LMFDB - Group of Dirichlet characters of modulus 4640

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(4640)

gp:g = idealstar(,4640,2)

magma:G := FullDirichletGroup(4640);

Character group

Order	=	1792	comment:Order sage:G.order() gp:g.no magma:Order(G);
Structure	=	$C_{2}\times C_{4}\times C_{4}\times C_{56}$	comment:Group structure sage:sorted(g.order() for g in G.gens()) gp:g.cyc magma:PrimaryInvariants(AbelianGroup(G));
Generators	=	$\chi_{4640}(4351,\cdot)$, $\chi_{4640}(581,\cdot)$, $\chi_{4640}(1857,\cdot)$, $\chi_{4640}(321,\cdot)$	comment:Generators sage:G.gens() gp:g.gen magma:Generators(G);

First 32 of 1792 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	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{4640}(1,\cdot)$	4640.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{4640}(3,\cdot)$	4640.ha	56	yes	$-1$	$1$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{47}{56}\right)$	$e\left(\frac{5}{56}\right)$	$1$	$e\left(\frac{13}{56}\right)$	$e\left(\frac{51}{56}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{17}{56}\right)$
$\chi_{4640}(7,\cdot)$	4640.ez	28	no	$1$	$1$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{3}{14}\right)$	$i$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{3}{7}\right)$
$\chi_{4640}(9,\cdot)$	4640.fh	28	no	$1$	$1$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{5}{28}\right)$	$1$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{17}{28}\right)$
$\chi_{4640}(11,\cdot)$	4640.hl	56	no	$1$	$1$	$e\left(\frac{47}{56}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{53}{56}\right)$	$e\left(\frac{25}{56}\right)$	$i$	$e\left(\frac{51}{56}\right)$	$e\left(\frac{17}{56}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{29}{56}\right)$
$\chi_{4640}(13,\cdot)$	4640.hw	56	yes	$-1$	$1$	$e\left(\frac{5}{56}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{25}{56}\right)$	$e\left(\frac{53}{56}\right)$	$-i$	$e\left(\frac{23}{56}\right)$	$e\left(\frac{17}{56}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{15}{56}\right)$
$\chi_{4640}(17,\cdot)$	4640.cp	4	no	$1$	$1$	$1$	$i$	$1$	$i$	$-i$	$1$	$-i$	$i$	$-i$	$1$
$\chi_{4640}(19,\cdot)$	4640.hi	56	yes	$1$	$1$	$e\left(\frac{13}{56}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{51}{56}\right)$	$e\left(\frac{23}{56}\right)$	$-i$	$e\left(\frac{29}{56}\right)$	$e\left(\frac{47}{56}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{39}{56}\right)$
$\chi_{4640}(21,\cdot)$	4640.hn	56	no	$-1$	$1$	$e\left(\frac{51}{56}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{17}{56}\right)$	$e\left(\frac{17}{56}\right)$	$i$	$e\left(\frac{47}{56}\right)$	$e\left(\frac{25}{56}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{41}{56}\right)$
$\chi_{4640}(23,\cdot)$	4640.ez	28	no	$1$	$1$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{5}{14}\right)$	$-i$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{5}{7}\right)$
$\chi_{4640}(27,\cdot)$	4640.ha	56	yes	$-1$	$1$	$e\left(\frac{17}{56}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{29}{56}\right)$	$e\left(\frac{15}{56}\right)$	$1$	$e\left(\frac{39}{56}\right)$	$e\left(\frac{41}{56}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{51}{56}\right)$
$\chi_{4640}(31,\cdot)$	4640.gh	28	no	$1$	$1$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{9}{14}\right)$	$-i$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{1}{28}\right)$
$\chi_{4640}(33,\cdot)$	4640.fx	28	no	$-1$	$1$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{15}{28}\right)$	$i$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{23}{28}\right)$
$\chi_{4640}(37,\cdot)$	4640.hy	56	yes	$1$	$1$	$e\left(\frac{37}{56}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{17}{56}\right)$	$e\left(\frac{31}{56}\right)$	$1$	$e\left(\frac{19}{56}\right)$	$e\left(\frac{25}{56}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{55}{56}\right)$
$\chi_{4640}(39,\cdot)$	4640.fa	28	no	$1$	$1$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{1}{28}\right)$	$-i$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{4}{7}\right)$
$\chi_{4640}(41,\cdot)$	4640.r	4	no	$-1$	$1$	$-1$	$-1$	$1$	$1$	$-i$	$i$	$-1$	$1$	$-1$	$-1$
$\chi_{4640}(43,\cdot)$	4640.hz	56	yes	$-1$	$1$	$e\left(\frac{53}{56}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{13}{56}\right)$	$e\left(\frac{55}{56}\right)$	$1$	$e\left(\frac{31}{56}\right)$	$e\left(\frac{1}{56}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{47}{56}\right)$
$\chi_{4640}(47,\cdot)$	4640.ev	28	no	$-1$	$1$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{9}{28}\right)$	$-1$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{1}{7}\right)$
$\chi_{4640}(49,\cdot)$	4640.eg	14	no	$1$	$1$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{3}{7}\right)$	$-1$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{6}{7}\right)$
$\chi_{4640}(51,\cdot)$	4640.ho	56	no	$-1$	$1$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{5}{56}\right)$	$e\left(\frac{47}{56}\right)$	$1$	$e\left(\frac{55}{56}\right)$	$e\left(\frac{9}{56}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{17}{56}\right)$
$\chi_{4640}(53,\cdot)$	4640.gx	56	yes	$-1$	$1$	$e\left(\frac{31}{56}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{15}{56}\right)$	$e\left(\frac{43}{56}\right)$	$i$	$e\left(\frac{25}{56}\right)$	$e\left(\frac{55}{56}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{37}{56}\right)$
$\chi_{4640}(57,\cdot)$	4640.cl	4	no	$-1$	$1$	$1$	$-i$	$1$	$-i$	$-1$	$-i$	$-i$	$-i$	$i$	$1$
$\chi_{4640}(59,\cdot)$	4640.dp	8	no	$-1$	$1$	$e\left(\frac{3}{8}\right)$	$i$	$-i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{8}\right)$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{8}\right)$	$-i$	$e\left(\frac{1}{8}\right)$
$\chi_{4640}(61,\cdot)$	4640.hk	56	no	$-1$	$1$	$e\left(\frac{1}{56}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{19}{56}\right)$	$e\left(\frac{47}{56}\right)$	$i$	$e\left(\frac{13}{56}\right)$	$e\left(\frac{51}{56}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{3}{56}\right)$
$\chi_{4640}(63,\cdot)$	4640.fo	28	no	$1$	$1$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{11}{28}\right)$	$i$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{1}{28}\right)$
$\chi_{4640}(67,\cdot)$	4640.hv	56	yes	$1$	$1$	$e\left(\frac{9}{56}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{17}{56}\right)$	$e\left(\frac{45}{56}\right)$	$i$	$e\left(\frac{47}{56}\right)$	$e\left(\frac{53}{56}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{27}{56}\right)$
$\chi_{4640}(69,\cdot)$	4640.hj	56	yes	$-1$	$1$	$e\left(\frac{19}{56}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{53}{56}\right)$	$e\left(\frac{25}{56}\right)$	$-i$	$e\left(\frac{51}{56}\right)$	$e\left(\frac{45}{56}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{1}{56}\right)$
$\chi_{4640}(71,\cdot)$	4640.fe	28	no	$-1$	$1$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{9}{28}\right)$	$-1$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{11}{28}\right)$
$\chi_{4640}(73,\cdot)$	4640.fl	28	no	$1$	$1$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{6}{7}\right)$	$1$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{27}{28}\right)$
$\chi_{4640}(77,\cdot)$	4640.gu	56	yes	$1$	$1$	$e\left(\frac{55}{56}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{23}{56}\right)$	$e\left(\frac{37}{56}\right)$	$-1$	$e\left(\frac{29}{56}\right)$	$e\left(\frac{47}{56}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{53}{56}\right)$
$\chi_{4640}(79,\cdot)$	4640.fi	28	no	$1$	$1$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{13}{14}\right)$	$i$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{17}{28}\right)$
$\chi_{4640}(81,\cdot)$	4640.el	14	no	$1$	$1$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{5}{14}\right)$	$1$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{3}{14}\right)$

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Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$ over number fields
Genus 2 curves
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Modulus	$4640$
Structure	\(C_{2}\times C_{4}\times C_{4}\times C_{56}\)
Order	$1792$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)
\(\chi_{4640}(1,\cdot)\)	4640.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{4640}(3,\cdot)\)	4640.ha	56	yes	\(-1\)	\(1\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{47}{56}\right)\)	\(e\left(\frac{5}{56}\right)\)	\(1\)	\(e\left(\frac{13}{56}\right)\)	\(e\left(\frac{51}{56}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{17}{56}\right)\)
\(\chi_{4640}(7,\cdot)\)	4640.ez	28	no	\(1\)	\(1\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(i\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{3}{7}\right)\)
\(\chi_{4640}(9,\cdot)\)	4640.fh	28	no	\(1\)	\(1\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(1\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{17}{28}\right)\)
\(\chi_{4640}(11,\cdot)\)	4640.hl	56	no	\(1\)	\(1\)	\(e\left(\frac{47}{56}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{53}{56}\right)\)	\(e\left(\frac{25}{56}\right)\)	\(i\)	\(e\left(\frac{51}{56}\right)\)	\(e\left(\frac{17}{56}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{29}{56}\right)\)
\(\chi_{4640}(13,\cdot)\)	4640.hw	56	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{56}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{25}{56}\right)\)	\(e\left(\frac{53}{56}\right)\)	\(-i\)	\(e\left(\frac{23}{56}\right)\)	\(e\left(\frac{17}{56}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{15}{56}\right)\)
\(\chi_{4640}(17,\cdot)\)	4640.cp	4	no	\(1\)	\(1\)	\(1\)	\(i\)	\(1\)	\(i\)	\(-i\)	\(1\)	\(-i\)	\(i\)	\(-i\)	\(1\)
\(\chi_{4640}(19,\cdot)\)	4640.hi	56	yes	\(1\)	\(1\)	\(e\left(\frac{13}{56}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{51}{56}\right)\)	\(e\left(\frac{23}{56}\right)\)	\(-i\)	\(e\left(\frac{29}{56}\right)\)	\(e\left(\frac{47}{56}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{39}{56}\right)\)
\(\chi_{4640}(21,\cdot)\)	4640.hn	56	no	\(-1\)	\(1\)	\(e\left(\frac{51}{56}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{17}{56}\right)\)	\(e\left(\frac{17}{56}\right)\)	\(i\)	\(e\left(\frac{47}{56}\right)\)	\(e\left(\frac{25}{56}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{41}{56}\right)\)
\(\chi_{4640}(23,\cdot)\)	4640.ez	28	no	\(1\)	\(1\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(-i\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{4640}(27,\cdot)\)	4640.ha	56	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{56}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{29}{56}\right)\)	\(e\left(\frac{15}{56}\right)\)	\(1\)	\(e\left(\frac{39}{56}\right)\)	\(e\left(\frac{41}{56}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{51}{56}\right)\)
\(\chi_{4640}(31,\cdot)\)	4640.gh	28	no	\(1\)	\(1\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(-i\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{1}{28}\right)\)
\(\chi_{4640}(33,\cdot)\)	4640.fx	28	no	\(-1\)	\(1\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(i\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{23}{28}\right)\)
\(\chi_{4640}(37,\cdot)\)	4640.hy	56	yes	\(1\)	\(1\)	\(e\left(\frac{37}{56}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{17}{56}\right)\)	\(e\left(\frac{31}{56}\right)\)	\(1\)	\(e\left(\frac{19}{56}\right)\)	\(e\left(\frac{25}{56}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{55}{56}\right)\)
\(\chi_{4640}(39,\cdot)\)	4640.fa	28	no	\(1\)	\(1\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(-i\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)
\(\chi_{4640}(41,\cdot)\)	4640.r	4	no	\(-1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(1\)	\(-i\)	\(i\)	\(-1\)	\(1\)	\(-1\)	\(-1\)
\(\chi_{4640}(43,\cdot)\)	4640.hz	56	yes	\(-1\)	\(1\)	\(e\left(\frac{53}{56}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{13}{56}\right)\)	\(e\left(\frac{55}{56}\right)\)	\(1\)	\(e\left(\frac{31}{56}\right)\)	\(e\left(\frac{1}{56}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{47}{56}\right)\)
\(\chi_{4640}(47,\cdot)\)	4640.ev	28	no	\(-1\)	\(1\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(-1\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{1}{7}\right)\)
\(\chi_{4640}(49,\cdot)\)	4640.eg	14	no	\(1\)	\(1\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(-1\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)
\(\chi_{4640}(51,\cdot)\)	4640.ho	56	no	\(-1\)	\(1\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{5}{56}\right)\)	\(e\left(\frac{47}{56}\right)\)	\(1\)	\(e\left(\frac{55}{56}\right)\)	\(e\left(\frac{9}{56}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{17}{56}\right)\)
\(\chi_{4640}(53,\cdot)\)	4640.gx	56	yes	\(-1\)	\(1\)	\(e\left(\frac{31}{56}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{15}{56}\right)\)	\(e\left(\frac{43}{56}\right)\)	\(i\)	\(e\left(\frac{25}{56}\right)\)	\(e\left(\frac{55}{56}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{37}{56}\right)\)
\(\chi_{4640}(57,\cdot)\)	4640.cl	4	no	\(-1\)	\(1\)	\(1\)	\(-i\)	\(1\)	\(-i\)	\(-1\)	\(-i\)	\(-i\)	\(-i\)	\(i\)	\(1\)
\(\chi_{4640}(59,\cdot)\)	4640.dp	8	no	\(-1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(i\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{4640}(61,\cdot)\)	4640.hk	56	no	\(-1\)	\(1\)	\(e\left(\frac{1}{56}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{19}{56}\right)\)	\(e\left(\frac{47}{56}\right)\)	\(i\)	\(e\left(\frac{13}{56}\right)\)	\(e\left(\frac{51}{56}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{3}{56}\right)\)
\(\chi_{4640}(63,\cdot)\)	4640.fo	28	no	\(1\)	\(1\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(i\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{1}{28}\right)\)
\(\chi_{4640}(67,\cdot)\)	4640.hv	56	yes	\(1\)	\(1\)	\(e\left(\frac{9}{56}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{17}{56}\right)\)	\(e\left(\frac{45}{56}\right)\)	\(i\)	\(e\left(\frac{47}{56}\right)\)	\(e\left(\frac{53}{56}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{27}{56}\right)\)
\(\chi_{4640}(69,\cdot)\)	4640.hj	56	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{56}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{53}{56}\right)\)	\(e\left(\frac{25}{56}\right)\)	\(-i\)	\(e\left(\frac{51}{56}\right)\)	\(e\left(\frac{45}{56}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{1}{56}\right)\)
\(\chi_{4640}(71,\cdot)\)	4640.fe	28	no	\(-1\)	\(1\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(-1\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{11}{28}\right)\)
\(\chi_{4640}(73,\cdot)\)	4640.fl	28	no	\(1\)	\(1\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(1\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{27}{28}\right)\)
\(\chi_{4640}(77,\cdot)\)	4640.gu	56	yes	\(1\)	\(1\)	\(e\left(\frac{55}{56}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{23}{56}\right)\)	\(e\left(\frac{37}{56}\right)\)	\(-1\)	\(e\left(\frac{29}{56}\right)\)	\(e\left(\frac{47}{56}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{53}{56}\right)\)
\(\chi_{4640}(79,\cdot)\)	4640.fi	28	no	\(1\)	\(1\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(i\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{17}{28}\right)\)
\(\chi_{4640}(81,\cdot)\)	4640.el	14	no	\(1\)	\(1\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(1\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)

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