LMFDB - Group of Dirichlet characters of modulus 1872

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1872)

pari: g = idealstar(,1872,2)

Character group

sage: G.order() pari: g.no
Order	=	576
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{12}\times C_{12}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{1872}(703,\cdot)$, $\chi_{1872}(469,\cdot)$, $\chi_{1872}(209,\cdot)$, $\chi_{1872}(145,\cdot)$

First 32 of 576 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	$-1$	$1$	$5$	$7$	$11$	$17$	$19$	$23$	$25$	$29$	$31$	$35$
$\chi_{1872}(1,\cdot)$	1872.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1872}(5,\cdot)$	1872.hh	12	yes	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{12}\right)$	$i$
$\chi_{1872}(7,\cdot)$	1872.gh	12	no	$1$	$1$	$e\left(\frac{1}{12}\right)$	$i$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{12}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{1872}(11,\cdot)$	1872.eo	12	yes	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{12}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$i$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{1872}(17,\cdot)$	1872.dx	6	no	$-1$	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{5}{6}\right)$
$\chi_{1872}(19,\cdot)$	1872.ed	12	no	$1$	$1$	$-1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{11}{12}\right)$	$i$	$e\left(\frac{1}{12}\right)$
$\chi_{1872}(23,\cdot)$	1872.dq	6	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{1872}(25,\cdot)$	1872.cn	6	no	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$-1$
$\chi_{1872}(29,\cdot)$	1872.gt	12	yes	$-1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{6}\right)$	$i$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$-i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{1872}(31,\cdot)$	1872.fg	12	no	$1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{12}\right)$	$-1$	$i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$-1$
$\chi_{1872}(35,\cdot)$	1872.fc	12	no	$1$	$1$	$i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{5}{12}\right)$	$-1$	$e\left(\frac{7}{12}\right)$
$\chi_{1872}(37,\cdot)$	1872.eb	12	no	$-1$	$1$	$-1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{12}\right)$	$i$	$e\left(\frac{5}{12}\right)$
$\chi_{1872}(41,\cdot)$	1872.fu	12	no	$1$	$1$	$e\left(\frac{5}{12}\right)$	$i$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{12}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{1872}(43,\cdot)$	1872.er	12	yes	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$-1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{12}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{1872}(47,\cdot)$	1872.gl	12	no	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{12}\right)$	$1$	$-i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{12}\right)$	$1$
$\chi_{1872}(49,\cdot)$	1872.cx	6	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{1872}(53,\cdot)$	1872.z	4	no	$-1$	$1$	$-i$	$-1$	$-i$	$-1$	$-i$	$1$	$-1$	$i$	$1$	$i$
$\chi_{1872}(55,\cdot)$	1872.bw	6	no	$-1$	$1$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$
$\chi_{1872}(59,\cdot)$	1872.eo	12	yes	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{12}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$i$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{1872}(61,\cdot)$	1872.eq	12	yes	$1$	$1$	$e\left(\frac{1}{12}\right)$	$-1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{12}\right)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{1872}(67,\cdot)$	1872.hk	12	yes	$1$	$1$	$e\left(\frac{1}{6}\right)$	$i$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{1872}(71,\cdot)$	1872.fq	12	no	$-1$	$1$	$-i$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$i$	$e\left(\frac{5}{6}\right)$
$\chi_{1872}(73,\cdot)$	1872.bc	4	no	$-1$	$1$	$-i$	$-i$	$i$	$-1$	$-i$	$-1$	$-1$	$-1$	$i$	$-1$
$\chi_{1872}(77,\cdot)$	1872.eu	12	yes	$-1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{12}\right)$	$-1$	$-i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$-i$
$\chi_{1872}(79,\cdot)$	1872.cp	6	no	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$-1$
$\chi_{1872}(83,\cdot)$	1872.ej	12	yes	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{12}\right)$	$i$
$\chi_{1872}(85,\cdot)$	1872.hn	12	yes	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{12}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$-i$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{1872}(89,\cdot)$	1872.fm	12	no	$1$	$1$	$i$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$i$	$e\left(\frac{2}{3}\right)$
$\chi_{1872}(95,\cdot)$	1872.cf	6	no	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{1872}(97,\cdot)$	1872.fw	12	no	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$i$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{12}\right)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{1872}(101,\cdot)$	1872.fb	12	yes	$-1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{3}\right)$	$i$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{1872}(103,\cdot)$	1872.ci	6	no	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$1$

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Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Modulus	$1872$
Structure	\(C_{2}\times C_{2}\times C_{12}\times C_{12}\)
Order	$576$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(35\)
\(\chi_{1872}(1,\cdot)\)	1872.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1872}(5,\cdot)\)	1872.hh	12	yes	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(i\)
\(\chi_{1872}(7,\cdot)\)	1872.gh	12	no	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(i\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{1872}(11,\cdot)\)	1872.eo	12	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(i\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{1872}(17,\cdot)\)	1872.dx	6	no	\(-1\)	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{1872}(19,\cdot)\)	1872.ed	12	no	\(1\)	\(1\)	\(-1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(i\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{1872}(23,\cdot)\)	1872.dq	6	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{1872}(25,\cdot)\)	1872.cn	6	no	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)
\(\chi_{1872}(29,\cdot)\)	1872.gt	12	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(i\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{1872}(31,\cdot)\)	1872.fg	12	no	\(1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-1\)	\(i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(-1\)
\(\chi_{1872}(35,\cdot)\)	1872.fc	12	no	\(1\)	\(1\)	\(i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{5}{12}\right)\)	\(-1\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{1872}(37,\cdot)\)	1872.eb	12	no	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(i\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{1872}(41,\cdot)\)	1872.fu	12	no	\(1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(i\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{1872}(43,\cdot)\)	1872.er	12	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(-1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{1872}(47,\cdot)\)	1872.gl	12	no	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(1\)	\(-i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(1\)
\(\chi_{1872}(49,\cdot)\)	1872.cx	6	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{1872}(53,\cdot)\)	1872.z	4	no	\(-1\)	\(1\)	\(-i\)	\(-1\)	\(-i\)	\(-1\)	\(-i\)	\(1\)	\(-1\)	\(i\)	\(1\)	\(i\)
\(\chi_{1872}(55,\cdot)\)	1872.bw	6	no	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{1872}(59,\cdot)\)	1872.eo	12	yes	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(i\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{1872}(61,\cdot)\)	1872.eq	12	yes	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(-1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{1872}(67,\cdot)\)	1872.hk	12	yes	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(i\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{1872}(71,\cdot)\)	1872.fq	12	no	\(-1\)	\(1\)	\(-i\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(i\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{1872}(73,\cdot)\)	1872.bc	4	no	\(-1\)	\(1\)	\(-i\)	\(-i\)	\(i\)	\(-1\)	\(-i\)	\(-1\)	\(-1\)	\(-1\)	\(i\)	\(-1\)
\(\chi_{1872}(77,\cdot)\)	1872.eu	12	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-1\)	\(-i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-i\)
\(\chi_{1872}(79,\cdot)\)	1872.cp	6	no	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)
\(\chi_{1872}(83,\cdot)\)	1872.ej	12	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(i\)
\(\chi_{1872}(85,\cdot)\)	1872.hn	12	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-i\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{1872}(89,\cdot)\)	1872.fm	12	no	\(1\)	\(1\)	\(i\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(i\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{1872}(95,\cdot)\)	1872.cf	6	no	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{1872}(97,\cdot)\)	1872.fw	12	no	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(i\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{1872}(101,\cdot)\)	1872.fb	12	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(i\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{1872}(103,\cdot)\)	1872.ci	6	no	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

Properties

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Character group

First 32 of 576 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.