LMFDB - Group of Dirichlet characters of modulus 175

Show commands: PariGP / SageMath

sage: H = DirichletGroup(175)

pari: g = idealstar(,175,2)

Character group

sage: G.order() pari: g.no
Order	=	120
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{60}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{175}(127,\cdot)$, $\chi_{175}(101,\cdot)$

First 32 of 120 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	$-1$	$1$	$2$	$3$	$4$	$6$	$8$	$9$	$11$	$12$	$13$	$16$
$\chi_{175}(1,\cdot)$	175.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{175}(2,\cdot)$	175.w	60	yes	$-1$	$1$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{13}{15}\right)$
$\chi_{175}(3,\cdot)$	175.x	60	yes	$1$	$1$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{11}{15}\right)$
$\chi_{175}(4,\cdot)$	175.t	30	yes	$1$	$1$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{11}{15}\right)$
$\chi_{175}(6,\cdot)$	175.l	10	yes	$-1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{175}(8,\cdot)$	175.r	20	no	$-1$	$1$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{175}(9,\cdot)$	175.t	30	yes	$1$	$1$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{15}\right)$
$\chi_{175}(11,\cdot)$	175.q	15	yes	$1$	$1$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{8}{15}\right)$
$\chi_{175}(12,\cdot)$	175.x	60	yes	$1$	$1$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{7}{15}\right)$
$\chi_{175}(13,\cdot)$	175.s	20	yes	$1$	$1$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{175}(16,\cdot)$	175.q	15	yes	$1$	$1$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{15}\right)$
$\chi_{175}(17,\cdot)$	175.x	60	yes	$1$	$1$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{14}{15}\right)$
$\chi_{175}(18,\cdot)$	175.p	12	no	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$i$	$e\left(\frac{1}{3}\right)$
$\chi_{175}(19,\cdot)$	175.u	30	yes	$-1$	$1$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{4}{15}\right)$
$\chi_{175}(22,\cdot)$	175.r	20	no	$-1$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{175}(23,\cdot)$	175.w	60	yes	$-1$	$1$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{13}{15}\right)$
$\chi_{175}(24,\cdot)$	175.j	6	no	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$
$\chi_{175}(26,\cdot)$	175.i	6	no	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$
$\chi_{175}(27,\cdot)$	175.s	20	yes	$1$	$1$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{175}(29,\cdot)$	175.n	10	no	$1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{175}(31,\cdot)$	175.v	30	yes	$-1$	$1$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{14}{15}\right)$
$\chi_{175}(32,\cdot)$	175.p	12	no	$-1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$-i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{12}\right)$	$-i$	$e\left(\frac{1}{3}\right)$
$\chi_{175}(33,\cdot)$	175.x	60	yes	$1$	$1$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{4}{15}\right)$
$\chi_{175}(34,\cdot)$	175.m	10	yes	$-1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{175}(36,\cdot)$	175.h	5	no	$1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{175}(37,\cdot)$	175.w	60	yes	$-1$	$1$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{7}{15}\right)$
$\chi_{175}(38,\cdot)$	175.x	60	yes	$1$	$1$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{2}{15}\right)$
$\chi_{175}(39,\cdot)$	175.t	30	yes	$1$	$1$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{8}{15}\right)$
$\chi_{175}(41,\cdot)$	175.l	10	yes	$-1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{175}(43,\cdot)$	175.g	4	no	$-1$	$1$	$-i$	$i$	$-1$	$1$	$i$	$-1$	$1$	$-i$	$i$	$1$
$\chi_{175}(44,\cdot)$	175.t	30	yes	$1$	$1$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{4}{15}\right)$
$\chi_{175}(46,\cdot)$	175.q	15	yes	$1$	$1$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{11}{15}\right)$

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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	$175$
Structure	\(C_{2}\times C_{60}\)
Order	$120$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(8\)	\(9\)	\(11\)	\(12\)	\(13\)	\(16\)
\(\chi_{175}(1,\cdot)\)	175.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{175}(2,\cdot)\)	175.w	60	yes	\(-1\)	\(1\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{13}{15}\right)\)
\(\chi_{175}(3,\cdot)\)	175.x	60	yes	\(1\)	\(1\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{11}{15}\right)\)
\(\chi_{175}(4,\cdot)\)	175.t	30	yes	\(1\)	\(1\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{11}{15}\right)\)
\(\chi_{175}(6,\cdot)\)	175.l	10	yes	\(-1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{175}(8,\cdot)\)	175.r	20	no	\(-1\)	\(1\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{175}(9,\cdot)\)	175.t	30	yes	\(1\)	\(1\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{15}\right)\)
\(\chi_{175}(11,\cdot)\)	175.q	15	yes	\(1\)	\(1\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{8}{15}\right)\)
\(\chi_{175}(12,\cdot)\)	175.x	60	yes	\(1\)	\(1\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{7}{15}\right)\)
\(\chi_{175}(13,\cdot)\)	175.s	20	yes	\(1\)	\(1\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{175}(16,\cdot)\)	175.q	15	yes	\(1\)	\(1\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{15}\right)\)
\(\chi_{175}(17,\cdot)\)	175.x	60	yes	\(1\)	\(1\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{14}{15}\right)\)
\(\chi_{175}(18,\cdot)\)	175.p	12	no	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(i\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{175}(19,\cdot)\)	175.u	30	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{4}{15}\right)\)
\(\chi_{175}(22,\cdot)\)	175.r	20	no	\(-1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{175}(23,\cdot)\)	175.w	60	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{13}{15}\right)\)
\(\chi_{175}(24,\cdot)\)	175.j	6	no	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{175}(26,\cdot)\)	175.i	6	no	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{175}(27,\cdot)\)	175.s	20	yes	\(1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{175}(29,\cdot)\)	175.n	10	no	\(1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{175}(31,\cdot)\)	175.v	30	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{14}{15}\right)\)
\(\chi_{175}(32,\cdot)\)	175.p	12	no	\(-1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(-i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{175}(33,\cdot)\)	175.x	60	yes	\(1\)	\(1\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{4}{15}\right)\)
\(\chi_{175}(34,\cdot)\)	175.m	10	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{175}(36,\cdot)\)	175.h	5	no	\(1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{175}(37,\cdot)\)	175.w	60	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{7}{15}\right)\)
\(\chi_{175}(38,\cdot)\)	175.x	60	yes	\(1\)	\(1\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{2}{15}\right)\)
\(\chi_{175}(39,\cdot)\)	175.t	30	yes	\(1\)	\(1\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{8}{15}\right)\)
\(\chi_{175}(41,\cdot)\)	175.l	10	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{175}(43,\cdot)\)	175.g	4	no	\(-1\)	\(1\)	\(-i\)	\(i\)	\(-1\)	\(1\)	\(i\)	\(-1\)	\(1\)	\(-i\)	\(i\)	\(1\)
\(\chi_{175}(44,\cdot)\)	175.t	30	yes	\(1\)	\(1\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{4}{15}\right)\)
\(\chi_{175}(46,\cdot)\)	175.q	15	yes	\(1\)	\(1\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{11}{15}\right)\)

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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.