}{75}\right)$$ $$e\left(\frac{74}{75}\right)$$ $$e\left(\frac{8}{75}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{21}{25}\right)$$ $$e\left(\frac{43}{75}\right)$$ $$e\left(\frac{56}{75}\right)$$
$$\chi_{151}(22,\cdot)$$ 151.k 75 Yes $$1$$ $$1$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{14}{25}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{34}{75}\right)$$ $$e\left(\frac{7}{75}\right)$$ $$e\left(\frac{19}{75}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{3}{25}\right)$$ $$e\left(\frac{74}{75}\right)$$ $$e\left(\frac{58}{75}\right)$$
$$\chi_{151}(23,\cdot)$$ 151.i 30 Yes $$-1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$1$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{1}{15}\right)$$
$$\chi_{151}(24,\cdot)$$ 151.j 50 Yes $$-1$$ $$1$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{7}{50}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{7}{25}\right)$$ $$e\left(\frac{47}{50}\right)$$ $$e\left(\frac{49}{50}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{7}{25}\right)$$ $$e\left(\frac{2}{25}\right)$$ $$e\left(\frac{9}{25}\right)$$
$$\chi_{151}(25,\cdot)$$ 151.k 75 Yes $$1$$ $$1$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{24}{25}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{19}{75}\right)$$ $$e\left(\frac{37}{75}\right)$$ $$e\left(\frac{4}{75}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{23}{25}\right)$$ $$e\left(\frac{59}{75}\right)$$ $$e\left(\frac{28}{75}\right)$$
$$\chi_{151}(26,\cdot)$$ 151.j 50 Yes $$-1$$ $$1$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{47}{50}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{22}{25}\right)$$ $$e\left(\frac{37}{50}\right)$$ $$e\left(\frac{29}{50}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{22}{25}\right)$$ $$e\left(\frac{17}{25}\right)$$ $$e\left(\frac{14}{25}\right)$$
$$\chi_{151}(27,\cdot)$$ 151.j 50 Yes $$-1$$ $$1$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{11}{50}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{11}{25}\right)$$ $$e\left(\frac{31}{50}\right)$$ $$e\left(\frac{27}{50}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{11}{25}\right)$$ $$e\left(\frac{21}{25}\right)$$ $$e\left(\frac{7}{25}\right)$$
$$\chi_{151}(28,\cdot)$$ 151.j 50 Yes $$-1$$ $$1$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{39}{50}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{14}{25}\right)$$ $$e\left(\frac{19}{50}\right)$$ $$e\left(\frac{23}{50}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{14}{25}\right)$$ $$e\left(\frac{4}{25}\right)$$ $$e\left(\frac{18}{25}\right)$$
$$\chi_{151}(29,\cdot)$$ 151.h 25 Yes $$1$$ $$1$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{14}{25}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{3}{25}\right)$$ $$e\left(\frac{19}{25}\right)$$ $$e\left(\frac{23}{25}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{3}{25}\right)$$ $$e\left(\frac{8}{25}\right)$$ $$e\left(\frac{11}{25}\right)$$
$$\chi_{151}(30,\cdot)$$ 151.l 150 Yes $$-1$$ $$1$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{1}{50}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{28}{75}\right)$$ $$e\left(\frac{113}{150}\right)$$ $$e\left(\frac{71}{150}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{1}{25}\right)$$ $$e\left(\frac{8}{75}\right)$$ $$e\left(\frac{61}{75}\right)$$
$$\chi_{151}(31,\cdot)$$ 151.k 75 Yes $$1$$ $$1$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{3}{25}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{68}{75}\right)$$ $$e\left(\frac{14}{75}\right)$$ $$e\left(\frac{38}{75}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{6}{25}\right)$$ $$e\left(\frac{73}{75}\right)$$ $$e\left(\frac{41}{75}\right)$$
$$\chi_{151}(32,\cdot)$$ 151.c 3 Yes $$1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$