Properties

Modulus 320
Structure \(C_{16}\times C_{4}\times C_{2}\)
Order 128

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(320)
 
pari: g = idealstar(,320,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 128
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{16}\times C_{4}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{320}(261,\cdot)$, $\chi_{320}(257,\cdot)$, $\chi_{320}(191,\cdot)$

First 32 of 128 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 3 7 9 11 13 17 19 21 23 27
\(\chi_{320}(1,\cdot)\) 320.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{320}(3,\cdot)\) 320.bj 16 yes \(1\) \(1\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{1}{16}\right)\) \(1\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{15}{16}\right)\)
\(\chi_{320}(7,\cdot)\) 320.ba 8 no \(1\) \(1\) \(e\left(\frac{1}{8}\right)\) \(1\) \(i\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(-i\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(1\) \(e\left(\frac{3}{8}\right)\)
\(\chi_{320}(9,\cdot)\) 320.z 8 no \(1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(i\) \(i\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(1\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(-i\) \(e\left(\frac{7}{8}\right)\)
\(\chi_{320}(11,\cdot)\) 320.bg 16 no \(-1\) \(1\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{11}{16}\right)\) \(-i\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{5}{16}\right)\)
\(\chi_{320}(13,\cdot)\) 320.bi 16 yes \(-1\) \(1\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{5}{16}\right)\) \(1\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{3}{16}\right)\)
\(\chi_{320}(17,\cdot)\) 320.t 4 no \(-1\) \(1\) \(1\) \(-i\) \(1\) \(-i\) \(1\) \(i\) \(-i\) \(-i\) \(i\) \(1\)
\(\chi_{320}(19,\cdot)\) 320.bh 16 yes \(-1\) \(1\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{1}{16}\right)\) \(-i\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{15}{16}\right)\)
\(\chi_{320}(21,\cdot)\) 320.be 16 no \(1\) \(1\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{3}{16}\right)\) \(-i\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{16}\right)\)
\(\chi_{320}(23,\cdot)\) 320.ba 8 no \(1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(1\) \(-i\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(i\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(1\) \(e\left(\frac{1}{8}\right)\)
\(\chi_{320}(27,\cdot)\) 320.bj 16 yes \(1\) \(1\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{3}{16}\right)\) \(1\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{13}{16}\right)\)
\(\chi_{320}(29,\cdot)\) 320.bf 16 yes \(1\) \(1\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{13}{16}\right)\) \(-i\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{11}{16}\right)\)
\(\chi_{320}(31,\cdot)\) 320.g 2 no \(-1\) \(1\) \(1\) \(-1\) \(1\) \(1\) \(-1\) \(1\) \(1\) \(-1\) \(-1\) \(1\)
\(\chi_{320}(33,\cdot)\) 320.m 4 no \(-1\) \(1\) \(-i\) \(-i\) \(-1\) \(-1\) \(-i\) \(-i\) \(1\) \(-1\) \(i\) \(i\)
\(\chi_{320}(37,\cdot)\) 320.bi 16 yes \(-1\) \(1\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{3}{16}\right)\) \(1\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{5}{16}\right)\)
\(\chi_{320}(39,\cdot)\) 320.y 8 no \(-1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(i\) \(-i\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(1\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(-i\) \(e\left(\frac{1}{8}\right)\)
\(\chi_{320}(41,\cdot)\) 320.x 8 no \(1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(-i\) \(i\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(-1\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(i\) \(e\left(\frac{7}{8}\right)\)
\(\chi_{320}(43,\cdot)\) 320.bd 16 yes \(1\) \(1\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(-1\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{9}{16}\right)\)
\(\chi_{320}(47,\cdot)\) 320.j 4 no \(1\) \(1\) \(-1\) \(i\) \(1\) \(i\) \(1\) \(i\) \(i\) \(-i\) \(-i\) \(-1\)
\(\chi_{320}(49,\cdot)\) 320.q 4 no \(1\) \(1\) \(i\) \(1\) \(-1\) \(i\) \(i\) \(-1\) \(-i\) \(i\) \(1\) \(-i\)
\(\chi_{320}(51,\cdot)\) 320.bg 16 no \(-1\) \(1\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{1}{16}\right)\) \(i\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{15}{16}\right)\)
\(\chi_{320}(53,\cdot)\) 320.bc 16 yes \(-1\) \(1\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{15}{16}\right)\) \(-1\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{9}{16}\right)\)
\(\chi_{320}(57,\cdot)\) 320.v 8 no \(-1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(-1\) \(i\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(-i\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(-1\) \(e\left(\frac{7}{8}\right)\)
\(\chi_{320}(59,\cdot)\) 320.bh 16 yes \(-1\) \(1\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(i\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{9}{16}\right)\)
\(\chi_{320}(61,\cdot)\) 320.be 16 no \(1\) \(1\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{13}{16}\right)\) \(i\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{11}{16}\right)\)
\(\chi_{320}(63,\cdot)\) 320.n 4 no \(1\) \(1\) \(-i\) \(i\) \(-1\) \(-1\) \(i\) \(-i\) \(1\) \(1\) \(-i\) \(i\)
\(\chi_{320}(67,\cdot)\) 320.bd 16 yes \(1\) \(1\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{9}{16}\right)\) \(-1\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{7}{16}\right)\)
\(\chi_{320}(69,\cdot)\) 320.bf 16 yes \(1\) \(1\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(i\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{1}{16}\right)\)
\(\chi_{320}(71,\cdot)\) 320.w 8 no \(-1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(-i\) \(-i\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(-1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(i\) \(e\left(\frac{1}{8}\right)\)
\(\chi_{320}(73,\cdot)\) 320.v 8 no \(-1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(-1\) \(-i\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(i\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(-1\) \(e\left(\frac{1}{8}\right)\)
\(\chi_{320}(77,\cdot)\) 320.bc 16 yes \(-1\) \(1\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{13}{16}\right)\) \(-1\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{11}{16}\right)\)
\(\chi_{320}(79,\cdot)\) 320.k 4 no \(-1\) \(1\) \(-i\) \(-1\) \(-1\) \(-i\) \(i\) \(-1\) \(i\) \(i\) \(-1\) \(i\)