LMFDB - Group of Dirichlet characters of modulus 725

Show commands: PariGP / SageMath

sage: H = DirichletGroup(725)

pari: g = idealstar(,725,2)

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	=	$\chi_{725}(552,\cdot)$, $\chi_{725}(176,\cdot)$

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	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$11$	$12$	$13$
$\chi_{725}(1,\cdot)$	725.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{725}(2,\cdot)$	725.bn	140	yes	$1$	$1$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{97}{140}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{83}{140}\right)$
$\chi_{725}(3,\cdot)$	725.bi	140	yes	$1$	$1$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{9}{140}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{121}{140}\right)$
$\chi_{725}(4,\cdot)$	725.bh	70	yes	$1$	$1$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{13}{70}\right)$
$\chi_{725}(6,\cdot)$	725.bf	70	yes	$1$	$1$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{16}{35}\right)$
$\chi_{725}(7,\cdot)$	725.z	28	no	$-1$	$1$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{5}{7}\right)$	$i$	$e\left(\frac{13}{28}\right)$
$\chi_{725}(8,\cdot)$	725.bn	140	yes	$1$	$1$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{11}{140}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{109}{140}\right)$
$\chi_{725}(9,\cdot)$	725.bh	70	yes	$1$	$1$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{51}{70}\right)$
$\chi_{725}(11,\cdot)$	725.bj	140	yes	$-1$	$1$	$e\left(\frac{97}{140}\right)$	$e\left(\frac{9}{140}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{11}{140}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{17}{140}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{19}{70}\right)$
$\chi_{725}(12,\cdot)$	725.x	20	yes	$1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{10}\right)$	$i$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{20}\right)$
$\chi_{725}(13,\cdot)$	725.bl	140	yes	$-1$	$1$	$e\left(\frac{83}{140}\right)$	$e\left(\frac{121}{140}\right)$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{109}{140}\right)$	$e\left(\frac{51}{70}\right)$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{87}{140}\right)$
$\chi_{725}(14,\cdot)$	725.bk	140	yes	$-1$	$1$	$e\left(\frac{107}{140}\right)$	$e\left(\frac{59}{140}\right)$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{41}{140}\right)$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{57}{140}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{2}{35}\right)$
$\chi_{725}(16,\cdot)$	725.be	35	yes	$1$	$1$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{13}{35}\right)$
$\chi_{725}(17,\cdot)$	725.s	20	yes	$1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{10}\right)$	$i$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{17}{20}\right)$
$\chi_{725}(18,\cdot)$	725.y	28	no	$1$	$1$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{23}{28}\right)$	$-1$	$e\left(\frac{9}{28}\right)$
$\chi_{725}(19,\cdot)$	725.bk	140	yes	$-1$	$1$	$e\left(\frac{31}{140}\right)$	$e\left(\frac{127}{140}\right)$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{93}{140}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{61}{140}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{31}{35}\right)$
$\chi_{725}(21,\cdot)$	725.bj	140	yes	$-1$	$1$	$e\left(\frac{29}{140}\right)$	$e\left(\frac{33}{140}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{87}{140}\right)$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{109}{140}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{23}{70}\right)$
$\chi_{725}(22,\cdot)$	725.bl	140	yes	$-1$	$1$	$e\left(\frac{109}{140}\right)$	$e\left(\frac{83}{140}\right)$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{47}{140}\right)$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{121}{140}\right)$
$\chi_{725}(23,\cdot)$	725.bm	140	yes	$-1$	$1$	$e\left(\frac{37}{140}\right)$	$e\left(\frac{59}{140}\right)$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{111}{140}\right)$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{43}{140}\right)$
$\chi_{725}(24,\cdot)$	725.r	14	no	$1$	$1$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{7}\right)$	$-1$	$e\left(\frac{9}{14}\right)$
$\chi_{725}(26,\cdot)$	725.bb	28	no	$-1$	$1$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{27}{28}\right)$	$-i$	$e\left(\frac{3}{14}\right)$
$\chi_{725}(27,\cdot)$	725.bi	140	yes	$1$	$1$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{27}{140}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{83}{140}\right)$
$\chi_{725}(28,\cdot)$	725.u	20	yes	$-1$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{5}\right)$	$-i$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{13}{20}\right)$
$\chi_{725}(31,\cdot)$	725.bj	140	yes	$-1$	$1$	$e\left(\frac{61}{140}\right)$	$e\left(\frac{137}{140}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{43}{140}\right)$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{41}{140}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{17}{70}\right)$
$\chi_{725}(32,\cdot)$	725.y	28	no	$1$	$1$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{13}{28}\right)$	$-1$	$e\left(\frac{27}{28}\right)$
$\chi_{725}(33,\cdot)$	725.bl	140	yes	$-1$	$1$	$e\left(\frac{31}{140}\right)$	$e\left(\frac{57}{140}\right)$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{93}{140}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{19}{140}\right)$
$\chi_{725}(34,\cdot)$	725.bh	70	yes	$1$	$1$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{31}{70}\right)$
$\chi_{725}(36,\cdot)$	725.be	35	yes	$1$	$1$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{32}{35}\right)$
$\chi_{725}(37,\cdot)$	725.bi	140	yes	$1$	$1$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{17}{70}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{123}{140}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{67}{140}\right)$
$\chi_{725}(38,\cdot)$	725.bl	140	yes	$-1$	$1$	$e\left(\frac{43}{140}\right)$	$e\left(\frac{61}{140}\right)$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{129}{140}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{67}{140}\right)$
$\chi_{725}(39,\cdot)$	725.bk	140	yes	$-1$	$1$	$e\left(\frac{17}{140}\right)$	$e\left(\frac{29}{140}\right)$	$e\left(\frac{17}{70}\right)$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{51}{140}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{47}{140}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{17}{35}\right)$
$\chi_{725}(41,\cdot)$	725.w	20	yes	$-1$	$1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{10}\right)$	$1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{3}{10}\right)$

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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	$725$
Structure	\(C_{4}\times C_{140}\)
Order	$560$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(7\)	\(8\)	\(9\)	\(11\)	\(12\)	\(13\)
\(\chi_{725}(1,\cdot)\)	725.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{725}(2,\cdot)\)	725.bn	140	yes	\(1\)	\(1\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{97}{140}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{83}{140}\right)\)
\(\chi_{725}(3,\cdot)\)	725.bi	140	yes	\(1\)	\(1\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{9}{140}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{121}{140}\right)\)
\(\chi_{725}(4,\cdot)\)	725.bh	70	yes	\(1\)	\(1\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{13}{70}\right)\)
\(\chi_{725}(6,\cdot)\)	725.bf	70	yes	\(1\)	\(1\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{16}{35}\right)\)
\(\chi_{725}(7,\cdot)\)	725.z	28	no	\(-1\)	\(1\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(i\)	\(e\left(\frac{13}{28}\right)\)
\(\chi_{725}(8,\cdot)\)	725.bn	140	yes	\(1\)	\(1\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{11}{140}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{109}{140}\right)\)
\(\chi_{725}(9,\cdot)\)	725.bh	70	yes	\(1\)	\(1\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{51}{70}\right)\)
\(\chi_{725}(11,\cdot)\)	725.bj	140	yes	\(-1\)	\(1\)	\(e\left(\frac{97}{140}\right)\)	\(e\left(\frac{9}{140}\right)\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{11}{140}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{17}{140}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{19}{70}\right)\)
\(\chi_{725}(12,\cdot)\)	725.x	20	yes	\(1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(i\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{20}\right)\)
\(\chi_{725}(13,\cdot)\)	725.bl	140	yes	\(-1\)	\(1\)	\(e\left(\frac{83}{140}\right)\)	\(e\left(\frac{121}{140}\right)\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{109}{140}\right)\)	\(e\left(\frac{51}{70}\right)\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{87}{140}\right)\)
\(\chi_{725}(14,\cdot)\)	725.bk	140	yes	\(-1\)	\(1\)	\(e\left(\frac{107}{140}\right)\)	\(e\left(\frac{59}{140}\right)\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{41}{140}\right)\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{57}{140}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{2}{35}\right)\)
\(\chi_{725}(16,\cdot)\)	725.be	35	yes	\(1\)	\(1\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{13}{35}\right)\)
\(\chi_{725}(17,\cdot)\)	725.s	20	yes	\(1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(i\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)
\(\chi_{725}(18,\cdot)\)	725.y	28	no	\(1\)	\(1\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(-1\)	\(e\left(\frac{9}{28}\right)\)
\(\chi_{725}(19,\cdot)\)	725.bk	140	yes	\(-1\)	\(1\)	\(e\left(\frac{31}{140}\right)\)	\(e\left(\frac{127}{140}\right)\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{93}{140}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{61}{140}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{31}{35}\right)\)
\(\chi_{725}(21,\cdot)\)	725.bj	140	yes	\(-1\)	\(1\)	\(e\left(\frac{29}{140}\right)\)	\(e\left(\frac{33}{140}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{87}{140}\right)\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{109}{140}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{23}{70}\right)\)
\(\chi_{725}(22,\cdot)\)	725.bl	140	yes	\(-1\)	\(1\)	\(e\left(\frac{109}{140}\right)\)	\(e\left(\frac{83}{140}\right)\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{47}{140}\right)\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{121}{140}\right)\)
\(\chi_{725}(23,\cdot)\)	725.bm	140	yes	\(-1\)	\(1\)	\(e\left(\frac{37}{140}\right)\)	\(e\left(\frac{59}{140}\right)\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{111}{140}\right)\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{43}{140}\right)\)
\(\chi_{725}(24,\cdot)\)	725.r	14	no	\(1\)	\(1\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(-1\)	\(e\left(\frac{9}{14}\right)\)
\(\chi_{725}(26,\cdot)\)	725.bb	28	no	\(-1\)	\(1\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(-i\)	\(e\left(\frac{3}{14}\right)\)
\(\chi_{725}(27,\cdot)\)	725.bi	140	yes	\(1\)	\(1\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{27}{140}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{83}{140}\right)\)
\(\chi_{725}(28,\cdot)\)	725.u	20	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(-i\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)
\(\chi_{725}(31,\cdot)\)	725.bj	140	yes	\(-1\)	\(1\)	\(e\left(\frac{61}{140}\right)\)	\(e\left(\frac{137}{140}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{43}{140}\right)\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{41}{140}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{17}{70}\right)\)
\(\chi_{725}(32,\cdot)\)	725.y	28	no	\(1\)	\(1\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(-1\)	\(e\left(\frac{27}{28}\right)\)
\(\chi_{725}(33,\cdot)\)	725.bl	140	yes	\(-1\)	\(1\)	\(e\left(\frac{31}{140}\right)\)	\(e\left(\frac{57}{140}\right)\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{93}{140}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{19}{140}\right)\)
\(\chi_{725}(34,\cdot)\)	725.bh	70	yes	\(1\)	\(1\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{31}{70}\right)\)
\(\chi_{725}(36,\cdot)\)	725.be	35	yes	\(1\)	\(1\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{32}{35}\right)\)
\(\chi_{725}(37,\cdot)\)	725.bi	140	yes	\(1\)	\(1\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{17}{70}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{123}{140}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{67}{140}\right)\)
\(\chi_{725}(38,\cdot)\)	725.bl	140	yes	\(-1\)	\(1\)	\(e\left(\frac{43}{140}\right)\)	\(e\left(\frac{61}{140}\right)\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{129}{140}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{67}{140}\right)\)
\(\chi_{725}(39,\cdot)\)	725.bk	140	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{140}\right)\)	\(e\left(\frac{29}{140}\right)\)	\(e\left(\frac{17}{70}\right)\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{51}{140}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{47}{140}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{17}{35}\right)\)
\(\chi_{725}(41,\cdot)\)	725.w	20	yes	\(-1\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(1\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)

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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.