LMFDB - Group of Dirichlet characters of modulus 445

Show commands: PariGP / SageMath

sage: H = DirichletGroup(445)

pari: g = idealstar(,445,2)

Character group

sage: G.order() pari: g.no
Order	=	352
sage: H.invariants() pari: g.cyc
Structure	=	$C_{4}\times C_{88}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{445}(357,\cdot)$, $\chi_{445}(181,\cdot)$

First 32 of 352 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	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$11$	$12$	$13$
$\chi_{445}(1,\cdot)$	445.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{445}(2,\cdot)$	445.u	44	yes	$-1$	$1$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{3}{11}\right)$	$i$	$e\left(\frac{41}{44}\right)$
$\chi_{445}(3,\cdot)$	445.z	88	yes	$1$	$1$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{23}{88}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{17}{88}\right)$	$e\left(\frac{59}{88}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{45}{88}\right)$
$\chi_{445}(4,\cdot)$	445.r	22	yes	$1$	$1$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{6}{11}\right)$	$-1$	$e\left(\frac{19}{22}\right)$
$\chi_{445}(6,\cdot)$	445.y	88	no	$-1$	$1$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{17}{88}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{25}{88}\right)$	$e\left(\frac{57}{88}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{39}{88}\right)$
$\chi_{445}(7,\cdot)$	445.ba	88	yes	$1$	$1$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{59}{88}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{57}{88}\right)$	$e\left(\frac{71}{88}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{81}{88}\right)$
$\chi_{445}(8,\cdot)$	445.u	44	yes	$-1$	$1$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{9}{11}\right)$	$-i$	$e\left(\frac{35}{44}\right)$
$\chi_{445}(9,\cdot)$	445.x	44	yes	$1$	$1$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{10}{11}\right)$	$i$	$e\left(\frac{1}{44}\right)$
$\chi_{445}(11,\cdot)$	445.p	22	no	$1$	$1$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{2}{11}\right)$	$-1$	$e\left(\frac{21}{22}\right)$
$\chi_{445}(12,\cdot)$	445.l	8	yes	$1$	$1$	$i$	$e\left(\frac{1}{8}\right)$	$-1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{8}\right)$	$-i$	$i$	$-1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{445}(13,\cdot)$	445.ba	88	yes	$1$	$1$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{45}{88}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{39}{88}\right)$	$e\left(\frac{81}{88}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{23}{88}\right)$
$\chi_{445}(14,\cdot)$	445.bb	88	yes	$-1$	$1$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{53}{88}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{65}{88}\right)$	$e\left(\frac{69}{88}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{75}{88}\right)$
$\chi_{445}(16,\cdot)$	445.o	11	no	$1$	$1$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{1}{11}\right)$	$1$	$e\left(\frac{8}{11}\right)$
$\chi_{445}(17,\cdot)$	445.t	44	yes	$-1$	$1$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{8}{11}\right)$	$-1$	$e\left(\frac{7}{22}\right)$
$\chi_{445}(18,\cdot)$	445.t	44	yes	$-1$	$1$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{2}{11}\right)$	$-1$	$e\left(\frac{21}{22}\right)$
$\chi_{445}(19,\cdot)$	445.bb	88	yes	$-1$	$1$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{79}{88}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{67}{88}\right)$	$e\left(\frac{63}{88}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{57}{88}\right)$
$\chi_{445}(21,\cdot)$	445.s	44	no	$1$	$1$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{3}{11}\right)$	$-i$	$e\left(\frac{19}{44}\right)$
$\chi_{445}(22,\cdot)$	445.v	44	yes	$-1$	$1$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{5}{11}\right)$	$-i$	$e\left(\frac{39}{44}\right)$
$\chi_{445}(23,\cdot)$	445.z	88	yes	$1$	$1$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{79}{88}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{1}{88}\right)$	$e\left(\frac{19}{88}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{13}{88}\right)$
$\chi_{445}(24,\cdot)$	445.bb	88	yes	$-1$	$1$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{5}{88}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{41}{88}\right)$	$e\left(\frac{53}{88}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{27}{88}\right)$
$\chi_{445}(26,\cdot)$	445.y	88	no	$-1$	$1$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{39}{88}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{47}{88}\right)$	$e\left(\frac{79}{88}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{17}{88}\right)$
$\chi_{445}(27,\cdot)$	445.z	88	yes	$1$	$1$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{69}{88}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{51}{88}\right)$	$e\left(\frac{1}{88}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{47}{88}\right)$
$\chi_{445}(28,\cdot)$	445.z	88	yes	$1$	$1$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{47}{88}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{73}{88}\right)$	$e\left(\frac{67}{88}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{69}{88}\right)$
$\chi_{445}(29,\cdot)$	445.bb	88	yes	$-1$	$1$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{15}{88}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{35}{88}\right)$	$e\left(\frac{71}{88}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{81}{88}\right)$
$\chi_{445}(31,\cdot)$	445.y	88	no	$-1$	$1$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{31}{88}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{87}{88}\right)$	$e\left(\frac{47}{88}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{9}{88}\right)$
$\chi_{445}(32,\cdot)$	445.u	44	yes	$-1$	$1$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{4}{11}\right)$	$i$	$e\left(\frac{29}{44}\right)$
$\chi_{445}(33,\cdot)$	445.z	88	yes	$1$	$1$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{19}{88}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{37}{88}\right)$	$e\left(\frac{87}{88}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{41}{88}\right)$
$\chi_{445}(34,\cdot)$	445.e	4	yes	$1$	$1$	$-1$	$-i$	$1$	$i$	$-i$	$-1$	$-1$	$1$	$-i$	$i$
$\chi_{445}(36,\cdot)$	445.s	44	no	$1$	$1$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{5}{11}\right)$	$-i$	$e\left(\frac{39}{44}\right)$
$\chi_{445}(37,\cdot)$	445.m	8	yes	$1$	$1$	$i$	$e\left(\frac{7}{8}\right)$	$-1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{8}\right)$	$-i$	$-i$	$-1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{445}(38,\cdot)$	445.ba	88	yes	$1$	$1$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{73}{88}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{75}{88}\right)$	$e\left(\frac{61}{88}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{51}{88}\right)$
$\chi_{445}(39,\cdot)$	445.r	22	yes	$1$	$1$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{10}{11}\right)$	$-1$	$e\left(\frac{17}{22}\right)$

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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	$445$
Structure	\(C_{4}\times C_{88}\)
Order	$352$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(7\)	\(8\)	\(9\)	\(11\)	\(12\)	\(13\)
\(\chi_{445}(1,\cdot)\)	445.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{445}(2,\cdot)\)	445.u	44	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(i\)	\(e\left(\frac{41}{44}\right)\)
\(\chi_{445}(3,\cdot)\)	445.z	88	yes	\(1\)	\(1\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{23}{88}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{17}{88}\right)\)	\(e\left(\frac{59}{88}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{45}{88}\right)\)
\(\chi_{445}(4,\cdot)\)	445.r	22	yes	\(1\)	\(1\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(-1\)	\(e\left(\frac{19}{22}\right)\)
\(\chi_{445}(6,\cdot)\)	445.y	88	no	\(-1\)	\(1\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{17}{88}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{25}{88}\right)\)	\(e\left(\frac{57}{88}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{39}{88}\right)\)
\(\chi_{445}(7,\cdot)\)	445.ba	88	yes	\(1\)	\(1\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{59}{88}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{57}{88}\right)\)	\(e\left(\frac{71}{88}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{81}{88}\right)\)
\(\chi_{445}(8,\cdot)\)	445.u	44	yes	\(-1\)	\(1\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(-i\)	\(e\left(\frac{35}{44}\right)\)
\(\chi_{445}(9,\cdot)\)	445.x	44	yes	\(1\)	\(1\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(i\)	\(e\left(\frac{1}{44}\right)\)
\(\chi_{445}(11,\cdot)\)	445.p	22	no	\(1\)	\(1\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(-1\)	\(e\left(\frac{21}{22}\right)\)
\(\chi_{445}(12,\cdot)\)	445.l	8	yes	\(1\)	\(1\)	\(i\)	\(e\left(\frac{1}{8}\right)\)	\(-1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(-i\)	\(i\)	\(-1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{445}(13,\cdot)\)	445.ba	88	yes	\(1\)	\(1\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{45}{88}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{39}{88}\right)\)	\(e\left(\frac{81}{88}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{23}{88}\right)\)
\(\chi_{445}(14,\cdot)\)	445.bb	88	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{53}{88}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{65}{88}\right)\)	\(e\left(\frac{69}{88}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{75}{88}\right)\)
\(\chi_{445}(16,\cdot)\)	445.o	11	no	\(1\)	\(1\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(1\)	\(e\left(\frac{8}{11}\right)\)
\(\chi_{445}(17,\cdot)\)	445.t	44	yes	\(-1\)	\(1\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(-1\)	\(e\left(\frac{7}{22}\right)\)
\(\chi_{445}(18,\cdot)\)	445.t	44	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(-1\)	\(e\left(\frac{21}{22}\right)\)
\(\chi_{445}(19,\cdot)\)	445.bb	88	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{79}{88}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{67}{88}\right)\)	\(e\left(\frac{63}{88}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{57}{88}\right)\)
\(\chi_{445}(21,\cdot)\)	445.s	44	no	\(1\)	\(1\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(-i\)	\(e\left(\frac{19}{44}\right)\)
\(\chi_{445}(22,\cdot)\)	445.v	44	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(-i\)	\(e\left(\frac{39}{44}\right)\)
\(\chi_{445}(23,\cdot)\)	445.z	88	yes	\(1\)	\(1\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{79}{88}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{1}{88}\right)\)	\(e\left(\frac{19}{88}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{13}{88}\right)\)
\(\chi_{445}(24,\cdot)\)	445.bb	88	yes	\(-1\)	\(1\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{5}{88}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{41}{88}\right)\)	\(e\left(\frac{53}{88}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{27}{88}\right)\)
\(\chi_{445}(26,\cdot)\)	445.y	88	no	\(-1\)	\(1\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{39}{88}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{47}{88}\right)\)	\(e\left(\frac{79}{88}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{17}{88}\right)\)
\(\chi_{445}(27,\cdot)\)	445.z	88	yes	\(1\)	\(1\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{69}{88}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{51}{88}\right)\)	\(e\left(\frac{1}{88}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{47}{88}\right)\)
\(\chi_{445}(28,\cdot)\)	445.z	88	yes	\(1\)	\(1\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{47}{88}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{73}{88}\right)\)	\(e\left(\frac{67}{88}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{69}{88}\right)\)
\(\chi_{445}(29,\cdot)\)	445.bb	88	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{15}{88}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{35}{88}\right)\)	\(e\left(\frac{71}{88}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{81}{88}\right)\)
\(\chi_{445}(31,\cdot)\)	445.y	88	no	\(-1\)	\(1\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{31}{88}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{87}{88}\right)\)	\(e\left(\frac{47}{88}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{9}{88}\right)\)
\(\chi_{445}(32,\cdot)\)	445.u	44	yes	\(-1\)	\(1\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(i\)	\(e\left(\frac{29}{44}\right)\)
\(\chi_{445}(33,\cdot)\)	445.z	88	yes	\(1\)	\(1\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{19}{88}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{37}{88}\right)\)	\(e\left(\frac{87}{88}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{41}{88}\right)\)
\(\chi_{445}(34,\cdot)\)	445.e	4	yes	\(1\)	\(1\)	\(-1\)	\(-i\)	\(1\)	\(i\)	\(-i\)	\(-1\)	\(-1\)	\(1\)	\(-i\)	\(i\)
\(\chi_{445}(36,\cdot)\)	445.s	44	no	\(1\)	\(1\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(-i\)	\(e\left(\frac{39}{44}\right)\)
\(\chi_{445}(37,\cdot)\)	445.m	8	yes	\(1\)	\(1\)	\(i\)	\(e\left(\frac{7}{8}\right)\)	\(-1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(-i\)	\(-i\)	\(-1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{445}(38,\cdot)\)	445.ba	88	yes	\(1\)	\(1\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{73}{88}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{75}{88}\right)\)	\(e\left(\frac{61}{88}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{51}{88}\right)\)
\(\chi_{445}(39,\cdot)\)	445.r	22	yes	\(1\)	\(1\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(-1\)	\(e\left(\frac{17}{22}\right)\)

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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.