LMFDB - Group of Dirichlet characters of modulus 253

Show commands: PariGP / SageMath

sage: H = DirichletGroup(253)

pari: g = idealstar(,253,2)

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	=	$\chi_{253}(24,\cdot)$, $\chi_{253}(166,\cdot)$

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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$12$
$\chi_{253}(1,\cdot)$	253.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{253}(2,\cdot)$	253.o	110	yes	$-1$	$1$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{59}{110}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{9}{11}\right)$
$\chi_{253}(3,\cdot)$	253.m	55	yes	$1$	$1$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{6}{11}\right)$
$\chi_{253}(4,\cdot)$	253.m	55	yes	$1$	$1$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{7}{11}\right)$
$\chi_{253}(5,\cdot)$	253.p	110	yes	$-1$	$1$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{71}{110}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{10}{11}\right)$
$\chi_{253}(6,\cdot)$	253.o	110	yes	$-1$	$1$	$e\left(\frac{59}{110}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{67}{110}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{4}{11}\right)$
$\chi_{253}(7,\cdot)$	253.n	110	yes	$1$	$1$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{3}{11}\right)$
$\chi_{253}(8,\cdot)$	253.o	110	yes	$-1$	$1$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{67}{110}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{59}{110}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{5}{11}\right)$
$\chi_{253}(9,\cdot)$	253.m	55	yes	$1$	$1$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{1}{11}\right)$
$\chi_{253}(10,\cdot)$	253.l	22	yes	$1$	$1$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{8}{11}\right)$
$\chi_{253}(12,\cdot)$	253.i	11	no	$1$	$1$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{2}{11}\right)$
$\chi_{253}(13,\cdot)$	253.o	110	yes	$-1$	$1$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{13}{110}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{8}{11}\right)$
$\chi_{253}(14,\cdot)$	253.p	110	yes	$-1$	$1$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{1}{11}\right)$
$\chi_{253}(15,\cdot)$	253.p	110	yes	$-1$	$1$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{5}{11}\right)$
$\chi_{253}(16,\cdot)$	253.m	55	yes	$1$	$1$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{3}{11}\right)$
$\chi_{253}(17,\cdot)$	253.n	110	yes	$1$	$1$	$e\left(\frac{59}{110}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{67}{110}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{4}{11}\right)$
$\chi_{253}(18,\cdot)$	253.o	110	yes	$-1$	$1$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{13}{110}\right)$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{10}{11}\right)$
$\chi_{253}(19,\cdot)$	253.n	110	yes	$1$	$1$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{97}{110}\right)$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{109}{110}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{7}{11}\right)$
$\chi_{253}(20,\cdot)$	253.p	110	yes	$-1$	$1$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{6}{11}\right)$
$\chi_{253}(21,\cdot)$	253.l	22	yes	$1$	$1$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{9}{11}\right)$
$\chi_{253}(24,\cdot)$	253.g	10	no	$-1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{5}\right)$	$-1$	$1$
$\chi_{253}(25,\cdot)$	253.m	55	yes	$1$	$1$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{9}{11}\right)$
$\chi_{253}(26,\cdot)$	253.m	55	yes	$1$	$1$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{6}{11}\right)$
$\chi_{253}(27,\cdot)$	253.m	55	yes	$1$	$1$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{7}{11}\right)$
$\chi_{253}(28,\cdot)$	253.n	110	yes	$1$	$1$	$e\left(\frac{109}{110}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{71}{110}\right)$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{10}{11}\right)$
$\chi_{253}(29,\cdot)$	253.o	110	yes	$-1$	$1$	$e\left(\frac{37}{110}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{49}{110}\right)$	$e\left(\frac{1}{110}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{4}{11}\right)$
$\chi_{253}(30,\cdot)$	253.n	110	yes	$1$	$1$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{7}{110}\right)$	$e\left(\frac{27}{110}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{3}{11}\right)$
$\chi_{253}(31,\cdot)$	253.m	55	yes	$1$	$1$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{5}{11}\right)$
$\chi_{253}(32,\cdot)$	253.k	22	yes	$-1$	$1$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{1}{11}\right)$
$\chi_{253}(34,\cdot)$	253.j	22	no	$-1$	$1$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{2}{11}\right)$
$\chi_{253}(35,\cdot)$	253.o	110	yes	$-1$	$1$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{2}{11}\right)$
$\chi_{253}(36,\cdot)$	253.m	55	yes	$1$	$1$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{8}{11}\right)$

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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	$253$
Structure	\(C_{2}\times C_{110}\)
Order	$220$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(12\)
\(\chi_{253}(1,\cdot)\)	253.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{253}(2,\cdot)\)	253.o	110	yes	\(-1\)	\(1\)	\(e\left(\frac{31}{110}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{59}{110}\right)\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{93}{110}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)
\(\chi_{253}(3,\cdot)\)	253.m	55	yes	\(1\)	\(1\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)
\(\chi_{253}(4,\cdot)\)	253.m	55	yes	\(1\)	\(1\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)
\(\chi_{253}(5,\cdot)\)	253.p	110	yes	\(-1\)	\(1\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{71}{110}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{73}{110}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)
\(\chi_{253}(6,\cdot)\)	253.o	110	yes	\(-1\)	\(1\)	\(e\left(\frac{59}{110}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{93}{110}\right)\)	\(e\left(\frac{67}{110}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)
\(\chi_{253}(7,\cdot)\)	253.n	110	yes	\(1\)	\(1\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{73}{110}\right)\)	\(e\left(\frac{93}{110}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{31}{110}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)
\(\chi_{253}(8,\cdot)\)	253.o	110	yes	\(-1\)	\(1\)	\(e\left(\frac{93}{110}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{67}{110}\right)\)	\(e\left(\frac{31}{110}\right)\)	\(e\left(\frac{59}{110}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)
\(\chi_{253}(9,\cdot)\)	253.m	55	yes	\(1\)	\(1\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)
\(\chi_{253}(10,\cdot)\)	253.l	22	yes	\(1\)	\(1\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)
\(\chi_{253}(12,\cdot)\)	253.i	11	no	\(1\)	\(1\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)
\(\chi_{253}(13,\cdot)\)	253.o	110	yes	\(-1\)	\(1\)	\(e\left(\frac{41}{110}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{39}{110}\right)\)	\(e\left(\frac{87}{110}\right)\)	\(e\left(\frac{13}{110}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)
\(\chi_{253}(14,\cdot)\)	253.p	110	yes	\(-1\)	\(1\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{17}{110}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{81}{110}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)
\(\chi_{253}(15,\cdot)\)	253.p	110	yes	\(-1\)	\(1\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{63}{110}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)
\(\chi_{253}(16,\cdot)\)	253.m	55	yes	\(1\)	\(1\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)
\(\chi_{253}(17,\cdot)\)	253.n	110	yes	\(1\)	\(1\)	\(e\left(\frac{59}{110}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{101}{110}\right)\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{67}{110}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)
\(\chi_{253}(18,\cdot)\)	253.o	110	yes	\(-1\)	\(1\)	\(e\left(\frac{87}{110}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{13}{110}\right)\)	\(e\left(\frac{29}{110}\right)\)	\(e\left(\frac{41}{110}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)
\(\chi_{253}(19,\cdot)\)	253.n	110	yes	\(1\)	\(1\)	\(e\left(\frac{73}{110}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{97}{110}\right)\)	\(e\left(\frac{107}{110}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{109}{110}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)
\(\chi_{253}(20,\cdot)\)	253.p	110	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{69}{110}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{57}{110}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)
\(\chi_{253}(21,\cdot)\)	253.l	22	yes	\(1\)	\(1\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)
\(\chi_{253}(24,\cdot)\)	253.g	10	no	\(-1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(-1\)	\(1\)
\(\chi_{253}(25,\cdot)\)	253.m	55	yes	\(1\)	\(1\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)
\(\chi_{253}(26,\cdot)\)	253.m	55	yes	\(1\)	\(1\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)
\(\chi_{253}(27,\cdot)\)	253.m	55	yes	\(1\)	\(1\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)
\(\chi_{253}(28,\cdot)\)	253.n	110	yes	\(1\)	\(1\)	\(e\left(\frac{109}{110}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{71}{110}\right)\)	\(e\left(\frac{101}{110}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{107}{110}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)
\(\chi_{253}(29,\cdot)\)	253.o	110	yes	\(-1\)	\(1\)	\(e\left(\frac{37}{110}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{3}{110}\right)\)	\(e\left(\frac{49}{110}\right)\)	\(e\left(\frac{1}{110}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)
\(\chi_{253}(30,\cdot)\)	253.n	110	yes	\(1\)	\(1\)	\(e\left(\frac{3}{110}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{7}{110}\right)\)	\(e\left(\frac{27}{110}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)
\(\chi_{253}(31,\cdot)\)	253.m	55	yes	\(1\)	\(1\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)
\(\chi_{253}(32,\cdot)\)	253.k	22	yes	\(-1\)	\(1\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)
\(\chi_{253}(34,\cdot)\)	253.j	22	no	\(-1\)	\(1\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)
\(\chi_{253}(35,\cdot)\)	253.o	110	yes	\(-1\)	\(1\)	\(e\left(\frac{101}{110}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{29}{110}\right)\)	\(e\left(\frac{107}{110}\right)\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)
\(\chi_{253}(36,\cdot)\)	253.m	55	yes	\(1\)	\(1\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)

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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.