LMFDB - Group of Dirichlet characters of modulus 352

Show commands: PariGP / SageMath

sage: H = DirichletGroup(352)

pari: g = idealstar(,352,2)

Character group

sage: G.order() pari: g.no
Order	=	160
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{40}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{352}(287,\cdot)$, $\chi_{352}(133,\cdot)$, $\chi_{352}(321,\cdot)$

First 32 of 160 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	$-1$	$1$	$3$	$5$	$7$	$9$	$13$	$15$	$17$	$19$	$21$	$23$
$\chi_{352}(1,\cdot)$	352.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{352}(3,\cdot)$	352.bd	40	yes	$-1$	$1$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{7}{8}\right)$	$-i$
$\chi_{352}(5,\cdot)$	352.bf	40	yes	$1$	$1$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{5}{8}\right)$	$-i$
$\chi_{352}(7,\cdot)$	352.bb	20	no	$1$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{20}\right)$	$-i$	$1$
$\chi_{352}(9,\cdot)$	352.ba	20	no	$1$	$1$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{20}\right)$	$-i$	$-1$
$\chi_{352}(13,\cdot)$	352.be	40	yes	$-1$	$1$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{7}{8}\right)$	$i$
$\chi_{352}(15,\cdot)$	352.t	10	no	$-1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$	$-1$	$-1$
$\chi_{352}(17,\cdot)$	352.x	10	no	$-1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{5}\right)$	$1$	$1$
$\chi_{352}(19,\cdot)$	352.bc	40	yes	$1$	$1$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{7}{8}\right)$	$-i$
$\chi_{352}(21,\cdot)$	352.o	8	yes	$-1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$	$-i$	$-i$	$e\left(\frac{7}{8}\right)$	$-1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$	$-i$
$\chi_{352}(23,\cdot)$	352.k	4	no	$-1$	$1$	$-i$	$-i$	$1$	$-1$	$i$	$-1$	$1$	$-i$	$-i$	$1$
$\chi_{352}(25,\cdot)$	352.ba	20	no	$1$	$1$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{20}\right)$	$i$	$-1$
$\chi_{352}(27,\cdot)$	352.bd	40	yes	$-1$	$1$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{5}{8}\right)$	$i$
$\chi_{352}(29,\cdot)$	352.be	40	yes	$-1$	$1$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{3}{8}\right)$	$i$
$\chi_{352}(31,\cdot)$	352.v	10	no	$-1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{10}\right)$	$1$	$-1$
$\chi_{352}(35,\cdot)$	352.bc	40	yes	$1$	$1$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{3}{8}\right)$	$-i$
$\chi_{352}(37,\cdot)$	352.bf	40	yes	$1$	$1$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{5}{8}\right)$	$-i$
$\chi_{352}(39,\cdot)$	352.bb	20	no	$1$	$1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{19}{20}\right)$	$-i$	$1$
$\chi_{352}(41,\cdot)$	352.y	20	no	$-1$	$1$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{20}\right)$	$i$	$-1$
$\chi_{352}(43,\cdot)$	352.q	8	yes	$1$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{8}\right)$	$i$	$-i$	$e\left(\frac{7}{8}\right)$	$1$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{8}\right)$	$i$
$\chi_{352}(45,\cdot)$	352.n	8	no	$1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{8}\right)$	$-i$	$i$	$e\left(\frac{1}{8}\right)$	$-1$	$-1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{8}\right)$	$i$
$\chi_{352}(47,\cdot)$	352.t	10	no	$-1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{5}\right)$	$-1$	$-1$
$\chi_{352}(49,\cdot)$	352.w	10	no	$1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{10}\right)$	$-1$	$1$
$\chi_{352}(51,\cdot)$	352.bc	40	yes	$1$	$1$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{7}{8}\right)$	$-i$
$\chi_{352}(53,\cdot)$	352.bf	40	yes	$1$	$1$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{1}{8}\right)$	$-i$
$\chi_{352}(57,\cdot)$	352.y	20	no	$-1$	$1$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{20}\right)$	$-i$	$-1$
$\chi_{352}(59,\cdot)$	352.bd	40	yes	$-1$	$1$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{5}{8}\right)$	$i$
$\chi_{352}(61,\cdot)$	352.be	40	yes	$-1$	$1$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{3}{8}\right)$	$i$
$\chi_{352}(63,\cdot)$	352.u	10	no	$1$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{5}\right)$	$-1$	$-1$
$\chi_{352}(65,\cdot)$	352.h	2	no	$-1$	$1$	$1$	$1$	$-1$	$1$	$-1$	$1$	$-1$	$-1$	$-1$	$1$
$\chi_{352}(67,\cdot)$	352.p	8	no	$-1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{8}\right)$	$i$	$i$	$e\left(\frac{5}{8}\right)$	$1$	$-1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{8}\right)$	$-i$
$\chi_{352}(69,\cdot)$	352.bf	40	yes	$1$	$1$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{5}{8}\right)$	$-i$

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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	$352$
Structure	\(C_{2}\times C_{2}\times C_{40}\)
Order	$160$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)	\(23\)
\(\chi_{352}(1,\cdot)\)	352.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{352}(3,\cdot)\)	352.bd	40	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(-i\)
\(\chi_{352}(5,\cdot)\)	352.bf	40	yes	\(1\)	\(1\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(-i\)
\(\chi_{352}(7,\cdot)\)	352.bb	20	no	\(1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(-i\)	\(1\)
\(\chi_{352}(9,\cdot)\)	352.ba	20	no	\(1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(-i\)	\(-1\)
\(\chi_{352}(13,\cdot)\)	352.be	40	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(i\)
\(\chi_{352}(15,\cdot)\)	352.t	10	no	\(-1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(-1\)	\(-1\)
\(\chi_{352}(17,\cdot)\)	352.x	10	no	\(-1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(1\)	\(1\)
\(\chi_{352}(19,\cdot)\)	352.bc	40	yes	\(1\)	\(1\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(-i\)
\(\chi_{352}(21,\cdot)\)	352.o	8	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(-i\)	\(-i\)	\(e\left(\frac{7}{8}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(-i\)
\(\chi_{352}(23,\cdot)\)	352.k	4	no	\(-1\)	\(1\)	\(-i\)	\(-i\)	\(1\)	\(-1\)	\(i\)	\(-1\)	\(1\)	\(-i\)	\(-i\)	\(1\)
\(\chi_{352}(25,\cdot)\)	352.ba	20	no	\(1\)	\(1\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(i\)	\(-1\)
\(\chi_{352}(27,\cdot)\)	352.bd	40	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(i\)
\(\chi_{352}(29,\cdot)\)	352.be	40	yes	\(-1\)	\(1\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(i\)
\(\chi_{352}(31,\cdot)\)	352.v	10	no	\(-1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(1\)	\(-1\)
\(\chi_{352}(35,\cdot)\)	352.bc	40	yes	\(1\)	\(1\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(-i\)
\(\chi_{352}(37,\cdot)\)	352.bf	40	yes	\(1\)	\(1\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(-i\)
\(\chi_{352}(39,\cdot)\)	352.bb	20	no	\(1\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(-i\)	\(1\)
\(\chi_{352}(41,\cdot)\)	352.y	20	no	\(-1\)	\(1\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(i\)	\(-1\)
\(\chi_{352}(43,\cdot)\)	352.q	8	yes	\(1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(i\)	\(-i\)	\(e\left(\frac{7}{8}\right)\)	\(1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(i\)
\(\chi_{352}(45,\cdot)\)	352.n	8	no	\(1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(-i\)	\(i\)	\(e\left(\frac{1}{8}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(i\)
\(\chi_{352}(47,\cdot)\)	352.t	10	no	\(-1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(-1\)	\(-1\)
\(\chi_{352}(49,\cdot)\)	352.w	10	no	\(1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(-1\)	\(1\)
\(\chi_{352}(51,\cdot)\)	352.bc	40	yes	\(1\)	\(1\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(-i\)
\(\chi_{352}(53,\cdot)\)	352.bf	40	yes	\(1\)	\(1\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(-i\)
\(\chi_{352}(57,\cdot)\)	352.y	20	no	\(-1\)	\(1\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(-i\)	\(-1\)
\(\chi_{352}(59,\cdot)\)	352.bd	40	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(i\)
\(\chi_{352}(61,\cdot)\)	352.be	40	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(i\)
\(\chi_{352}(63,\cdot)\)	352.u	10	no	\(1\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(-1\)	\(-1\)
\(\chi_{352}(65,\cdot)\)	352.h	2	no	\(-1\)	\(1\)	\(1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(-1\)	\(-1\)	\(1\)
\(\chi_{352}(67,\cdot)\)	352.p	8	no	\(-1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(i\)	\(i\)	\(e\left(\frac{5}{8}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(-i\)
\(\chi_{352}(69,\cdot)\)	352.bf	40	yes	\(1\)	\(1\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(-i\)

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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.