LMFDB - Group of Dirichlet characters of modulus 451

sage:H = DirichletGroup(451)

pari:g = idealstar(,451,2)

Character group

sage:G.order() pari:g.no
Order	=	400
sage:H.invariants() pari:g.cyc
Structure	=	$C_{10}\times C_{40}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{451}(288,\cdot)$, $\chi_{451}(375,\cdot)$

First 32 of 400 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$12$
$\chi_{451}(1,\cdot)$	451.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{451}(2,\cdot)$	451.br	20	yes	$-1$	$1$	$1$	$e\left(\frac{11}{20}\right)$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{20}\right)$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{11}{20}\right)$
$\chi_{451}(3,\cdot)$	451.cd	40	yes	$-1$	$1$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{1}{20}\right)$	$1$	$e\left(\frac{1}{8}\right)$
$\chi_{451}(4,\cdot)$	451.bf	10	yes	$1$	$1$	$1$	$e\left(\frac{1}{10}\right)$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{10}\right)$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{451}(5,\cdot)$	451.bp	20	yes	$1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{20}\right)$	$i$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{17}{20}\right)$
$\chi_{451}(6,\cdot)$	451.ca	40	yes	$1$	$1$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{27}{40}\right)$
$\chi_{451}(7,\cdot)$	451.bz	40	yes	$1$	$1$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{1}{10}\right)$	$i$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{13}{40}\right)$
$\chi_{451}(8,\cdot)$	451.br	20	yes	$-1$	$1$	$1$	$e\left(\frac{13}{20}\right)$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{20}\right)$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{13}{20}\right)$
$\chi_{451}(9,\cdot)$	451.bq	20	yes	$1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{10}\right)$	$1$	$i$
$\chi_{451}(10,\cdot)$	451.be	10	yes	$-1$	$1$	$e\left(\frac{7}{10}\right)$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{10}\right)$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{451}(12,\cdot)$	451.bv	40	no	$-1$	$1$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{13}{20}\right)$	$i$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{9}{40}\right)$
$\chi_{451}(13,\cdot)$	451.bt	40	yes	$1$	$1$	$i$	$e\left(\frac{17}{40}\right)$	$-1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{37}{40}\right)$	$-i$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{37}{40}\right)$
$\chi_{451}(14,\cdot)$	451.cd	40	yes	$-1$	$1$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{11}{20}\right)$	$1$	$e\left(\frac{7}{8}\right)$
$\chi_{451}(15,\cdot)$	451.bs	40	yes	$-1$	$1$	$i$	$e\left(\frac{19}{40}\right)$	$-1$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{19}{40}\right)$	$-i$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{39}{40}\right)$
$\chi_{451}(16,\cdot)$	451.l	5	yes	$1$	$1$	$1$	$e\left(\frac{1}{5}\right)$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{5}\right)$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{451}(17,\cdot)$	451.bz	40	yes	$1$	$1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{7}{10}\right)$	$-i$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{11}{40}\right)$
$\chi_{451}(18,\cdot)$	451.x	10	yes	$-1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{10}\right)$	$-1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{451}(19,\cdot)$	451.cb	40	yes	$1$	$1$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{40}\right)$
$\chi_{451}(20,\cdot)$	451.bo	20	yes	$1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{10}\right)$	$i$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{19}{20}\right)$
$\chi_{451}(21,\cdot)$	451.bi	20	yes	$-1$	$1$	$e\left(\frac{3}{5}\right)$	$i$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{4}{5}\right)$	$-1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{20}\right)$
$\chi_{451}(23,\cdot)$	451.q	10	no	$1$	$1$	$e\left(\frac{2}{5}\right)$	$-1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{5}\right)$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{451}(24,\cdot)$	451.cb	40	yes	$1$	$1$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{31}{40}\right)$
$\chi_{451}(25,\cdot)$	451.s	10	yes	$1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{10}\right)$	$-1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{451}(26,\cdot)$	451.bs	40	yes	$-1$	$1$	$i$	$e\left(\frac{39}{40}\right)$	$-1$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{39}{40}\right)$	$-i$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{19}{40}\right)$
$\chi_{451}(27,\cdot)$	451.cd	40	yes	$-1$	$1$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{3}{20}\right)$	$1$	$e\left(\frac{3}{8}\right)$
$\chi_{451}(28,\cdot)$	451.ca	40	yes	$1$	$1$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{17}{40}\right)$
$\chi_{451}(29,\cdot)$	451.bt	40	yes	$1$	$1$	$i$	$e\left(\frac{9}{40}\right)$	$-1$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{29}{40}\right)$	$-i$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{29}{40}\right)$
$\chi_{451}(30,\cdot)$	451.bt	40	yes	$1$	$1$	$i$	$e\left(\frac{1}{40}\right)$	$-1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{21}{40}\right)$	$-i$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{21}{40}\right)$
$\chi_{451}(31,\cdot)$	451.s	10	yes	$1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{10}\right)$	$-1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{451}(32,\cdot)$	451.f	4	yes	$-1$	$1$	$1$	$-i$	$1$	$-1$	$-i$	$i$	$1$	$-1$	$-1$	$-i$
$\chi_{451}(34,\cdot)$	451.bv	40	no	$-1$	$1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{1}{20}\right)$	$i$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{33}{40}\right)$
$\chi_{451}(35,\cdot)$	451.bt	40	yes	$1$	$1$	$-i$	$e\left(\frac{27}{40}\right)$	$-1$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{7}{40}\right)$	$i$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{40}\right)$

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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 $\F_{q}$
Belyi maps

Modulus	$451$
Structure	\(C_{10}\times C_{40}\)
Order	$400$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(12\)
\(\chi_{451}(1,\cdot)\)	451.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{451}(2,\cdot)\)	451.br	20	yes	\(-1\)	\(1\)	\(1\)	\(e\left(\frac{11}{20}\right)\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{11}{20}\right)\)
\(\chi_{451}(3,\cdot)\)	451.cd	40	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(1\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{451}(4,\cdot)\)	451.bf	10	yes	\(1\)	\(1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{451}(5,\cdot)\)	451.bp	20	yes	\(1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(i\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{17}{20}\right)\)
\(\chi_{451}(6,\cdot)\)	451.ca	40	yes	\(1\)	\(1\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{27}{40}\right)\)
\(\chi_{451}(7,\cdot)\)	451.bz	40	yes	\(1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(i\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{13}{40}\right)\)
\(\chi_{451}(8,\cdot)\)	451.br	20	yes	\(-1\)	\(1\)	\(1\)	\(e\left(\frac{13}{20}\right)\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)
\(\chi_{451}(9,\cdot)\)	451.bq	20	yes	\(1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(1\)	\(i\)
\(\chi_{451}(10,\cdot)\)	451.be	10	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{451}(12,\cdot)\)	451.bv	40	no	\(-1\)	\(1\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(i\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{9}{40}\right)\)
\(\chi_{451}(13,\cdot)\)	451.bt	40	yes	\(1\)	\(1\)	\(i\)	\(e\left(\frac{17}{40}\right)\)	\(-1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(-i\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{37}{40}\right)\)
\(\chi_{451}(14,\cdot)\)	451.cd	40	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(1\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{451}(15,\cdot)\)	451.bs	40	yes	\(-1\)	\(1\)	\(i\)	\(e\left(\frac{19}{40}\right)\)	\(-1\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(-i\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{39}{40}\right)\)
\(\chi_{451}(16,\cdot)\)	451.l	5	yes	\(1\)	\(1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{451}(17,\cdot)\)	451.bz	40	yes	\(1\)	\(1\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(-i\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{11}{40}\right)\)
\(\chi_{451}(18,\cdot)\)	451.x	10	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(-1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{451}(19,\cdot)\)	451.cb	40	yes	\(1\)	\(1\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{40}\right)\)
\(\chi_{451}(20,\cdot)\)	451.bo	20	yes	\(1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(i\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{19}{20}\right)\)
\(\chi_{451}(21,\cdot)\)	451.bi	20	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(i\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(-1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{9}{20}\right)\)
\(\chi_{451}(23,\cdot)\)	451.q	10	no	\(1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(-1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{451}(24,\cdot)\)	451.cb	40	yes	\(1\)	\(1\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{31}{40}\right)\)
\(\chi_{451}(25,\cdot)\)	451.s	10	yes	\(1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(-1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{451}(26,\cdot)\)	451.bs	40	yes	\(-1\)	\(1\)	\(i\)	\(e\left(\frac{39}{40}\right)\)	\(-1\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(-i\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{19}{40}\right)\)
\(\chi_{451}(27,\cdot)\)	451.cd	40	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(1\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{451}(28,\cdot)\)	451.ca	40	yes	\(1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{17}{40}\right)\)
\(\chi_{451}(29,\cdot)\)	451.bt	40	yes	\(1\)	\(1\)	\(i\)	\(e\left(\frac{9}{40}\right)\)	\(-1\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(-i\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{29}{40}\right)\)
\(\chi_{451}(30,\cdot)\)	451.bt	40	yes	\(1\)	\(1\)	\(i\)	\(e\left(\frac{1}{40}\right)\)	\(-1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(-i\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{21}{40}\right)\)
\(\chi_{451}(31,\cdot)\)	451.s	10	yes	\(1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(-1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{451}(32,\cdot)\)	451.f	4	yes	\(-1\)	\(1\)	\(1\)	\(-i\)	\(1\)	\(-1\)	\(-i\)	\(i\)	\(1\)	\(-1\)	\(-1\)	\(-i\)
\(\chi_{451}(34,\cdot)\)	451.bv	40	no	\(-1\)	\(1\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(i\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{33}{40}\right)\)
\(\chi_{451}(35,\cdot)\)	451.bt	40	yes	\(1\)	\(1\)	\(-i\)	\(e\left(\frac{27}{40}\right)\)	\(-1\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(i\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{40}\right)\)

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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.