LMFDB - Group of Dirichlet characters of modulus 1682

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(1682)

gp:g = idealstar(,1682,2)

magma:G := FullDirichletGroup(1682);

Character group

Order	=	812	comment:Order sage:G.order() gp:g.no magma:Order(G);
Structure	=	$C_{812}$	comment:Group structure sage:sorted(g.order() for g in G.gens()) gp:g.cyc magma:PrimaryInvariants(AbelianGroup(G));
Generators	=	$\chi_{1682}(843,\cdot)$	comment:Generators sage:G.gens() gp:g.gen magma:Generators(G);

First 32 of 812 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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{1682}(1,\cdot)$	1682.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1682}(3,\cdot)$	1682.l	812	no	$-1$	$1$	$e\left(\frac{109}{812}\right)$	$e\left(\frac{293}{406}\right)$	$e\left(\frac{134}{203}\right)$	$e\left(\frac{109}{406}\right)$	$e\left(\frac{461}{812}\right)$	$e\left(\frac{325}{406}\right)$	$e\left(\frac{695}{812}\right)$	$e\left(\frac{19}{116}\right)$	$e\left(\frac{269}{812}\right)$	$e\left(\frac{645}{812}\right)$
$\chi_{1682}(5,\cdot)$	1682.k	406	no	$1$	$1$	$e\left(\frac{293}{406}\right)$	$e\left(\frac{65}{203}\right)$	$e\left(\frac{171}{203}\right)$	$e\left(\frac{90}{203}\right)$	$e\left(\frac{51}{406}\right)$	$e\left(\frac{43}{203}\right)$	$e\left(\frac{17}{406}\right)$	$e\left(\frac{25}{58}\right)$	$e\left(\frac{183}{406}\right)$	$e\left(\frac{229}{406}\right)$
$\chi_{1682}(7,\cdot)$	1682.j	203	no	$1$	$1$	$e\left(\frac{134}{203}\right)$	$e\left(\frac{171}{203}\right)$	$e\left(\frac{22}{203}\right)$	$e\left(\frac{65}{203}\right)$	$e\left(\frac{103}{203}\right)$	$e\left(\frac{110}{203}\right)$	$e\left(\frac{102}{203}\right)$	$e\left(\frac{5}{29}\right)$	$e\left(\frac{83}{203}\right)$	$e\left(\frac{156}{203}\right)$
$\chi_{1682}(9,\cdot)$	1682.k	406	no	$1$	$1$	$e\left(\frac{109}{406}\right)$	$e\left(\frac{90}{203}\right)$	$e\left(\frac{65}{203}\right)$	$e\left(\frac{109}{203}\right)$	$e\left(\frac{55}{406}\right)$	$e\left(\frac{122}{203}\right)$	$e\left(\frac{289}{406}\right)$	$e\left(\frac{19}{58}\right)$	$e\left(\frac{269}{406}\right)$	$e\left(\frac{239}{406}\right)$
$\chi_{1682}(11,\cdot)$	1682.l	812	no	$-1$	$1$	$e\left(\frac{461}{812}\right)$	$e\left(\frac{51}{406}\right)$	$e\left(\frac{103}{203}\right)$	$e\left(\frac{55}{406}\right)$	$e\left(\frac{65}{812}\right)$	$e\left(\frac{15}{406}\right)$	$e\left(\frac{563}{812}\right)$	$e\left(\frac{91}{116}\right)$	$e\left(\frac{281}{812}\right)$	$e\left(\frac{61}{812}\right)$
$\chi_{1682}(13,\cdot)$	1682.k	406	no	$1$	$1$	$e\left(\frac{325}{406}\right)$	$e\left(\frac{43}{203}\right)$	$e\left(\frac{110}{203}\right)$	$e\left(\frac{122}{203}\right)$	$e\left(\frac{15}{406}\right)$	$e\left(\frac{144}{203}\right)$	$e\left(\frac{5}{406}\right)$	$e\left(\frac{21}{58}\right)$	$e\left(\frac{221}{406}\right)$	$e\left(\frac{139}{406}\right)$
$\chi_{1682}(15,\cdot)$	1682.l	812	no	$-1$	$1$	$e\left(\frac{695}{812}\right)$	$e\left(\frac{17}{406}\right)$	$e\left(\frac{102}{203}\right)$	$e\left(\frac{289}{406}\right)$	$e\left(\frac{563}{812}\right)$	$e\left(\frac{5}{406}\right)$	$e\left(\frac{729}{812}\right)$	$e\left(\frac{69}{116}\right)$	$e\left(\frac{635}{812}\right)$	$e\left(\frac{291}{812}\right)$
$\chi_{1682}(17,\cdot)$	1682.i	116	no	$-1$	$1$	$e\left(\frac{19}{116}\right)$	$e\left(\frac{25}{58}\right)$	$e\left(\frac{5}{29}\right)$	$e\left(\frac{19}{58}\right)$	$e\left(\frac{91}{116}\right)$	$e\left(\frac{21}{58}\right)$	$e\left(\frac{69}{116}\right)$	$e\left(\frac{103}{116}\right)$	$e\left(\frac{115}{116}\right)$	$e\left(\frac{39}{116}\right)$
$\chi_{1682}(19,\cdot)$	1682.l	812	no	$-1$	$1$	$e\left(\frac{269}{812}\right)$	$e\left(\frac{183}{406}\right)$	$e\left(\frac{83}{203}\right)$	$e\left(\frac{269}{406}\right)$	$e\left(\frac{281}{812}\right)$	$e\left(\frac{221}{406}\right)$	$e\left(\frac{635}{812}\right)$	$e\left(\frac{115}{116}\right)$	$e\left(\frac{53}{812}\right)$	$e\left(\frac{601}{812}\right)$
$\chi_{1682}(21,\cdot)$	1682.l	812	no	$-1$	$1$	$e\left(\frac{645}{812}\right)$	$e\left(\frac{229}{406}\right)$	$e\left(\frac{156}{203}\right)$	$e\left(\frac{239}{406}\right)$	$e\left(\frac{61}{812}\right)$	$e\left(\frac{139}{406}\right)$	$e\left(\frac{291}{812}\right)$	$e\left(\frac{39}{116}\right)$	$e\left(\frac{601}{812}\right)$	$e\left(\frac{457}{812}\right)$
$\chi_{1682}(23,\cdot)$	1682.j	203	no	$1$	$1$	$e\left(\frac{144}{203}\right)$	$e\left(\frac{5}{203}\right)$	$e\left(\frac{60}{203}\right)$	$e\left(\frac{85}{203}\right)$	$e\left(\frac{41}{203}\right)$	$e\left(\frac{97}{203}\right)$	$e\left(\frac{149}{203}\right)$	$e\left(\frac{11}{29}\right)$	$e\left(\frac{171}{203}\right)$	$e\left(\frac{1}{203}\right)$
$\chi_{1682}(25,\cdot)$	1682.j	203	no	$1$	$1$	$e\left(\frac{90}{203}\right)$	$e\left(\frac{130}{203}\right)$	$e\left(\frac{139}{203}\right)$	$e\left(\frac{180}{203}\right)$	$e\left(\frac{51}{203}\right)$	$e\left(\frac{86}{203}\right)$	$e\left(\frac{17}{203}\right)$	$e\left(\frac{25}{29}\right)$	$e\left(\frac{183}{203}\right)$	$e\left(\frac{26}{203}\right)$
$\chi_{1682}(27,\cdot)$	1682.l	812	no	$-1$	$1$	$e\left(\frac{327}{812}\right)$	$e\left(\frac{67}{406}\right)$	$e\left(\frac{199}{203}\right)$	$e\left(\frac{327}{406}\right)$	$e\left(\frac{571}{812}\right)$	$e\left(\frac{163}{406}\right)$	$e\left(\frac{461}{812}\right)$	$e\left(\frac{57}{116}\right)$	$e\left(\frac{807}{812}\right)$	$e\left(\frac{311}{812}\right)$
$\chi_{1682}(31,\cdot)$	1682.l	812	no	$-1$	$1$	$e\left(\frac{341}{812}\right)$	$e\left(\frac{235}{406}\right)$	$e\left(\frac{192}{203}\right)$	$e\left(\frac{341}{406}\right)$	$e\left(\frac{809}{812}\right)$	$e\left(\frac{93}{406}\right)$	$e\left(\frac{811}{812}\right)$	$e\left(\frac{19}{116}\right)$	$e\left(\frac{37}{812}\right)$	$e\left(\frac{297}{812}\right)$
$\chi_{1682}(33,\cdot)$	1682.k	406	no	$1$	$1$	$e\left(\frac{285}{406}\right)$	$e\left(\frac{172}{203}\right)$	$e\left(\frac{34}{203}\right)$	$e\left(\frac{82}{203}\right)$	$e\left(\frac{263}{406}\right)$	$e\left(\frac{170}{203}\right)$	$e\left(\frac{223}{406}\right)$	$e\left(\frac{55}{58}\right)$	$e\left(\frac{275}{406}\right)$	$e\left(\frac{353}{406}\right)$
$\chi_{1682}(35,\cdot)$	1682.k	406	no	$1$	$1$	$e\left(\frac{155}{406}\right)$	$e\left(\frac{33}{203}\right)$	$e\left(\frac{193}{203}\right)$	$e\left(\frac{155}{203}\right)$	$e\left(\frac{257}{406}\right)$	$e\left(\frac{153}{203}\right)$	$e\left(\frac{221}{406}\right)$	$e\left(\frac{35}{58}\right)$	$e\left(\frac{349}{406}\right)$	$e\left(\frac{135}{406}\right)$
$\chi_{1682}(37,\cdot)$	1682.l	812	no	$-1$	$1$	$e\left(\frac{547}{812}\right)$	$e\left(\frac{271}{406}\right)$	$e\left(\frac{2}{203}\right)$	$e\left(\frac{141}{406}\right)$	$e\left(\frac{19}{812}\right)$	$e\left(\frac{223}{406}\right)$	$e\left(\frac{277}{812}\right)$	$e\left(\frac{73}{116}\right)$	$e\left(\frac{307}{812}\right)$	$e\left(\frac{555}{812}\right)$
$\chi_{1682}(39,\cdot)$	1682.l	812	no	$-1$	$1$	$e\left(\frac{759}{812}\right)$	$e\left(\frac{379}{406}\right)$	$e\left(\frac{41}{203}\right)$	$e\left(\frac{353}{406}\right)$	$e\left(\frac{491}{812}\right)$	$e\left(\frac{207}{406}\right)$	$e\left(\frac{705}{812}\right)$	$e\left(\frac{61}{116}\right)$	$e\left(\frac{711}{812}\right)$	$e\left(\frac{111}{812}\right)$
$\chi_{1682}(41,\cdot)$	1682.c	4	no	$-1$	$1$	$i$	$-1$	$1$	$-1$	$i$	$-1$	$-i$	$i$	$i$	$i$
$\chi_{1682}(43,\cdot)$	1682.l	812	no	$-1$	$1$	$e\left(\frac{233}{812}\right)$	$e\left(\frac{157}{406}\right)$	$e\left(\frac{130}{203}\right)$	$e\left(\frac{233}{406}\right)$	$e\left(\frac{17}{812}\right)$	$e\left(\frac{285}{406}\right)$	$e\left(\frac{547}{812}\right)$	$e\left(\frac{47}{116}\right)$	$e\left(\frac{61}{812}\right)$	$e\left(\frac{753}{812}\right)$
$\chi_{1682}(45,\cdot)$	1682.j	203	no	$1$	$1$	$e\left(\frac{201}{203}\right)$	$e\left(\frac{155}{203}\right)$	$e\left(\frac{33}{203}\right)$	$e\left(\frac{199}{203}\right)$	$e\left(\frac{53}{203}\right)$	$e\left(\frac{165}{203}\right)$	$e\left(\frac{153}{203}\right)$	$e\left(\frac{22}{29}\right)$	$e\left(\frac{23}{203}\right)$	$e\left(\frac{31}{203}\right)$
$\chi_{1682}(47,\cdot)$	1682.l	812	no	$-1$	$1$	$e\left(\frac{643}{812}\right)$	$e\left(\frac{205}{406}\right)$	$e\left(\frac{12}{203}\right)$	$e\left(\frac{237}{406}\right)$	$e\left(\frac{723}{812}\right)$	$e\left(\frac{323}{406}\right)$	$e\left(\frac{241}{812}\right)$	$e\left(\frac{61}{116}\right)$	$e\left(\frac{15}{812}\right)$	$e\left(\frac{691}{812}\right)$
$\chi_{1682}(49,\cdot)$	1682.j	203	no	$1$	$1$	$e\left(\frac{65}{203}\right)$	$e\left(\frac{139}{203}\right)$	$e\left(\frac{44}{203}\right)$	$e\left(\frac{130}{203}\right)$	$e\left(\frac{3}{203}\right)$	$e\left(\frac{17}{203}\right)$	$e\left(\frac{1}{203}\right)$	$e\left(\frac{10}{29}\right)$	$e\left(\frac{166}{203}\right)$	$e\left(\frac{109}{203}\right)$
$\chi_{1682}(51,\cdot)$	1682.k	406	no	$1$	$1$	$e\left(\frac{121}{406}\right)$	$e\left(\frac{31}{203}\right)$	$e\left(\frac{169}{203}\right)$	$e\left(\frac{121}{203}\right)$	$e\left(\frac{143}{406}\right)$	$e\left(\frac{33}{203}\right)$	$e\left(\frac{183}{406}\right)$	$e\left(\frac{3}{58}\right)$	$e\left(\frac{131}{406}\right)$	$e\left(\frac{53}{406}\right)$
$\chi_{1682}(53,\cdot)$	1682.j	203	no	$1$	$1$	$e\left(\frac{3}{203}\right)$	$e\left(\frac{72}{203}\right)$	$e\left(\frac{52}{203}\right)$	$e\left(\frac{6}{203}\right)$	$e\left(\frac{22}{203}\right)$	$e\left(\frac{57}{203}\right)$	$e\left(\frac{75}{203}\right)$	$e\left(\frac{25}{29}\right)$	$e\left(\frac{67}{203}\right)$	$e\left(\frac{55}{203}\right)$
$\chi_{1682}(55,\cdot)$	1682.l	812	no	$-1$	$1$	$e\left(\frac{235}{812}\right)$	$e\left(\frac{181}{406}\right)$	$e\left(\frac{71}{203}\right)$	$e\left(\frac{235}{406}\right)$	$e\left(\frac{167}{812}\right)$	$e\left(\frac{101}{406}\right)$	$e\left(\frac{597}{812}\right)$	$e\left(\frac{25}{116}\right)$	$e\left(\frac{647}{812}\right)$	$e\left(\frac{519}{812}\right)$
$\chi_{1682}(57,\cdot)$	1682.h	58	no	$1$	$1$	$e\left(\frac{27}{58}\right)$	$e\left(\frac{5}{29}\right)$	$e\left(\frac{2}{29}\right)$	$e\left(\frac{27}{29}\right)$	$e\left(\frac{53}{58}\right)$	$e\left(\frac{10}{29}\right)$	$e\left(\frac{37}{58}\right)$	$e\left(\frac{9}{58}\right)$	$e\left(\frac{23}{58}\right)$	$e\left(\frac{31}{58}\right)$
$\chi_{1682}(59,\cdot)$	1682.g	29	no	$1$	$1$	$e\left(\frac{1}{29}\right)$	$e\left(\frac{24}{29}\right)$	$e\left(\frac{27}{29}\right)$	$e\left(\frac{2}{29}\right)$	$e\left(\frac{17}{29}\right)$	$e\left(\frac{19}{29}\right)$	$e\left(\frac{25}{29}\right)$	$e\left(\frac{10}{29}\right)$	$e\left(\frac{3}{29}\right)$	$e\left(\frac{28}{29}\right)$
$\chi_{1682}(61,\cdot)$	1682.l	812	no	$-1$	$1$	$e\left(\frac{389}{812}\right)$	$e\left(\frac{405}{406}\right)$	$e\left(\frac{197}{203}\right)$	$e\left(\frac{389}{406}\right)$	$e\left(\frac{349}{812}\right)$	$e\left(\frac{143}{406}\right)$	$e\left(\frac{387}{812}\right)$	$e\left(\frac{71}{116}\right)$	$e\left(\frac{297}{812}\right)$	$e\left(\frac{365}{812}\right)$
$\chi_{1682}(63,\cdot)$	1682.e	14	no	$1$	$1$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{3}{14}\right)$	$-1$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{5}{14}\right)$
$\chi_{1682}(65,\cdot)$	1682.j	203	no	$1$	$1$	$e\left(\frac{106}{203}\right)$	$e\left(\frac{108}{203}\right)$	$e\left(\frac{78}{203}\right)$	$e\left(\frac{9}{203}\right)$	$e\left(\frac{33}{203}\right)$	$e\left(\frac{187}{203}\right)$	$e\left(\frac{11}{203}\right)$	$e\left(\frac{23}{29}\right)$	$e\left(\frac{202}{203}\right)$	$e\left(\frac{184}{203}\right)$

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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	$1682$
Structure	\(C_{812}\)
Order	$812$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{1682}(1,\cdot)\)	1682.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1682}(3,\cdot)\)	1682.l	812	no	\(-1\)	\(1\)	\(e\left(\frac{109}{812}\right)\)	\(e\left(\frac{293}{406}\right)\)	\(e\left(\frac{134}{203}\right)\)	\(e\left(\frac{109}{406}\right)\)	\(e\left(\frac{461}{812}\right)\)	\(e\left(\frac{325}{406}\right)\)	\(e\left(\frac{695}{812}\right)\)	\(e\left(\frac{19}{116}\right)\)	\(e\left(\frac{269}{812}\right)\)	\(e\left(\frac{645}{812}\right)\)
\(\chi_{1682}(5,\cdot)\)	1682.k	406	no	\(1\)	\(1\)	\(e\left(\frac{293}{406}\right)\)	\(e\left(\frac{65}{203}\right)\)	\(e\left(\frac{171}{203}\right)\)	\(e\left(\frac{90}{203}\right)\)	\(e\left(\frac{51}{406}\right)\)	\(e\left(\frac{43}{203}\right)\)	\(e\left(\frac{17}{406}\right)\)	\(e\left(\frac{25}{58}\right)\)	\(e\left(\frac{183}{406}\right)\)	\(e\left(\frac{229}{406}\right)\)
\(\chi_{1682}(7,\cdot)\)	1682.j	203	no	\(1\)	\(1\)	\(e\left(\frac{134}{203}\right)\)	\(e\left(\frac{171}{203}\right)\)	\(e\left(\frac{22}{203}\right)\)	\(e\left(\frac{65}{203}\right)\)	\(e\left(\frac{103}{203}\right)\)	\(e\left(\frac{110}{203}\right)\)	\(e\left(\frac{102}{203}\right)\)	\(e\left(\frac{5}{29}\right)\)	\(e\left(\frac{83}{203}\right)\)	\(e\left(\frac{156}{203}\right)\)
\(\chi_{1682}(9,\cdot)\)	1682.k	406	no	\(1\)	\(1\)	\(e\left(\frac{109}{406}\right)\)	\(e\left(\frac{90}{203}\right)\)	\(e\left(\frac{65}{203}\right)\)	\(e\left(\frac{109}{203}\right)\)	\(e\left(\frac{55}{406}\right)\)	\(e\left(\frac{122}{203}\right)\)	\(e\left(\frac{289}{406}\right)\)	\(e\left(\frac{19}{58}\right)\)	\(e\left(\frac{269}{406}\right)\)	\(e\left(\frac{239}{406}\right)\)
\(\chi_{1682}(11,\cdot)\)	1682.l	812	no	\(-1\)	\(1\)	\(e\left(\frac{461}{812}\right)\)	\(e\left(\frac{51}{406}\right)\)	\(e\left(\frac{103}{203}\right)\)	\(e\left(\frac{55}{406}\right)\)	\(e\left(\frac{65}{812}\right)\)	\(e\left(\frac{15}{406}\right)\)	\(e\left(\frac{563}{812}\right)\)	\(e\left(\frac{91}{116}\right)\)	\(e\left(\frac{281}{812}\right)\)	\(e\left(\frac{61}{812}\right)\)
\(\chi_{1682}(13,\cdot)\)	1682.k	406	no	\(1\)	\(1\)	\(e\left(\frac{325}{406}\right)\)	\(e\left(\frac{43}{203}\right)\)	\(e\left(\frac{110}{203}\right)\)	\(e\left(\frac{122}{203}\right)\)	\(e\left(\frac{15}{406}\right)\)	\(e\left(\frac{144}{203}\right)\)	\(e\left(\frac{5}{406}\right)\)	\(e\left(\frac{21}{58}\right)\)	\(e\left(\frac{221}{406}\right)\)	\(e\left(\frac{139}{406}\right)\)
\(\chi_{1682}(15,\cdot)\)	1682.l	812	no	\(-1\)	\(1\)	\(e\left(\frac{695}{812}\right)\)	\(e\left(\frac{17}{406}\right)\)	\(e\left(\frac{102}{203}\right)\)	\(e\left(\frac{289}{406}\right)\)	\(e\left(\frac{563}{812}\right)\)	\(e\left(\frac{5}{406}\right)\)	\(e\left(\frac{729}{812}\right)\)	\(e\left(\frac{69}{116}\right)\)	\(e\left(\frac{635}{812}\right)\)	\(e\left(\frac{291}{812}\right)\)
\(\chi_{1682}(17,\cdot)\)	1682.i	116	no	\(-1\)	\(1\)	\(e\left(\frac{19}{116}\right)\)	\(e\left(\frac{25}{58}\right)\)	\(e\left(\frac{5}{29}\right)\)	\(e\left(\frac{19}{58}\right)\)	\(e\left(\frac{91}{116}\right)\)	\(e\left(\frac{21}{58}\right)\)	\(e\left(\frac{69}{116}\right)\)	\(e\left(\frac{103}{116}\right)\)	\(e\left(\frac{115}{116}\right)\)	\(e\left(\frac{39}{116}\right)\)
\(\chi_{1682}(19,\cdot)\)	1682.l	812	no	\(-1\)	\(1\)	\(e\left(\frac{269}{812}\right)\)	\(e\left(\frac{183}{406}\right)\)	\(e\left(\frac{83}{203}\right)\)	\(e\left(\frac{269}{406}\right)\)	\(e\left(\frac{281}{812}\right)\)	\(e\left(\frac{221}{406}\right)\)	\(e\left(\frac{635}{812}\right)\)	\(e\left(\frac{115}{116}\right)\)	\(e\left(\frac{53}{812}\right)\)	\(e\left(\frac{601}{812}\right)\)
\(\chi_{1682}(21,\cdot)\)	1682.l	812	no	\(-1\)	\(1\)	\(e\left(\frac{645}{812}\right)\)	\(e\left(\frac{229}{406}\right)\)	\(e\left(\frac{156}{203}\right)\)	\(e\left(\frac{239}{406}\right)\)	\(e\left(\frac{61}{812}\right)\)	\(e\left(\frac{139}{406}\right)\)	\(e\left(\frac{291}{812}\right)\)	\(e\left(\frac{39}{116}\right)\)	\(e\left(\frac{601}{812}\right)\)	\(e\left(\frac{457}{812}\right)\)
\(\chi_{1682}(23,\cdot)\)	1682.j	203	no	\(1\)	\(1\)	\(e\left(\frac{144}{203}\right)\)	\(e\left(\frac{5}{203}\right)\)	\(e\left(\frac{60}{203}\right)\)	\(e\left(\frac{85}{203}\right)\)	\(e\left(\frac{41}{203}\right)\)	\(e\left(\frac{97}{203}\right)\)	\(e\left(\frac{149}{203}\right)\)	\(e\left(\frac{11}{29}\right)\)	\(e\left(\frac{171}{203}\right)\)	\(e\left(\frac{1}{203}\right)\)
\(\chi_{1682}(25,\cdot)\)	1682.j	203	no	\(1\)	\(1\)	\(e\left(\frac{90}{203}\right)\)	\(e\left(\frac{130}{203}\right)\)	\(e\left(\frac{139}{203}\right)\)	\(e\left(\frac{180}{203}\right)\)	\(e\left(\frac{51}{203}\right)\)	\(e\left(\frac{86}{203}\right)\)	\(e\left(\frac{17}{203}\right)\)	\(e\left(\frac{25}{29}\right)\)	\(e\left(\frac{183}{203}\right)\)	\(e\left(\frac{26}{203}\right)\)
\(\chi_{1682}(27,\cdot)\)	1682.l	812	no	\(-1\)	\(1\)	\(e\left(\frac{327}{812}\right)\)	\(e\left(\frac{67}{406}\right)\)	\(e\left(\frac{199}{203}\right)\)	\(e\left(\frac{327}{406}\right)\)	\(e\left(\frac{571}{812}\right)\)	\(e\left(\frac{163}{406}\right)\)	\(e\left(\frac{461}{812}\right)\)	\(e\left(\frac{57}{116}\right)\)	\(e\left(\frac{807}{812}\right)\)	\(e\left(\frac{311}{812}\right)\)
\(\chi_{1682}(31,\cdot)\)	1682.l	812	no	\(-1\)	\(1\)	\(e\left(\frac{341}{812}\right)\)	\(e\left(\frac{235}{406}\right)\)	\(e\left(\frac{192}{203}\right)\)	\(e\left(\frac{341}{406}\right)\)	\(e\left(\frac{809}{812}\right)\)	\(e\left(\frac{93}{406}\right)\)	\(e\left(\frac{811}{812}\right)\)	\(e\left(\frac{19}{116}\right)\)	\(e\left(\frac{37}{812}\right)\)	\(e\left(\frac{297}{812}\right)\)
\(\chi_{1682}(33,\cdot)\)	1682.k	406	no	\(1\)	\(1\)	\(e\left(\frac{285}{406}\right)\)	\(e\left(\frac{172}{203}\right)\)	\(e\left(\frac{34}{203}\right)\)	\(e\left(\frac{82}{203}\right)\)	\(e\left(\frac{263}{406}\right)\)	\(e\left(\frac{170}{203}\right)\)	\(e\left(\frac{223}{406}\right)\)	\(e\left(\frac{55}{58}\right)\)	\(e\left(\frac{275}{406}\right)\)	\(e\left(\frac{353}{406}\right)\)
\(\chi_{1682}(35,\cdot)\)	1682.k	406	no	\(1\)	\(1\)	\(e\left(\frac{155}{406}\right)\)	\(e\left(\frac{33}{203}\right)\)	\(e\left(\frac{193}{203}\right)\)	\(e\left(\frac{155}{203}\right)\)	\(e\left(\frac{257}{406}\right)\)	\(e\left(\frac{153}{203}\right)\)	\(e\left(\frac{221}{406}\right)\)	\(e\left(\frac{35}{58}\right)\)	\(e\left(\frac{349}{406}\right)\)	\(e\left(\frac{135}{406}\right)\)
\(\chi_{1682}(37,\cdot)\)	1682.l	812	no	\(-1\)	\(1\)	\(e\left(\frac{547}{812}\right)\)	\(e\left(\frac{271}{406}\right)\)	\(e\left(\frac{2}{203}\right)\)	\(e\left(\frac{141}{406}\right)\)	\(e\left(\frac{19}{812}\right)\)	\(e\left(\frac{223}{406}\right)\)	\(e\left(\frac{277}{812}\right)\)	\(e\left(\frac{73}{116}\right)\)	\(e\left(\frac{307}{812}\right)\)	\(e\left(\frac{555}{812}\right)\)
\(\chi_{1682}(39,\cdot)\)	1682.l	812	no	\(-1\)	\(1\)	\(e\left(\frac{759}{812}\right)\)	\(e\left(\frac{379}{406}\right)\)	\(e\left(\frac{41}{203}\right)\)	\(e\left(\frac{353}{406}\right)\)	\(e\left(\frac{491}{812}\right)\)	\(e\left(\frac{207}{406}\right)\)	\(e\left(\frac{705}{812}\right)\)	\(e\left(\frac{61}{116}\right)\)	\(e\left(\frac{711}{812}\right)\)	\(e\left(\frac{111}{812}\right)\)
\(\chi_{1682}(41,\cdot)\)	1682.c	4	no	\(-1\)	\(1\)	\(i\)	\(-1\)	\(1\)	\(-1\)	\(i\)	\(-1\)	\(-i\)	\(i\)	\(i\)	\(i\)
\(\chi_{1682}(43,\cdot)\)	1682.l	812	no	\(-1\)	\(1\)	\(e\left(\frac{233}{812}\right)\)	\(e\left(\frac{157}{406}\right)\)	\(e\left(\frac{130}{203}\right)\)	\(e\left(\frac{233}{406}\right)\)	\(e\left(\frac{17}{812}\right)\)	\(e\left(\frac{285}{406}\right)\)	\(e\left(\frac{547}{812}\right)\)	\(e\left(\frac{47}{116}\right)\)	\(e\left(\frac{61}{812}\right)\)	\(e\left(\frac{753}{812}\right)\)
\(\chi_{1682}(45,\cdot)\)	1682.j	203	no	\(1\)	\(1\)	\(e\left(\frac{201}{203}\right)\)	\(e\left(\frac{155}{203}\right)\)	\(e\left(\frac{33}{203}\right)\)	\(e\left(\frac{199}{203}\right)\)	\(e\left(\frac{53}{203}\right)\)	\(e\left(\frac{165}{203}\right)\)	\(e\left(\frac{153}{203}\right)\)	\(e\left(\frac{22}{29}\right)\)	\(e\left(\frac{23}{203}\right)\)	\(e\left(\frac{31}{203}\right)\)
\(\chi_{1682}(47,\cdot)\)	1682.l	812	no	\(-1\)	\(1\)	\(e\left(\frac{643}{812}\right)\)	\(e\left(\frac{205}{406}\right)\)	\(e\left(\frac{12}{203}\right)\)	\(e\left(\frac{237}{406}\right)\)	\(e\left(\frac{723}{812}\right)\)	\(e\left(\frac{323}{406}\right)\)	\(e\left(\frac{241}{812}\right)\)	\(e\left(\frac{61}{116}\right)\)	\(e\left(\frac{15}{812}\right)\)	\(e\left(\frac{691}{812}\right)\)
\(\chi_{1682}(49,\cdot)\)	1682.j	203	no	\(1\)	\(1\)	\(e\left(\frac{65}{203}\right)\)	\(e\left(\frac{139}{203}\right)\)	\(e\left(\frac{44}{203}\right)\)	\(e\left(\frac{130}{203}\right)\)	\(e\left(\frac{3}{203}\right)\)	\(e\left(\frac{17}{203}\right)\)	\(e\left(\frac{1}{203}\right)\)	\(e\left(\frac{10}{29}\right)\)	\(e\left(\frac{166}{203}\right)\)	\(e\left(\frac{109}{203}\right)\)
\(\chi_{1682}(51,\cdot)\)	1682.k	406	no	\(1\)	\(1\)	\(e\left(\frac{121}{406}\right)\)	\(e\left(\frac{31}{203}\right)\)	\(e\left(\frac{169}{203}\right)\)	\(e\left(\frac{121}{203}\right)\)	\(e\left(\frac{143}{406}\right)\)	\(e\left(\frac{33}{203}\right)\)	\(e\left(\frac{183}{406}\right)\)	\(e\left(\frac{3}{58}\right)\)	\(e\left(\frac{131}{406}\right)\)	\(e\left(\frac{53}{406}\right)\)
\(\chi_{1682}(53,\cdot)\)	1682.j	203	no	\(1\)	\(1\)	\(e\left(\frac{3}{203}\right)\)	\(e\left(\frac{72}{203}\right)\)	\(e\left(\frac{52}{203}\right)\)	\(e\left(\frac{6}{203}\right)\)	\(e\left(\frac{22}{203}\right)\)	\(e\left(\frac{57}{203}\right)\)	\(e\left(\frac{75}{203}\right)\)	\(e\left(\frac{25}{29}\right)\)	\(e\left(\frac{67}{203}\right)\)	\(e\left(\frac{55}{203}\right)\)
\(\chi_{1682}(55,\cdot)\)	1682.l	812	no	\(-1\)	\(1\)	\(e\left(\frac{235}{812}\right)\)	\(e\left(\frac{181}{406}\right)\)	\(e\left(\frac{71}{203}\right)\)	\(e\left(\frac{235}{406}\right)\)	\(e\left(\frac{167}{812}\right)\)	\(e\left(\frac{101}{406}\right)\)	\(e\left(\frac{597}{812}\right)\)	\(e\left(\frac{25}{116}\right)\)	\(e\left(\frac{647}{812}\right)\)	\(e\left(\frac{519}{812}\right)\)
\(\chi_{1682}(57,\cdot)\)	1682.h	58	no	\(1\)	\(1\)	\(e\left(\frac{27}{58}\right)\)	\(e\left(\frac{5}{29}\right)\)	\(e\left(\frac{2}{29}\right)\)	\(e\left(\frac{27}{29}\right)\)	\(e\left(\frac{53}{58}\right)\)	\(e\left(\frac{10}{29}\right)\)	\(e\left(\frac{37}{58}\right)\)	\(e\left(\frac{9}{58}\right)\)	\(e\left(\frac{23}{58}\right)\)	\(e\left(\frac{31}{58}\right)\)
\(\chi_{1682}(59,\cdot)\)	1682.g	29	no	\(1\)	\(1\)	\(e\left(\frac{1}{29}\right)\)	\(e\left(\frac{24}{29}\right)\)	\(e\left(\frac{27}{29}\right)\)	\(e\left(\frac{2}{29}\right)\)	\(e\left(\frac{17}{29}\right)\)	\(e\left(\frac{19}{29}\right)\)	\(e\left(\frac{25}{29}\right)\)	\(e\left(\frac{10}{29}\right)\)	\(e\left(\frac{3}{29}\right)\)	\(e\left(\frac{28}{29}\right)\)
\(\chi_{1682}(61,\cdot)\)	1682.l	812	no	\(-1\)	\(1\)	\(e\left(\frac{389}{812}\right)\)	\(e\left(\frac{405}{406}\right)\)	\(e\left(\frac{197}{203}\right)\)	\(e\left(\frac{389}{406}\right)\)	\(e\left(\frac{349}{812}\right)\)	\(e\left(\frac{143}{406}\right)\)	\(e\left(\frac{387}{812}\right)\)	\(e\left(\frac{71}{116}\right)\)	\(e\left(\frac{297}{812}\right)\)	\(e\left(\frac{365}{812}\right)\)
\(\chi_{1682}(63,\cdot)\)	1682.e	14	no	\(1\)	\(1\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(-1\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{5}{14}\right)\)
\(\chi_{1682}(65,\cdot)\)	1682.j	203	no	\(1\)	\(1\)	\(e\left(\frac{106}{203}\right)\)	\(e\left(\frac{108}{203}\right)\)	\(e\left(\frac{78}{203}\right)\)	\(e\left(\frac{9}{203}\right)\)	\(e\left(\frac{33}{203}\right)\)	\(e\left(\frac{187}{203}\right)\)	\(e\left(\frac{11}{203}\right)\)	\(e\left(\frac{23}{29}\right)\)	\(e\left(\frac{202}{203}\right)\)	\(e\left(\frac{184}{203}\right)\)

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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.