LMFDB - Group of Dirichlet characters of modulus 403

Show commands: PariGP / SageMath

sage: H = DirichletGroup(403)

pari: g = idealstar(,403,2)

Character group

sage: G.order() pari: g.no
Order	=	360
sage: H.invariants() pari: g.cyc
Structure	=	$C_{6}\times C_{60}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{403}(249,\cdot)$, $\chi_{403}(313,\cdot)$

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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{403}(1,\cdot)$	403.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{403}(2,\cdot)$	403.ce	60	yes	$-1$	$1$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{17}{30}\right)$	$-i$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{59}{60}\right)$
$\chi_{403}(3,\cdot)$	403.bv	30	yes	$-1$	$1$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{403}(4,\cdot)$	403.bs	30	yes	$1$	$1$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{2}{15}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{29}{30}\right)$
$\chi_{403}(5,\cdot)$	403.bb	12	yes	$-1$	$1$	$-i$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{11}{12}\right)$	$i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{403}(6,\cdot)$	403.ba	12	yes	$1$	$1$	$e\left(\frac{5}{12}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{11}{12}\right)$	$i$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{403}(7,\cdot)$	403.ca	60	yes	$-1$	$1$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{53}{60}\right)$
$\chi_{403}(8,\cdot)$	403.bm	20	yes	$-1$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{10}\right)$	$i$	$i$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{19}{20}\right)$
$\chi_{403}(9,\cdot)$	403.bk	15	yes	$1$	$1$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{403}(10,\cdot)$	403.bp	30	yes	$1$	$1$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{17}{30}\right)$
$\chi_{403}(11,\cdot)$	403.ch	60	yes	$1$	$1$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{43}{60}\right)$
$\chi_{403}(12,\cdot)$	403.by	30	yes	$-1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{1}{15}\right)$
$\chi_{403}(14,\cdot)$	403.bi	15	no	$1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{13}{15}\right)$
$\chi_{403}(15,\cdot)$	403.cb	60	yes	$1$	$1$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{23}{30}\right)$	$-i$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{41}{60}\right)$
$\chi_{403}(16,\cdot)$	403.bl	15	yes	$1$	$1$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{4}{15}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{14}{15}\right)$
$\chi_{403}(17,\cdot)$	403.bu	30	yes	$-1$	$1$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{8}{15}\right)$
$\chi_{403}(18,\cdot)$	403.cg	60	yes	$-1$	$1$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{11}{60}\right)$
$\chi_{403}(19,\cdot)$	403.ca	60	yes	$-1$	$1$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{59}{60}\right)$
$\chi_{403}(20,\cdot)$	403.cf	60	yes	$-1$	$1$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{7}{12}\right)$	$i$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{11}{20}\right)$
$\chi_{403}(21,\cdot)$	403.cd	60	yes	$1$	$1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{59}{60}\right)$
$\chi_{403}(22,\cdot)$	403.bv	30	yes	$-1$	$1$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{403}(23,\cdot)$	403.bq	30	yes	$-1$	$1$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{13}{15}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{8}{15}\right)$
$\chi_{403}(24,\cdot)$	403.cc	60	yes	$1$	$1$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{11}{12}\right)$	$-i$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{20}\right)$
$\chi_{403}(25,\cdot)$	403.l	6	yes	$1$	$1$	$-1$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{403}(27,\cdot)$	403.x	10	no	$-1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{4}{5}\right)$	$1$	$-1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{403}(28,\cdot)$	403.cf	60	yes	$-1$	$1$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{5}{12}\right)$	$-i$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{17}{20}\right)$
$\chi_{403}(29,\cdot)$	403.bw	30	yes	$-1$	$1$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{15}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{7}{30}\right)$
$\chi_{403}(30,\cdot)$	403.t	6	yes	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{403}(32,\cdot)$	403.bd	12	no	$-1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$-i$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{12}\right)$	$i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{403}(33,\cdot)$	403.ce	60	yes	$-1$	$1$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{7}{30}\right)$	$i$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{49}{60}\right)$
$\chi_{403}(34,\cdot)$	403.cd	60	yes	$1$	$1$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{31}{60}\right)$
$\chi_{403}(35,\cdot)$	403.bl	15	yes	$1$	$1$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{2}{15}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{7}{15}\right)$

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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	$403$
Structure	\(C_{6}\times C_{60}\)
Order	$360$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{403}(1,\cdot)\)	403.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{403}(2,\cdot)\)	403.ce	60	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(-i\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{59}{60}\right)\)
\(\chi_{403}(3,\cdot)\)	403.bv	30	yes	\(-1\)	\(1\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{403}(4,\cdot)\)	403.bs	30	yes	\(1\)	\(1\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{29}{30}\right)\)
\(\chi_{403}(5,\cdot)\)	403.bb	12	yes	\(-1\)	\(1\)	\(-i\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{403}(6,\cdot)\)	403.ba	12	yes	\(1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(i\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{403}(7,\cdot)\)	403.ca	60	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{53}{60}\right)\)
\(\chi_{403}(8,\cdot)\)	403.bm	20	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(i\)	\(i\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)
\(\chi_{403}(9,\cdot)\)	403.bk	15	yes	\(1\)	\(1\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{403}(10,\cdot)\)	403.bp	30	yes	\(1\)	\(1\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{17}{30}\right)\)
\(\chi_{403}(11,\cdot)\)	403.ch	60	yes	\(1\)	\(1\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{43}{60}\right)\)
\(\chi_{403}(12,\cdot)\)	403.by	30	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)
\(\chi_{403}(14,\cdot)\)	403.bi	15	no	\(1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)
\(\chi_{403}(15,\cdot)\)	403.cb	60	yes	\(1\)	\(1\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(-i\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{41}{60}\right)\)
\(\chi_{403}(16,\cdot)\)	403.bl	15	yes	\(1\)	\(1\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)
\(\chi_{403}(17,\cdot)\)	403.bu	30	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)
\(\chi_{403}(18,\cdot)\)	403.cg	60	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{11}{60}\right)\)
\(\chi_{403}(19,\cdot)\)	403.ca	60	yes	\(-1\)	\(1\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{59}{60}\right)\)
\(\chi_{403}(20,\cdot)\)	403.cf	60	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(i\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{11}{20}\right)\)
\(\chi_{403}(21,\cdot)\)	403.cd	60	yes	\(1\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{59}{60}\right)\)
\(\chi_{403}(22,\cdot)\)	403.bv	30	yes	\(-1\)	\(1\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{403}(23,\cdot)\)	403.bq	30	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)
\(\chi_{403}(24,\cdot)\)	403.cc	60	yes	\(1\)	\(1\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(-i\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{20}\right)\)
\(\chi_{403}(25,\cdot)\)	403.l	6	yes	\(1\)	\(1\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{403}(27,\cdot)\)	403.x	10	no	\(-1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{403}(28,\cdot)\)	403.cf	60	yes	\(-1\)	\(1\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(-i\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)
\(\chi_{403}(29,\cdot)\)	403.bw	30	yes	\(-1\)	\(1\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{7}{30}\right)\)
\(\chi_{403}(30,\cdot)\)	403.t	6	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{403}(32,\cdot)\)	403.bd	12	no	\(-1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-i\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{403}(33,\cdot)\)	403.ce	60	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(i\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{49}{60}\right)\)
\(\chi_{403}(34,\cdot)\)	403.cd	60	yes	\(1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{31}{60}\right)\)
\(\chi_{403}(35,\cdot)\)	403.bl	15	yes	\(1\)	\(1\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)

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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.