LMFDB - Group of Dirichlet Characters of Modulus 104

Show commands for: SageMath / Pari/GP

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed

sage: H = DirichletGroup_conrey(104)

pari: g = idealstar(,104,2)

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	=	$\chi_{104}(41,\cdot)$, $\chi_{104}(79,\cdot)$, $\chi_{104}(53,\cdot)$

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.

	orbit label	order	primitive	-1	1	3	5	7	9	11	15	17	19	21	23
$\chi_{104}(1,\cdot)$	104.a	1	No	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{104}(3,\cdot)$	104.n	6	Yes	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{5}{6}\right)$
$\chi_{104}(5,\cdot)$	104.j	4	Yes	$-1$	$1$	$-1$	$i$	$i$	$1$	$-i$	$-i$	$-1$	$i$	$-i$	$-1$
$\chi_{104}(7,\cdot)$	104.w	12	No	$1$	$1$	$e\left(\frac{1}{6}\right)$	$i$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{12}\right)$	$-i$	$e\left(\frac{2}{3}\right)$
$\chi_{104}(9,\cdot)$	104.i	3	No	$1$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$
$\chi_{104}(11,\cdot)$	104.u	12	Yes	$1$	$1$	$e\left(\frac{1}{3}\right)$	$-i$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{12}\right)$	$i$	$e\left(\frac{1}{3}\right)$
$\chi_{104}(15,\cdot)$	104.w	12	No	$1$	$1$	$e\left(\frac{5}{6}\right)$	$-i$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{12}\right)$	$i$	$e\left(\frac{1}{3}\right)$
$\chi_{104}(17,\cdot)$	104.o	6	No	$1$	$1$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$
$\chi_{104}(19,\cdot)$	104.u	12	Yes	$1$	$1$	$e\left(\frac{2}{3}\right)$	$i$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{12}\right)$	$-i$	$e\left(\frac{2}{3}\right)$
$\chi_{104}(21,\cdot)$	104.j	4	Yes	$-1$	$1$	$-1$	$-i$	$-i$	$1$	$i$	$i$	$-1$	$-i$	$i$	$-1$
$\chi_{104}(23,\cdot)$	104.q	6	No	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{5}{6}\right)$
$\chi_{104}(25,\cdot)$	104.f	2	No	$1$	$1$	$1$	$-1$	$-1$	$1$	$-1$	$-1$	$1$	$-1$	$-1$	$1$
$\chi_{104}(27,\cdot)$	104.g	2	No	$-1$	$1$	$1$	$-1$	$-1$	$1$	$1$	$-1$	$1$	$1$	$-1$	$-1$
$\chi_{104}(29,\cdot)$	104.r	6	Yes	$1$	$1$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{3}\right)$
$\chi_{104}(31,\cdot)$	104.k	4	No	$1$	$1$	$-1$	$-i$	$-i$	$1$	$-i$	$i$	$-1$	$i$	$i$	$1$
$\chi_{104}(33,\cdot)$	104.v	12	No	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$i$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{12}\right)$	$-i$	$e\left(\frac{1}{6}\right)$
$\chi_{104}(35,\cdot)$	104.n	6	Yes	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{1}{6}\right)$
$\chi_{104}(37,\cdot)$	104.x	12	Yes	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$-i$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{12}\right)$	$i$	$e\left(\frac{5}{6}\right)$
$\chi_{104}(41,\cdot)$	104.v	12	No	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$-i$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{12}\right)$	$i$	$e\left(\frac{5}{6}\right)$
$\chi_{104}(43,\cdot)$	104.p	6	Yes	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{6}\right)$
$\chi_{104}(45,\cdot)$	104.x	12	Yes	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$i$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{12}\right)$	$-i$	$e\left(\frac{1}{6}\right)$
$\chi_{104}(47,\cdot)$	104.k	4	No	$1$	$1$	$-1$	$i$	$i$	$1$	$i$	$-i$	$-1$	$-i$	$-i$	$1$
$\chi_{104}(49,\cdot)$	104.o	6	No	$1$	$1$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{3}\right)$
$\chi_{104}(51,\cdot)$	104.h	2	Yes	$-1$	$1$	$1$	$1$	$1$	$1$	$-1$	$1$	$1$	$-1$	$1$	$-1$
$\chi_{104}(53,\cdot)$	104.b	2	No	$1$	$1$	$-1$	$-1$	$1$	$1$	$-1$	$1$	$1$	$-1$	$-1$	$1$
$\chi_{104}(55,\cdot)$	104.t	6	No	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{5}{6}\right)$
$\chi_{104}(57,\cdot)$	104.l	4	No	$-1$	$1$	$1$	$-i$	$i$	$1$	$i$	$-i$	$-1$	$-i$	$i$	$-1$
$\chi_{104}(59,\cdot)$	104.u	12	Yes	$1$	$1$	$e\left(\frac{2}{3}\right)$	$-i$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{12}\right)$	$i$	$e\left(\frac{2}{3}\right)$
$\chi_{104}(61,\cdot)$	104.r	6	Yes	$1$	$1$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$
$\chi_{104}(63,\cdot)$	104.w	12	No	$1$	$1$	$e\left(\frac{5}{6}\right)$	$i$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{12}\right)$	$-i$	$e\left(\frac{1}{3}\right)$
$\chi_{104}(67,\cdot)$	104.u	12	Yes	$1$	$1$	$e\left(\frac{1}{3}\right)$	$i$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{12}\right)$	$-i$	$e\left(\frac{1}{3}\right)$
$\chi_{104}(69,\cdot)$	104.s	6	Yes	$1$	$1$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$

Introduction	Features
Universe	News

	orbit label	order	primitive	-1	1	3	5	7	9	11	15	17	19	21	23
\(\chi_{104}(1,\cdot)\)	104.a	1	No	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{104}(3,\cdot)\)	104.n	6	Yes	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{104}(5,\cdot)\)	104.j	4	Yes	\(-1\)	\(1\)	\(-1\)	\(i\)	\(i\)	\(1\)	\(-i\)	\(-i\)	\(-1\)	\(i\)	\(-i\)	\(-1\)
\(\chi_{104}(7,\cdot)\)	104.w	12	No	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(i\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-i\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{104}(9,\cdot)\)	104.i	3	No	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{104}(11,\cdot)\)	104.u	12	Yes	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(-i\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(i\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{104}(15,\cdot)\)	104.w	12	No	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(-i\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(i\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{104}(17,\cdot)\)	104.o	6	No	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{104}(19,\cdot)\)	104.u	12	Yes	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(i\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-i\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{104}(21,\cdot)\)	104.j	4	Yes	\(-1\)	\(1\)	\(-1\)	\(-i\)	\(-i\)	\(1\)	\(i\)	\(i\)	\(-1\)	\(-i\)	\(i\)	\(-1\)
\(\chi_{104}(23,\cdot)\)	104.q	6	No	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{104}(25,\cdot)\)	104.f	2	No	\(1\)	\(1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(-1\)	\(-1\)	\(1\)
\(\chi_{104}(27,\cdot)\)	104.g	2	No	\(-1\)	\(1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(1\)	\(-1\)	\(1\)	\(1\)	\(-1\)	\(-1\)
\(\chi_{104}(29,\cdot)\)	104.r	6	Yes	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{104}(31,\cdot)\)	104.k	4	No	\(1\)	\(1\)	\(-1\)	\(-i\)	\(-i\)	\(1\)	\(-i\)	\(i\)	\(-1\)	\(i\)	\(i\)	\(1\)
\(\chi_{104}(33,\cdot)\)	104.v	12	No	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(i\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{104}(35,\cdot)\)	104.n	6	Yes	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{104}(37,\cdot)\)	104.x	12	Yes	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(-i\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(i\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{104}(41,\cdot)\)	104.v	12	No	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(-i\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(i\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{104}(43,\cdot)\)	104.p	6	Yes	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{104}(45,\cdot)\)	104.x	12	Yes	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(i\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{104}(47,\cdot)\)	104.k	4	No	\(1\)	\(1\)	\(-1\)	\(i\)	\(i\)	\(1\)	\(i\)	\(-i\)	\(-1\)	\(-i\)	\(-i\)	\(1\)
\(\chi_{104}(49,\cdot)\)	104.o	6	No	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{104}(51,\cdot)\)	104.h	2	Yes	\(-1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(-1\)	\(1\)	\(1\)	\(-1\)	\(1\)	\(-1\)
\(\chi_{104}(53,\cdot)\)	104.b	2	No	\(1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(1\)	\(-1\)	\(1\)	\(1\)	\(-1\)	\(-1\)	\(1\)
\(\chi_{104}(55,\cdot)\)	104.t	6	No	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{104}(57,\cdot)\)	104.l	4	No	\(-1\)	\(1\)	\(1\)	\(-i\)	\(i\)	\(1\)	\(i\)	\(-i\)	\(-1\)	\(-i\)	\(i\)	\(-1\)
\(\chi_{104}(59,\cdot)\)	104.u	12	Yes	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(-i\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(i\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{104}(61,\cdot)\)	104.r	6	Yes	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{104}(63,\cdot)\)	104.w	12	No	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(i\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{104}(67,\cdot)\)	104.u	12	Yes	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(i\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{104}(69,\cdot)\)	104.s	6	Yes	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)

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L-functions

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Character group

First 32 of 48 characters

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Modulus	104
Structure	\(C_{12}\times C_{2}\times C_{2}\)
Order	48