Properties

 Modulus $1950$ Structure $$C_{2}\times C_{4}\times C_{60}$$ Order $480$

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Show commands: PariGP / SageMath

sage: H = DirichletGroup(1950)

pari: g = idealstar(,1950,2)

Character group

 sage: G.order()  pari: g.no Order = 480 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{4}\times C_{60}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{1950}(1301,\cdot)$, $\chi_{1950}(1327,\cdot)$, $\chi_{1950}(301,\cdot)$

First 32 of 480 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 $$-1$$ $$1$$ $$7$$ $$11$$ $$17$$ $$19$$ $$23$$ $$29$$ $$31$$ $$37$$ $$41$$ $$43$$
$$\chi_{1950}(1,\cdot)$$ 1950.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{1950}(7,\cdot)$$ 1950.bl 12 no $$1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$i$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$
$$\chi_{1950}(11,\cdot)$$ 1950.cw 60 no $$1$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{1950}(17,\cdot)$$ 1950.cz 60 no $$1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{1}{12}\right)$$
$$\chi_{1950}(19,\cdot)$$ 1950.cx 60 no $$-1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{1950}(23,\cdot)$$ 1950.cz 60 no $$1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{53}{60}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{11}{12}\right)$$
$$\chi_{1950}(29,\cdot)$$ 1950.cn 30 no $$-1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{1950}(31,\cdot)$$ 1950.cd 20 no $$-1$$ $$1$$ $$i$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$-1$$
$$\chi_{1950}(37,\cdot)$$ 1950.cq 60 no $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{11}{12}\right)$$
$$\chi_{1950}(41,\cdot)$$ 1950.cw 60 no $$1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{1950}(43,\cdot)$$ 1950.bs 12 no $$-1$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{7}{12}\right)$$
$$\chi_{1950}(47,\cdot)$$ 1950.ch 20 no $$-1$$ $$1$$ $$1$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$i$$
$$\chi_{1950}(49,\cdot)$$ 1950.y 6 no $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{1950}(53,\cdot)$$ 1950.cg 20 no $$1$$ $$1$$ $$-i$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$i$$
$$\chi_{1950}(59,\cdot)$$ 1950.cu 60 no $$1$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{43}{60}\right)$$ $$e\left(\frac{13}{60}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{1950}(61,\cdot)$$ 1950.bw 15 no $$1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{1950}(67,\cdot)$$ 1950.da 60 no $$1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{37}{60}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{11}{12}\right)$$
$$\chi_{1950}(71,\cdot)$$ 1950.cw 60 no $$1$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{53}{60}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{1950}(73,\cdot)$$ 1950.by 20 no $$1$$ $$1$$ $$-1$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$-i$$
$$\chi_{1950}(77,\cdot)$$ 1950.bz 20 no $$1$$ $$1$$ $$-i$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$-i$$
$$\chi_{1950}(79,\cdot)$$ 1950.bd 10 no $$1$$ $$1$$ $$-1$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$-1$$
$$\chi_{1950}(83,\cdot)$$ 1950.ch 20 no $$-1$$ $$1$$ $$1$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$-i$$
$$\chi_{1950}(89,\cdot)$$ 1950.cu 60 no $$1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{1950}(97,\cdot)$$ 1950.da 60 no $$1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{53}{60}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{49}{60}\right)$$ $$e\left(\frac{7}{12}\right)$$
$$\chi_{1950}(101,\cdot)$$ 1950.ba 6 no $$-1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{1950}(103,\cdot)$$ 1950.cf 20 no $$-1$$ $$1$$ $$i$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$i$$
$$\chi_{1950}(107,\cdot)$$ 1950.bt 12 no $$1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{12}\right)$$
$$\chi_{1950}(109,\cdot)$$ 1950.cb 20 no $$-1$$ $$1$$ $$-i$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$1$$
$$\chi_{1950}(113,\cdot)$$ 1950.cs 60 no $$1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{37}{60}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{13}{60}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{7}{12}\right)$$
$$\chi_{1950}(119,\cdot)$$ 1950.cu 60 no $$1$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{37}{60}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{1950}(121,\cdot)$$ 1950.cm 30 no $$1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{1950}(127,\cdot)$$ 1950.ct 60 no $$-1$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{53}{60}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{5}{12}\right)$$
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