LMFDB - Group of Dirichlet characters of modulus 834

sage:H = DirichletGroup(834)

pari:g = idealstar(,834,2)

Character group

sage:G.order() pari:g.no
Order	=	276
sage:H.invariants() pari:g.cyc
Structure	=	$C_{2}\times C_{138}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{834}(557,\cdot)$, $\chi_{834}(697,\cdot)$

First 32 of 276 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	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$
$\chi_{834}(1,\cdot)$	834.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{834}(5,\cdot)$	834.n	138	no	$-1$	$1$	$e\left(\frac{13}{138}\right)$	$e\left(\frac{11}{69}\right)$	$e\left(\frac{119}{138}\right)$	$e\left(\frac{61}{69}\right)$	$e\left(\frac{25}{138}\right)$	$e\left(\frac{1}{69}\right)$	$e\left(\frac{15}{46}\right)$	$e\left(\frac{13}{69}\right)$	$e\left(\frac{11}{138}\right)$	$e\left(\frac{62}{69}\right)$
$\chi_{834}(7,\cdot)$	834.m	69	no	$1$	$1$	$e\left(\frac{11}{69}\right)$	$e\left(\frac{8}{69}\right)$	$e\left(\frac{37}{69}\right)$	$e\left(\frac{13}{69}\right)$	$e\left(\frac{53}{69}\right)$	$e\left(\frac{7}{69}\right)$	$e\left(\frac{18}{23}\right)$	$e\left(\frac{22}{69}\right)$	$e\left(\frac{4}{69}\right)$	$e\left(\frac{20}{69}\right)$
$\chi_{834}(11,\cdot)$	834.n	138	no	$-1$	$1$	$e\left(\frac{119}{138}\right)$	$e\left(\frac{37}{69}\right)$	$e\left(\frac{49}{138}\right)$	$e\left(\frac{17}{69}\right)$	$e\left(\frac{59}{138}\right)$	$e\left(\frac{41}{69}\right)$	$e\left(\frac{17}{46}\right)$	$e\left(\frac{50}{69}\right)$	$e\left(\frac{37}{138}\right)$	$e\left(\frac{58}{69}\right)$
$\chi_{834}(13,\cdot)$	834.m	69	no	$1$	$1$	$e\left(\frac{61}{69}\right)$	$e\left(\frac{13}{69}\right)$	$e\left(\frac{17}{69}\right)$	$e\left(\frac{47}{69}\right)$	$e\left(\frac{43}{69}\right)$	$e\left(\frac{20}{69}\right)$	$e\left(\frac{12}{23}\right)$	$e\left(\frac{53}{69}\right)$	$e\left(\frac{41}{69}\right)$	$e\left(\frac{67}{69}\right)$
$\chi_{834}(17,\cdot)$	834.o	138	no	$1$	$1$	$e\left(\frac{25}{138}\right)$	$e\left(\frac{53}{69}\right)$	$e\left(\frac{59}{138}\right)$	$e\left(\frac{43}{69}\right)$	$e\left(\frac{32}{69}\right)$	$e\left(\frac{41}{138}\right)$	$e\left(\frac{10}{23}\right)$	$e\left(\frac{25}{69}\right)$	$e\left(\frac{53}{138}\right)$	$e\left(\frac{29}{69}\right)$
$\chi_{834}(19,\cdot)$	834.p	138	no	$-1$	$1$	$e\left(\frac{1}{69}\right)$	$e\left(\frac{7}{69}\right)$	$e\left(\frac{41}{69}\right)$	$e\left(\frac{20}{69}\right)$	$e\left(\frac{41}{138}\right)$	$e\left(\frac{133}{138}\right)$	$e\left(\frac{43}{46}\right)$	$e\left(\frac{2}{69}\right)$	$e\left(\frac{38}{69}\right)$	$e\left(\frac{52}{69}\right)$
$\chi_{834}(23,\cdot)$	834.k	46	no	$1$	$1$	$e\left(\frac{15}{46}\right)$	$e\left(\frac{18}{23}\right)$	$e\left(\frac{17}{46}\right)$	$e\left(\frac{12}{23}\right)$	$e\left(\frac{10}{23}\right)$	$e\left(\frac{43}{46}\right)$	$e\left(\frac{18}{23}\right)$	$e\left(\frac{15}{23}\right)$	$e\left(\frac{41}{46}\right)$	$e\left(\frac{22}{23}\right)$
$\chi_{834}(25,\cdot)$	834.m	69	no	$1$	$1$	$e\left(\frac{13}{69}\right)$	$e\left(\frac{22}{69}\right)$	$e\left(\frac{50}{69}\right)$	$e\left(\frac{53}{69}\right)$	$e\left(\frac{25}{69}\right)$	$e\left(\frac{2}{69}\right)$	$e\left(\frac{15}{23}\right)$	$e\left(\frac{26}{69}\right)$	$e\left(\frac{11}{69}\right)$	$e\left(\frac{55}{69}\right)$
$\chi_{834}(29,\cdot)$	834.n	138	no	$-1$	$1$	$e\left(\frac{11}{138}\right)$	$e\left(\frac{4}{69}\right)$	$e\left(\frac{37}{138}\right)$	$e\left(\frac{41}{69}\right)$	$e\left(\frac{53}{138}\right)$	$e\left(\frac{38}{69}\right)$	$e\left(\frac{41}{46}\right)$	$e\left(\frac{11}{69}\right)$	$e\left(\frac{73}{138}\right)$	$e\left(\frac{10}{69}\right)$
$\chi_{834}(31,\cdot)$	834.m	69	no	$1$	$1$	$e\left(\frac{62}{69}\right)$	$e\left(\frac{20}{69}\right)$	$e\left(\frac{58}{69}\right)$	$e\left(\frac{67}{69}\right)$	$e\left(\frac{29}{69}\right)$	$e\left(\frac{52}{69}\right)$	$e\left(\frac{22}{23}\right)$	$e\left(\frac{55}{69}\right)$	$e\left(\frac{10}{69}\right)$	$e\left(\frac{50}{69}\right)$
$\chi_{834}(35,\cdot)$	834.n	138	no	$-1$	$1$	$e\left(\frac{35}{138}\right)$	$e\left(\frac{19}{69}\right)$	$e\left(\frac{55}{138}\right)$	$e\left(\frac{5}{69}\right)$	$e\left(\frac{131}{138}\right)$	$e\left(\frac{8}{69}\right)$	$e\left(\frac{5}{46}\right)$	$e\left(\frac{35}{69}\right)$	$e\left(\frac{19}{138}\right)$	$e\left(\frac{13}{69}\right)$
$\chi_{834}(37,\cdot)$	834.m	69	no	$1$	$1$	$e\left(\frac{59}{69}\right)$	$e\left(\frac{68}{69}\right)$	$e\left(\frac{4}{69}\right)$	$e\left(\frac{7}{69}\right)$	$e\left(\frac{2}{69}\right)$	$e\left(\frac{25}{69}\right)$	$e\left(\frac{15}{23}\right)$	$e\left(\frac{49}{69}\right)$	$e\left(\frac{34}{69}\right)$	$e\left(\frac{32}{69}\right)$
$\chi_{834}(41,\cdot)$	834.n	138	no	$-1$	$1$	$e\left(\frac{61}{138}\right)$	$e\left(\frac{41}{69}\right)$	$e\left(\frac{17}{138}\right)$	$e\left(\frac{58}{69}\right)$	$e\left(\frac{43}{138}\right)$	$e\left(\frac{10}{69}\right)$	$e\left(\frac{35}{46}\right)$	$e\left(\frac{61}{69}\right)$	$e\left(\frac{41}{138}\right)$	$e\left(\frac{68}{69}\right)$
$\chi_{834}(43,\cdot)$	834.f	6	no	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{834}(47,\cdot)$	834.n	138	no	$-1$	$1$	$e\left(\frac{79}{138}\right)$	$e\left(\frac{35}{69}\right)$	$e\left(\frac{65}{138}\right)$	$e\left(\frac{31}{69}\right)$	$e\left(\frac{67}{138}\right)$	$e\left(\frac{22}{69}\right)$	$e\left(\frac{31}{46}\right)$	$e\left(\frac{10}{69}\right)$	$e\left(\frac{35}{138}\right)$	$e\left(\frac{53}{69}\right)$
$\chi_{834}(49,\cdot)$	834.m	69	no	$1$	$1$	$e\left(\frac{22}{69}\right)$	$e\left(\frac{16}{69}\right)$	$e\left(\frac{5}{69}\right)$	$e\left(\frac{26}{69}\right)$	$e\left(\frac{37}{69}\right)$	$e\left(\frac{14}{69}\right)$	$e\left(\frac{13}{23}\right)$	$e\left(\frac{44}{69}\right)$	$e\left(\frac{8}{69}\right)$	$e\left(\frac{40}{69}\right)$
$\chi_{834}(53,\cdot)$	834.o	138	no	$1$	$1$	$e\left(\frac{109}{138}\right)$	$e\left(\frac{2}{69}\right)$	$e\left(\frac{53}{138}\right)$	$e\left(\frac{55}{69}\right)$	$e\left(\frac{65}{69}\right)$	$e\left(\frac{107}{138}\right)$	$e\left(\frac{16}{23}\right)$	$e\left(\frac{40}{69}\right)$	$e\left(\frac{71}{138}\right)$	$e\left(\frac{5}{69}\right)$
$\chi_{834}(55,\cdot)$	834.i	23	no	$1$	$1$	$e\left(\frac{22}{23}\right)$	$e\left(\frac{16}{23}\right)$	$e\left(\frac{5}{23}\right)$	$e\left(\frac{3}{23}\right)$	$e\left(\frac{14}{23}\right)$	$e\left(\frac{14}{23}\right)$	$e\left(\frac{16}{23}\right)$	$e\left(\frac{21}{23}\right)$	$e\left(\frac{8}{23}\right)$	$e\left(\frac{17}{23}\right)$
$\chi_{834}(59,\cdot)$	834.k	46	no	$1$	$1$	$e\left(\frac{27}{46}\right)$	$e\left(\frac{14}{23}\right)$	$e\left(\frac{3}{46}\right)$	$e\left(\frac{17}{23}\right)$	$e\left(\frac{18}{23}\right)$	$e\left(\frac{13}{46}\right)$	$e\left(\frac{14}{23}\right)$	$e\left(\frac{4}{23}\right)$	$e\left(\frac{37}{46}\right)$	$e\left(\frac{12}{23}\right)$
$\chi_{834}(61,\cdot)$	834.p	138	no	$-1$	$1$	$e\left(\frac{4}{69}\right)$	$e\left(\frac{28}{69}\right)$	$e\left(\frac{26}{69}\right)$	$e\left(\frac{11}{69}\right)$	$e\left(\frac{95}{138}\right)$	$e\left(\frac{49}{138}\right)$	$e\left(\frac{11}{46}\right)$	$e\left(\frac{8}{69}\right)$	$e\left(\frac{14}{69}\right)$	$e\left(\frac{1}{69}\right)$
$\chi_{834}(65,\cdot)$	834.l	46	no	$-1$	$1$	$e\left(\frac{45}{46}\right)$	$e\left(\frac{8}{23}\right)$	$e\left(\frac{5}{46}\right)$	$e\left(\frac{13}{23}\right)$	$e\left(\frac{37}{46}\right)$	$e\left(\frac{7}{23}\right)$	$e\left(\frac{39}{46}\right)$	$e\left(\frac{22}{23}\right)$	$e\left(\frac{31}{46}\right)$	$e\left(\frac{20}{23}\right)$
$\chi_{834}(67,\cdot)$	834.m	69	no	$1$	$1$	$e\left(\frac{67}{69}\right)$	$e\left(\frac{55}{69}\right)$	$e\left(\frac{56}{69}\right)$	$e\left(\frac{29}{69}\right)$	$e\left(\frac{28}{69}\right)$	$e\left(\frac{5}{69}\right)$	$e\left(\frac{3}{23}\right)$	$e\left(\frac{65}{69}\right)$	$e\left(\frac{62}{69}\right)$	$e\left(\frac{34}{69}\right)$
$\chi_{834}(71,\cdot)$	834.n	138	no	$-1$	$1$	$e\left(\frac{59}{138}\right)$	$e\left(\frac{34}{69}\right)$	$e\left(\frac{73}{138}\right)$	$e\left(\frac{38}{69}\right)$	$e\left(\frac{71}{138}\right)$	$e\left(\frac{47}{69}\right)$	$e\left(\frac{15}{46}\right)$	$e\left(\frac{59}{69}\right)$	$e\left(\frac{103}{138}\right)$	$e\left(\frac{16}{69}\right)$
$\chi_{834}(73,\cdot)$	834.p	138	no	$-1$	$1$	$e\left(\frac{37}{69}\right)$	$e\left(\frac{52}{69}\right)$	$e\left(\frac{68}{69}\right)$	$e\left(\frac{50}{69}\right)$	$e\left(\frac{137}{138}\right)$	$e\left(\frac{91}{138}\right)$	$e\left(\frac{27}{46}\right)$	$e\left(\frac{5}{69}\right)$	$e\left(\frac{26}{69}\right)$	$e\left(\frac{61}{69}\right)$
$\chi_{834}(77,\cdot)$	834.l	46	no	$-1$	$1$	$e\left(\frac{1}{46}\right)$	$e\left(\frac{15}{23}\right)$	$e\left(\frac{41}{46}\right)$	$e\left(\frac{10}{23}\right)$	$e\left(\frac{9}{46}\right)$	$e\left(\frac{16}{23}\right)$	$e\left(\frac{7}{46}\right)$	$e\left(\frac{1}{23}\right)$	$e\left(\frac{15}{46}\right)$	$e\left(\frac{3}{23}\right)$
$\chi_{834}(79,\cdot)$	834.i	23	no	$1$	$1$	$e\left(\frac{9}{23}\right)$	$e\left(\frac{17}{23}\right)$	$e\left(\frac{1}{23}\right)$	$e\left(\frac{19}{23}\right)$	$e\left(\frac{12}{23}\right)$	$e\left(\frac{12}{23}\right)$	$e\left(\frac{17}{23}\right)$	$e\left(\frac{18}{23}\right)$	$e\left(\frac{20}{23}\right)$	$e\left(\frac{8}{23}\right)$
$\chi_{834}(83,\cdot)$	834.n	138	no	$-1$	$1$	$e\left(\frac{73}{138}\right)$	$e\left(\frac{14}{69}\right)$	$e\left(\frac{95}{138}\right)$	$e\left(\frac{40}{69}\right)$	$e\left(\frac{13}{138}\right)$	$e\left(\frac{64}{69}\right)$	$e\left(\frac{17}{46}\right)$	$e\left(\frac{4}{69}\right)$	$e\left(\frac{83}{138}\right)$	$e\left(\frac{35}{69}\right)$
$\chi_{834}(85,\cdot)$	834.p	138	no	$-1$	$1$	$e\left(\frac{19}{69}\right)$	$e\left(\frac{64}{69}\right)$	$e\left(\frac{20}{69}\right)$	$e\left(\frac{35}{69}\right)$	$e\left(\frac{89}{138}\right)$	$e\left(\frac{43}{138}\right)$	$e\left(\frac{35}{46}\right)$	$e\left(\frac{38}{69}\right)$	$e\left(\frac{32}{69}\right)$	$e\left(\frac{22}{69}\right)$
$\chi_{834}(89,\cdot)$	834.n	138	no	$-1$	$1$	$e\left(\frac{43}{138}\right)$	$e\left(\frac{47}{69}\right)$	$e\left(\frac{107}{138}\right)$	$e\left(\frac{16}{69}\right)$	$e\left(\frac{19}{138}\right)$	$e\left(\frac{67}{69}\right)$	$e\left(\frac{39}{46}\right)$	$e\left(\frac{43}{69}\right)$	$e\left(\frac{47}{138}\right)$	$e\left(\frac{14}{69}\right)$
$\chi_{834}(91,\cdot)$	834.i	23	no	$1$	$1$	$e\left(\frac{1}{23}\right)$	$e\left(\frac{7}{23}\right)$	$e\left(\frac{18}{23}\right)$	$e\left(\frac{20}{23}\right)$	$e\left(\frac{9}{23}\right)$	$e\left(\frac{9}{23}\right)$	$e\left(\frac{7}{23}\right)$	$e\left(\frac{2}{23}\right)$	$e\left(\frac{15}{23}\right)$	$e\left(\frac{6}{23}\right)$
$\chi_{834}(95,\cdot)$	834.k	46	no	$1$	$1$	$e\left(\frac{5}{46}\right)$	$e\left(\frac{6}{23}\right)$	$e\left(\frac{21}{46}\right)$	$e\left(\frac{4}{23}\right)$	$e\left(\frac{11}{23}\right)$	$e\left(\frac{45}{46}\right)$	$e\left(\frac{6}{23}\right)$	$e\left(\frac{5}{23}\right)$	$e\left(\frac{29}{46}\right)$	$e\left(\frac{15}{23}\right)$

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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	$834$
Structure	\(C_{2}\times C_{138}\)
Order	$276$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)
\(\chi_{834}(1,\cdot)\)	834.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{834}(5,\cdot)\)	834.n	138	no	\(-1\)	\(1\)	\(e\left(\frac{13}{138}\right)\)	\(e\left(\frac{11}{69}\right)\)	\(e\left(\frac{119}{138}\right)\)	\(e\left(\frac{61}{69}\right)\)	\(e\left(\frac{25}{138}\right)\)	\(e\left(\frac{1}{69}\right)\)	\(e\left(\frac{15}{46}\right)\)	\(e\left(\frac{13}{69}\right)\)	\(e\left(\frac{11}{138}\right)\)	\(e\left(\frac{62}{69}\right)\)
\(\chi_{834}(7,\cdot)\)	834.m	69	no	\(1\)	\(1\)	\(e\left(\frac{11}{69}\right)\)	\(e\left(\frac{8}{69}\right)\)	\(e\left(\frac{37}{69}\right)\)	\(e\left(\frac{13}{69}\right)\)	\(e\left(\frac{53}{69}\right)\)	\(e\left(\frac{7}{69}\right)\)	\(e\left(\frac{18}{23}\right)\)	\(e\left(\frac{22}{69}\right)\)	\(e\left(\frac{4}{69}\right)\)	\(e\left(\frac{20}{69}\right)\)
\(\chi_{834}(11,\cdot)\)	834.n	138	no	\(-1\)	\(1\)	\(e\left(\frac{119}{138}\right)\)	\(e\left(\frac{37}{69}\right)\)	\(e\left(\frac{49}{138}\right)\)	\(e\left(\frac{17}{69}\right)\)	\(e\left(\frac{59}{138}\right)\)	\(e\left(\frac{41}{69}\right)\)	\(e\left(\frac{17}{46}\right)\)	\(e\left(\frac{50}{69}\right)\)	\(e\left(\frac{37}{138}\right)\)	\(e\left(\frac{58}{69}\right)\)
\(\chi_{834}(13,\cdot)\)	834.m	69	no	\(1\)	\(1\)	\(e\left(\frac{61}{69}\right)\)	\(e\left(\frac{13}{69}\right)\)	\(e\left(\frac{17}{69}\right)\)	\(e\left(\frac{47}{69}\right)\)	\(e\left(\frac{43}{69}\right)\)	\(e\left(\frac{20}{69}\right)\)	\(e\left(\frac{12}{23}\right)\)	\(e\left(\frac{53}{69}\right)\)	\(e\left(\frac{41}{69}\right)\)	\(e\left(\frac{67}{69}\right)\)
\(\chi_{834}(17,\cdot)\)	834.o	138	no	\(1\)	\(1\)	\(e\left(\frac{25}{138}\right)\)	\(e\left(\frac{53}{69}\right)\)	\(e\left(\frac{59}{138}\right)\)	\(e\left(\frac{43}{69}\right)\)	\(e\left(\frac{32}{69}\right)\)	\(e\left(\frac{41}{138}\right)\)	\(e\left(\frac{10}{23}\right)\)	\(e\left(\frac{25}{69}\right)\)	\(e\left(\frac{53}{138}\right)\)	\(e\left(\frac{29}{69}\right)\)
\(\chi_{834}(19,\cdot)\)	834.p	138	no	\(-1\)	\(1\)	\(e\left(\frac{1}{69}\right)\)	\(e\left(\frac{7}{69}\right)\)	\(e\left(\frac{41}{69}\right)\)	\(e\left(\frac{20}{69}\right)\)	\(e\left(\frac{41}{138}\right)\)	\(e\left(\frac{133}{138}\right)\)	\(e\left(\frac{43}{46}\right)\)	\(e\left(\frac{2}{69}\right)\)	\(e\left(\frac{38}{69}\right)\)	\(e\left(\frac{52}{69}\right)\)
\(\chi_{834}(23,\cdot)\)	834.k	46	no	\(1\)	\(1\)	\(e\left(\frac{15}{46}\right)\)	\(e\left(\frac{18}{23}\right)\)	\(e\left(\frac{17}{46}\right)\)	\(e\left(\frac{12}{23}\right)\)	\(e\left(\frac{10}{23}\right)\)	\(e\left(\frac{43}{46}\right)\)	\(e\left(\frac{18}{23}\right)\)	\(e\left(\frac{15}{23}\right)\)	\(e\left(\frac{41}{46}\right)\)	\(e\left(\frac{22}{23}\right)\)
\(\chi_{834}(25,\cdot)\)	834.m	69	no	\(1\)	\(1\)	\(e\left(\frac{13}{69}\right)\)	\(e\left(\frac{22}{69}\right)\)	\(e\left(\frac{50}{69}\right)\)	\(e\left(\frac{53}{69}\right)\)	\(e\left(\frac{25}{69}\right)\)	\(e\left(\frac{2}{69}\right)\)	\(e\left(\frac{15}{23}\right)\)	\(e\left(\frac{26}{69}\right)\)	\(e\left(\frac{11}{69}\right)\)	\(e\left(\frac{55}{69}\right)\)
\(\chi_{834}(29,\cdot)\)	834.n	138	no	\(-1\)	\(1\)	\(e\left(\frac{11}{138}\right)\)	\(e\left(\frac{4}{69}\right)\)	\(e\left(\frac{37}{138}\right)\)	\(e\left(\frac{41}{69}\right)\)	\(e\left(\frac{53}{138}\right)\)	\(e\left(\frac{38}{69}\right)\)	\(e\left(\frac{41}{46}\right)\)	\(e\left(\frac{11}{69}\right)\)	\(e\left(\frac{73}{138}\right)\)	\(e\left(\frac{10}{69}\right)\)
\(\chi_{834}(31,\cdot)\)	834.m	69	no	\(1\)	\(1\)	\(e\left(\frac{62}{69}\right)\)	\(e\left(\frac{20}{69}\right)\)	\(e\left(\frac{58}{69}\right)\)	\(e\left(\frac{67}{69}\right)\)	\(e\left(\frac{29}{69}\right)\)	\(e\left(\frac{52}{69}\right)\)	\(e\left(\frac{22}{23}\right)\)	\(e\left(\frac{55}{69}\right)\)	\(e\left(\frac{10}{69}\right)\)	\(e\left(\frac{50}{69}\right)\)
\(\chi_{834}(35,\cdot)\)	834.n	138	no	\(-1\)	\(1\)	\(e\left(\frac{35}{138}\right)\)	\(e\left(\frac{19}{69}\right)\)	\(e\left(\frac{55}{138}\right)\)	\(e\left(\frac{5}{69}\right)\)	\(e\left(\frac{131}{138}\right)\)	\(e\left(\frac{8}{69}\right)\)	\(e\left(\frac{5}{46}\right)\)	\(e\left(\frac{35}{69}\right)\)	\(e\left(\frac{19}{138}\right)\)	\(e\left(\frac{13}{69}\right)\)
\(\chi_{834}(37,\cdot)\)	834.m	69	no	\(1\)	\(1\)	\(e\left(\frac{59}{69}\right)\)	\(e\left(\frac{68}{69}\right)\)	\(e\left(\frac{4}{69}\right)\)	\(e\left(\frac{7}{69}\right)\)	\(e\left(\frac{2}{69}\right)\)	\(e\left(\frac{25}{69}\right)\)	\(e\left(\frac{15}{23}\right)\)	\(e\left(\frac{49}{69}\right)\)	\(e\left(\frac{34}{69}\right)\)	\(e\left(\frac{32}{69}\right)\)
\(\chi_{834}(41,\cdot)\)	834.n	138	no	\(-1\)	\(1\)	\(e\left(\frac{61}{138}\right)\)	\(e\left(\frac{41}{69}\right)\)	\(e\left(\frac{17}{138}\right)\)	\(e\left(\frac{58}{69}\right)\)	\(e\left(\frac{43}{138}\right)\)	\(e\left(\frac{10}{69}\right)\)	\(e\left(\frac{35}{46}\right)\)	\(e\left(\frac{61}{69}\right)\)	\(e\left(\frac{41}{138}\right)\)	\(e\left(\frac{68}{69}\right)\)
\(\chi_{834}(43,\cdot)\)	834.f	6	no	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{834}(47,\cdot)\)	834.n	138	no	\(-1\)	\(1\)	\(e\left(\frac{79}{138}\right)\)	\(e\left(\frac{35}{69}\right)\)	\(e\left(\frac{65}{138}\right)\)	\(e\left(\frac{31}{69}\right)\)	\(e\left(\frac{67}{138}\right)\)	\(e\left(\frac{22}{69}\right)\)	\(e\left(\frac{31}{46}\right)\)	\(e\left(\frac{10}{69}\right)\)	\(e\left(\frac{35}{138}\right)\)	\(e\left(\frac{53}{69}\right)\)
\(\chi_{834}(49,\cdot)\)	834.m	69	no	\(1\)	\(1\)	\(e\left(\frac{22}{69}\right)\)	\(e\left(\frac{16}{69}\right)\)	\(e\left(\frac{5}{69}\right)\)	\(e\left(\frac{26}{69}\right)\)	\(e\left(\frac{37}{69}\right)\)	\(e\left(\frac{14}{69}\right)\)	\(e\left(\frac{13}{23}\right)\)	\(e\left(\frac{44}{69}\right)\)	\(e\left(\frac{8}{69}\right)\)	\(e\left(\frac{40}{69}\right)\)
\(\chi_{834}(53,\cdot)\)	834.o	138	no	\(1\)	\(1\)	\(e\left(\frac{109}{138}\right)\)	\(e\left(\frac{2}{69}\right)\)	\(e\left(\frac{53}{138}\right)\)	\(e\left(\frac{55}{69}\right)\)	\(e\left(\frac{65}{69}\right)\)	\(e\left(\frac{107}{138}\right)\)	\(e\left(\frac{16}{23}\right)\)	\(e\left(\frac{40}{69}\right)\)	\(e\left(\frac{71}{138}\right)\)	\(e\left(\frac{5}{69}\right)\)
\(\chi_{834}(55,\cdot)\)	834.i	23	no	\(1\)	\(1\)	\(e\left(\frac{22}{23}\right)\)	\(e\left(\frac{16}{23}\right)\)	\(e\left(\frac{5}{23}\right)\)	\(e\left(\frac{3}{23}\right)\)	\(e\left(\frac{14}{23}\right)\)	\(e\left(\frac{14}{23}\right)\)	\(e\left(\frac{16}{23}\right)\)	\(e\left(\frac{21}{23}\right)\)	\(e\left(\frac{8}{23}\right)\)	\(e\left(\frac{17}{23}\right)\)
\(\chi_{834}(59,\cdot)\)	834.k	46	no	\(1\)	\(1\)	\(e\left(\frac{27}{46}\right)\)	\(e\left(\frac{14}{23}\right)\)	\(e\left(\frac{3}{46}\right)\)	\(e\left(\frac{17}{23}\right)\)	\(e\left(\frac{18}{23}\right)\)	\(e\left(\frac{13}{46}\right)\)	\(e\left(\frac{14}{23}\right)\)	\(e\left(\frac{4}{23}\right)\)	\(e\left(\frac{37}{46}\right)\)	\(e\left(\frac{12}{23}\right)\)
\(\chi_{834}(61,\cdot)\)	834.p	138	no	\(-1\)	\(1\)	\(e\left(\frac{4}{69}\right)\)	\(e\left(\frac{28}{69}\right)\)	\(e\left(\frac{26}{69}\right)\)	\(e\left(\frac{11}{69}\right)\)	\(e\left(\frac{95}{138}\right)\)	\(e\left(\frac{49}{138}\right)\)	\(e\left(\frac{11}{46}\right)\)	\(e\left(\frac{8}{69}\right)\)	\(e\left(\frac{14}{69}\right)\)	\(e\left(\frac{1}{69}\right)\)
\(\chi_{834}(65,\cdot)\)	834.l	46	no	\(-1\)	\(1\)	\(e\left(\frac{45}{46}\right)\)	\(e\left(\frac{8}{23}\right)\)	\(e\left(\frac{5}{46}\right)\)	\(e\left(\frac{13}{23}\right)\)	\(e\left(\frac{37}{46}\right)\)	\(e\left(\frac{7}{23}\right)\)	\(e\left(\frac{39}{46}\right)\)	\(e\left(\frac{22}{23}\right)\)	\(e\left(\frac{31}{46}\right)\)	\(e\left(\frac{20}{23}\right)\)
\(\chi_{834}(67,\cdot)\)	834.m	69	no	\(1\)	\(1\)	\(e\left(\frac{67}{69}\right)\)	\(e\left(\frac{55}{69}\right)\)	\(e\left(\frac{56}{69}\right)\)	\(e\left(\frac{29}{69}\right)\)	\(e\left(\frac{28}{69}\right)\)	\(e\left(\frac{5}{69}\right)\)	\(e\left(\frac{3}{23}\right)\)	\(e\left(\frac{65}{69}\right)\)	\(e\left(\frac{62}{69}\right)\)	\(e\left(\frac{34}{69}\right)\)
\(\chi_{834}(71,\cdot)\)	834.n	138	no	\(-1\)	\(1\)	\(e\left(\frac{59}{138}\right)\)	\(e\left(\frac{34}{69}\right)\)	\(e\left(\frac{73}{138}\right)\)	\(e\left(\frac{38}{69}\right)\)	\(e\left(\frac{71}{138}\right)\)	\(e\left(\frac{47}{69}\right)\)	\(e\left(\frac{15}{46}\right)\)	\(e\left(\frac{59}{69}\right)\)	\(e\left(\frac{103}{138}\right)\)	\(e\left(\frac{16}{69}\right)\)
\(\chi_{834}(73,\cdot)\)	834.p	138	no	\(-1\)	\(1\)	\(e\left(\frac{37}{69}\right)\)	\(e\left(\frac{52}{69}\right)\)	\(e\left(\frac{68}{69}\right)\)	\(e\left(\frac{50}{69}\right)\)	\(e\left(\frac{137}{138}\right)\)	\(e\left(\frac{91}{138}\right)\)	\(e\left(\frac{27}{46}\right)\)	\(e\left(\frac{5}{69}\right)\)	\(e\left(\frac{26}{69}\right)\)	\(e\left(\frac{61}{69}\right)\)
\(\chi_{834}(77,\cdot)\)	834.l	46	no	\(-1\)	\(1\)	\(e\left(\frac{1}{46}\right)\)	\(e\left(\frac{15}{23}\right)\)	\(e\left(\frac{41}{46}\right)\)	\(e\left(\frac{10}{23}\right)\)	\(e\left(\frac{9}{46}\right)\)	\(e\left(\frac{16}{23}\right)\)	\(e\left(\frac{7}{46}\right)\)	\(e\left(\frac{1}{23}\right)\)	\(e\left(\frac{15}{46}\right)\)	\(e\left(\frac{3}{23}\right)\)
\(\chi_{834}(79,\cdot)\)	834.i	23	no	\(1\)	\(1\)	\(e\left(\frac{9}{23}\right)\)	\(e\left(\frac{17}{23}\right)\)	\(e\left(\frac{1}{23}\right)\)	\(e\left(\frac{19}{23}\right)\)	\(e\left(\frac{12}{23}\right)\)	\(e\left(\frac{12}{23}\right)\)	\(e\left(\frac{17}{23}\right)\)	\(e\left(\frac{18}{23}\right)\)	\(e\left(\frac{20}{23}\right)\)	\(e\left(\frac{8}{23}\right)\)
\(\chi_{834}(83,\cdot)\)	834.n	138	no	\(-1\)	\(1\)	\(e\left(\frac{73}{138}\right)\)	\(e\left(\frac{14}{69}\right)\)	\(e\left(\frac{95}{138}\right)\)	\(e\left(\frac{40}{69}\right)\)	\(e\left(\frac{13}{138}\right)\)	\(e\left(\frac{64}{69}\right)\)	\(e\left(\frac{17}{46}\right)\)	\(e\left(\frac{4}{69}\right)\)	\(e\left(\frac{83}{138}\right)\)	\(e\left(\frac{35}{69}\right)\)
\(\chi_{834}(85,\cdot)\)	834.p	138	no	\(-1\)	\(1\)	\(e\left(\frac{19}{69}\right)\)	\(e\left(\frac{64}{69}\right)\)	\(e\left(\frac{20}{69}\right)\)	\(e\left(\frac{35}{69}\right)\)	\(e\left(\frac{89}{138}\right)\)	\(e\left(\frac{43}{138}\right)\)	\(e\left(\frac{35}{46}\right)\)	\(e\left(\frac{38}{69}\right)\)	\(e\left(\frac{32}{69}\right)\)	\(e\left(\frac{22}{69}\right)\)
\(\chi_{834}(89,\cdot)\)	834.n	138	no	\(-1\)	\(1\)	\(e\left(\frac{43}{138}\right)\)	\(e\left(\frac{47}{69}\right)\)	\(e\left(\frac{107}{138}\right)\)	\(e\left(\frac{16}{69}\right)\)	\(e\left(\frac{19}{138}\right)\)	\(e\left(\frac{67}{69}\right)\)	\(e\left(\frac{39}{46}\right)\)	\(e\left(\frac{43}{69}\right)\)	\(e\left(\frac{47}{138}\right)\)	\(e\left(\frac{14}{69}\right)\)
\(\chi_{834}(91,\cdot)\)	834.i	23	no	\(1\)	\(1\)	\(e\left(\frac{1}{23}\right)\)	\(e\left(\frac{7}{23}\right)\)	\(e\left(\frac{18}{23}\right)\)	\(e\left(\frac{20}{23}\right)\)	\(e\left(\frac{9}{23}\right)\)	\(e\left(\frac{9}{23}\right)\)	\(e\left(\frac{7}{23}\right)\)	\(e\left(\frac{2}{23}\right)\)	\(e\left(\frac{15}{23}\right)\)	\(e\left(\frac{6}{23}\right)\)
\(\chi_{834}(95,\cdot)\)	834.k	46	no	\(1\)	\(1\)	\(e\left(\frac{5}{46}\right)\)	\(e\left(\frac{6}{23}\right)\)	\(e\left(\frac{21}{46}\right)\)	\(e\left(\frac{4}{23}\right)\)	\(e\left(\frac{11}{23}\right)\)	\(e\left(\frac{45}{46}\right)\)	\(e\left(\frac{6}{23}\right)\)	\(e\left(\frac{5}{23}\right)\)	\(e\left(\frac{29}{46}\right)\)	\(e\left(\frac{15}{23}\right)\)

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L-functions

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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.