Properties

Modulus $328$
Structure \(C_{40}\times C_{2}\times C_{2}\)
Order $160$

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Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(328)
 
pari: g = idealstar(,328,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 160
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{40}\times C_{2}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{328}(247,\cdot)$, $\chi_{328}(165,\cdot)$, $\chi_{328}(129,\cdot)$

First 32 of 160 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 \(-1\) \(1\) \(3\) \(5\) \(7\) \(9\) \(11\) \(13\) \(15\) \(17\) \(19\) \(21\)
\(\chi_{328}(1,\cdot)\) 328.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{328}(3,\cdot)\) 328.p 8 yes \(1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(-i\) \(e\left(\frac{1}{8}\right)\) \(i\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(-i\)
\(\chi_{328}(5,\cdot)\) 328.y 20 yes \(1\) \(1\) \(-i\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{9}{20}\right)\) \(-1\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{1}{5}\right)\)
\(\chi_{328}(7,\cdot)\) 328.bc 40 no \(1\) \(1\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{21}{40}\right)\) \(i\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{13}{20}\right)\)
\(\chi_{328}(9,\cdot)\) 328.j 4 no \(1\) \(1\) \(i\) \(-1\) \(i\) \(-1\) \(i\) \(i\) \(-i\) \(-i\) \(-i\) \(-1\)
\(\chi_{328}(11,\cdot)\) 328.bd 40 yes \(1\) \(1\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{17}{40}\right)\) \(i\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{11}{20}\right)\)
\(\chi_{328}(13,\cdot)\) 328.bf 40 yes \(-1\) \(1\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{9}{40}\right)\) \(i\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{7}{20}\right)\)
\(\chi_{328}(15,\cdot)\) 328.bc 40 no \(1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{23}{40}\right)\) \(-i\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{19}{20}\right)\)
\(\chi_{328}(17,\cdot)\) 328.be 40 no \(-1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{7}{40}\right)\) \(-i\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{11}{20}\right)\)
\(\chi_{328}(19,\cdot)\) 328.bd 40 yes \(1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{11}{40}\right)\) \(-i\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{13}{20}\right)\)
\(\chi_{328}(21,\cdot)\) 328.y 20 yes \(1\) \(1\) \(-i\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{13}{20}\right)\) \(-1\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{328}(23,\cdot)\) 328.v 10 no \(-1\) \(1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{3}{5}\right)\)
\(\chi_{328}(25,\cdot)\) 328.s 10 no \(1\) \(1\) \(-1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(1\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{328}(27,\cdot)\) 328.p 8 yes \(1\) \(1\) \(e\left(\frac{7}{8}\right)\) \(i\) \(e\left(\frac{3}{8}\right)\) \(-i\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(i\)
\(\chi_{328}(29,\cdot)\) 328.bf 40 yes \(-1\) \(1\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{33}{40}\right)\) \(i\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{19}{20}\right)\)
\(\chi_{328}(31,\cdot)\) 328.v 10 no \(-1\) \(1\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{4}{5}\right)\)
\(\chi_{328}(33,\cdot)\) 328.ba 20 no \(1\) \(1\) \(-i\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{11}{20}\right)\) \(-1\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{3}{10}\right)\)
\(\chi_{328}(35,\cdot)\) 328.bd 40 yes \(1\) \(1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{39}{40}\right)\) \(-i\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{17}{20}\right)\)
\(\chi_{328}(37,\cdot)\) 328.u 10 yes \(1\) \(1\) \(-1\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(1\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{7}{10}\right)\)
\(\chi_{328}(39,\cdot)\) 328.bb 20 no \(-1\) \(1\) \(-i\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{7}{20}\right)\) \(-1\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{1}{10}\right)\)
\(\chi_{328}(43,\cdot)\) 328.z 20 yes \(-1\) \(1\) \(-i\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{17}{20}\right)\) \(-1\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{3}{5}\right)\)
\(\chi_{328}(45,\cdot)\) 328.w 10 yes \(1\) \(1\) \(1\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{7}{10}\right)\)
\(\chi_{328}(47,\cdot)\) 328.bc 40 no \(1\) \(1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{19}{40}\right)\) \(-i\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{7}{20}\right)\)
\(\chi_{328}(49,\cdot)\) 328.ba 20 no \(1\) \(1\) \(i\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{20}\right)\) \(-1\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{3}{10}\right)\)
\(\chi_{328}(51,\cdot)\) 328.x 10 yes \(-1\) \(1\) \(1\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{10}\right)\)
\(\chi_{328}(53,\cdot)\) 328.bf 40 yes \(-1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{13}{40}\right)\) \(i\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{19}{20}\right)\)
\(\chi_{328}(55,\cdot)\) 328.q 8 no \(1\) \(1\) \(e\left(\frac{7}{8}\right)\) \(-i\) \(e\left(\frac{7}{8}\right)\) \(-i\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(-i\)
\(\chi_{328}(57,\cdot)\) 328.m 5 no \(1\) \(1\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{328}(59,\cdot)\) 328.x 10 yes \(-1\) \(1\) \(1\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{10}\right)\)
\(\chi_{328}(61,\cdot)\) 328.y 20 yes \(1\) \(1\) \(i\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{20}\right)\) \(-1\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{328}(63,\cdot)\) 328.bc 40 no \(1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{31}{40}\right)\) \(-i\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{3}{20}\right)\)
\(\chi_{328}(65,\cdot)\) 328.be 40 no \(-1\) \(1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{27}{40}\right)\) \(-i\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{11}{20}\right)\)