LMFDB - Group of Dirichlet characters of modulus 440

Show commands: PariGP / SageMath

sage: H = DirichletGroup(440)

pari: g = idealstar(,440,2)

Character group

sage: G.order() pari: g.no
Order	=	160
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{20}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{440}(111,\cdot)$, $\chi_{440}(221,\cdot)$, $\chi_{440}(177,\cdot)$, $\chi_{440}(321,\cdot)$

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	$-1$	$1$	$3$	$7$	$9$	$13$	$17$	$19$	$21$	$23$	$27$	$29$
$\chi_{440}(1,\cdot)$	440.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{440}(3,\cdot)$	440.bs	20	yes	$1$	$1$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{9}{10}\right)$	$-1$	$-i$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{440}(7,\cdot)$	440.bt	20	no	$-1$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{10}\right)$	$-1$	$i$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{440}(9,\cdot)$	440.bn	10	no	$1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{5}\right)$	$1$	$-1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{440}(13,\cdot)$	440.bu	20	yes	$1$	$1$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{10}\right)$	$1$	$i$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{440}(17,\cdot)$	440.bo	20	no	$1$	$1$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{5}\right)$	$-1$	$-i$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{440}(19,\cdot)$	440.bm	10	yes	$1$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{9}{10}\right)$	$1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{440}(21,\cdot)$	440.d	2	no	$-1$	$1$	$-1$	$-1$	$1$	$1$	$-1$	$1$	$1$	$1$	$-1$	$1$
$\chi_{440}(23,\cdot)$	440.x	4	no	$1$	$1$	$-i$	$i$	$-1$	$i$	$-i$	$1$	$1$	$-i$	$i$	$-1$
$\chi_{440}(27,\cdot)$	440.bs	20	yes	$1$	$1$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{7}{10}\right)$	$-1$	$i$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{440}(29,\cdot)$	440.ba	10	yes	$-1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$	$1$	$-1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{440}(31,\cdot)$	440.bk	10	no	$-1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{10}\right)$	$1$	$-1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{440}(37,\cdot)$	440.bp	20	yes	$-1$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{5}\right)$	$-1$	$-i$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{440}(39,\cdot)$	440.bc	10	no	$1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{5}\right)$	$-1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{440}(41,\cdot)$	440.bf	10	no	$-1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{10}\right)$	$-1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{440}(43,\cdot)$	440.w	4	yes	$-1$	$1$	$i$	$-i$	$-1$	$i$	$i$	$1$	$1$	$-i$	$-i$	$-1$
$\chi_{440}(47,\cdot)$	440.bq	20	no	$1$	$1$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{2}{5}\right)$	$1$	$i$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{440}(49,\cdot)$	440.bn	10	no	$1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{5}\right)$	$1$	$-1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{440}(51,\cdot)$	440.z	10	no	$1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{10}\right)$	$1$	$-1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{440}(53,\cdot)$	440.bp	20	yes	$-1$	$1$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{4}{5}\right)$	$-1$	$i$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{440}(57,\cdot)$	440.bo	20	no	$1$	$1$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{4}{5}\right)$	$-1$	$-i$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{440}(59,\cdot)$	440.bh	10	yes	$-1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{5}\right)$	$-1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{440}(61,\cdot)$	440.bl	10	no	$-1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{5}\right)$	$1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{440}(63,\cdot)$	440.bt	20	no	$-1$	$1$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{9}{10}\right)$	$-1$	$-i$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{440}(67,\cdot)$	440.r	4	no	$1$	$1$	$-i$	$-i$	$-1$	$i$	$i$	$-1$	$-1$	$i$	$i$	$1$
$\chi_{440}(69,\cdot)$	440.bd	10	yes	$1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{10}\right)$	$-1$	$-1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{440}(71,\cdot)$	440.bk	10	no	$-1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{10}\right)$	$1$	$-1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{440}(73,\cdot)$	440.bo	20	no	$1$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{5}\right)$	$-1$	$i$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{440}(79,\cdot)$	440.bc	10	no	$1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$-1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{440}(81,\cdot)$	440.y	5	no	$1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$	$1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{440}(83,\cdot)$	440.br	20	yes	$-1$	$1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{5}\right)$	$1$	$-i$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{440}(87,\cdot)$	440.q	4	no	$-1$	$1$	$i$	$i$	$-1$	$i$	$-i$	$-1$	$-1$	$i$	$-i$	$1$

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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	$440$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{20}\)
Order	$160$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(13\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)	\(29\)
\(\chi_{440}(1,\cdot)\)	440.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{440}(3,\cdot)\)	440.bs	20	yes	\(1\)	\(1\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(-1\)	\(-i\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{440}(7,\cdot)\)	440.bt	20	no	\(-1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(-1\)	\(i\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{440}(9,\cdot)\)	440.bn	10	no	\(1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{440}(13,\cdot)\)	440.bu	20	yes	\(1\)	\(1\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(1\)	\(i\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{440}(17,\cdot)\)	440.bo	20	no	\(1\)	\(1\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(-1\)	\(-i\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{440}(19,\cdot)\)	440.bm	10	yes	\(1\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{440}(21,\cdot)\)	440.d	2	no	\(-1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(1\)	\(-1\)	\(1\)	\(1\)	\(1\)	\(-1\)	\(1\)
\(\chi_{440}(23,\cdot)\)	440.x	4	no	\(1\)	\(1\)	\(-i\)	\(i\)	\(-1\)	\(i\)	\(-i\)	\(1\)	\(1\)	\(-i\)	\(i\)	\(-1\)
\(\chi_{440}(27,\cdot)\)	440.bs	20	yes	\(1\)	\(1\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(-1\)	\(i\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{440}(29,\cdot)\)	440.ba	10	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{440}(31,\cdot)\)	440.bk	10	no	\(-1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{440}(37,\cdot)\)	440.bp	20	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(-1\)	\(-i\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{440}(39,\cdot)\)	440.bc	10	no	\(1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{440}(41,\cdot)\)	440.bf	10	no	\(-1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{440}(43,\cdot)\)	440.w	4	yes	\(-1\)	\(1\)	\(i\)	\(-i\)	\(-1\)	\(i\)	\(i\)	\(1\)	\(1\)	\(-i\)	\(-i\)	\(-1\)
\(\chi_{440}(47,\cdot)\)	440.bq	20	no	\(1\)	\(1\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(1\)	\(i\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{440}(49,\cdot)\)	440.bn	10	no	\(1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{440}(51,\cdot)\)	440.z	10	no	\(1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{440}(53,\cdot)\)	440.bp	20	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(-1\)	\(i\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{440}(57,\cdot)\)	440.bo	20	no	\(1\)	\(1\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(-1\)	\(-i\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{440}(59,\cdot)\)	440.bh	10	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{440}(61,\cdot)\)	440.bl	10	no	\(-1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{440}(63,\cdot)\)	440.bt	20	no	\(-1\)	\(1\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(-1\)	\(-i\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{440}(67,\cdot)\)	440.r	4	no	\(1\)	\(1\)	\(-i\)	\(-i\)	\(-1\)	\(i\)	\(i\)	\(-1\)	\(-1\)	\(i\)	\(i\)	\(1\)
\(\chi_{440}(69,\cdot)\)	440.bd	10	yes	\(1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{440}(71,\cdot)\)	440.bk	10	no	\(-1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{440}(73,\cdot)\)	440.bo	20	no	\(1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(-1\)	\(i\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{440}(79,\cdot)\)	440.bc	10	no	\(1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{440}(81,\cdot)\)	440.y	5	no	\(1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{440}(83,\cdot)\)	440.br	20	yes	\(-1\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(1\)	\(-i\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{440}(87,\cdot)\)	440.q	4	no	\(-1\)	\(1\)	\(i\)	\(i\)	\(-1\)	\(i\)	\(-i\)	\(-1\)	\(-1\)	\(i\)	\(-i\)	\(1\)

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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.