LMFDB - Group of Dirichlet characters of modulus 548

Show commands: PariGP / SageMath

sage: H = DirichletGroup(548)

pari: g = idealstar(,548,2)

Character group

sage: G.order() pari: g.no
Order	=	272
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{136}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{548}(275,\cdot)$, $\chi_{548}(277,\cdot)$

First 32 of 272 characters

Each row describes a character. When available, the columns show the orbit label, order of the character, whether the character is primitive, and several values of the character.

Character	Orbit	Order	Primitive	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{548}(1,\cdot)$	548.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{548}(3,\cdot)$	548.o	136	yes	$1$	$1$	$e\left(\frac{69}{136}\right)$	$e\left(\frac{75}{136}\right)$	$e\left(\frac{55}{68}\right)$	$e\left(\frac{1}{68}\right)$	$e\left(\frac{27}{68}\right)$	$e\left(\frac{25}{136}\right)$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{19}{68}\right)$	$e\left(\frac{57}{68}\right)$	$e\left(\frac{43}{136}\right)$
$\chi_{548}(5,\cdot)$	548.p	136	no	$-1$	$1$	$e\left(\frac{75}{136}\right)$	$e\left(\frac{49}{136}\right)$	$e\left(\frac{11}{68}\right)$	$e\left(\frac{7}{68}\right)$	$e\left(\frac{19}{68}\right)$	$e\left(\frac{107}{136}\right)$	$e\left(\frac{31}{34}\right)$	$e\left(\frac{65}{68}\right)$	$e\left(\frac{25}{68}\right)$	$e\left(\frac{97}{136}\right)$
$\chi_{548}(7,\cdot)$	548.m	68	yes	$-1$	$1$	$e\left(\frac{55}{68}\right)$	$e\left(\frac{11}{68}\right)$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{21}{34}\right)$	$e\left(\frac{3}{17}\right)$	$e\left(\frac{49}{68}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{25}{34}\right)$	$e\left(\frac{12}{17}\right)$	$e\left(\frac{19}{68}\right)$
$\chi_{548}(9,\cdot)$	548.n	68	no	$1$	$1$	$e\left(\frac{1}{68}\right)$	$e\left(\frac{7}{68}\right)$	$e\left(\frac{21}{34}\right)$	$e\left(\frac{1}{34}\right)$	$e\left(\frac{27}{34}\right)$	$e\left(\frac{25}{68}\right)$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{19}{34}\right)$	$e\left(\frac{23}{34}\right)$	$e\left(\frac{43}{68}\right)$
$\chi_{548}(11,\cdot)$	548.m	68	yes	$-1$	$1$	$e\left(\frac{27}{68}\right)$	$e\left(\frac{19}{68}\right)$	$e\left(\frac{3}{17}\right)$	$e\left(\frac{27}{34}\right)$	$e\left(\frac{16}{17}\right)$	$e\left(\frac{29}{68}\right)$	$e\left(\frac{23}{34}\right)$	$e\left(\frac{3}{34}\right)$	$e\left(\frac{13}{17}\right)$	$e\left(\frac{39}{68}\right)$
$\chi_{548}(13,\cdot)$	548.p	136	no	$-1$	$1$	$e\left(\frac{25}{136}\right)$	$e\left(\frac{107}{136}\right)$	$e\left(\frac{49}{68}\right)$	$e\left(\frac{25}{68}\right)$	$e\left(\frac{29}{68}\right)$	$e\left(\frac{81}{136}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{67}{68}\right)$	$e\left(\frac{31}{68}\right)$	$e\left(\frac{123}{136}\right)$
$\chi_{548}(15,\cdot)$	548.j	34	yes	$-1$	$1$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{31}{34}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{23}{34}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{4}{17}\right)$	$e\left(\frac{7}{34}\right)$	$e\left(\frac{1}{34}\right)$
$\chi_{548}(17,\cdot)$	548.n	68	no	$1$	$1$	$e\left(\frac{19}{68}\right)$	$e\left(\frac{65}{68}\right)$	$e\left(\frac{25}{34}\right)$	$e\left(\frac{19}{34}\right)$	$e\left(\frac{3}{34}\right)$	$e\left(\frac{67}{68}\right)$	$e\left(\frac{4}{17}\right)$	$e\left(\frac{21}{34}\right)$	$e\left(\frac{29}{34}\right)$	$e\left(\frac{1}{68}\right)$
$\chi_{548}(19,\cdot)$	548.m	68	yes	$-1$	$1$	$e\left(\frac{57}{68}\right)$	$e\left(\frac{25}{68}\right)$	$e\left(\frac{12}{17}\right)$	$e\left(\frac{23}{34}\right)$	$e\left(\frac{13}{17}\right)$	$e\left(\frac{31}{68}\right)$	$e\left(\frac{7}{34}\right)$	$e\left(\frac{29}{34}\right)$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{37}{68}\right)$
$\chi_{548}(21,\cdot)$	548.p	136	no	$-1$	$1$	$e\left(\frac{43}{136}\right)$	$e\left(\frac{97}{136}\right)$	$e\left(\frac{19}{68}\right)$	$e\left(\frac{43}{68}\right)$	$e\left(\frac{39}{68}\right)$	$e\left(\frac{123}{136}\right)$	$e\left(\frac{1}{34}\right)$	$e\left(\frac{1}{68}\right)$	$e\left(\frac{37}{68}\right)$	$e\left(\frac{81}{136}\right)$
$\chi_{548}(23,\cdot)$	548.o	136	yes	$1$	$1$	$e\left(\frac{57}{136}\right)$	$e\left(\frac{127}{136}\right)$	$e\left(\frac{7}{68}\right)$	$e\left(\frac{57}{68}\right)$	$e\left(\frac{43}{68}\right)$	$e\left(\frac{133}{136}\right)$	$e\left(\frac{6}{17}\right)$	$e\left(\frac{63}{68}\right)$	$e\left(\frac{53}{68}\right)$	$e\left(\frac{71}{136}\right)$
$\chi_{548}(25,\cdot)$	548.n	68	no	$1$	$1$	$e\left(\frac{7}{68}\right)$	$e\left(\frac{49}{68}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{7}{34}\right)$	$e\left(\frac{19}{34}\right)$	$e\left(\frac{39}{68}\right)$	$e\left(\frac{14}{17}\right)$	$e\left(\frac{31}{34}\right)$	$e\left(\frac{25}{34}\right)$	$e\left(\frac{29}{68}\right)$
$\chi_{548}(27,\cdot)$	548.o	136	yes	$1$	$1$	$e\left(\frac{71}{136}\right)$	$e\left(\frac{89}{136}\right)$	$e\left(\frac{29}{68}\right)$	$e\left(\frac{3}{68}\right)$	$e\left(\frac{13}{68}\right)$	$e\left(\frac{75}{136}\right)$	$e\left(\frac{3}{17}\right)$	$e\left(\frac{57}{68}\right)$	$e\left(\frac{35}{68}\right)$	$e\left(\frac{129}{136}\right)$
$\chi_{548}(29,\cdot)$	548.p	136	no	$-1$	$1$	$e\left(\frac{91}{136}\right)$	$e\left(\frac{25}{136}\right)$	$e\left(\frac{7}{68}\right)$	$e\left(\frac{23}{68}\right)$	$e\left(\frac{43}{68}\right)$	$e\left(\frac{99}{136}\right)$	$e\left(\frac{29}{34}\right)$	$e\left(\frac{29}{68}\right)$	$e\left(\frac{53}{68}\right)$	$e\left(\frac{105}{136}\right)$
$\chi_{548}(31,\cdot)$	548.o	136	yes	$1$	$1$	$e\left(\frac{5}{136}\right)$	$e\left(\frac{35}{136}\right)$	$e\left(\frac{3}{68}\right)$	$e\left(\frac{5}{68}\right)$	$e\left(\frac{67}{68}\right)$	$e\left(\frac{57}{136}\right)$	$e\left(\frac{5}{17}\right)$	$e\left(\frac{27}{68}\right)$	$e\left(\frac{13}{68}\right)$	$e\left(\frac{11}{136}\right)$
$\chi_{548}(33,\cdot)$	548.p	136	no	$-1$	$1$	$e\left(\frac{123}{136}\right)$	$e\left(\frac{113}{136}\right)$	$e\left(\frac{67}{68}\right)$	$e\left(\frac{55}{68}\right)$	$e\left(\frac{23}{68}\right)$	$e\left(\frac{83}{136}\right)$	$e\left(\frac{25}{34}\right)$	$e\left(\frac{25}{68}\right)$	$e\left(\frac{41}{68}\right)$	$e\left(\frac{121}{136}\right)$
$\chi_{548}(35,\cdot)$	548.o	136	yes	$1$	$1$	$e\left(\frac{49}{136}\right)$	$e\left(\frac{71}{136}\right)$	$e\left(\frac{43}{68}\right)$	$e\left(\frac{49}{68}\right)$	$e\left(\frac{31}{68}\right)$	$e\left(\frac{69}{136}\right)$	$e\left(\frac{15}{17}\right)$	$e\left(\frac{47}{68}\right)$	$e\left(\frac{5}{68}\right)$	$e\left(\frac{135}{136}\right)$
$\chi_{548}(37,\cdot)$	548.e	4	no	$1$	$1$	$-i$	$i$	$-1$	$-1$	$-1$	$-i$	$1$	$-1$	$-1$	$i$
$\chi_{548}(39,\cdot)$	548.m	68	yes	$-1$	$1$	$e\left(\frac{47}{68}\right)$	$e\left(\frac{23}{68}\right)$	$e\left(\frac{9}{17}\right)$	$e\left(\frac{13}{34}\right)$	$e\left(\frac{14}{17}\right)$	$e\left(\frac{53}{68}\right)$	$e\left(\frac{1}{34}\right)$	$e\left(\frac{9}{34}\right)$	$e\left(\frac{5}{17}\right)$	$e\left(\frac{15}{68}\right)$
$\chi_{548}(41,\cdot)$	548.g	8	no	$-1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$	$-i$	$-i$	$-i$	$e\left(\frac{7}{8}\right)$	$-1$	$i$	$i$	$e\left(\frac{5}{8}\right)$
$\chi_{548}(43,\cdot)$	548.o	136	yes	$1$	$1$	$e\left(\frac{29}{136}\right)$	$e\left(\frac{67}{136}\right)$	$e\left(\frac{31}{68}\right)$	$e\left(\frac{29}{68}\right)$	$e\left(\frac{35}{68}\right)$	$e\left(\frac{113}{136}\right)$	$e\left(\frac{12}{17}\right)$	$e\left(\frac{7}{68}\right)$	$e\left(\frac{21}{68}\right)$	$e\left(\frac{91}{136}\right)$
$\chi_{548}(45,\cdot)$	548.p	136	no	$-1$	$1$	$e\left(\frac{77}{136}\right)$	$e\left(\frac{63}{136}\right)$	$e\left(\frac{53}{68}\right)$	$e\left(\frac{9}{68}\right)$	$e\left(\frac{5}{68}\right)$	$e\left(\frac{21}{136}\right)$	$e\left(\frac{1}{34}\right)$	$e\left(\frac{35}{68}\right)$	$e\left(\frac{3}{68}\right)$	$e\left(\frac{47}{136}\right)$
$\chi_{548}(47,\cdot)$	548.o	136	yes	$1$	$1$	$e\left(\frac{87}{136}\right)$	$e\left(\frac{65}{136}\right)$	$e\left(\frac{25}{68}\right)$	$e\left(\frac{19}{68}\right)$	$e\left(\frac{37}{68}\right)$	$e\left(\frac{67}{136}\right)$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{21}{68}\right)$	$e\left(\frac{63}{68}\right)$	$e\left(\frac{1}{136}\right)$
$\chi_{548}(49,\cdot)$	548.l	34	no	$1$	$1$	$e\left(\frac{21}{34}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{16}{17}\right)$	$e\left(\frac{4}{17}\right)$	$e\left(\frac{6}{17}\right)$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{16}{17}\right)$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{7}{17}\right)$	$e\left(\frac{19}{34}\right)$
$\chi_{548}(51,\cdot)$	548.o	136	yes	$1$	$1$	$e\left(\frac{107}{136}\right)$	$e\left(\frac{69}{136}\right)$	$e\left(\frac{37}{68}\right)$	$e\left(\frac{39}{68}\right)$	$e\left(\frac{33}{68}\right)$	$e\left(\frac{23}{136}\right)$	$e\left(\frac{5}{17}\right)$	$e\left(\frac{61}{68}\right)$	$e\left(\frac{47}{68}\right)$	$e\left(\frac{45}{136}\right)$
$\chi_{548}(53,\cdot)$	548.p	136	no	$-1$	$1$	$e\left(\frac{131}{136}\right)$	$e\left(\frac{33}{136}\right)$	$e\left(\frac{31}{68}\right)$	$e\left(\frac{63}{68}\right)$	$e\left(\frac{35}{68}\right)$	$e\left(\frac{11}{136}\right)$	$e\left(\frac{7}{34}\right)$	$e\left(\frac{41}{68}\right)$	$e\left(\frac{21}{68}\right)$	$e\left(\frac{57}{136}\right)$
$\chi_{548}(55,\cdot)$	548.o	136	yes	$1$	$1$	$e\left(\frac{129}{136}\right)$	$e\left(\frac{87}{136}\right)$	$e\left(\frac{23}{68}\right)$	$e\left(\frac{61}{68}\right)$	$e\left(\frac{15}{68}\right)$	$e\left(\frac{29}{136}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{3}{68}\right)$	$e\left(\frac{9}{68}\right)$	$e\left(\frac{39}{136}\right)$
$\chi_{548}(57,\cdot)$	548.p	136	no	$-1$	$1$	$e\left(\frac{47}{136}\right)$	$e\left(\frac{125}{136}\right)$	$e\left(\frac{35}{68}\right)$	$e\left(\frac{47}{68}\right)$	$e\left(\frac{11}{68}\right)$	$e\left(\frac{87}{136}\right)$	$e\left(\frac{9}{34}\right)$	$e\left(\frac{9}{68}\right)$	$e\left(\frac{61}{68}\right)$	$e\left(\frac{117}{136}\right)$
$\chi_{548}(59,\cdot)$	548.k	34	yes	$-1$	$1$	$e\left(\frac{9}{34}\right)$	$e\left(\frac{6}{17}\right)$	$e\left(\frac{21}{34}\right)$	$e\left(\frac{9}{17}\right)$	$e\left(\frac{27}{34}\right)$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{21}{34}\right)$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{23}{34}\right)$	$e\left(\frac{15}{17}\right)$
$\chi_{548}(61,\cdot)$	548.n	68	no	$1$	$1$	$e\left(\frac{67}{68}\right)$	$e\left(\frac{61}{68}\right)$	$e\left(\frac{13}{34}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{7}{34}\right)$	$e\left(\frac{43}{68}\right)$	$e\left(\frac{15}{17}\right)$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{25}{68}\right)$
$\chi_{548}(63,\cdot)$	548.j	34	yes	$-1$	$1$	$e\left(\frac{14}{17}\right)$	$e\left(\frac{9}{34}\right)$	$e\left(\frac{3}{34}\right)$	$e\left(\frac{11}{17}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{3}{34}\right)$	$e\left(\frac{3}{34}\right)$	$e\left(\frac{5}{17}\right)$	$e\left(\frac{13}{34}\right)$	$e\left(\frac{31}{34}\right)$

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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	$548$
Structure	\(C_{2}\times C_{136}\)
Order	$272$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{548}(1,\cdot)\)	548.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{548}(3,\cdot)\)	548.o	136	yes	\(1\)	\(1\)	\(e\left(\frac{69}{136}\right)\)	\(e\left(\frac{75}{136}\right)\)	\(e\left(\frac{55}{68}\right)\)	\(e\left(\frac{1}{68}\right)\)	\(e\left(\frac{27}{68}\right)\)	\(e\left(\frac{25}{136}\right)\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{19}{68}\right)\)	\(e\left(\frac{57}{68}\right)\)	\(e\left(\frac{43}{136}\right)\)
\(\chi_{548}(5,\cdot)\)	548.p	136	no	\(-1\)	\(1\)	\(e\left(\frac{75}{136}\right)\)	\(e\left(\frac{49}{136}\right)\)	\(e\left(\frac{11}{68}\right)\)	\(e\left(\frac{7}{68}\right)\)	\(e\left(\frac{19}{68}\right)\)	\(e\left(\frac{107}{136}\right)\)	\(e\left(\frac{31}{34}\right)\)	\(e\left(\frac{65}{68}\right)\)	\(e\left(\frac{25}{68}\right)\)	\(e\left(\frac{97}{136}\right)\)
\(\chi_{548}(7,\cdot)\)	548.m	68	yes	\(-1\)	\(1\)	\(e\left(\frac{55}{68}\right)\)	\(e\left(\frac{11}{68}\right)\)	\(e\left(\frac{8}{17}\right)\)	\(e\left(\frac{21}{34}\right)\)	\(e\left(\frac{3}{17}\right)\)	\(e\left(\frac{49}{68}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{25}{34}\right)\)	\(e\left(\frac{12}{17}\right)\)	\(e\left(\frac{19}{68}\right)\)
\(\chi_{548}(9,\cdot)\)	548.n	68	no	\(1\)	\(1\)	\(e\left(\frac{1}{68}\right)\)	\(e\left(\frac{7}{68}\right)\)	\(e\left(\frac{21}{34}\right)\)	\(e\left(\frac{1}{34}\right)\)	\(e\left(\frac{27}{34}\right)\)	\(e\left(\frac{25}{68}\right)\)	\(e\left(\frac{2}{17}\right)\)	\(e\left(\frac{19}{34}\right)\)	\(e\left(\frac{23}{34}\right)\)	\(e\left(\frac{43}{68}\right)\)
\(\chi_{548}(11,\cdot)\)	548.m	68	yes	\(-1\)	\(1\)	\(e\left(\frac{27}{68}\right)\)	\(e\left(\frac{19}{68}\right)\)	\(e\left(\frac{3}{17}\right)\)	\(e\left(\frac{27}{34}\right)\)	\(e\left(\frac{16}{17}\right)\)	\(e\left(\frac{29}{68}\right)\)	\(e\left(\frac{23}{34}\right)\)	\(e\left(\frac{3}{34}\right)\)	\(e\left(\frac{13}{17}\right)\)	\(e\left(\frac{39}{68}\right)\)
\(\chi_{548}(13,\cdot)\)	548.p	136	no	\(-1\)	\(1\)	\(e\left(\frac{25}{136}\right)\)	\(e\left(\frac{107}{136}\right)\)	\(e\left(\frac{49}{68}\right)\)	\(e\left(\frac{25}{68}\right)\)	\(e\left(\frac{29}{68}\right)\)	\(e\left(\frac{81}{136}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{67}{68}\right)\)	\(e\left(\frac{31}{68}\right)\)	\(e\left(\frac{123}{136}\right)\)
\(\chi_{548}(15,\cdot)\)	548.j	34	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{31}{34}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{2}{17}\right)\)	\(e\left(\frac{23}{34}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{4}{17}\right)\)	\(e\left(\frac{7}{34}\right)\)	\(e\left(\frac{1}{34}\right)\)
\(\chi_{548}(17,\cdot)\)	548.n	68	no	\(1\)	\(1\)	\(e\left(\frac{19}{68}\right)\)	\(e\left(\frac{65}{68}\right)\)	\(e\left(\frac{25}{34}\right)\)	\(e\left(\frac{19}{34}\right)\)	\(e\left(\frac{3}{34}\right)\)	\(e\left(\frac{67}{68}\right)\)	\(e\left(\frac{4}{17}\right)\)	\(e\left(\frac{21}{34}\right)\)	\(e\left(\frac{29}{34}\right)\)	\(e\left(\frac{1}{68}\right)\)
\(\chi_{548}(19,\cdot)\)	548.m	68	yes	\(-1\)	\(1\)	\(e\left(\frac{57}{68}\right)\)	\(e\left(\frac{25}{68}\right)\)	\(e\left(\frac{12}{17}\right)\)	\(e\left(\frac{23}{34}\right)\)	\(e\left(\frac{13}{17}\right)\)	\(e\left(\frac{31}{68}\right)\)	\(e\left(\frac{7}{34}\right)\)	\(e\left(\frac{29}{34}\right)\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{37}{68}\right)\)
\(\chi_{548}(21,\cdot)\)	548.p	136	no	\(-1\)	\(1\)	\(e\left(\frac{43}{136}\right)\)	\(e\left(\frac{97}{136}\right)\)	\(e\left(\frac{19}{68}\right)\)	\(e\left(\frac{43}{68}\right)\)	\(e\left(\frac{39}{68}\right)\)	\(e\left(\frac{123}{136}\right)\)	\(e\left(\frac{1}{34}\right)\)	\(e\left(\frac{1}{68}\right)\)	\(e\left(\frac{37}{68}\right)\)	\(e\left(\frac{81}{136}\right)\)
\(\chi_{548}(23,\cdot)\)	548.o	136	yes	\(1\)	\(1\)	\(e\left(\frac{57}{136}\right)\)	\(e\left(\frac{127}{136}\right)\)	\(e\left(\frac{7}{68}\right)\)	\(e\left(\frac{57}{68}\right)\)	\(e\left(\frac{43}{68}\right)\)	\(e\left(\frac{133}{136}\right)\)	\(e\left(\frac{6}{17}\right)\)	\(e\left(\frac{63}{68}\right)\)	\(e\left(\frac{53}{68}\right)\)	\(e\left(\frac{71}{136}\right)\)
\(\chi_{548}(25,\cdot)\)	548.n	68	no	\(1\)	\(1\)	\(e\left(\frac{7}{68}\right)\)	\(e\left(\frac{49}{68}\right)\)	\(e\left(\frac{11}{34}\right)\)	\(e\left(\frac{7}{34}\right)\)	\(e\left(\frac{19}{34}\right)\)	\(e\left(\frac{39}{68}\right)\)	\(e\left(\frac{14}{17}\right)\)	\(e\left(\frac{31}{34}\right)\)	\(e\left(\frac{25}{34}\right)\)	\(e\left(\frac{29}{68}\right)\)
\(\chi_{548}(27,\cdot)\)	548.o	136	yes	\(1\)	\(1\)	\(e\left(\frac{71}{136}\right)\)	\(e\left(\frac{89}{136}\right)\)	\(e\left(\frac{29}{68}\right)\)	\(e\left(\frac{3}{68}\right)\)	\(e\left(\frac{13}{68}\right)\)	\(e\left(\frac{75}{136}\right)\)	\(e\left(\frac{3}{17}\right)\)	\(e\left(\frac{57}{68}\right)\)	\(e\left(\frac{35}{68}\right)\)	\(e\left(\frac{129}{136}\right)\)
\(\chi_{548}(29,\cdot)\)	548.p	136	no	\(-1\)	\(1\)	\(e\left(\frac{91}{136}\right)\)	\(e\left(\frac{25}{136}\right)\)	\(e\left(\frac{7}{68}\right)\)	\(e\left(\frac{23}{68}\right)\)	\(e\left(\frac{43}{68}\right)\)	\(e\left(\frac{99}{136}\right)\)	\(e\left(\frac{29}{34}\right)\)	\(e\left(\frac{29}{68}\right)\)	\(e\left(\frac{53}{68}\right)\)	\(e\left(\frac{105}{136}\right)\)
\(\chi_{548}(31,\cdot)\)	548.o	136	yes	\(1\)	\(1\)	\(e\left(\frac{5}{136}\right)\)	\(e\left(\frac{35}{136}\right)\)	\(e\left(\frac{3}{68}\right)\)	\(e\left(\frac{5}{68}\right)\)	\(e\left(\frac{67}{68}\right)\)	\(e\left(\frac{57}{136}\right)\)	\(e\left(\frac{5}{17}\right)\)	\(e\left(\frac{27}{68}\right)\)	\(e\left(\frac{13}{68}\right)\)	\(e\left(\frac{11}{136}\right)\)
\(\chi_{548}(33,\cdot)\)	548.p	136	no	\(-1\)	\(1\)	\(e\left(\frac{123}{136}\right)\)	\(e\left(\frac{113}{136}\right)\)	\(e\left(\frac{67}{68}\right)\)	\(e\left(\frac{55}{68}\right)\)	\(e\left(\frac{23}{68}\right)\)	\(e\left(\frac{83}{136}\right)\)	\(e\left(\frac{25}{34}\right)\)	\(e\left(\frac{25}{68}\right)\)	\(e\left(\frac{41}{68}\right)\)	\(e\left(\frac{121}{136}\right)\)
\(\chi_{548}(35,\cdot)\)	548.o	136	yes	\(1\)	\(1\)	\(e\left(\frac{49}{136}\right)\)	\(e\left(\frac{71}{136}\right)\)	\(e\left(\frac{43}{68}\right)\)	\(e\left(\frac{49}{68}\right)\)	\(e\left(\frac{31}{68}\right)\)	\(e\left(\frac{69}{136}\right)\)	\(e\left(\frac{15}{17}\right)\)	\(e\left(\frac{47}{68}\right)\)	\(e\left(\frac{5}{68}\right)\)	\(e\left(\frac{135}{136}\right)\)
\(\chi_{548}(37,\cdot)\)	548.e	4	no	\(1\)	\(1\)	\(-i\)	\(i\)	\(-1\)	\(-1\)	\(-1\)	\(-i\)	\(1\)	\(-1\)	\(-1\)	\(i\)
\(\chi_{548}(39,\cdot)\)	548.m	68	yes	\(-1\)	\(1\)	\(e\left(\frac{47}{68}\right)\)	\(e\left(\frac{23}{68}\right)\)	\(e\left(\frac{9}{17}\right)\)	\(e\left(\frac{13}{34}\right)\)	\(e\left(\frac{14}{17}\right)\)	\(e\left(\frac{53}{68}\right)\)	\(e\left(\frac{1}{34}\right)\)	\(e\left(\frac{9}{34}\right)\)	\(e\left(\frac{5}{17}\right)\)	\(e\left(\frac{15}{68}\right)\)
\(\chi_{548}(41,\cdot)\)	548.g	8	no	\(-1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(-i\)	\(-i\)	\(-i\)	\(e\left(\frac{7}{8}\right)\)	\(-1\)	\(i\)	\(i\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{548}(43,\cdot)\)	548.o	136	yes	\(1\)	\(1\)	\(e\left(\frac{29}{136}\right)\)	\(e\left(\frac{67}{136}\right)\)	\(e\left(\frac{31}{68}\right)\)	\(e\left(\frac{29}{68}\right)\)	\(e\left(\frac{35}{68}\right)\)	\(e\left(\frac{113}{136}\right)\)	\(e\left(\frac{12}{17}\right)\)	\(e\left(\frac{7}{68}\right)\)	\(e\left(\frac{21}{68}\right)\)	\(e\left(\frac{91}{136}\right)\)
\(\chi_{548}(45,\cdot)\)	548.p	136	no	\(-1\)	\(1\)	\(e\left(\frac{77}{136}\right)\)	\(e\left(\frac{63}{136}\right)\)	\(e\left(\frac{53}{68}\right)\)	\(e\left(\frac{9}{68}\right)\)	\(e\left(\frac{5}{68}\right)\)	\(e\left(\frac{21}{136}\right)\)	\(e\left(\frac{1}{34}\right)\)	\(e\left(\frac{35}{68}\right)\)	\(e\left(\frac{3}{68}\right)\)	\(e\left(\frac{47}{136}\right)\)
\(\chi_{548}(47,\cdot)\)	548.o	136	yes	\(1\)	\(1\)	\(e\left(\frac{87}{136}\right)\)	\(e\left(\frac{65}{136}\right)\)	\(e\left(\frac{25}{68}\right)\)	\(e\left(\frac{19}{68}\right)\)	\(e\left(\frac{37}{68}\right)\)	\(e\left(\frac{67}{136}\right)\)	\(e\left(\frac{2}{17}\right)\)	\(e\left(\frac{21}{68}\right)\)	\(e\left(\frac{63}{68}\right)\)	\(e\left(\frac{1}{136}\right)\)
\(\chi_{548}(49,\cdot)\)	548.l	34	no	\(1\)	\(1\)	\(e\left(\frac{21}{34}\right)\)	\(e\left(\frac{11}{34}\right)\)	\(e\left(\frac{16}{17}\right)\)	\(e\left(\frac{4}{17}\right)\)	\(e\left(\frac{6}{17}\right)\)	\(e\left(\frac{15}{34}\right)\)	\(e\left(\frac{16}{17}\right)\)	\(e\left(\frac{8}{17}\right)\)	\(e\left(\frac{7}{17}\right)\)	\(e\left(\frac{19}{34}\right)\)
\(\chi_{548}(51,\cdot)\)	548.o	136	yes	\(1\)	\(1\)	\(e\left(\frac{107}{136}\right)\)	\(e\left(\frac{69}{136}\right)\)	\(e\left(\frac{37}{68}\right)\)	\(e\left(\frac{39}{68}\right)\)	\(e\left(\frac{33}{68}\right)\)	\(e\left(\frac{23}{136}\right)\)	\(e\left(\frac{5}{17}\right)\)	\(e\left(\frac{61}{68}\right)\)	\(e\left(\frac{47}{68}\right)\)	\(e\left(\frac{45}{136}\right)\)
\(\chi_{548}(53,\cdot)\)	548.p	136	no	\(-1\)	\(1\)	\(e\left(\frac{131}{136}\right)\)	\(e\left(\frac{33}{136}\right)\)	\(e\left(\frac{31}{68}\right)\)	\(e\left(\frac{63}{68}\right)\)	\(e\left(\frac{35}{68}\right)\)	\(e\left(\frac{11}{136}\right)\)	\(e\left(\frac{7}{34}\right)\)	\(e\left(\frac{41}{68}\right)\)	\(e\left(\frac{21}{68}\right)\)	\(e\left(\frac{57}{136}\right)\)
\(\chi_{548}(55,\cdot)\)	548.o	136	yes	\(1\)	\(1\)	\(e\left(\frac{129}{136}\right)\)	\(e\left(\frac{87}{136}\right)\)	\(e\left(\frac{23}{68}\right)\)	\(e\left(\frac{61}{68}\right)\)	\(e\left(\frac{15}{68}\right)\)	\(e\left(\frac{29}{136}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{3}{68}\right)\)	\(e\left(\frac{9}{68}\right)\)	\(e\left(\frac{39}{136}\right)\)
\(\chi_{548}(57,\cdot)\)	548.p	136	no	\(-1\)	\(1\)	\(e\left(\frac{47}{136}\right)\)	\(e\left(\frac{125}{136}\right)\)	\(e\left(\frac{35}{68}\right)\)	\(e\left(\frac{47}{68}\right)\)	\(e\left(\frac{11}{68}\right)\)	\(e\left(\frac{87}{136}\right)\)	\(e\left(\frac{9}{34}\right)\)	\(e\left(\frac{9}{68}\right)\)	\(e\left(\frac{61}{68}\right)\)	\(e\left(\frac{117}{136}\right)\)
\(\chi_{548}(59,\cdot)\)	548.k	34	yes	\(-1\)	\(1\)	\(e\left(\frac{9}{34}\right)\)	\(e\left(\frac{6}{17}\right)\)	\(e\left(\frac{21}{34}\right)\)	\(e\left(\frac{9}{17}\right)\)	\(e\left(\frac{27}{34}\right)\)	\(e\left(\frac{2}{17}\right)\)	\(e\left(\frac{21}{34}\right)\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{23}{34}\right)\)	\(e\left(\frac{15}{17}\right)\)
\(\chi_{548}(61,\cdot)\)	548.n	68	no	\(1\)	\(1\)	\(e\left(\frac{67}{68}\right)\)	\(e\left(\frac{61}{68}\right)\)	\(e\left(\frac{13}{34}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{7}{34}\right)\)	\(e\left(\frac{43}{68}\right)\)	\(e\left(\frac{15}{17}\right)\)	\(e\left(\frac{15}{34}\right)\)	\(e\left(\frac{11}{34}\right)\)	\(e\left(\frac{25}{68}\right)\)
\(\chi_{548}(63,\cdot)\)	548.j	34	yes	\(-1\)	\(1\)	\(e\left(\frac{14}{17}\right)\)	\(e\left(\frac{9}{34}\right)\)	\(e\left(\frac{3}{34}\right)\)	\(e\left(\frac{11}{17}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{3}{34}\right)\)	\(e\left(\frac{3}{34}\right)\)	\(e\left(\frac{5}{17}\right)\)	\(e\left(\frac{13}{34}\right)\)	\(e\left(\frac{31}{34}\right)\)

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L-functions

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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.