Properties

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

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Show commands: Pari/GP / 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 = \(C_{60}\times C_{4}\times C_{2}\)
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 \(-1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{5}{12}\right)\)