LMFDB - Group of Dirichlet characters of modulus 2856

Show commands: PariGP / SageMath

sage: H = DirichletGroup(2856)

pari: g = idealstar(,2856,2)

Character group

sage: G.order() pari: g.no
Order	=	768
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{2}\times C_{48}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{2856}(2143,\cdot)$, $\chi_{2856}(1429,\cdot)$, $\chi_{2856}(953,\cdot)$, $\chi_{2856}(409,\cdot)$, $\chi_{2856}(2689,\cdot)$

First 32 of 768 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	$-1$	$1$	$5$	$11$	$13$	$19$	$23$	$25$	$29$	$31$	$37$	$41$
$\chi_{2856}(1,\cdot)$	2856.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{2856}(5,\cdot)$	2856.fr	48	yes	$-1$	$1$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{25}{48}\right)$	$i$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{7}{16}\right)$
$\chi_{2856}(11,\cdot)$	2856.gd	48	yes	$-1$	$1$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{11}{48}\right)$	$i$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{5}{16}\right)$
$\chi_{2856}(13,\cdot)$	2856.br	4	no	$-1$	$1$	$i$	$i$	$1$	$-1$	$-i$	$-1$	$-i$	$-i$	$-i$	$i$
$\chi_{2856}(19,\cdot)$	2856.fc	24	no	$1$	$1$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{11}{24}\right)$	$-1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{2856}(23,\cdot)$	2856.fq	48	no	$-1$	$1$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{43}{48}\right)$	$-i$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{13}{16}\right)$
$\chi_{2856}(25,\cdot)$	2856.fd	24	no	$1$	$1$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{1}{24}\right)$	$-1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{2856}(29,\cdot)$	2856.es	16	no	$1$	$1$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{11}{16}\right)$	$-i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{7}{16}\right)$
$\chi_{2856}(31,\cdot)$	2856.fo	48	no	$-1$	$1$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{5}{48}\right)$	$-i$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{11}{16}\right)$
$\chi_{2856}(37,\cdot)$	2856.fp	48	no	$-1$	$1$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{13}{48}\right)$	$-i$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{11}{16}\right)$
$\chi_{2856}(41,\cdot)$	2856.ej	16	no	$-1$	$1$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{5}{16}\right)$	$i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{9}{16}\right)$
$\chi_{2856}(43,\cdot)$	2856.dq	8	no	$-1$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{8}\right)$	$1$	$-i$	$e\left(\frac{3}{8}\right)$	$i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{2856}(47,\cdot)$	2856.dz	12	no	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{12}\right)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$-i$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{12}\right)$	$-i$
$\chi_{2856}(53,\cdot)$	2856.fg	24	yes	$-1$	$1$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{19}{24}\right)$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{2856}(55,\cdot)$	2856.bk	4	no	$1$	$1$	$i$	$-i$	$-1$	$-1$	$-i$	$-1$	$-i$	$-i$	$-i$	$-i$
$\chi_{2856}(59,\cdot)$	2856.ez	24	yes	$-1$	$1$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{13}{24}\right)$	$-1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{2856}(61,\cdot)$	2856.fv	48	no	$1$	$1$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{7}{48}\right)$	$-i$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{9}{16}\right)$
$\chi_{2856}(65,\cdot)$	2856.fw	48	no	$1$	$1$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{37}{48}\right)$	$i$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{11}{16}\right)$
$\chi_{2856}(67,\cdot)$	2856.ce	6	no	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$-1$
$\chi_{2856}(71,\cdot)$	2856.ev	16	no	$-1$	$1$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{7}{16}\right)$	$i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{3}{16}\right)$
$\chi_{2856}(73,\cdot)$	2856.fy	48	no	$1$	$1$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{41}{48}\right)$	$-i$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{15}{16}\right)$
$\chi_{2856}(79,\cdot)$	2856.fu	48	no	$1$	$1$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{43}{48}\right)$	$-i$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{13}{16}\right)$
$\chi_{2856}(83,\cdot)$	2856.dg	8	yes	$-1$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{8}\right)$	$-1$	$-i$	$e\left(\frac{5}{8}\right)$	$-i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{2856}(89,\cdot)$	2856.ds	12	no	$1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{12}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$i$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{12}\right)$	$i$
$\chi_{2856}(95,\cdot)$	2856.fq	48	no	$-1$	$1$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{47}{48}\right)$	$-i$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{9}{16}\right)$
$\chi_{2856}(97,\cdot)$	2856.en	16	no	$1$	$1$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{11}{16}\right)$	$-i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{7}{16}\right)$
$\chi_{2856}(101,\cdot)$	2856.ci	6	yes	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$-1$
$\chi_{2856}(103,\cdot)$	2856.cu	6	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-1$
$\chi_{2856}(107,\cdot)$	2856.gd	48	yes	$-1$	$1$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{1}{48}\right)$	$-i$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{15}{16}\right)$
$\chi_{2856}(109,\cdot)$	2856.fp	48	no	$-1$	$1$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{47}{48}\right)$	$i$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{9}{16}\right)$
$\chi_{2856}(113,\cdot)$	2856.ep	16	no	$1$	$1$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{9}{16}\right)$	$-i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{5}{16}\right)$
$\chi_{2856}(115,\cdot)$	2856.ea	12	no	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{12}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$-i$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{12}\right)$	$i$

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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	$2856$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{2}\times C_{48}\)
Order	$768$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(11\)	\(13\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{2856}(1,\cdot)\)	2856.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{2856}(5,\cdot)\)	2856.fr	48	yes	\(-1\)	\(1\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(i\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{7}{16}\right)\)
\(\chi_{2856}(11,\cdot)\)	2856.gd	48	yes	\(-1\)	\(1\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(i\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{5}{16}\right)\)
\(\chi_{2856}(13,\cdot)\)	2856.br	4	no	\(-1\)	\(1\)	\(i\)	\(i\)	\(1\)	\(-1\)	\(-i\)	\(-1\)	\(-i\)	\(-i\)	\(-i\)	\(i\)
\(\chi_{2856}(19,\cdot)\)	2856.fc	24	no	\(1\)	\(1\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(-1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{2856}(23,\cdot)\)	2856.fq	48	no	\(-1\)	\(1\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(-i\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{13}{16}\right)\)
\(\chi_{2856}(25,\cdot)\)	2856.fd	24	no	\(1\)	\(1\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(-1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{2856}(29,\cdot)\)	2856.es	16	no	\(1\)	\(1\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(-i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)
\(\chi_{2856}(31,\cdot)\)	2856.fo	48	no	\(-1\)	\(1\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(-i\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{11}{16}\right)\)
\(\chi_{2856}(37,\cdot)\)	2856.fp	48	no	\(-1\)	\(1\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(-i\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{11}{16}\right)\)
\(\chi_{2856}(41,\cdot)\)	2856.ej	16	no	\(-1\)	\(1\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)
\(\chi_{2856}(43,\cdot)\)	2856.dq	8	no	\(-1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(1\)	\(-i\)	\(e\left(\frac{3}{8}\right)\)	\(i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{2856}(47,\cdot)\)	2856.dz	12	no	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-i\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(-i\)
\(\chi_{2856}(53,\cdot)\)	2856.fg	24	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{2856}(55,\cdot)\)	2856.bk	4	no	\(1\)	\(1\)	\(i\)	\(-i\)	\(-1\)	\(-1\)	\(-i\)	\(-1\)	\(-i\)	\(-i\)	\(-i\)	\(-i\)
\(\chi_{2856}(59,\cdot)\)	2856.ez	24	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(-1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{2856}(61,\cdot)\)	2856.fv	48	no	\(1\)	\(1\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(-i\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{9}{16}\right)\)
\(\chi_{2856}(65,\cdot)\)	2856.fw	48	no	\(1\)	\(1\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(i\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{11}{16}\right)\)
\(\chi_{2856}(67,\cdot)\)	2856.ce	6	no	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)
\(\chi_{2856}(71,\cdot)\)	2856.ev	16	no	\(-1\)	\(1\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)
\(\chi_{2856}(73,\cdot)\)	2856.fy	48	no	\(1\)	\(1\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(-i\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{15}{16}\right)\)
\(\chi_{2856}(79,\cdot)\)	2856.fu	48	no	\(1\)	\(1\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(-i\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{13}{16}\right)\)
\(\chi_{2856}(83,\cdot)\)	2856.dg	8	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(-1\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)	\(-i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{2856}(89,\cdot)\)	2856.ds	12	no	\(1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(i\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(i\)
\(\chi_{2856}(95,\cdot)\)	2856.fq	48	no	\(-1\)	\(1\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(-i\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{9}{16}\right)\)
\(\chi_{2856}(97,\cdot)\)	2856.en	16	no	\(1\)	\(1\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(-i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)
\(\chi_{2856}(101,\cdot)\)	2856.ci	6	yes	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)
\(\chi_{2856}(103,\cdot)\)	2856.cu	6	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)
\(\chi_{2856}(107,\cdot)\)	2856.gd	48	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(-i\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{15}{16}\right)\)
\(\chi_{2856}(109,\cdot)\)	2856.fp	48	no	\(-1\)	\(1\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(i\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{9}{16}\right)\)
\(\chi_{2856}(113,\cdot)\)	2856.ep	16	no	\(1\)	\(1\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)
\(\chi_{2856}(115,\cdot)\)	2856.ea	12	no	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-i\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(i\)

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