LMFDB - Group of Dirichlet characters of modulus 475

Show commands: PariGP / SageMath

sage: H = DirichletGroup(475)

pari: g = idealstar(,475,2)

Character group

sage: G.order() pari: g.no
Order	=	360
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{180}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{475}(77,\cdot)$, $\chi_{475}(401,\cdot)$

First 32 of 360 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	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$11$	$12$	$13$
$\chi_{475}(1,\cdot)$	475.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{475}(2,\cdot)$	475.bi	180	yes	$1$	$1$	$e\left(\frac{19}{180}\right)$	$e\left(\frac{13}{180}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{41}{180}\right)$
$\chi_{475}(3,\cdot)$	475.bi	180	yes	$1$	$1$	$e\left(\frac{13}{180}\right)$	$e\left(\frac{151}{180}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{47}{180}\right)$
$\chi_{475}(4,\cdot)$	475.bg	90	yes	$1$	$1$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{41}{90}\right)$
$\chi_{475}(6,\cdot)$	475.bc	45	yes	$1$	$1$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{22}{45}\right)$
$\chi_{475}(7,\cdot)$	475.q	12	no	$-1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$i$	$-i$	$e\left(\frac{1}{6}\right)$	$1$	$i$	$e\left(\frac{5}{12}\right)$
$\chi_{475}(8,\cdot)$	475.be	60	yes	$1$	$1$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{8}{15}\right)$	$-i$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{41}{60}\right)$
$\chi_{475}(9,\cdot)$	475.bg	90	yes	$1$	$1$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{47}{90}\right)$
$\chi_{475}(11,\cdot)$	475.r	15	yes	$1$	$1$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{11}{15}\right)$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{8}{15}\right)$
$\chi_{475}(12,\cdot)$	475.be	60	yes	$1$	$1$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{4}{15}\right)$	$i$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{43}{60}\right)$
$\chi_{475}(13,\cdot)$	475.bi	180	yes	$1$	$1$	$e\left(\frac{41}{180}\right)$	$e\left(\frac{47}{180}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{79}{180}\right)$
$\chi_{475}(14,\cdot)$	475.bh	90	yes	$-1$	$1$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{29}{45}\right)$
$\chi_{475}(16,\cdot)$	475.bc	45	yes	$1$	$1$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{41}{45}\right)$
$\chi_{475}(17,\cdot)$	475.bj	180	yes	$-1$	$1$	$e\left(\frac{37}{180}\right)$	$e\left(\frac{139}{180}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{23}{180}\right)$
$\chi_{475}(18,\cdot)$	475.g	4	no	$1$	$1$	$i$	$-i$	$-1$	$1$	$-i$	$-i$	$-1$	$1$	$i$	$-i$
$\chi_{475}(21,\cdot)$	475.bf	90	yes	$-1$	$1$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{61}{90}\right)$
$\chi_{475}(22,\cdot)$	475.bi	180	yes	$1$	$1$	$e\left(\frac{103}{180}\right)$	$e\left(\frac{61}{180}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{137}{180}\right)$
$\chi_{475}(23,\cdot)$	475.bj	180	yes	$-1$	$1$	$e\left(\frac{119}{180}\right)$	$e\left(\frac{53}{180}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{1}{180}\right)$
$\chi_{475}(24,\cdot)$	475.u	18	no	$1$	$1$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{17}{18}\right)$
$\chi_{475}(26,\cdot)$	475.e	3	no	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$e\left(\frac{2}{3}\right)$
$\chi_{475}(27,\cdot)$	475.be	60	yes	$1$	$1$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{11}{15}\right)$	$i$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{47}{60}\right)$
$\chi_{475}(28,\cdot)$	475.bj	180	yes	$-1$	$1$	$e\left(\frac{143}{180}\right)$	$e\left(\frac{41}{180}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{157}{180}\right)$
$\chi_{475}(29,\cdot)$	475.bh	90	yes	$-1$	$1$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{28}{45}\right)$
$\chi_{475}(31,\cdot)$	475.y	30	yes	$-1$	$1$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{13}{15}\right)$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{23}{30}\right)$
$\chi_{475}(32,\cdot)$	475.bb	36	no	$1$	$1$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{36}\right)$
$\chi_{475}(33,\cdot)$	475.bi	180	yes	$1$	$1$	$e\left(\frac{97}{180}\right)$	$e\left(\frac{19}{180}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{143}{180}\right)$
$\chi_{475}(34,\cdot)$	475.bh	90	yes	$-1$	$1$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{16}{45}\right)$
$\chi_{475}(36,\cdot)$	475.bc	45	yes	$1$	$1$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{44}{45}\right)$
$\chi_{475}(37,\cdot)$	475.v	20	yes	$1$	$1$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{5}\right)$	$i$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{20}\right)$
$\chi_{475}(39,\cdot)$	475.n	10	no	$1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$-1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{475}(41,\cdot)$	475.bf	90	yes	$-1$	$1$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{37}{90}\right)$
$\chi_{475}(42,\cdot)$	475.bj	180	yes	$-1$	$1$	$e\left(\frac{137}{180}\right)$	$e\left(\frac{179}{180}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{163}{180}\right)$

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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	$475$
Structure	\(C_{2}\times C_{180}\)
Order	$360$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(7\)	\(8\)	\(9\)	\(11\)	\(12\)	\(13\)
\(\chi_{475}(1,\cdot)\)	475.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{475}(2,\cdot)\)	475.bi	180	yes	\(1\)	\(1\)	\(e\left(\frac{19}{180}\right)\)	\(e\left(\frac{13}{180}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{41}{180}\right)\)
\(\chi_{475}(3,\cdot)\)	475.bi	180	yes	\(1\)	\(1\)	\(e\left(\frac{13}{180}\right)\)	\(e\left(\frac{151}{180}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{47}{180}\right)\)
\(\chi_{475}(4,\cdot)\)	475.bg	90	yes	\(1\)	\(1\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{41}{90}\right)\)
\(\chi_{475}(6,\cdot)\)	475.bc	45	yes	\(1\)	\(1\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{22}{45}\right)\)
\(\chi_{475}(7,\cdot)\)	475.q	12	no	\(-1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(i\)	\(-i\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(i\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{475}(8,\cdot)\)	475.be	60	yes	\(1\)	\(1\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(-i\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{41}{60}\right)\)
\(\chi_{475}(9,\cdot)\)	475.bg	90	yes	\(1\)	\(1\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{47}{90}\right)\)
\(\chi_{475}(11,\cdot)\)	475.r	15	yes	\(1\)	\(1\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{8}{15}\right)\)
\(\chi_{475}(12,\cdot)\)	475.be	60	yes	\(1\)	\(1\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(i\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{43}{60}\right)\)
\(\chi_{475}(13,\cdot)\)	475.bi	180	yes	\(1\)	\(1\)	\(e\left(\frac{41}{180}\right)\)	\(e\left(\frac{47}{180}\right)\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{79}{180}\right)\)
\(\chi_{475}(14,\cdot)\)	475.bh	90	yes	\(-1\)	\(1\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{29}{45}\right)\)
\(\chi_{475}(16,\cdot)\)	475.bc	45	yes	\(1\)	\(1\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{41}{45}\right)\)
\(\chi_{475}(17,\cdot)\)	475.bj	180	yes	\(-1\)	\(1\)	\(e\left(\frac{37}{180}\right)\)	\(e\left(\frac{139}{180}\right)\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{23}{180}\right)\)
\(\chi_{475}(18,\cdot)\)	475.g	4	no	\(1\)	\(1\)	\(i\)	\(-i\)	\(-1\)	\(1\)	\(-i\)	\(-i\)	\(-1\)	\(1\)	\(i\)	\(-i\)
\(\chi_{475}(21,\cdot)\)	475.bf	90	yes	\(-1\)	\(1\)	\(e\left(\frac{59}{90}\right)\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{61}{90}\right)\)
\(\chi_{475}(22,\cdot)\)	475.bi	180	yes	\(1\)	\(1\)	\(e\left(\frac{103}{180}\right)\)	\(e\left(\frac{61}{180}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{137}{180}\right)\)
\(\chi_{475}(23,\cdot)\)	475.bj	180	yes	\(-1\)	\(1\)	\(e\left(\frac{119}{180}\right)\)	\(e\left(\frac{53}{180}\right)\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{1}{180}\right)\)
\(\chi_{475}(24,\cdot)\)	475.u	18	no	\(1\)	\(1\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{17}{18}\right)\)
\(\chi_{475}(26,\cdot)\)	475.e	3	no	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{475}(27,\cdot)\)	475.be	60	yes	\(1\)	\(1\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(i\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{47}{60}\right)\)
\(\chi_{475}(28,\cdot)\)	475.bj	180	yes	\(-1\)	\(1\)	\(e\left(\frac{143}{180}\right)\)	\(e\left(\frac{41}{180}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{157}{180}\right)\)
\(\chi_{475}(29,\cdot)\)	475.bh	90	yes	\(-1\)	\(1\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{28}{45}\right)\)
\(\chi_{475}(31,\cdot)\)	475.y	30	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{23}{30}\right)\)
\(\chi_{475}(32,\cdot)\)	475.bb	36	no	\(1\)	\(1\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{36}\right)\)
\(\chi_{475}(33,\cdot)\)	475.bi	180	yes	\(1\)	\(1\)	\(e\left(\frac{97}{180}\right)\)	\(e\left(\frac{19}{180}\right)\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{143}{180}\right)\)
\(\chi_{475}(34,\cdot)\)	475.bh	90	yes	\(-1\)	\(1\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{16}{45}\right)\)
\(\chi_{475}(36,\cdot)\)	475.bc	45	yes	\(1\)	\(1\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{44}{45}\right)\)
\(\chi_{475}(37,\cdot)\)	475.v	20	yes	\(1\)	\(1\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(i\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)
\(\chi_{475}(39,\cdot)\)	475.n	10	no	\(1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(-1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{475}(41,\cdot)\)	475.bf	90	yes	\(-1\)	\(1\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{71}{90}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{37}{90}\right)\)
\(\chi_{475}(42,\cdot)\)	475.bj	180	yes	\(-1\)	\(1\)	\(e\left(\frac{137}{180}\right)\)	\(e\left(\frac{179}{180}\right)\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{163}{180}\right)\)

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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.