Properties

Modulus $210$
Structure \(C_{12}\times C_{2}\times C_{2}\)
Order $48$

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(210)
 
pari: g = idealstar(,210,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 48
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{12}\times C_{2}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{210}(73,\cdot)$, $\chi_{210}(139,\cdot)$, $\chi_{210}(71,\cdot)$

First 32 of 48 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 \(-1\) \(1\) \(11\) \(13\) \(17\) \(19\) \(23\) \(29\) \(31\) \(37\) \(41\) \(43\)
\(\chi_{210}(1,\cdot)\) 210.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{210}(11,\cdot)\) 210.s 6 no \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(1\)
\(\chi_{210}(13,\cdot)\) 210.m 4 no \(1\) \(1\) \(1\) \(-i\) \(i\) \(1\) \(i\) \(-1\) \(-1\) \(-i\) \(-1\) \(i\)
\(\chi_{210}(17,\cdot)\) 210.w 12 no \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(i\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{12}\right)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{12}\right)\) \(1\) \(-i\)
\(\chi_{210}(19,\cdot)\) 210.p 6 no \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(-1\)
\(\chi_{210}(23,\cdot)\) 210.x 12 no \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(i\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{12}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{12}\right)\) \(-1\) \(i\)
\(\chi_{210}(29,\cdot)\) 210.c 2 no \(-1\) \(1\) \(-1\) \(-1\) \(1\) \(1\) \(1\) \(-1\) \(1\) \(-1\) \(-1\) \(-1\)
\(\chi_{210}(31,\cdot)\) 210.o 6 no \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(1\)
\(\chi_{210}(37,\cdot)\) 210.v 12 no \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(-i\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{12}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{11}{12}\right)\) \(1\) \(-i\)
\(\chi_{210}(41,\cdot)\) 210.b 2 no \(1\) \(1\) \(-1\) \(-1\) \(1\) \(-1\) \(-1\) \(-1\) \(-1\) \(1\) \(1\) \(1\)
\(\chi_{210}(43,\cdot)\) 210.l 4 no \(-1\) \(1\) \(1\) \(i\) \(-i\) \(-1\) \(i\) \(-1\) \(1\) \(-i\) \(1\) \(i\)
\(\chi_{210}(47,\cdot)\) 210.w 12 no \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(i\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{12}\right)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{12}\right)\) \(1\) \(-i\)
\(\chi_{210}(53,\cdot)\) 210.x 12 no \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(i\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{12}\right)\) \(-1\) \(i\)
\(\chi_{210}(59,\cdot)\) 210.t 6 no \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(-1\)
\(\chi_{210}(61,\cdot)\) 210.o 6 no \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(1\)
\(\chi_{210}(67,\cdot)\) 210.v 12 no \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(-i\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{12}\right)\) \(1\) \(-i\)
\(\chi_{210}(71,\cdot)\) 210.e 2 no \(-1\) \(1\) \(-1\) \(1\) \(-1\) \(1\) \(-1\) \(-1\) \(1\) \(1\) \(-1\) \(1\)
\(\chi_{210}(73,\cdot)\) 210.u 12 no \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(-i\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{12}\right)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(-1\) \(i\)
\(\chi_{210}(79,\cdot)\) 210.n 6 no \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(-1\)
\(\chi_{210}(83,\cdot)\) 210.k 4 no \(-1\) \(1\) \(-1\) \(-i\) \(-i\) \(1\) \(-i\) \(1\) \(-1\) \(-i\) \(1\) \(i\)
\(\chi_{210}(89,\cdot)\) 210.t 6 no \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(-1\)
\(\chi_{210}(97,\cdot)\) 210.m 4 no \(1\) \(1\) \(1\) \(i\) \(-i\) \(1\) \(-i\) \(-1\) \(-1\) \(i\) \(-1\) \(-i\)
\(\chi_{210}(101,\cdot)\) 210.r 6 no \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\)
\(\chi_{210}(103,\cdot)\) 210.u 12 no \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(-i\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{12}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{12}\right)\) \(-1\) \(i\)
\(\chi_{210}(107,\cdot)\) 210.x 12 no \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(-i\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{11}{12}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{11}{12}\right)\) \(-1\) \(-i\)
\(\chi_{210}(109,\cdot)\) 210.n 6 no \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(-1\)
\(\chi_{210}(113,\cdot)\) 210.j 4 no \(1\) \(1\) \(-1\) \(i\) \(i\) \(-1\) \(-i\) \(1\) \(1\) \(-i\) \(-1\) \(i\)
\(\chi_{210}(121,\cdot)\) 210.i 3 no \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\)
\(\chi_{210}(127,\cdot)\) 210.l 4 no \(-1\) \(1\) \(1\) \(-i\) \(i\) \(-1\) \(-i\) \(-1\) \(1\) \(i\) \(1\) \(-i\)
\(\chi_{210}(131,\cdot)\) 210.r 6 no \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\)
\(\chi_{210}(137,\cdot)\) 210.x 12 no \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(-i\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{12}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{12}\right)\) \(-1\) \(-i\)
\(\chi_{210}(139,\cdot)\) 210.h 2 no \(-1\) \(1\) \(1\) \(1\) \(1\) \(-1\) \(-1\) \(1\) \(-1\) \(-1\) \(-1\) \(-1\)