LMFDB - Group of Dirichlet characters of modulus 1450

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1450)

pari: g = idealstar(,1450,2)

Character group

sage: G.order() pari: g.no
Order	=	560
sage: H.invariants() pari: g.cyc
Structure	=	$C_{4}\times C_{140}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{1450}(1277,\cdot)$, $\chi_{1450}(901,\cdot)$

First 32 of 560 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	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{1450}(1,\cdot)$	1450.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1450}(3,\cdot)$	1450.bn	140	no	$1$	$1$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{9}{140}\right)$	$e\left(\frac{121}{140}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{127}{140}\right)$	$e\left(\frac{33}{140}\right)$	$e\left(\frac{59}{140}\right)$	$e\left(\frac{1}{35}\right)$
$\chi_{1450}(7,\cdot)$	1450.ba	28	no	$-1$	$1$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{13}{28}\right)$	$i$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{19}{28}\right)$
$\chi_{1450}(9,\cdot)$	1450.bh	70	no	$1$	$1$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{51}{70}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{2}{35}\right)$
$\chi_{1450}(11,\cdot)$	1450.bj	140	no	$-1$	$1$	$e\left(\frac{9}{140}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{17}{140}\right)$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{61}{140}\right)$	$e\left(\frac{109}{140}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{27}{140}\right)$
$\chi_{1450}(13,\cdot)$	1450.bk	140	no	$-1$	$1$	$e\left(\frac{121}{140}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{51}{70}\right)$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{87}{140}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{43}{140}\right)$	$e\left(\frac{83}{140}\right)$
$\chi_{1450}(17,\cdot)$	1450.x	20	no	$1$	$1$	$e\left(\frac{3}{10}\right)$	$i$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{1450}(19,\cdot)$	1450.bm	140	no	$-1$	$1$	$e\left(\frac{127}{140}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{61}{140}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{13}{140}\right)$	$e\left(\frac{37}{140}\right)$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{101}{140}\right)$
$\chi_{1450}(21,\cdot)$	1450.bj	140	no	$-1$	$1$	$e\left(\frac{33}{140}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{109}{140}\right)$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{37}{140}\right)$	$e\left(\frac{73}{140}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{99}{140}\right)$
$\chi_{1450}(23,\cdot)$	1450.bl	140	no	$-1$	$1$	$e\left(\frac{59}{140}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{43}{140}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{47}{140}\right)$	$e\left(\frac{37}{140}\right)$
$\chi_{1450}(27,\cdot)$	1450.bn	140	no	$1$	$1$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{27}{140}\right)$	$e\left(\frac{83}{140}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{101}{140}\right)$	$e\left(\frac{99}{140}\right)$	$e\left(\frac{37}{140}\right)$	$e\left(\frac{3}{35}\right)$
$\chi_{1450}(31,\cdot)$	1450.bj	140	no	$-1$	$1$	$e\left(\frac{137}{140}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{41}{140}\right)$	$e\left(\frac{17}{70}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{73}{140}\right)$	$e\left(\frac{57}{140}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{131}{140}\right)$
$\chi_{1450}(33,\cdot)$	1450.bk	140	no	$-1$	$1$	$e\left(\frac{57}{140}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{19}{140}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{11}{140}\right)$	$e\left(\frac{31}{140}\right)$
$\chi_{1450}(37,\cdot)$	1450.bn	140	no	$1$	$1$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{123}{140}\right)$	$e\left(\frac{67}{140}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{140}\right)$	$e\left(\frac{31}{140}\right)$	$e\left(\frac{13}{140}\right)$	$e\left(\frac{2}{35}\right)$
$\chi_{1450}(39,\cdot)$	1450.bm	140	no	$-1$	$1$	$e\left(\frac{29}{140}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{47}{140}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{111}{140}\right)$	$e\left(\frac{79}{140}\right)$	$e\left(\frac{51}{70}\right)$	$e\left(\frac{87}{140}\right)$
$\chi_{1450}(41,\cdot)$	1450.w	20	no	$-1$	$1$	$e\left(\frac{13}{20}\right)$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{19}{20}\right)$
$\chi_{1450}(43,\cdot)$	1450.y	28	no	$1$	$1$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{17}{28}\right)$	$-1$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{5}{7}\right)$
$\chi_{1450}(47,\cdot)$	1450.bn	140	no	$1$	$1$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{59}{140}\right)$	$e\left(\frac{31}{140}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{117}{140}\right)$	$e\left(\frac{123}{140}\right)$	$e\left(\frac{29}{140}\right)$	$e\left(\frac{26}{35}\right)$
$\chi_{1450}(49,\cdot)$	1450.r	14	no	$1$	$1$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{13}{14}\right)$	$-1$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{5}{14}\right)$
$\chi_{1450}(51,\cdot)$	1450.q	14	no	$1$	$1$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{5}{7}\right)$	$-1$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{13}{14}\right)$
$\chi_{1450}(53,\cdot)$	1450.bl	140	no	$-1$	$1$	$e\left(\frac{123}{140}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{111}{140}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{79}{140}\right)$	$e\left(\frac{89}{140}\right)$
$\chi_{1450}(57,\cdot)$	1450.g	4	no	$-1$	$1$	$i$	$i$	$-1$	$-1$	$-i$	$-i$	$1$	$-1$	$-i$	$-i$
$\chi_{1450}(59,\cdot)$	1450.n	10	no	$1$	$1$	$e\left(\frac{9}{10}\right)$	$-1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{1450}(61,\cdot)$	1450.bj	140	no	$-1$	$1$	$e\left(\frac{69}{140}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{37}{140}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{140}\right)$	$e\left(\frac{89}{140}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{67}{140}\right)$
$\chi_{1450}(63,\cdot)$	1450.bk	140	no	$-1$	$1$	$e\left(\frac{81}{140}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{11}{70}\right)$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{27}{140}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{23}{140}\right)$	$e\left(\frac{103}{140}\right)$
$\chi_{1450}(67,\cdot)$	1450.bk	140	no	$-1$	$1$	$e\left(\frac{47}{140}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{109}{140}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{41}{140}\right)$	$e\left(\frac{1}{140}\right)$
$\chi_{1450}(69,\cdot)$	1450.bm	140	no	$-1$	$1$	$e\left(\frac{107}{140}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{101}{140}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{33}{140}\right)$	$e\left(\frac{137}{140}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{41}{140}\right)$
$\chi_{1450}(71,\cdot)$	1450.bf	70	no	$1$	$1$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{17}{70}\right)$
$\chi_{1450}(73,\cdot)$	1450.bi	140	no	$1$	$1$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{127}{140}\right)$	$e\left(\frac{113}{140}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{81}{140}\right)$	$e\left(\frac{139}{140}\right)$	$e\left(\frac{47}{140}\right)$	$e\left(\frac{1}{70}\right)$
$\chi_{1450}(77,\cdot)$	1450.bi	140	no	$1$	$1$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{117}{140}\right)$	$e\left(\frac{103}{140}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{111}{140}\right)$	$e\left(\frac{9}{140}\right)$	$e\left(\frac{137}{140}\right)$	$e\left(\frac{61}{70}\right)$
$\chi_{1450}(79,\cdot)$	1450.bm	140	no	$-1$	$1$	$e\left(\frac{103}{140}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{109}{140}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{37}{140}\right)$	$e\left(\frac{73}{140}\right)$	$e\left(\frac{17}{70}\right)$	$e\left(\frac{29}{140}\right)$
$\chi_{1450}(81,\cdot)$	1450.be	35	no	$1$	$1$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{4}{35}\right)$

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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 $\F_{q}$

Modulus	$1450$
Structure	\(C_{4}\times C_{140}\)
Order	$560$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)
\(\chi_{1450}(1,\cdot)\)	1450.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1450}(3,\cdot)\)	1450.bn	140	no	\(1\)	\(1\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{9}{140}\right)\)	\(e\left(\frac{121}{140}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{127}{140}\right)\)	\(e\left(\frac{33}{140}\right)\)	\(e\left(\frac{59}{140}\right)\)	\(e\left(\frac{1}{35}\right)\)
\(\chi_{1450}(7,\cdot)\)	1450.ba	28	no	\(-1\)	\(1\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(i\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{19}{28}\right)\)
\(\chi_{1450}(9,\cdot)\)	1450.bh	70	no	\(1\)	\(1\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{51}{70}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{2}{35}\right)\)
\(\chi_{1450}(11,\cdot)\)	1450.bj	140	no	\(-1\)	\(1\)	\(e\left(\frac{9}{140}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{17}{140}\right)\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{61}{140}\right)\)	\(e\left(\frac{109}{140}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{27}{140}\right)\)
\(\chi_{1450}(13,\cdot)\)	1450.bk	140	no	\(-1\)	\(1\)	\(e\left(\frac{121}{140}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{51}{70}\right)\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{87}{140}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{43}{140}\right)\)	\(e\left(\frac{83}{140}\right)\)
\(\chi_{1450}(17,\cdot)\)	1450.x	20	no	\(1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(i\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{1450}(19,\cdot)\)	1450.bm	140	no	\(-1\)	\(1\)	\(e\left(\frac{127}{140}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{61}{140}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{13}{140}\right)\)	\(e\left(\frac{37}{140}\right)\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{101}{140}\right)\)
\(\chi_{1450}(21,\cdot)\)	1450.bj	140	no	\(-1\)	\(1\)	\(e\left(\frac{33}{140}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{109}{140}\right)\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{37}{140}\right)\)	\(e\left(\frac{73}{140}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{99}{140}\right)\)
\(\chi_{1450}(23,\cdot)\)	1450.bl	140	no	\(-1\)	\(1\)	\(e\left(\frac{59}{140}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{43}{140}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{47}{140}\right)\)	\(e\left(\frac{37}{140}\right)\)
\(\chi_{1450}(27,\cdot)\)	1450.bn	140	no	\(1\)	\(1\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{27}{140}\right)\)	\(e\left(\frac{83}{140}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{101}{140}\right)\)	\(e\left(\frac{99}{140}\right)\)	\(e\left(\frac{37}{140}\right)\)	\(e\left(\frac{3}{35}\right)\)
\(\chi_{1450}(31,\cdot)\)	1450.bj	140	no	\(-1\)	\(1\)	\(e\left(\frac{137}{140}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{41}{140}\right)\)	\(e\left(\frac{17}{70}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{73}{140}\right)\)	\(e\left(\frac{57}{140}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{131}{140}\right)\)
\(\chi_{1450}(33,\cdot)\)	1450.bk	140	no	\(-1\)	\(1\)	\(e\left(\frac{57}{140}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{19}{140}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{11}{140}\right)\)	\(e\left(\frac{31}{140}\right)\)
\(\chi_{1450}(37,\cdot)\)	1450.bn	140	no	\(1\)	\(1\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{123}{140}\right)\)	\(e\left(\frac{67}{140}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{9}{140}\right)\)	\(e\left(\frac{31}{140}\right)\)	\(e\left(\frac{13}{140}\right)\)	\(e\left(\frac{2}{35}\right)\)
\(\chi_{1450}(39,\cdot)\)	1450.bm	140	no	\(-1\)	\(1\)	\(e\left(\frac{29}{140}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{47}{140}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{111}{140}\right)\)	\(e\left(\frac{79}{140}\right)\)	\(e\left(\frac{51}{70}\right)\)	\(e\left(\frac{87}{140}\right)\)
\(\chi_{1450}(41,\cdot)\)	1450.w	20	no	\(-1\)	\(1\)	\(e\left(\frac{13}{20}\right)\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{19}{20}\right)\)
\(\chi_{1450}(43,\cdot)\)	1450.y	28	no	\(1\)	\(1\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(-1\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{1450}(47,\cdot)\)	1450.bn	140	no	\(1\)	\(1\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{59}{140}\right)\)	\(e\left(\frac{31}{140}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{117}{140}\right)\)	\(e\left(\frac{123}{140}\right)\)	\(e\left(\frac{29}{140}\right)\)	\(e\left(\frac{26}{35}\right)\)
\(\chi_{1450}(49,\cdot)\)	1450.r	14	no	\(1\)	\(1\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(-1\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{5}{14}\right)\)
\(\chi_{1450}(51,\cdot)\)	1450.q	14	no	\(1\)	\(1\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(-1\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)
\(\chi_{1450}(53,\cdot)\)	1450.bl	140	no	\(-1\)	\(1\)	\(e\left(\frac{123}{140}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{111}{140}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{79}{140}\right)\)	\(e\left(\frac{89}{140}\right)\)
\(\chi_{1450}(57,\cdot)\)	1450.g	4	no	\(-1\)	\(1\)	\(i\)	\(i\)	\(-1\)	\(-1\)	\(-i\)	\(-i\)	\(1\)	\(-1\)	\(-i\)	\(-i\)
\(\chi_{1450}(59,\cdot)\)	1450.n	10	no	\(1\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(-1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{1450}(61,\cdot)\)	1450.bj	140	no	\(-1\)	\(1\)	\(e\left(\frac{69}{140}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{37}{140}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{140}\right)\)	\(e\left(\frac{89}{140}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{67}{140}\right)\)
\(\chi_{1450}(63,\cdot)\)	1450.bk	140	no	\(-1\)	\(1\)	\(e\left(\frac{81}{140}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{11}{70}\right)\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{27}{140}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{23}{140}\right)\)	\(e\left(\frac{103}{140}\right)\)
\(\chi_{1450}(67,\cdot)\)	1450.bk	140	no	\(-1\)	\(1\)	\(e\left(\frac{47}{140}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{109}{140}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{41}{140}\right)\)	\(e\left(\frac{1}{140}\right)\)
\(\chi_{1450}(69,\cdot)\)	1450.bm	140	no	\(-1\)	\(1\)	\(e\left(\frac{107}{140}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{101}{140}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{33}{140}\right)\)	\(e\left(\frac{137}{140}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{41}{140}\right)\)
\(\chi_{1450}(71,\cdot)\)	1450.bf	70	no	\(1\)	\(1\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{17}{70}\right)\)
\(\chi_{1450}(73,\cdot)\)	1450.bi	140	no	\(1\)	\(1\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{127}{140}\right)\)	\(e\left(\frac{113}{140}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{81}{140}\right)\)	\(e\left(\frac{139}{140}\right)\)	\(e\left(\frac{47}{140}\right)\)	\(e\left(\frac{1}{70}\right)\)
\(\chi_{1450}(77,\cdot)\)	1450.bi	140	no	\(1\)	\(1\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{117}{140}\right)\)	\(e\left(\frac{103}{140}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{111}{140}\right)\)	\(e\left(\frac{9}{140}\right)\)	\(e\left(\frac{137}{140}\right)\)	\(e\left(\frac{61}{70}\right)\)
\(\chi_{1450}(79,\cdot)\)	1450.bm	140	no	\(-1\)	\(1\)	\(e\left(\frac{103}{140}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{109}{140}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{37}{140}\right)\)	\(e\left(\frac{73}{140}\right)\)	\(e\left(\frac{17}{70}\right)\)	\(e\left(\frac{29}{140}\right)\)
\(\chi_{1450}(81,\cdot)\)	1450.be	35	no	\(1\)	\(1\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{4}{35}\right)\)

Introduction

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.