LMFDB - Group of Dirichlet characters of modulus 10304

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(10304)

gp:g = idealstar(,10304,2)

magma:G = FullDirichletGroup(10304);

Character group

Order	=	4224	comment:Order sage:G.order() gp:g.no magma:Order(G);
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{528}$	comment:Group structure sage:sorted(g.order() for g in G.gens()) gp:g.cyc magma:PrimaryInvariants(G);
Generators	=	$\chi_{10304}(9983,\cdot)$, $\chi_{10304}(645,\cdot)$, $\chi_{10304}(1473,\cdot)$, $\chi_{10304}(6721,\cdot)$	comment:Generators sage:G.gens() gp:g.gen magma:Generators(G);

First 32 of 4224 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	$-1$	$1$	$3$	$5$	$9$	$11$	$13$	$15$	$17$	$19$	$25$	$27$
$\chi_{10304}(1,\cdot)$	10304.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{10304}(3,\cdot)$	10304.fz	528	yes	$1$	$1$	$e\left(\frac{457}{528}\right)$	$e\left(\frac{395}{528}\right)$	$e\left(\frac{193}{264}\right)$	$e\left(\frac{343}{528}\right)$	$e\left(\frac{87}{176}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{67}{132}\right)$	$e\left(\frac{293}{528}\right)$	$e\left(\frac{131}{264}\right)$	$e\left(\frac{105}{176}\right)$
$\chi_{10304}(5,\cdot)$	10304.ga	528	yes	$1$	$1$	$e\left(\frac{395}{528}\right)$	$e\left(\frac{145}{528}\right)$	$e\left(\frac{131}{264}\right)$	$e\left(\frac{29}{528}\right)$	$e\left(\frac{13}{176}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{119}{132}\right)$	$e\left(\frac{151}{528}\right)$	$e\left(\frac{145}{264}\right)$	$e\left(\frac{43}{176}\right)$
$\chi_{10304}(9,\cdot)$	10304.ft	264	no	$1$	$1$	$e\left(\frac{193}{264}\right)$	$e\left(\frac{131}{264}\right)$	$e\left(\frac{61}{132}\right)$	$e\left(\frac{79}{264}\right)$	$e\left(\frac{87}{88}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{29}{264}\right)$	$e\left(\frac{131}{132}\right)$	$e\left(\frac{17}{88}\right)$
$\chi_{10304}(11,\cdot)$	10304.gc	528	yes	$1$	$1$	$e\left(\frac{343}{528}\right)$	$e\left(\frac{29}{528}\right)$	$e\left(\frac{79}{264}\right)$	$e\left(\frac{217}{528}\right)$	$e\left(\frac{73}{176}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{37}{132}\right)$	$e\left(\frac{83}{528}\right)$	$e\left(\frac{29}{264}\right)$	$e\left(\frac{167}{176}\right)$
$\chi_{10304}(13,\cdot)$	10304.fg	176	yes	$-1$	$1$	$e\left(\frac{87}{176}\right)$	$e\left(\frac{13}{176}\right)$	$e\left(\frac{87}{88}\right)$	$e\left(\frac{73}{176}\right)$	$e\left(\frac{83}{176}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{107}{176}\right)$	$e\left(\frac{13}{88}\right)$	$e\left(\frac{85}{176}\right)$
$\chi_{10304}(15,\cdot)$	10304.dn	44	no	$1$	$1$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{37}{44}\right)$
$\chi_{10304}(17,\cdot)$	10304.fe	132	no	$1$	$1$	$e\left(\frac{67}{132}\right)$	$e\left(\frac{119}{132}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{37}{132}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{113}{132}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{23}{44}\right)$
$\chi_{10304}(19,\cdot)$	10304.fw	528	yes	$-1$	$1$	$e\left(\frac{293}{528}\right)$	$e\left(\frac{151}{528}\right)$	$e\left(\frac{29}{264}\right)$	$e\left(\frac{83}{528}\right)$	$e\left(\frac{107}{176}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{113}{132}\right)$	$e\left(\frac{505}{528}\right)$	$e\left(\frac{151}{264}\right)$	$e\left(\frac{117}{176}\right)$
$\chi_{10304}(25,\cdot)$	10304.ft	264	no	$1$	$1$	$e\left(\frac{131}{264}\right)$	$e\left(\frac{145}{264}\right)$	$e\left(\frac{131}{132}\right)$	$e\left(\frac{29}{264}\right)$	$e\left(\frac{13}{88}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{151}{264}\right)$	$e\left(\frac{13}{132}\right)$	$e\left(\frac{43}{88}\right)$
$\chi_{10304}(27,\cdot)$	10304.fk	176	yes	$1$	$1$	$e\left(\frac{105}{176}\right)$	$e\left(\frac{43}{176}\right)$	$e\left(\frac{17}{88}\right)$	$e\left(\frac{167}{176}\right)$	$e\left(\frac{85}{176}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{117}{176}\right)$	$e\left(\frac{43}{88}\right)$	$e\left(\frac{139}{176}\right)$
$\chi_{10304}(29,\cdot)$	10304.fm	176	no	$1$	$1$	$e\left(\frac{27}{176}\right)$	$e\left(\frac{89}{176}\right)$	$e\left(\frac{27}{88}\right)$	$e\left(\frac{141}{176}\right)$	$e\left(\frac{135}{176}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{15}{176}\right)$	$e\left(\frac{1}{88}\right)$	$e\left(\frac{81}{176}\right)$
$\chi_{10304}(31,\cdot)$	10304.eh	66	no	$1$	$1$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{13}{22}\right)$
$\chi_{10304}(33,\cdot)$	10304.el	66	no	$1$	$1$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{6}{11}\right)$
$\chi_{10304}(37,\cdot)$	10304.fy	528	yes	$-1$	$1$	$e\left(\frac{155}{528}\right)$	$e\left(\frac{97}{528}\right)$	$e\left(\frac{155}{264}\right)$	$e\left(\frac{389}{528}\right)$	$e\left(\frac{141}{176}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{101}{132}\right)$	$e\left(\frac{487}{528}\right)$	$e\left(\frac{97}{264}\right)$	$e\left(\frac{155}{176}\right)$
$\chi_{10304}(39,\cdot)$	10304.fp	264	no	$-1$	$1$	$e\left(\frac{95}{264}\right)$	$e\left(\frac{217}{264}\right)$	$e\left(\frac{95}{132}\right)$	$e\left(\frac{17}{264}\right)$	$e\left(\frac{85}{88}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{43}{264}\right)$	$e\left(\frac{85}{132}\right)$	$e\left(\frac{7}{88}\right)$
$\chi_{10304}(41,\cdot)$	10304.eu	88	no	$-1$	$1$	$e\left(\frac{75}{88}\right)$	$e\left(\frac{81}{88}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{25}{88}\right)$	$e\left(\frac{23}{88}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{71}{88}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{49}{88}\right)$
$\chi_{10304}(43,\cdot)$	10304.fh	176	no	$1$	$1$	$e\left(\frac{101}{176}\right)$	$e\left(\frac{7}{176}\right)$	$e\left(\frac{13}{88}\right)$	$e\left(\frac{107}{176}\right)$	$e\left(\frac{65}{176}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{105}{176}\right)$	$e\left(\frac{7}{88}\right)$	$e\left(\frac{127}{176}\right)$
$\chi_{10304}(45,\cdot)$	10304.dw	48	yes	$1$	$1$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{1}{16}\right)$	$i$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{7}{16}\right)$
$\chi_{10304}(47,\cdot)$	10304.bz	12	no	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$-i$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$-i$
$\chi_{10304}(51,\cdot)$	10304.gc	528	yes	$1$	$1$	$e\left(\frac{197}{528}\right)$	$e\left(\frac{343}{528}\right)$	$e\left(\frac{197}{264}\right)$	$e\left(\frac{491}{528}\right)$	$e\left(\frac{123}{176}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{119}{132}\right)$	$e\left(\frac{217}{528}\right)$	$e\left(\frac{79}{264}\right)$	$e\left(\frac{21}{176}\right)$
$\chi_{10304}(53,\cdot)$	10304.fy	528	yes	$-1$	$1$	$e\left(\frac{223}{528}\right)$	$e\left(\frac{269}{528}\right)$	$e\left(\frac{223}{264}\right)$	$e\left(\frac{1}{528}\right)$	$e\left(\frac{137}{176}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{61}{132}\right)$	$e\left(\frac{251}{528}\right)$	$e\left(\frac{5}{264}\right)$	$e\left(\frac{47}{176}\right)$
$\chi_{10304}(55,\cdot)$	10304.eq	88	no	$1$	$1$	$e\left(\frac{35}{88}\right)$	$e\left(\frac{29}{88}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{41}{88}\right)$	$e\left(\frac{43}{88}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{39}{88}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{17}{88}\right)$
$\chi_{10304}(57,\cdot)$	10304.er	88	no	$-1$	$1$	$e\left(\frac{37}{88}\right)$	$e\left(\frac{3}{88}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{71}{88}\right)$	$e\left(\frac{9}{88}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{45}{88}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{23}{88}\right)$
$\chi_{10304}(59,\cdot)$	10304.fz	528	yes	$1$	$1$	$e\left(\frac{19}{528}\right)$	$e\left(\frac{281}{528}\right)$	$e\left(\frac{19}{264}\right)$	$e\left(\frac{109}{528}\right)$	$e\left(\frac{61}{176}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{49}{132}\right)$	$e\left(\frac{167}{528}\right)$	$e\left(\frac{17}{264}\right)$	$e\left(\frac{19}{176}\right)$
$\chi_{10304}(61,\cdot)$	10304.ga	528	yes	$1$	$1$	$e\left(\frac{401}{528}\right)$	$e\left(\frac{67}{528}\right)$	$e\left(\frac{137}{264}\right)$	$e\left(\frac{119}{528}\right)$	$e\left(\frac{23}{176}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{65}{132}\right)$	$e\left(\frac{37}{528}\right)$	$e\left(\frac{67}{264}\right)$	$e\left(\frac{49}{176}\right)$
$\chi_{10304}(65,\cdot)$	10304.ej	66	no	$-1$	$1$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{8}{11}\right)$
$\chi_{10304}(67,\cdot)$	10304.gc	528	yes	$1$	$1$	$e\left(\frac{97}{528}\right)$	$e\left(\frac{59}{528}\right)$	$e\left(\frac{97}{264}\right)$	$e\left(\frac{223}{528}\right)$	$e\left(\frac{15}{176}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{7}{132}\right)$	$e\left(\frac{5}{528}\right)$	$e\left(\frac{59}{264}\right)$	$e\left(\frac{97}{176}\right)$
$\chi_{10304}(71,\cdot)$	10304.es	88	no	$-1$	$1$	$e\left(\frac{73}{88}\right)$	$e\left(\frac{63}{88}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{39}{88}\right)$	$e\left(\frac{57}{88}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{21}{88}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{43}{88}\right)$
$\chi_{10304}(73,\cdot)$	10304.fv	264	no	$-1$	$1$	$e\left(\frac{53}{264}\right)$	$e\left(\frac{103}{264}\right)$	$e\left(\frac{53}{132}\right)$	$e\left(\frac{47}{264}\right)$	$e\left(\frac{59}{88}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{49}{264}\right)$	$e\left(\frac{103}{132}\right)$	$e\left(\frac{53}{88}\right)$
$\chi_{10304}(75,\cdot)$	10304.fz	528	yes	$1$	$1$	$e\left(\frac{191}{528}\right)$	$e\left(\frac{157}{528}\right)$	$e\left(\frac{191}{264}\right)$	$e\left(\frac{401}{528}\right)$	$e\left(\frac{113}{176}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{41}{132}\right)$	$e\left(\frac{67}{528}\right)$	$e\left(\frac{157}{264}\right)$	$e\left(\frac{15}{176}\right)$
$\chi_{10304}(79,\cdot)$	10304.ez	132	no	$1$	$1$	$e\left(\frac{101}{132}\right)$	$e\left(\frac{7}{132}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{41}{132}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{127}{132}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{13}{44}\right)$

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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 $\F_{q}$
Belyi maps

Modulus	$10304$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{528}\)
Order	$4224$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(25\)	\(27\)
\(\chi_{10304}(1,\cdot)\)	10304.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{10304}(3,\cdot)\)	10304.fz	528	yes	\(1\)	\(1\)	\(e\left(\frac{457}{528}\right)\)	\(e\left(\frac{395}{528}\right)\)	\(e\left(\frac{193}{264}\right)\)	\(e\left(\frac{343}{528}\right)\)	\(e\left(\frac{87}{176}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{67}{132}\right)\)	\(e\left(\frac{293}{528}\right)\)	\(e\left(\frac{131}{264}\right)\)	\(e\left(\frac{105}{176}\right)\)
\(\chi_{10304}(5,\cdot)\)	10304.ga	528	yes	\(1\)	\(1\)	\(e\left(\frac{395}{528}\right)\)	\(e\left(\frac{145}{528}\right)\)	\(e\left(\frac{131}{264}\right)\)	\(e\left(\frac{29}{528}\right)\)	\(e\left(\frac{13}{176}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{119}{132}\right)\)	\(e\left(\frac{151}{528}\right)\)	\(e\left(\frac{145}{264}\right)\)	\(e\left(\frac{43}{176}\right)\)
\(\chi_{10304}(9,\cdot)\)	10304.ft	264	no	\(1\)	\(1\)	\(e\left(\frac{193}{264}\right)\)	\(e\left(\frac{131}{264}\right)\)	\(e\left(\frac{61}{132}\right)\)	\(e\left(\frac{79}{264}\right)\)	\(e\left(\frac{87}{88}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{29}{264}\right)\)	\(e\left(\frac{131}{132}\right)\)	\(e\left(\frac{17}{88}\right)\)
\(\chi_{10304}(11,\cdot)\)	10304.gc	528	yes	\(1\)	\(1\)	\(e\left(\frac{343}{528}\right)\)	\(e\left(\frac{29}{528}\right)\)	\(e\left(\frac{79}{264}\right)\)	\(e\left(\frac{217}{528}\right)\)	\(e\left(\frac{73}{176}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{37}{132}\right)\)	\(e\left(\frac{83}{528}\right)\)	\(e\left(\frac{29}{264}\right)\)	\(e\left(\frac{167}{176}\right)\)
\(\chi_{10304}(13,\cdot)\)	10304.fg	176	yes	\(-1\)	\(1\)	\(e\left(\frac{87}{176}\right)\)	\(e\left(\frac{13}{176}\right)\)	\(e\left(\frac{87}{88}\right)\)	\(e\left(\frac{73}{176}\right)\)	\(e\left(\frac{83}{176}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{107}{176}\right)\)	\(e\left(\frac{13}{88}\right)\)	\(e\left(\frac{85}{176}\right)\)
\(\chi_{10304}(15,\cdot)\)	10304.dn	44	no	\(1\)	\(1\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{37}{44}\right)\)
\(\chi_{10304}(17,\cdot)\)	10304.fe	132	no	\(1\)	\(1\)	\(e\left(\frac{67}{132}\right)\)	\(e\left(\frac{119}{132}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{37}{132}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{113}{132}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{23}{44}\right)\)
\(\chi_{10304}(19,\cdot)\)	10304.fw	528	yes	\(-1\)	\(1\)	\(e\left(\frac{293}{528}\right)\)	\(e\left(\frac{151}{528}\right)\)	\(e\left(\frac{29}{264}\right)\)	\(e\left(\frac{83}{528}\right)\)	\(e\left(\frac{107}{176}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{113}{132}\right)\)	\(e\left(\frac{505}{528}\right)\)	\(e\left(\frac{151}{264}\right)\)	\(e\left(\frac{117}{176}\right)\)
\(\chi_{10304}(25,\cdot)\)	10304.ft	264	no	\(1\)	\(1\)	\(e\left(\frac{131}{264}\right)\)	\(e\left(\frac{145}{264}\right)\)	\(e\left(\frac{131}{132}\right)\)	\(e\left(\frac{29}{264}\right)\)	\(e\left(\frac{13}{88}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{151}{264}\right)\)	\(e\left(\frac{13}{132}\right)\)	\(e\left(\frac{43}{88}\right)\)
\(\chi_{10304}(27,\cdot)\)	10304.fk	176	yes	\(1\)	\(1\)	\(e\left(\frac{105}{176}\right)\)	\(e\left(\frac{43}{176}\right)\)	\(e\left(\frac{17}{88}\right)\)	\(e\left(\frac{167}{176}\right)\)	\(e\left(\frac{85}{176}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{117}{176}\right)\)	\(e\left(\frac{43}{88}\right)\)	\(e\left(\frac{139}{176}\right)\)
\(\chi_{10304}(29,\cdot)\)	10304.fm	176	no	\(1\)	\(1\)	\(e\left(\frac{27}{176}\right)\)	\(e\left(\frac{89}{176}\right)\)	\(e\left(\frac{27}{88}\right)\)	\(e\left(\frac{141}{176}\right)\)	\(e\left(\frac{135}{176}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{15}{176}\right)\)	\(e\left(\frac{1}{88}\right)\)	\(e\left(\frac{81}{176}\right)\)
\(\chi_{10304}(31,\cdot)\)	10304.eh	66	no	\(1\)	\(1\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{13}{22}\right)\)
\(\chi_{10304}(33,\cdot)\)	10304.el	66	no	\(1\)	\(1\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{6}{11}\right)\)
\(\chi_{10304}(37,\cdot)\)	10304.fy	528	yes	\(-1\)	\(1\)	\(e\left(\frac{155}{528}\right)\)	\(e\left(\frac{97}{528}\right)\)	\(e\left(\frac{155}{264}\right)\)	\(e\left(\frac{389}{528}\right)\)	\(e\left(\frac{141}{176}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{101}{132}\right)\)	\(e\left(\frac{487}{528}\right)\)	\(e\left(\frac{97}{264}\right)\)	\(e\left(\frac{155}{176}\right)\)
\(\chi_{10304}(39,\cdot)\)	10304.fp	264	no	\(-1\)	\(1\)	\(e\left(\frac{95}{264}\right)\)	\(e\left(\frac{217}{264}\right)\)	\(e\left(\frac{95}{132}\right)\)	\(e\left(\frac{17}{264}\right)\)	\(e\left(\frac{85}{88}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{43}{264}\right)\)	\(e\left(\frac{85}{132}\right)\)	\(e\left(\frac{7}{88}\right)\)
\(\chi_{10304}(41,\cdot)\)	10304.eu	88	no	\(-1\)	\(1\)	\(e\left(\frac{75}{88}\right)\)	\(e\left(\frac{81}{88}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{25}{88}\right)\)	\(e\left(\frac{23}{88}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{71}{88}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{49}{88}\right)\)
\(\chi_{10304}(43,\cdot)\)	10304.fh	176	no	\(1\)	\(1\)	\(e\left(\frac{101}{176}\right)\)	\(e\left(\frac{7}{176}\right)\)	\(e\left(\frac{13}{88}\right)\)	\(e\left(\frac{107}{176}\right)\)	\(e\left(\frac{65}{176}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{105}{176}\right)\)	\(e\left(\frac{7}{88}\right)\)	\(e\left(\frac{127}{176}\right)\)
\(\chi_{10304}(45,\cdot)\)	10304.dw	48	yes	\(1\)	\(1\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(i\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{7}{16}\right)\)
\(\chi_{10304}(47,\cdot)\)	10304.bz	12	no	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-i\)
\(\chi_{10304}(51,\cdot)\)	10304.gc	528	yes	\(1\)	\(1\)	\(e\left(\frac{197}{528}\right)\)	\(e\left(\frac{343}{528}\right)\)	\(e\left(\frac{197}{264}\right)\)	\(e\left(\frac{491}{528}\right)\)	\(e\left(\frac{123}{176}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{119}{132}\right)\)	\(e\left(\frac{217}{528}\right)\)	\(e\left(\frac{79}{264}\right)\)	\(e\left(\frac{21}{176}\right)\)
\(\chi_{10304}(53,\cdot)\)	10304.fy	528	yes	\(-1\)	\(1\)	\(e\left(\frac{223}{528}\right)\)	\(e\left(\frac{269}{528}\right)\)	\(e\left(\frac{223}{264}\right)\)	\(e\left(\frac{1}{528}\right)\)	\(e\left(\frac{137}{176}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{61}{132}\right)\)	\(e\left(\frac{251}{528}\right)\)	\(e\left(\frac{5}{264}\right)\)	\(e\left(\frac{47}{176}\right)\)
\(\chi_{10304}(55,\cdot)\)	10304.eq	88	no	\(1\)	\(1\)	\(e\left(\frac{35}{88}\right)\)	\(e\left(\frac{29}{88}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{41}{88}\right)\)	\(e\left(\frac{43}{88}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{39}{88}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{17}{88}\right)\)
\(\chi_{10304}(57,\cdot)\)	10304.er	88	no	\(-1\)	\(1\)	\(e\left(\frac{37}{88}\right)\)	\(e\left(\frac{3}{88}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{71}{88}\right)\)	\(e\left(\frac{9}{88}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{45}{88}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{23}{88}\right)\)
\(\chi_{10304}(59,\cdot)\)	10304.fz	528	yes	\(1\)	\(1\)	\(e\left(\frac{19}{528}\right)\)	\(e\left(\frac{281}{528}\right)\)	\(e\left(\frac{19}{264}\right)\)	\(e\left(\frac{109}{528}\right)\)	\(e\left(\frac{61}{176}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{49}{132}\right)\)	\(e\left(\frac{167}{528}\right)\)	\(e\left(\frac{17}{264}\right)\)	\(e\left(\frac{19}{176}\right)\)
\(\chi_{10304}(61,\cdot)\)	10304.ga	528	yes	\(1\)	\(1\)	\(e\left(\frac{401}{528}\right)\)	\(e\left(\frac{67}{528}\right)\)	\(e\left(\frac{137}{264}\right)\)	\(e\left(\frac{119}{528}\right)\)	\(e\left(\frac{23}{176}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{65}{132}\right)\)	\(e\left(\frac{37}{528}\right)\)	\(e\left(\frac{67}{264}\right)\)	\(e\left(\frac{49}{176}\right)\)
\(\chi_{10304}(65,\cdot)\)	10304.ej	66	no	\(-1\)	\(1\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{8}{11}\right)\)
\(\chi_{10304}(67,\cdot)\)	10304.gc	528	yes	\(1\)	\(1\)	\(e\left(\frac{97}{528}\right)\)	\(e\left(\frac{59}{528}\right)\)	\(e\left(\frac{97}{264}\right)\)	\(e\left(\frac{223}{528}\right)\)	\(e\left(\frac{15}{176}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{7}{132}\right)\)	\(e\left(\frac{5}{528}\right)\)	\(e\left(\frac{59}{264}\right)\)	\(e\left(\frac{97}{176}\right)\)
\(\chi_{10304}(71,\cdot)\)	10304.es	88	no	\(-1\)	\(1\)	\(e\left(\frac{73}{88}\right)\)	\(e\left(\frac{63}{88}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{39}{88}\right)\)	\(e\left(\frac{57}{88}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{21}{88}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{43}{88}\right)\)
\(\chi_{10304}(73,\cdot)\)	10304.fv	264	no	\(-1\)	\(1\)	\(e\left(\frac{53}{264}\right)\)	\(e\left(\frac{103}{264}\right)\)	\(e\left(\frac{53}{132}\right)\)	\(e\left(\frac{47}{264}\right)\)	\(e\left(\frac{59}{88}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{49}{264}\right)\)	\(e\left(\frac{103}{132}\right)\)	\(e\left(\frac{53}{88}\right)\)
\(\chi_{10304}(75,\cdot)\)	10304.fz	528	yes	\(1\)	\(1\)	\(e\left(\frac{191}{528}\right)\)	\(e\left(\frac{157}{528}\right)\)	\(e\left(\frac{191}{264}\right)\)	\(e\left(\frac{401}{528}\right)\)	\(e\left(\frac{113}{176}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{41}{132}\right)\)	\(e\left(\frac{67}{528}\right)\)	\(e\left(\frac{157}{264}\right)\)	\(e\left(\frac{15}{176}\right)\)
\(\chi_{10304}(79,\cdot)\)	10304.ez	132	no	\(1\)	\(1\)	\(e\left(\frac{101}{132}\right)\)	\(e\left(\frac{7}{132}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{41}{132}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{127}{132}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{13}{44}\right)\)

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