LMFDB - Group of Dirichlet characters of modulus 363

Show commands: PariGP / SageMath

sage: H = DirichletGroup(363)

pari: g = idealstar(,363,2)

Character group

sage: G.order() pari: g.no
Order	=	220
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{110}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{363}(122,\cdot)$, $\chi_{363}(244,\cdot)$

First 32 of 220 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	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$13$	$14$	$16$	$17$
$\chi_{363}(1,\cdot)$	363.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{363}(2,\cdot)$	363.p	110	yes	$1$	$1$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{19}{110}\right)$	$e\left(\frac{7}{110}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{52}{55}\right)$
$\chi_{363}(4,\cdot)$	363.m	55	no	$1$	$1$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{49}{55}\right)$
$\chi_{363}(5,\cdot)$	363.n	110	yes	$-1$	$1$	$e\left(\frac{19}{110}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{97}{110}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{51}{110}\right)$
$\chi_{363}(7,\cdot)$	363.o	110	no	$-1$	$1$	$e\left(\frac{7}{110}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{49}{110}\right)$	$e\left(\frac{21}{110}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{13}{110}\right)$
$\chi_{363}(8,\cdot)$	363.p	110	yes	$1$	$1$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{21}{110}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{79}{110}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{46}{55}\right)$
$\chi_{363}(10,\cdot)$	363.k	22	no	$-1$	$1$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{9}{22}\right)$
$\chi_{363}(13,\cdot)$	363.o	110	no	$-1$	$1$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{109}{110}\right)$
$\chi_{363}(14,\cdot)$	363.n	110	yes	$-1$	$1$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{97}{110}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{79}{110}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{7}{110}\right)$
$\chi_{363}(16,\cdot)$	363.m	55	no	$1$	$1$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{43}{55}\right)$
$\chi_{363}(17,\cdot)$	363.p	110	yes	$1$	$1$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{13}{110}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{109}{110}\right)$	$e\left(\frac{7}{110}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{18}{55}\right)$
$\chi_{363}(19,\cdot)$	363.o	110	no	$-1$	$1$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{23}{110}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{107}{110}\right)$
$\chi_{363}(20,\cdot)$	363.n	110	yes	$-1$	$1$	$e\left(\frac{21}{110}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{39}{110}\right)$
$\chi_{363}(23,\cdot)$	363.l	22	yes	$-1$	$1$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{15}{22}\right)$
$\chi_{363}(25,\cdot)$	363.m	55	no	$1$	$1$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{51}{55}\right)$
$\chi_{363}(26,\cdot)$	363.n	110	yes	$-1$	$1$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{13}{110}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{103}{110}\right)$
$\chi_{363}(28,\cdot)$	363.o	110	no	$-1$	$1$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{27}{110}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{1}{110}\right)$
$\chi_{363}(29,\cdot)$	363.p	110	yes	$1$	$1$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{67}{110}\right)$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{4}{55}\right)$
$\chi_{363}(31,\cdot)$	363.m	55	no	$1$	$1$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{17}{55}\right)$
$\chi_{363}(32,\cdot)$	363.j	22	yes	$1$	$1$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{8}{11}\right)$
$\chi_{363}(34,\cdot)$	363.i	11	no	$1$	$1$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{3}{11}\right)$
$\chi_{363}(35,\cdot)$	363.p	110	yes	$1$	$1$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{109}{110}\right)$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{43}{110}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{32}{55}\right)$
$\chi_{363}(37,\cdot)$	363.m	55	no	$1$	$1$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{39}{55}\right)$
$\chi_{363}(38,\cdot)$	363.n	110	yes	$-1$	$1$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{1}{110}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{67}{110}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{101}{110}\right)$
$\chi_{363}(40,\cdot)$	363.g	10	no	$-1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{10}\right)$	$-1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{363}(41,\cdot)$	363.p	110	yes	$1$	$1$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{13}{110}\right)$	$e\left(\frac{19}{110}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{41}{55}\right)$
$\chi_{363}(43,\cdot)$	363.k	22	no	$-1$	$1$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{3}{22}\right)$
$\chi_{363}(46,\cdot)$	363.o	110	no	$-1$	$1$	$e\left(\frac{71}{110}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{21}{110}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{69}{110}\right)$
$\chi_{363}(47,\cdot)$	363.n	110	yes	$-1$	$1$	$e\left(\frac{43}{110}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{19}{110}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{17}{110}\right)$
$\chi_{363}(49,\cdot)$	363.m	55	no	$1$	$1$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{13}{55}\right)$
$\chi_{363}(50,\cdot)$	363.p	110	yes	$1$	$1$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{37}{110}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{48}{55}\right)$
$\chi_{363}(52,\cdot)$	363.o	110	no	$-1$	$1$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{97}{110}\right)$

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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	$363$
Structure	\(C_{2}\times C_{110}\)
Order	$220$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(13\)	\(14\)	\(16\)	\(17\)
\(\chi_{363}(1,\cdot)\)	363.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{363}(2,\cdot)\)	363.p	110	yes	\(1\)	\(1\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{19}{110}\right)\)	\(e\left(\frac{7}{110}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{101}{110}\right)\)	\(e\left(\frac{63}{110}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{52}{55}\right)\)
\(\chi_{363}(4,\cdot)\)	363.m	55	no	\(1\)	\(1\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{49}{55}\right)\)
\(\chi_{363}(5,\cdot)\)	363.n	110	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{110}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{31}{110}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{57}{110}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{97}{110}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{51}{110}\right)\)
\(\chi_{363}(7,\cdot)\)	363.o	110	no	\(-1\)	\(1\)	\(e\left(\frac{7}{110}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{49}{110}\right)\)	\(e\left(\frac{21}{110}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{13}{110}\right)\)
\(\chi_{363}(8,\cdot)\)	363.p	110	yes	\(1\)	\(1\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{57}{110}\right)\)	\(e\left(\frac{21}{110}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{79}{110}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{46}{55}\right)\)
\(\chi_{363}(10,\cdot)\)	363.k	22	no	\(-1\)	\(1\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)
\(\chi_{363}(13,\cdot)\)	363.o	110	no	\(-1\)	\(1\)	\(e\left(\frac{101}{110}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{81}{110}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{109}{110}\right)\)
\(\chi_{363}(14,\cdot)\)	363.n	110	yes	\(-1\)	\(1\)	\(e\left(\frac{63}{110}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{97}{110}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{79}{110}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{7}{110}\right)\)
\(\chi_{363}(16,\cdot)\)	363.m	55	no	\(1\)	\(1\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{43}{55}\right)\)
\(\chi_{363}(17,\cdot)\)	363.p	110	yes	\(1\)	\(1\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{13}{110}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{109}{110}\right)\)	\(e\left(\frac{7}{110}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{18}{55}\right)\)
\(\chi_{363}(19,\cdot)\)	363.o	110	no	\(-1\)	\(1\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{31}{110}\right)\)	\(e\left(\frac{29}{110}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{23}{110}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{107}{110}\right)\)
\(\chi_{363}(20,\cdot)\)	363.n	110	yes	\(-1\)	\(1\)	\(e\left(\frac{21}{110}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{69}{110}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{63}{110}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{3}{110}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{39}{110}\right)\)
\(\chi_{363}(23,\cdot)\)	363.l	22	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)
\(\chi_{363}(25,\cdot)\)	363.m	55	no	\(1\)	\(1\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{51}{55}\right)\)
\(\chi_{363}(26,\cdot)\)	363.n	110	yes	\(-1\)	\(1\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{13}{110}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{31}{110}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{101}{110}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{103}{110}\right)\)
\(\chi_{363}(28,\cdot)\)	363.o	110	no	\(-1\)	\(1\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{63}{110}\right)\)	\(e\left(\frac{27}{110}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{29}{110}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{1}{110}\right)\)
\(\chi_{363}(29,\cdot)\)	363.p	110	yes	\(1\)	\(1\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{67}{110}\right)\)	\(e\left(\frac{81}{110}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{4}{55}\right)\)
\(\chi_{363}(31,\cdot)\)	363.m	55	no	\(1\)	\(1\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{17}{55}\right)\)
\(\chi_{363}(32,\cdot)\)	363.j	22	yes	\(1\)	\(1\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)
\(\chi_{363}(34,\cdot)\)	363.i	11	no	\(1\)	\(1\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)
\(\chi_{363}(35,\cdot)\)	363.p	110	yes	\(1\)	\(1\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{109}{110}\right)\)	\(e\left(\frac{17}{110}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{41}{110}\right)\)	\(e\left(\frac{43}{110}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{32}{55}\right)\)
\(\chi_{363}(37,\cdot)\)	363.m	55	no	\(1\)	\(1\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{39}{55}\right)\)
\(\chi_{363}(38,\cdot)\)	363.n	110	yes	\(-1\)	\(1\)	\(e\left(\frac{29}{110}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{1}{110}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{87}{110}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{67}{110}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{101}{110}\right)\)
\(\chi_{363}(40,\cdot)\)	363.g	10	no	\(-1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(-1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{363}(41,\cdot)\)	363.p	110	yes	\(1\)	\(1\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{107}{110}\right)\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{13}{110}\right)\)	\(e\left(\frac{19}{110}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{41}{55}\right)\)
\(\chi_{363}(43,\cdot)\)	363.k	22	no	\(-1\)	\(1\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)
\(\chi_{363}(46,\cdot)\)	363.o	110	no	\(-1\)	\(1\)	\(e\left(\frac{71}{110}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{57}{110}\right)\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{21}{110}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{69}{110}\right)\)
\(\chi_{363}(47,\cdot)\)	363.n	110	yes	\(-1\)	\(1\)	\(e\left(\frac{43}{110}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{19}{110}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{69}{110}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{17}{110}\right)\)
\(\chi_{363}(49,\cdot)\)	363.m	55	no	\(1\)	\(1\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{13}{55}\right)\)
\(\chi_{363}(50,\cdot)\)	363.p	110	yes	\(1\)	\(1\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{81}{110}\right)\)	\(e\left(\frac{53}{110}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{89}{110}\right)\)	\(e\left(\frac{37}{110}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{48}{55}\right)\)
\(\chi_{363}(52,\cdot)\)	363.o	110	no	\(-1\)	\(1\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{61}{110}\right)\)	\(e\left(\frac{89}{110}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{63}{110}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{97}{110}\right)\)

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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.