Properties

Modulus $960$
Structure \(C_{2}\times C_{2}\times C_{4}\times C_{16}\)
Order $256$

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Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(960)
 
pari: g = idealstar(,960,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 256
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{2}\times C_{2}\times C_{4}\times C_{16}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{960}(511,\cdot)$, $\chi_{960}(901,\cdot)$, $\chi_{960}(641,\cdot)$, $\chi_{960}(577,\cdot)$

First 32 of 256 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 \(-1\) \(1\) \(7\) \(11\) \(13\) \(17\) \(19\) \(23\) \(29\) \(31\) \(37\) \(41\)
\(\chi_{960}(1,\cdot)\) 960.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{960}(7,\cdot)\) 960.cc 8 no \(1\) \(1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(-i\) \(e\left(\frac{3}{8}\right)\) \(1\) \(e\left(\frac{3}{8}\right)\) \(-1\) \(e\left(\frac{7}{8}\right)\) \(-i\)
\(\chi_{960}(11,\cdot)\) 960.cn 16 no \(1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{11}{16}\right)\) \(i\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{15}{16}\right)\) \(1\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{7}{8}\right)\)
\(\chi_{960}(13,\cdot)\) 960.cq 16 no \(-1\) \(1\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{5}{16}\right)\) \(1\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{13}{16}\right)\) \(-1\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{1}{8}\right)\)
\(\chi_{960}(17,\cdot)\) 960.bf 4 no \(1\) \(1\) \(-i\) \(i\) \(1\) \(-i\) \(-i\) \(-i\) \(i\) \(1\) \(1\) \(1\)
\(\chi_{960}(19,\cdot)\) 960.co 16 no \(-1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{1}{16}\right)\) \(-i\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{13}{16}\right)\) \(1\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{1}{8}\right)\)
\(\chi_{960}(23,\cdot)\) 960.ca 8 no \(-1\) \(1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(-i\) \(e\left(\frac{1}{8}\right)\) \(-1\) \(e\left(\frac{5}{8}\right)\) \(-1\) \(e\left(\frac{5}{8}\right)\) \(-i\)
\(\chi_{960}(29,\cdot)\) 960.cl 16 yes \(-1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{13}{16}\right)\) \(i\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{1}{16}\right)\) \(-1\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{1}{8}\right)\)
\(\chi_{960}(31,\cdot)\) 960.g 2 no \(-1\) \(1\) \(-1\) \(1\) \(-1\) \(1\) \(1\) \(-1\) \(-1\) \(-1\) \(-1\) \(1\)
\(\chi_{960}(37,\cdot)\) 960.cq 16 no \(-1\) \(1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{3}{16}\right)\) \(1\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{11}{16}\right)\) \(-1\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{7}{8}\right)\)
\(\chi_{960}(41,\cdot)\) 960.bz 8 no \(-1\) \(1\) \(-i\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(1\) \(e\left(\frac{1}{8}\right)\) \(-i\) \(e\left(\frac{1}{8}\right)\) \(1\) \(e\left(\frac{7}{8}\right)\) \(-i\)
\(\chi_{960}(43,\cdot)\) 960.cg 16 no \(1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(-1\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{16}\right)\) \(1\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{3}{8}\right)\)
\(\chi_{960}(47,\cdot)\) 960.bd 4 no \(-1\) \(1\) \(i\) \(-i\) \(1\) \(-i\) \(i\) \(i\) \(i\) \(-1\) \(1\) \(1\)
\(\chi_{960}(49,\cdot)\) 960.bl 4 no \(1\) \(1\) \(1\) \(i\) \(i\) \(-1\) \(-i\) \(1\) \(-i\) \(1\) \(-i\) \(-1\)
\(\chi_{960}(53,\cdot)\) 960.cr 16 yes \(1\) \(1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{15}{16}\right)\) \(1\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{16}\right)\) \(-1\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{7}{8}\right)\)
\(\chi_{960}(59,\cdot)\) 960.cp 16 yes \(1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(-i\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{3}{16}\right)\) \(1\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{3}{8}\right)\)
\(\chi_{960}(61,\cdot)\) 960.ci 16 no \(1\) \(1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{13}{16}\right)\) \(i\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{1}{16}\right)\) \(-1\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{5}{8}\right)\)
\(\chi_{960}(67,\cdot)\) 960.cg 16 no \(1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{9}{16}\right)\) \(-1\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{9}{16}\right)\) \(1\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{5}{8}\right)\)
\(\chi_{960}(71,\cdot)\) 960.bx 8 no \(1\) \(1\) \(-i\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(1\) \(e\left(\frac{7}{8}\right)\) \(-i\) \(e\left(\frac{3}{8}\right)\) \(-1\) \(e\left(\frac{5}{8}\right)\) \(i\)
\(\chi_{960}(73,\cdot)\) 960.bp 8 no \(-1\) \(1\) \(-1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(i\) \(e\left(\frac{1}{8}\right)\) \(-1\) \(e\left(\frac{5}{8}\right)\) \(1\) \(e\left(\frac{1}{8}\right)\) \(i\)
\(\chi_{960}(77,\cdot)\) 960.cr 16 yes \(1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{13}{16}\right)\) \(1\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{16}\right)\) \(-1\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{5}{8}\right)\)
\(\chi_{960}(79,\cdot)\) 960.q 4 no \(-1\) \(1\) \(-1\) \(-i\) \(i\) \(-1\) \(i\) \(-1\) \(-i\) \(-1\) \(-i\) \(-1\)
\(\chi_{960}(83,\cdot)\) 960.ch 16 yes \(-1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{13}{16}\right)\) \(-1\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{13}{16}\right)\) \(1\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{5}{8}\right)\)
\(\chi_{960}(89,\cdot)\) 960.bu 8 no \(-1\) \(1\) \(-i\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(-1\) \(e\left(\frac{7}{8}\right)\) \(-i\) \(e\left(\frac{7}{8}\right)\) \(1\) \(e\left(\frac{5}{8}\right)\) \(i\)
\(\chi_{960}(91,\cdot)\) 960.cm 16 no \(-1\) \(1\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(-i\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{3}{16}\right)\) \(1\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{7}{8}\right)\)
\(\chi_{960}(97,\cdot)\) 960.x 4 no \(-1\) \(1\) \(i\) \(-1\) \(i\) \(i\) \(1\) \(-i\) \(1\) \(1\) \(-i\) \(1\)
\(\chi_{960}(101,\cdot)\) 960.cj 16 no \(-1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(i\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{11}{16}\right)\) \(-1\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{3}{8}\right)\)
\(\chi_{960}(103,\cdot)\) 960.bo 8 no \(1\) \(1\) \(-1\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(i\) \(e\left(\frac{7}{8}\right)\) \(-1\) \(e\left(\frac{7}{8}\right)\) \(-1\) \(e\left(\frac{7}{8}\right)\) \(-i\)
\(\chi_{960}(107,\cdot)\) 960.ch 16 yes \(-1\) \(1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{15}{16}\right)\) \(-1\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{15}{16}\right)\) \(1\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{7}{8}\right)\)
\(\chi_{960}(109,\cdot)\) 960.ck 16 no \(1\) \(1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{1}{16}\right)\) \(-i\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{13}{16}\right)\) \(-1\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{1}{8}\right)\)
\(\chi_{960}(113,\cdot)\) 960.bf 4 no \(1\) \(1\) \(i\) \(-i\) \(1\) \(i\) \(i\) \(i\) \(-i\) \(1\) \(1\) \(1\)
\(\chi_{960}(119,\cdot)\) 960.bs 8 no \(1\) \(1\) \(-i\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(-1\) \(e\left(\frac{1}{8}\right)\) \(-i\) \(e\left(\frac{5}{8}\right)\) \(-1\) \(e\left(\frac{7}{8}\right)\) \(-i\)
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