LMFDB - Group of Dirichlet characters of modulus 1013

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1013)

pari: g = idealstar(,1013,2)

Character group

sage: G.order() pari: g.no
Order	=	1012
sage: H.invariants() pari: g.cyc
Structure	=	$C_{1012}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{1013}(3,\cdot)$

First 32 of 1012 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{1013}(1,\cdot)$	1013.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1013}(2,\cdot)$	1013.i	92	yes	$-1$	$1$	$e\left(\frac{19}{92}\right)$	$e\left(\frac{33}{92}\right)$	$e\left(\frac{19}{46}\right)$	$e\left(\frac{49}{92}\right)$	$e\left(\frac{13}{23}\right)$	$e\left(\frac{45}{92}\right)$	$e\left(\frac{57}{92}\right)$	$e\left(\frac{33}{46}\right)$	$e\left(\frac{17}{23}\right)$	$e\left(\frac{3}{46}\right)$
$\chi_{1013}(3,\cdot)$	1013.l	1012	yes	$-1$	$1$	$e\left(\frac{33}{92}\right)$	$e\left(\frac{1}{1012}\right)$	$e\left(\frac{33}{46}\right)$	$e\left(\frac{757}{1012}\right)$	$e\left(\frac{91}{253}\right)$	$e\left(\frac{821}{1012}\right)$	$e\left(\frac{7}{92}\right)$	$e\left(\frac{1}{506}\right)$	$e\left(\frac{27}{253}\right)$	$e\left(\frac{27}{46}\right)$
$\chi_{1013}(4,\cdot)$	1013.h	46	yes	$1$	$1$	$e\left(\frac{19}{46}\right)$	$e\left(\frac{33}{46}\right)$	$e\left(\frac{19}{23}\right)$	$e\left(\frac{3}{46}\right)$	$e\left(\frac{3}{23}\right)$	$e\left(\frac{45}{46}\right)$	$e\left(\frac{11}{46}\right)$	$e\left(\frac{10}{23}\right)$	$e\left(\frac{11}{23}\right)$	$e\left(\frac{3}{23}\right)$
$\chi_{1013}(5,\cdot)$	1013.l	1012	yes	$-1$	$1$	$e\left(\frac{49}{92}\right)$	$e\left(\frac{757}{1012}\right)$	$e\left(\frac{3}{46}\right)$	$e\left(\frac{257}{1012}\right)$	$e\left(\frac{71}{253}\right)$	$e\left(\frac{129}{1012}\right)$	$e\left(\frac{55}{92}\right)$	$e\left(\frac{251}{506}\right)$	$e\left(\frac{199}{253}\right)$	$e\left(\frac{15}{46}\right)$
$\chi_{1013}(6,\cdot)$	1013.j	253	yes	$1$	$1$	$e\left(\frac{13}{23}\right)$	$e\left(\frac{91}{253}\right)$	$e\left(\frac{3}{23}\right)$	$e\left(\frac{71}{253}\right)$	$e\left(\frac{234}{253}\right)$	$e\left(\frac{76}{253}\right)$	$e\left(\frac{16}{23}\right)$	$e\left(\frac{182}{253}\right)$	$e\left(\frac{214}{253}\right)$	$e\left(\frac{15}{23}\right)$
$\chi_{1013}(7,\cdot)$	1013.l	1012	yes	$-1$	$1$	$e\left(\frac{45}{92}\right)$	$e\left(\frac{821}{1012}\right)$	$e\left(\frac{45}{46}\right)$	$e\left(\frac{129}{1012}\right)$	$e\left(\frac{76}{253}\right)$	$e\left(\frac{49}{1012}\right)$	$e\left(\frac{43}{92}\right)$	$e\left(\frac{315}{506}\right)$	$e\left(\frac{156}{253}\right)$	$e\left(\frac{41}{46}\right)$
$\chi_{1013}(8,\cdot)$	1013.i	92	yes	$-1$	$1$	$e\left(\frac{57}{92}\right)$	$e\left(\frac{7}{92}\right)$	$e\left(\frac{11}{46}\right)$	$e\left(\frac{55}{92}\right)$	$e\left(\frac{16}{23}\right)$	$e\left(\frac{43}{92}\right)$	$e\left(\frac{79}{92}\right)$	$e\left(\frac{7}{46}\right)$	$e\left(\frac{5}{23}\right)$	$e\left(\frac{9}{46}\right)$
$\chi_{1013}(9,\cdot)$	1013.k	506	yes	$1$	$1$	$e\left(\frac{33}{46}\right)$	$e\left(\frac{1}{506}\right)$	$e\left(\frac{10}{23}\right)$	$e\left(\frac{251}{506}\right)$	$e\left(\frac{182}{253}\right)$	$e\left(\frac{315}{506}\right)$	$e\left(\frac{7}{46}\right)$	$e\left(\frac{1}{253}\right)$	$e\left(\frac{54}{253}\right)$	$e\left(\frac{4}{23}\right)$
$\chi_{1013}(10,\cdot)$	1013.j	253	yes	$1$	$1$	$e\left(\frac{17}{23}\right)$	$e\left(\frac{27}{253}\right)$	$e\left(\frac{11}{23}\right)$	$e\left(\frac{199}{253}\right)$	$e\left(\frac{214}{253}\right)$	$e\left(\frac{156}{253}\right)$	$e\left(\frac{5}{23}\right)$	$e\left(\frac{54}{253}\right)$	$e\left(\frac{133}{253}\right)$	$e\left(\frac{9}{23}\right)$
$\chi_{1013}(11,\cdot)$	1013.h	46	yes	$1$	$1$	$e\left(\frac{3}{46}\right)$	$e\left(\frac{27}{46}\right)$	$e\left(\frac{3}{23}\right)$	$e\left(\frac{15}{46}\right)$	$e\left(\frac{15}{23}\right)$	$e\left(\frac{41}{46}\right)$	$e\left(\frac{9}{46}\right)$	$e\left(\frac{4}{23}\right)$	$e\left(\frac{9}{23}\right)$	$e\left(\frac{15}{23}\right)$
$\chi_{1013}(12,\cdot)$	1013.l	1012	yes	$-1$	$1$	$e\left(\frac{71}{92}\right)$	$e\left(\frac{727}{1012}\right)$	$e\left(\frac{25}{46}\right)$	$e\left(\frac{823}{1012}\right)$	$e\left(\frac{124}{253}\right)$	$e\left(\frac{799}{1012}\right)$	$e\left(\frac{29}{92}\right)$	$e\left(\frac{221}{506}\right)$	$e\left(\frac{148}{253}\right)$	$e\left(\frac{33}{46}\right)$
$\chi_{1013}(13,\cdot)$	1013.k	506	yes	$1$	$1$	$e\left(\frac{33}{46}\right)$	$e\left(\frac{415}{506}\right)$	$e\left(\frac{10}{23}\right)$	$e\left(\frac{435}{506}\right)$	$e\left(\frac{136}{253}\right)$	$e\left(\frac{177}{506}\right)$	$e\left(\frac{7}{46}\right)$	$e\left(\frac{162}{253}\right)$	$e\left(\frac{146}{253}\right)$	$e\left(\frac{4}{23}\right)$
$\chi_{1013}(14,\cdot)$	1013.j	253	yes	$1$	$1$	$e\left(\frac{16}{23}\right)$	$e\left(\frac{43}{253}\right)$	$e\left(\frac{9}{23}\right)$	$e\left(\frac{167}{253}\right)$	$e\left(\frac{219}{253}\right)$	$e\left(\frac{136}{253}\right)$	$e\left(\frac{2}{23}\right)$	$e\left(\frac{86}{253}\right)$	$e\left(\frac{90}{253}\right)$	$e\left(\frac{22}{23}\right)$
$\chi_{1013}(15,\cdot)$	1013.k	506	yes	$1$	$1$	$e\left(\frac{41}{46}\right)$	$e\left(\frac{379}{506}\right)$	$e\left(\frac{18}{23}\right)$	$e\left(\frac{1}{506}\right)$	$e\left(\frac{162}{253}\right)$	$e\left(\frac{475}{506}\right)$	$e\left(\frac{31}{46}\right)$	$e\left(\frac{126}{253}\right)$	$e\left(\frac{226}{253}\right)$	$e\left(\frac{21}{23}\right)$
$\chi_{1013}(16,\cdot)$	1013.f	23	yes	$1$	$1$	$e\left(\frac{19}{23}\right)$	$e\left(\frac{10}{23}\right)$	$e\left(\frac{15}{23}\right)$	$e\left(\frac{3}{23}\right)$	$e\left(\frac{6}{23}\right)$	$e\left(\frac{22}{23}\right)$	$e\left(\frac{11}{23}\right)$	$e\left(\frac{20}{23}\right)$	$e\left(\frac{22}{23}\right)$	$e\left(\frac{6}{23}\right)$
$\chi_{1013}(17,\cdot)$	1013.l	1012	yes	$-1$	$1$	$e\left(\frac{17}{92}\right)$	$e\left(\frac{349}{1012}\right)$	$e\left(\frac{17}{46}\right)$	$e\left(\frac{61}{1012}\right)$	$e\left(\frac{134}{253}\right)$	$e\left(\frac{133}{1012}\right)$	$e\left(\frac{51}{92}\right)$	$e\left(\frac{349}{506}\right)$	$e\left(\frac{62}{253}\right)$	$e\left(\frac{39}{46}\right)$
$\chi_{1013}(18,\cdot)$	1013.l	1012	yes	$-1$	$1$	$e\left(\frac{85}{92}\right)$	$e\left(\frac{365}{1012}\right)$	$e\left(\frac{39}{46}\right)$	$e\left(\frac{29}{1012}\right)$	$e\left(\frac{72}{253}\right)$	$e\left(\frac{113}{1012}\right)$	$e\left(\frac{71}{92}\right)$	$e\left(\frac{365}{506}\right)$	$e\left(\frac{241}{253}\right)$	$e\left(\frac{11}{46}\right)$
$\chi_{1013}(19,\cdot)$	1013.j	253	yes	$1$	$1$	$e\left(\frac{10}{23}\right)$	$e\left(\frac{116}{253}\right)$	$e\left(\frac{20}{23}\right)$	$e\left(\frac{21}{253}\right)$	$e\left(\frac{226}{253}\right)$	$e\left(\frac{108}{253}\right)$	$e\left(\frac{7}{23}\right)$	$e\left(\frac{232}{253}\right)$	$e\left(\frac{131}{253}\right)$	$e\left(\frac{8}{23}\right)$
$\chi_{1013}(20,\cdot)$	1013.l	1012	yes	$-1$	$1$	$e\left(\frac{87}{92}\right)$	$e\left(\frac{471}{1012}\right)$	$e\left(\frac{41}{46}\right)$	$e\left(\frac{323}{1012}\right)$	$e\left(\frac{104}{253}\right)$	$e\left(\frac{107}{1012}\right)$	$e\left(\frac{77}{92}\right)$	$e\left(\frac{471}{506}\right)$	$e\left(\frac{67}{253}\right)$	$e\left(\frac{21}{46}\right)$
$\chi_{1013}(21,\cdot)$	1013.k	506	yes	$1$	$1$	$e\left(\frac{39}{46}\right)$	$e\left(\frac{411}{506}\right)$	$e\left(\frac{16}{23}\right)$	$e\left(\frac{443}{506}\right)$	$e\left(\frac{167}{253}\right)$	$e\left(\frac{435}{506}\right)$	$e\left(\frac{25}{46}\right)$	$e\left(\frac{158}{253}\right)$	$e\left(\frac{183}{253}\right)$	$e\left(\frac{11}{23}\right)$
$\chi_{1013}(22,\cdot)$	1013.i	92	yes	$-1$	$1$	$e\left(\frac{25}{92}\right)$	$e\left(\frac{87}{92}\right)$	$e\left(\frac{25}{46}\right)$	$e\left(\frac{79}{92}\right)$	$e\left(\frac{5}{23}\right)$	$e\left(\frac{35}{92}\right)$	$e\left(\frac{75}{92}\right)$	$e\left(\frac{41}{46}\right)$	$e\left(\frac{3}{23}\right)$	$e\left(\frac{33}{46}\right)$
$\chi_{1013}(23,\cdot)$	1013.h	46	yes	$1$	$1$	$e\left(\frac{1}{46}\right)$	$e\left(\frac{9}{46}\right)$	$e\left(\frac{1}{23}\right)$	$e\left(\frac{5}{46}\right)$	$e\left(\frac{5}{23}\right)$	$e\left(\frac{29}{46}\right)$	$e\left(\frac{3}{46}\right)$	$e\left(\frac{9}{23}\right)$	$e\left(\frac{3}{23}\right)$	$e\left(\frac{5}{23}\right)$
$\chi_{1013}(24,\cdot)$	1013.k	506	yes	$1$	$1$	$e\left(\frac{45}{46}\right)$	$e\left(\frac{39}{506}\right)$	$e\left(\frac{22}{23}\right)$	$e\left(\frac{175}{506}\right)$	$e\left(\frac{14}{253}\right)$	$e\left(\frac{141}{506}\right)$	$e\left(\frac{43}{46}\right)$	$e\left(\frac{39}{253}\right)$	$e\left(\frac{82}{253}\right)$	$e\left(\frac{18}{23}\right)$
$\chi_{1013}(25,\cdot)$	1013.k	506	yes	$1$	$1$	$e\left(\frac{3}{46}\right)$	$e\left(\frac{251}{506}\right)$	$e\left(\frac{3}{23}\right)$	$e\left(\frac{257}{506}\right)$	$e\left(\frac{142}{253}\right)$	$e\left(\frac{129}{506}\right)$	$e\left(\frac{9}{46}\right)$	$e\left(\frac{251}{253}\right)$	$e\left(\frac{145}{253}\right)$	$e\left(\frac{15}{23}\right)$
$\chi_{1013}(26,\cdot)$	1013.l	1012	yes	$-1$	$1$	$e\left(\frac{85}{92}\right)$	$e\left(\frac{181}{1012}\right)$	$e\left(\frac{39}{46}\right)$	$e\left(\frac{397}{1012}\right)$	$e\left(\frac{26}{253}\right)$	$e\left(\frac{849}{1012}\right)$	$e\left(\frac{71}{92}\right)$	$e\left(\frac{181}{506}\right)$	$e\left(\frac{80}{253}\right)$	$e\left(\frac{11}{46}\right)$
$\chi_{1013}(27,\cdot)$	1013.l	1012	yes	$-1$	$1$	$e\left(\frac{7}{92}\right)$	$e\left(\frac{3}{1012}\right)$	$e\left(\frac{7}{46}\right)$	$e\left(\frac{247}{1012}\right)$	$e\left(\frac{20}{253}\right)$	$e\left(\frac{439}{1012}\right)$	$e\left(\frac{21}{92}\right)$	$e\left(\frac{3}{506}\right)$	$e\left(\frac{81}{253}\right)$	$e\left(\frac{35}{46}\right)$
$\chi_{1013}(28,\cdot)$	1013.l	1012	yes	$-1$	$1$	$e\left(\frac{83}{92}\right)$	$e\left(\frac{535}{1012}\right)$	$e\left(\frac{37}{46}\right)$	$e\left(\frac{195}{1012}\right)$	$e\left(\frac{109}{253}\right)$	$e\left(\frac{27}{1012}\right)$	$e\left(\frac{65}{92}\right)$	$e\left(\frac{29}{506}\right)$	$e\left(\frac{24}{253}\right)$	$e\left(\frac{1}{46}\right)$
$\chi_{1013}(29,\cdot)$	1013.l	1012	yes	$-1$	$1$	$e\left(\frac{17}{92}\right)$	$e\left(\frac{809}{1012}\right)$	$e\left(\frac{17}{46}\right)$	$e\left(\frac{153}{1012}\right)$	$e\left(\frac{249}{253}\right)$	$e\left(\frac{317}{1012}\right)$	$e\left(\frac{51}{92}\right)$	$e\left(\frac{303}{506}\right)$	$e\left(\frac{85}{253}\right)$	$e\left(\frac{39}{46}\right)$
$\chi_{1013}(30,\cdot)$	1013.l	1012	yes	$-1$	$1$	$e\left(\frac{9}{92}\right)$	$e\left(\frac{109}{1012}\right)$	$e\left(\frac{9}{46}\right)$	$e\left(\frac{541}{1012}\right)$	$e\left(\frac{52}{253}\right)$	$e\left(\frac{433}{1012}\right)$	$e\left(\frac{27}{92}\right)$	$e\left(\frac{109}{506}\right)$	$e\left(\frac{160}{253}\right)$	$e\left(\frac{45}{46}\right)$
$\chi_{1013}(31,\cdot)$	1013.l	1012	yes	$-1$	$1$	$e\left(\frac{29}{92}\right)$	$e\left(\frac{525}{1012}\right)$	$e\left(\frac{29}{46}\right)$	$e\left(\frac{721}{1012}\right)$	$e\left(\frac{211}{253}\right)$	$e\left(\frac{925}{1012}\right)$	$e\left(\frac{87}{92}\right)$	$e\left(\frac{19}{506}\right)$	$e\left(\frac{7}{253}\right)$	$e\left(\frac{7}{46}\right)$
$\chi_{1013}(32,\cdot)$	1013.i	92	yes	$-1$	$1$	$e\left(\frac{3}{92}\right)$	$e\left(\frac{73}{92}\right)$	$e\left(\frac{3}{46}\right)$	$e\left(\frac{61}{92}\right)$	$e\left(\frac{19}{23}\right)$	$e\left(\frac{41}{92}\right)$	$e\left(\frac{9}{92}\right)$	$e\left(\frac{27}{46}\right)$	$e\left(\frac{16}{23}\right)$	$e\left(\frac{15}{46}\right)$

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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	$1013$
Structure	\(C_{1012}\)
Order	$1012$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{1013}(1,\cdot)\)	1013.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1013}(2,\cdot)\)	1013.i	92	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{92}\right)\)	\(e\left(\frac{33}{92}\right)\)	\(e\left(\frac{19}{46}\right)\)	\(e\left(\frac{49}{92}\right)\)	\(e\left(\frac{13}{23}\right)\)	\(e\left(\frac{45}{92}\right)\)	\(e\left(\frac{57}{92}\right)\)	\(e\left(\frac{33}{46}\right)\)	\(e\left(\frac{17}{23}\right)\)	\(e\left(\frac{3}{46}\right)\)
\(\chi_{1013}(3,\cdot)\)	1013.l	1012	yes	\(-1\)	\(1\)	\(e\left(\frac{33}{92}\right)\)	\(e\left(\frac{1}{1012}\right)\)	\(e\left(\frac{33}{46}\right)\)	\(e\left(\frac{757}{1012}\right)\)	\(e\left(\frac{91}{253}\right)\)	\(e\left(\frac{821}{1012}\right)\)	\(e\left(\frac{7}{92}\right)\)	\(e\left(\frac{1}{506}\right)\)	\(e\left(\frac{27}{253}\right)\)	\(e\left(\frac{27}{46}\right)\)
\(\chi_{1013}(4,\cdot)\)	1013.h	46	yes	\(1\)	\(1\)	\(e\left(\frac{19}{46}\right)\)	\(e\left(\frac{33}{46}\right)\)	\(e\left(\frac{19}{23}\right)\)	\(e\left(\frac{3}{46}\right)\)	\(e\left(\frac{3}{23}\right)\)	\(e\left(\frac{45}{46}\right)\)	\(e\left(\frac{11}{46}\right)\)	\(e\left(\frac{10}{23}\right)\)	\(e\left(\frac{11}{23}\right)\)	\(e\left(\frac{3}{23}\right)\)
\(\chi_{1013}(5,\cdot)\)	1013.l	1012	yes	\(-1\)	\(1\)	\(e\left(\frac{49}{92}\right)\)	\(e\left(\frac{757}{1012}\right)\)	\(e\left(\frac{3}{46}\right)\)	\(e\left(\frac{257}{1012}\right)\)	\(e\left(\frac{71}{253}\right)\)	\(e\left(\frac{129}{1012}\right)\)	\(e\left(\frac{55}{92}\right)\)	\(e\left(\frac{251}{506}\right)\)	\(e\left(\frac{199}{253}\right)\)	\(e\left(\frac{15}{46}\right)\)
\(\chi_{1013}(6,\cdot)\)	1013.j	253	yes	\(1\)	\(1\)	\(e\left(\frac{13}{23}\right)\)	\(e\left(\frac{91}{253}\right)\)	\(e\left(\frac{3}{23}\right)\)	\(e\left(\frac{71}{253}\right)\)	\(e\left(\frac{234}{253}\right)\)	\(e\left(\frac{76}{253}\right)\)	\(e\left(\frac{16}{23}\right)\)	\(e\left(\frac{182}{253}\right)\)	\(e\left(\frac{214}{253}\right)\)	\(e\left(\frac{15}{23}\right)\)
\(\chi_{1013}(7,\cdot)\)	1013.l	1012	yes	\(-1\)	\(1\)	\(e\left(\frac{45}{92}\right)\)	\(e\left(\frac{821}{1012}\right)\)	\(e\left(\frac{45}{46}\right)\)	\(e\left(\frac{129}{1012}\right)\)	\(e\left(\frac{76}{253}\right)\)	\(e\left(\frac{49}{1012}\right)\)	\(e\left(\frac{43}{92}\right)\)	\(e\left(\frac{315}{506}\right)\)	\(e\left(\frac{156}{253}\right)\)	\(e\left(\frac{41}{46}\right)\)
\(\chi_{1013}(8,\cdot)\)	1013.i	92	yes	\(-1\)	\(1\)	\(e\left(\frac{57}{92}\right)\)	\(e\left(\frac{7}{92}\right)\)	\(e\left(\frac{11}{46}\right)\)	\(e\left(\frac{55}{92}\right)\)	\(e\left(\frac{16}{23}\right)\)	\(e\left(\frac{43}{92}\right)\)	\(e\left(\frac{79}{92}\right)\)	\(e\left(\frac{7}{46}\right)\)	\(e\left(\frac{5}{23}\right)\)	\(e\left(\frac{9}{46}\right)\)
\(\chi_{1013}(9,\cdot)\)	1013.k	506	yes	\(1\)	\(1\)	\(e\left(\frac{33}{46}\right)\)	\(e\left(\frac{1}{506}\right)\)	\(e\left(\frac{10}{23}\right)\)	\(e\left(\frac{251}{506}\right)\)	\(e\left(\frac{182}{253}\right)\)	\(e\left(\frac{315}{506}\right)\)	\(e\left(\frac{7}{46}\right)\)	\(e\left(\frac{1}{253}\right)\)	\(e\left(\frac{54}{253}\right)\)	\(e\left(\frac{4}{23}\right)\)
\(\chi_{1013}(10,\cdot)\)	1013.j	253	yes	\(1\)	\(1\)	\(e\left(\frac{17}{23}\right)\)	\(e\left(\frac{27}{253}\right)\)	\(e\left(\frac{11}{23}\right)\)	\(e\left(\frac{199}{253}\right)\)	\(e\left(\frac{214}{253}\right)\)	\(e\left(\frac{156}{253}\right)\)	\(e\left(\frac{5}{23}\right)\)	\(e\left(\frac{54}{253}\right)\)	\(e\left(\frac{133}{253}\right)\)	\(e\left(\frac{9}{23}\right)\)
\(\chi_{1013}(11,\cdot)\)	1013.h	46	yes	\(1\)	\(1\)	\(e\left(\frac{3}{46}\right)\)	\(e\left(\frac{27}{46}\right)\)	\(e\left(\frac{3}{23}\right)\)	\(e\left(\frac{15}{46}\right)\)	\(e\left(\frac{15}{23}\right)\)	\(e\left(\frac{41}{46}\right)\)	\(e\left(\frac{9}{46}\right)\)	\(e\left(\frac{4}{23}\right)\)	\(e\left(\frac{9}{23}\right)\)	\(e\left(\frac{15}{23}\right)\)
\(\chi_{1013}(12,\cdot)\)	1013.l	1012	yes	\(-1\)	\(1\)	\(e\left(\frac{71}{92}\right)\)	\(e\left(\frac{727}{1012}\right)\)	\(e\left(\frac{25}{46}\right)\)	\(e\left(\frac{823}{1012}\right)\)	\(e\left(\frac{124}{253}\right)\)	\(e\left(\frac{799}{1012}\right)\)	\(e\left(\frac{29}{92}\right)\)	\(e\left(\frac{221}{506}\right)\)	\(e\left(\frac{148}{253}\right)\)	\(e\left(\frac{33}{46}\right)\)
\(\chi_{1013}(13,\cdot)\)	1013.k	506	yes	\(1\)	\(1\)	\(e\left(\frac{33}{46}\right)\)	\(e\left(\frac{415}{506}\right)\)	\(e\left(\frac{10}{23}\right)\)	\(e\left(\frac{435}{506}\right)\)	\(e\left(\frac{136}{253}\right)\)	\(e\left(\frac{177}{506}\right)\)	\(e\left(\frac{7}{46}\right)\)	\(e\left(\frac{162}{253}\right)\)	\(e\left(\frac{146}{253}\right)\)	\(e\left(\frac{4}{23}\right)\)
\(\chi_{1013}(14,\cdot)\)	1013.j	253	yes	\(1\)	\(1\)	\(e\left(\frac{16}{23}\right)\)	\(e\left(\frac{43}{253}\right)\)	\(e\left(\frac{9}{23}\right)\)	\(e\left(\frac{167}{253}\right)\)	\(e\left(\frac{219}{253}\right)\)	\(e\left(\frac{136}{253}\right)\)	\(e\left(\frac{2}{23}\right)\)	\(e\left(\frac{86}{253}\right)\)	\(e\left(\frac{90}{253}\right)\)	\(e\left(\frac{22}{23}\right)\)
\(\chi_{1013}(15,\cdot)\)	1013.k	506	yes	\(1\)	\(1\)	\(e\left(\frac{41}{46}\right)\)	\(e\left(\frac{379}{506}\right)\)	\(e\left(\frac{18}{23}\right)\)	\(e\left(\frac{1}{506}\right)\)	\(e\left(\frac{162}{253}\right)\)	\(e\left(\frac{475}{506}\right)\)	\(e\left(\frac{31}{46}\right)\)	\(e\left(\frac{126}{253}\right)\)	\(e\left(\frac{226}{253}\right)\)	\(e\left(\frac{21}{23}\right)\)
\(\chi_{1013}(16,\cdot)\)	1013.f	23	yes	\(1\)	\(1\)	\(e\left(\frac{19}{23}\right)\)	\(e\left(\frac{10}{23}\right)\)	\(e\left(\frac{15}{23}\right)\)	\(e\left(\frac{3}{23}\right)\)	\(e\left(\frac{6}{23}\right)\)	\(e\left(\frac{22}{23}\right)\)	\(e\left(\frac{11}{23}\right)\)	\(e\left(\frac{20}{23}\right)\)	\(e\left(\frac{22}{23}\right)\)	\(e\left(\frac{6}{23}\right)\)
\(\chi_{1013}(17,\cdot)\)	1013.l	1012	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{92}\right)\)	\(e\left(\frac{349}{1012}\right)\)	\(e\left(\frac{17}{46}\right)\)	\(e\left(\frac{61}{1012}\right)\)	\(e\left(\frac{134}{253}\right)\)	\(e\left(\frac{133}{1012}\right)\)	\(e\left(\frac{51}{92}\right)\)	\(e\left(\frac{349}{506}\right)\)	\(e\left(\frac{62}{253}\right)\)	\(e\left(\frac{39}{46}\right)\)
\(\chi_{1013}(18,\cdot)\)	1013.l	1012	yes	\(-1\)	\(1\)	\(e\left(\frac{85}{92}\right)\)	\(e\left(\frac{365}{1012}\right)\)	\(e\left(\frac{39}{46}\right)\)	\(e\left(\frac{29}{1012}\right)\)	\(e\left(\frac{72}{253}\right)\)	\(e\left(\frac{113}{1012}\right)\)	\(e\left(\frac{71}{92}\right)\)	\(e\left(\frac{365}{506}\right)\)	\(e\left(\frac{241}{253}\right)\)	\(e\left(\frac{11}{46}\right)\)
\(\chi_{1013}(19,\cdot)\)	1013.j	253	yes	\(1\)	\(1\)	\(e\left(\frac{10}{23}\right)\)	\(e\left(\frac{116}{253}\right)\)	\(e\left(\frac{20}{23}\right)\)	\(e\left(\frac{21}{253}\right)\)	\(e\left(\frac{226}{253}\right)\)	\(e\left(\frac{108}{253}\right)\)	\(e\left(\frac{7}{23}\right)\)	\(e\left(\frac{232}{253}\right)\)	\(e\left(\frac{131}{253}\right)\)	\(e\left(\frac{8}{23}\right)\)
\(\chi_{1013}(20,\cdot)\)	1013.l	1012	yes	\(-1\)	\(1\)	\(e\left(\frac{87}{92}\right)\)	\(e\left(\frac{471}{1012}\right)\)	\(e\left(\frac{41}{46}\right)\)	\(e\left(\frac{323}{1012}\right)\)	\(e\left(\frac{104}{253}\right)\)	\(e\left(\frac{107}{1012}\right)\)	\(e\left(\frac{77}{92}\right)\)	\(e\left(\frac{471}{506}\right)\)	\(e\left(\frac{67}{253}\right)\)	\(e\left(\frac{21}{46}\right)\)
\(\chi_{1013}(21,\cdot)\)	1013.k	506	yes	\(1\)	\(1\)	\(e\left(\frac{39}{46}\right)\)	\(e\left(\frac{411}{506}\right)\)	\(e\left(\frac{16}{23}\right)\)	\(e\left(\frac{443}{506}\right)\)	\(e\left(\frac{167}{253}\right)\)	\(e\left(\frac{435}{506}\right)\)	\(e\left(\frac{25}{46}\right)\)	\(e\left(\frac{158}{253}\right)\)	\(e\left(\frac{183}{253}\right)\)	\(e\left(\frac{11}{23}\right)\)
\(\chi_{1013}(22,\cdot)\)	1013.i	92	yes	\(-1\)	\(1\)	\(e\left(\frac{25}{92}\right)\)	\(e\left(\frac{87}{92}\right)\)	\(e\left(\frac{25}{46}\right)\)	\(e\left(\frac{79}{92}\right)\)	\(e\left(\frac{5}{23}\right)\)	\(e\left(\frac{35}{92}\right)\)	\(e\left(\frac{75}{92}\right)\)	\(e\left(\frac{41}{46}\right)\)	\(e\left(\frac{3}{23}\right)\)	\(e\left(\frac{33}{46}\right)\)
\(\chi_{1013}(23,\cdot)\)	1013.h	46	yes	\(1\)	\(1\)	\(e\left(\frac{1}{46}\right)\)	\(e\left(\frac{9}{46}\right)\)	\(e\left(\frac{1}{23}\right)\)	\(e\left(\frac{5}{46}\right)\)	\(e\left(\frac{5}{23}\right)\)	\(e\left(\frac{29}{46}\right)\)	\(e\left(\frac{3}{46}\right)\)	\(e\left(\frac{9}{23}\right)\)	\(e\left(\frac{3}{23}\right)\)	\(e\left(\frac{5}{23}\right)\)
\(\chi_{1013}(24,\cdot)\)	1013.k	506	yes	\(1\)	\(1\)	\(e\left(\frac{45}{46}\right)\)	\(e\left(\frac{39}{506}\right)\)	\(e\left(\frac{22}{23}\right)\)	\(e\left(\frac{175}{506}\right)\)	\(e\left(\frac{14}{253}\right)\)	\(e\left(\frac{141}{506}\right)\)	\(e\left(\frac{43}{46}\right)\)	\(e\left(\frac{39}{253}\right)\)	\(e\left(\frac{82}{253}\right)\)	\(e\left(\frac{18}{23}\right)\)
\(\chi_{1013}(25,\cdot)\)	1013.k	506	yes	\(1\)	\(1\)	\(e\left(\frac{3}{46}\right)\)	\(e\left(\frac{251}{506}\right)\)	\(e\left(\frac{3}{23}\right)\)	\(e\left(\frac{257}{506}\right)\)	\(e\left(\frac{142}{253}\right)\)	\(e\left(\frac{129}{506}\right)\)	\(e\left(\frac{9}{46}\right)\)	\(e\left(\frac{251}{253}\right)\)	\(e\left(\frac{145}{253}\right)\)	\(e\left(\frac{15}{23}\right)\)
\(\chi_{1013}(26,\cdot)\)	1013.l	1012	yes	\(-1\)	\(1\)	\(e\left(\frac{85}{92}\right)\)	\(e\left(\frac{181}{1012}\right)\)	\(e\left(\frac{39}{46}\right)\)	\(e\left(\frac{397}{1012}\right)\)	\(e\left(\frac{26}{253}\right)\)	\(e\left(\frac{849}{1012}\right)\)	\(e\left(\frac{71}{92}\right)\)	\(e\left(\frac{181}{506}\right)\)	\(e\left(\frac{80}{253}\right)\)	\(e\left(\frac{11}{46}\right)\)
\(\chi_{1013}(27,\cdot)\)	1013.l	1012	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{92}\right)\)	\(e\left(\frac{3}{1012}\right)\)	\(e\left(\frac{7}{46}\right)\)	\(e\left(\frac{247}{1012}\right)\)	\(e\left(\frac{20}{253}\right)\)	\(e\left(\frac{439}{1012}\right)\)	\(e\left(\frac{21}{92}\right)\)	\(e\left(\frac{3}{506}\right)\)	\(e\left(\frac{81}{253}\right)\)	\(e\left(\frac{35}{46}\right)\)
\(\chi_{1013}(28,\cdot)\)	1013.l	1012	yes	\(-1\)	\(1\)	\(e\left(\frac{83}{92}\right)\)	\(e\left(\frac{535}{1012}\right)\)	\(e\left(\frac{37}{46}\right)\)	\(e\left(\frac{195}{1012}\right)\)	\(e\left(\frac{109}{253}\right)\)	\(e\left(\frac{27}{1012}\right)\)	\(e\left(\frac{65}{92}\right)\)	\(e\left(\frac{29}{506}\right)\)	\(e\left(\frac{24}{253}\right)\)	\(e\left(\frac{1}{46}\right)\)
\(\chi_{1013}(29,\cdot)\)	1013.l	1012	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{92}\right)\)	\(e\left(\frac{809}{1012}\right)\)	\(e\left(\frac{17}{46}\right)\)	\(e\left(\frac{153}{1012}\right)\)	\(e\left(\frac{249}{253}\right)\)	\(e\left(\frac{317}{1012}\right)\)	\(e\left(\frac{51}{92}\right)\)	\(e\left(\frac{303}{506}\right)\)	\(e\left(\frac{85}{253}\right)\)	\(e\left(\frac{39}{46}\right)\)
\(\chi_{1013}(30,\cdot)\)	1013.l	1012	yes	\(-1\)	\(1\)	\(e\left(\frac{9}{92}\right)\)	\(e\left(\frac{109}{1012}\right)\)	\(e\left(\frac{9}{46}\right)\)	\(e\left(\frac{541}{1012}\right)\)	\(e\left(\frac{52}{253}\right)\)	\(e\left(\frac{433}{1012}\right)\)	\(e\left(\frac{27}{92}\right)\)	\(e\left(\frac{109}{506}\right)\)	\(e\left(\frac{160}{253}\right)\)	\(e\left(\frac{45}{46}\right)\)
\(\chi_{1013}(31,\cdot)\)	1013.l	1012	yes	\(-1\)	\(1\)	\(e\left(\frac{29}{92}\right)\)	\(e\left(\frac{525}{1012}\right)\)	\(e\left(\frac{29}{46}\right)\)	\(e\left(\frac{721}{1012}\right)\)	\(e\left(\frac{211}{253}\right)\)	\(e\left(\frac{925}{1012}\right)\)	\(e\left(\frac{87}{92}\right)\)	\(e\left(\frac{19}{506}\right)\)	\(e\left(\frac{7}{253}\right)\)	\(e\left(\frac{7}{46}\right)\)
\(\chi_{1013}(32,\cdot)\)	1013.i	92	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{92}\right)\)	\(e\left(\frac{73}{92}\right)\)	\(e\left(\frac{3}{46}\right)\)	\(e\left(\frac{61}{92}\right)\)	\(e\left(\frac{19}{23}\right)\)	\(e\left(\frac{41}{92}\right)\)	\(e\left(\frac{9}{92}\right)\)	\(e\left(\frac{27}{46}\right)\)	\(e\left(\frac{16}{23}\right)\)	\(e\left(\frac{15}{46}\right)\)

Introduction

L-functions

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Character group

First 32 of 1012 characters

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.