Properties

Modulus 225
Structure \(C_{60}\times C_{2}\)
Order 120

Learn more about

Show commands for: Pari/GP / SageMath

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(225)
 
pari: g = idealstar(,225,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 120
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{60}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{225}(77,\cdot)$, $\chi_{225}(224,\cdot)$

First 32 of 120 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 4 7 8 11 13 14 16 17 19
\(\chi_{225}(1,\cdot)\) 225.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{225}(2,\cdot)\) 225.w 60 yes \(1\) \(1\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{9}{10}\right)\)
\(\chi_{225}(4,\cdot)\) 225.u 30 yes \(1\) \(1\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{4}{5}\right)\)
\(\chi_{225}(7,\cdot)\) 225.o 12 no \(-1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{12}\right)\) \(-i\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(i\) \(-1\)
\(\chi_{225}(8,\cdot)\) 225.s 20 no \(1\) \(1\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(-i\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{7}{10}\right)\)
\(\chi_{225}(11,\cdot)\) 225.t 30 yes \(-1\) \(1\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{225}(13,\cdot)\) 225.x 60 yes \(-1\) \(1\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{1}{10}\right)\)
\(\chi_{225}(14,\cdot)\) 225.v 30 yes \(-1\) \(1\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{225}(16,\cdot)\) 225.q 15 yes \(1\) \(1\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{3}{5}\right)\)
\(\chi_{225}(17,\cdot)\) 225.s 20 no \(1\) \(1\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(i\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{7}{10}\right)\)
\(\chi_{225}(19,\cdot)\) 225.m 10 no \(1\) \(1\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(-1\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{5}\right)\)
\(\chi_{225}(22,\cdot)\) 225.x 60 yes \(-1\) \(1\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{3}{10}\right)\)
\(\chi_{225}(23,\cdot)\) 225.w 60 yes \(1\) \(1\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{9}{10}\right)\)
\(\chi_{225}(26,\cdot)\) 225.c 2 no \(-1\) \(1\) \(-1\) \(1\) \(1\) \(-1\) \(-1\) \(1\) \(-1\) \(1\) \(-1\) \(1\)
\(\chi_{225}(28,\cdot)\) 225.r 20 no \(-1\) \(1\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(-i\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{3}{10}\right)\)
\(\chi_{225}(29,\cdot)\) 225.v 30 yes \(-1\) \(1\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{4}{5}\right)\)
\(\chi_{225}(31,\cdot)\) 225.q 15 yes \(1\) \(1\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{5}\right)\)
\(\chi_{225}(32,\cdot)\) 225.p 12 no \(1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{12}\right)\) \(i\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(-i\) \(-1\)
\(\chi_{225}(34,\cdot)\) 225.u 30 yes \(1\) \(1\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{3}{5}\right)\)
\(\chi_{225}(37,\cdot)\) 225.r 20 no \(-1\) \(1\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(i\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{1}{10}\right)\)
\(\chi_{225}(38,\cdot)\) 225.w 60 yes \(1\) \(1\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{1}{10}\right)\)
\(\chi_{225}(41,\cdot)\) 225.t 30 yes \(-1\) \(1\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{3}{5}\right)\)
\(\chi_{225}(43,\cdot)\) 225.o 12 no \(-1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{12}\right)\) \(i\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(-i\) \(-1\)
\(\chi_{225}(44,\cdot)\) 225.l 10 no \(-1\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(-1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{5}\right)\)
\(\chi_{225}(46,\cdot)\) 225.h 5 no \(1\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{4}{5}\right)\)
\(\chi_{225}(47,\cdot)\) 225.w 60 yes \(1\) \(1\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{3}{10}\right)\)
\(\chi_{225}(49,\cdot)\) 225.k 6 no \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(1\)
\(\chi_{225}(52,\cdot)\) 225.x 60 yes \(-1\) \(1\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{9}{10}\right)\)
\(\chi_{225}(53,\cdot)\) 225.s 20 no \(1\) \(1\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(-i\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{3}{10}\right)\)
\(\chi_{225}(56,\cdot)\) 225.t 30 yes \(-1\) \(1\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{5}\right)\)
\(\chi_{225}(58,\cdot)\) 225.x 60 yes \(-1\) \(1\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{7}{10}\right)\)
\(\chi_{225}(59,\cdot)\) 225.v 30 yes \(-1\) \(1\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{3}{5}\right)\)