LMFDB - Group of Dirichlet characters of modulus 3055

Show commands: PariGP / SageMath

sage: H = DirichletGroup(3055)

pari: g = idealstar(,3055,2)

Character group

sage: G.order() pari: g.no
Order	=	2208
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{4}\times C_{276}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{3055}(612,\cdot)$, $\chi_{3055}(236,\cdot)$, $\chi_{3055}(2731,\cdot)$

First 32 of 2208 characters

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

Character	Orbit	Order	Primitive	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$11$	$12$	$14$
$\chi_{3055}(1,\cdot)$	3055.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{3055}(2,\cdot)$	3055.da	276	yes	$1$	$1$	$e\left(\frac{26}{69}\right)$	$e\left(\frac{251}{276}\right)$	$e\left(\frac{52}{69}\right)$	$e\left(\frac{79}{276}\right)$	$e\left(\frac{95}{138}\right)$	$e\left(\frac{3}{23}\right)$	$e\left(\frac{113}{138}\right)$	$e\left(\frac{89}{276}\right)$	$e\left(\frac{61}{92}\right)$	$e\left(\frac{3}{46}\right)$
$\chi_{3055}(3,\cdot)$	3055.cx	276	yes	$-1$	$1$	$e\left(\frac{251}{276}\right)$	$e\left(\frac{77}{276}\right)$	$e\left(\frac{113}{138}\right)$	$e\left(\frac{13}{69}\right)$	$e\left(\frac{91}{276}\right)$	$e\left(\frac{67}{92}\right)$	$e\left(\frac{77}{138}\right)$	$e\left(\frac{26}{69}\right)$	$e\left(\frac{9}{92}\right)$	$e\left(\frac{11}{46}\right)$
$\chi_{3055}(4,\cdot)$	3055.cn	138	yes	$1$	$1$	$e\left(\frac{52}{69}\right)$	$e\left(\frac{113}{138}\right)$	$e\left(\frac{35}{69}\right)$	$e\left(\frac{79}{138}\right)$	$e\left(\frac{26}{69}\right)$	$e\left(\frac{6}{23}\right)$	$e\left(\frac{44}{69}\right)$	$e\left(\frac{89}{138}\right)$	$e\left(\frac{15}{46}\right)$	$e\left(\frac{3}{23}\right)$
$\chi_{3055}(6,\cdot)$	3055.cz	276	no	$-1$	$1$	$e\left(\frac{79}{276}\right)$	$e\left(\frac{13}{69}\right)$	$e\left(\frac{79}{138}\right)$	$e\left(\frac{131}{276}\right)$	$e\left(\frac{5}{276}\right)$	$e\left(\frac{79}{92}\right)$	$e\left(\frac{26}{69}\right)$	$e\left(\frac{193}{276}\right)$	$e\left(\frac{35}{46}\right)$	$e\left(\frac{7}{23}\right)$
$\chi_{3055}(7,\cdot)$	3055.cq	276	yes	$1$	$1$	$e\left(\frac{95}{138}\right)$	$e\left(\frac{91}{276}\right)$	$e\left(\frac{26}{69}\right)$	$e\left(\frac{5}{276}\right)$	$e\left(\frac{41}{69}\right)$	$e\left(\frac{3}{46}\right)$	$e\left(\frac{91}{138}\right)$	$e\left(\frac{79}{276}\right)$	$e\left(\frac{65}{92}\right)$	$e\left(\frac{13}{46}\right)$
$\chi_{3055}(8,\cdot)$	3055.by	92	yes	$1$	$1$	$e\left(\frac{3}{23}\right)$	$e\left(\frac{67}{92}\right)$	$e\left(\frac{6}{23}\right)$	$e\left(\frac{79}{92}\right)$	$e\left(\frac{3}{46}\right)$	$e\left(\frac{9}{23}\right)$	$e\left(\frac{21}{46}\right)$	$e\left(\frac{89}{92}\right)$	$e\left(\frac{91}{92}\right)$	$e\left(\frac{9}{46}\right)$
$\chi_{3055}(9,\cdot)$	3055.ck	138	yes	$1$	$1$	$e\left(\frac{113}{138}\right)$	$e\left(\frac{77}{138}\right)$	$e\left(\frac{44}{69}\right)$	$e\left(\frac{26}{69}\right)$	$e\left(\frac{91}{138}\right)$	$e\left(\frac{21}{46}\right)$	$e\left(\frac{8}{69}\right)$	$e\left(\frac{52}{69}\right)$	$e\left(\frac{9}{46}\right)$	$e\left(\frac{11}{23}\right)$
$\chi_{3055}(11,\cdot)$	3055.cy	276	no	$1$	$1$	$e\left(\frac{89}{276}\right)$	$e\left(\frac{26}{69}\right)$	$e\left(\frac{89}{138}\right)$	$e\left(\frac{193}{276}\right)$	$e\left(\frac{79}{276}\right)$	$e\left(\frac{89}{92}\right)$	$e\left(\frac{52}{69}\right)$	$e\left(\frac{41}{276}\right)$	$e\left(\frac{1}{46}\right)$	$e\left(\frac{14}{23}\right)$
$\chi_{3055}(12,\cdot)$	3055.ce	92	yes	$-1$	$1$	$e\left(\frac{61}{92}\right)$	$e\left(\frac{9}{92}\right)$	$e\left(\frac{15}{46}\right)$	$e\left(\frac{35}{46}\right)$	$e\left(\frac{65}{92}\right)$	$e\left(\frac{91}{92}\right)$	$e\left(\frac{9}{46}\right)$	$e\left(\frac{1}{46}\right)$	$e\left(\frac{39}{92}\right)$	$e\left(\frac{17}{46}\right)$
$\chi_{3055}(14,\cdot)$	3055.bu	46	no	$1$	$1$	$e\left(\frac{3}{46}\right)$	$e\left(\frac{11}{46}\right)$	$e\left(\frac{3}{23}\right)$	$e\left(\frac{7}{23}\right)$	$e\left(\frac{13}{46}\right)$	$e\left(\frac{9}{46}\right)$	$e\left(\frac{11}{23}\right)$	$e\left(\frac{14}{23}\right)$	$e\left(\frac{17}{46}\right)$	$e\left(\frac{8}{23}\right)$
$\chi_{3055}(16,\cdot)$	3055.bw	69	no	$1$	$1$	$e\left(\frac{35}{69}\right)$	$e\left(\frac{44}{69}\right)$	$e\left(\frac{1}{69}\right)$	$e\left(\frac{10}{69}\right)$	$e\left(\frac{52}{69}\right)$	$e\left(\frac{12}{23}\right)$	$e\left(\frac{19}{69}\right)$	$e\left(\frac{20}{69}\right)$	$e\left(\frac{15}{23}\right)$	$e\left(\frac{6}{23}\right)$
$\chi_{3055}(17,\cdot)$	3055.cu	276	yes	$-1$	$1$	$e\left(\frac{187}{276}\right)$	$e\left(\frac{103}{276}\right)$	$e\left(\frac{49}{138}\right)$	$e\left(\frac{7}{138}\right)$	$e\left(\frac{59}{276}\right)$	$e\left(\frac{3}{92}\right)$	$e\left(\frac{103}{138}\right)$	$e\left(\frac{83}{138}\right)$	$e\left(\frac{67}{92}\right)$	$e\left(\frac{41}{46}\right)$
$\chi_{3055}(18,\cdot)$	3055.ci	92	yes	$1$	$1$	$e\left(\frac{9}{46}\right)$	$e\left(\frac{43}{92}\right)$	$e\left(\frac{9}{23}\right)$	$e\left(\frac{61}{92}\right)$	$e\left(\frac{8}{23}\right)$	$e\left(\frac{27}{46}\right)$	$e\left(\frac{43}{46}\right)$	$e\left(\frac{7}{92}\right)$	$e\left(\frac{79}{92}\right)$	$e\left(\frac{25}{46}\right)$
$\chi_{3055}(19,\cdot)$	3055.ct	276	yes	$1$	$1$	$e\left(\frac{145}{276}\right)$	$e\left(\frac{101}{138}\right)$	$e\left(\frac{7}{138}\right)$	$e\left(\frac{71}{276}\right)$	$e\left(\frac{107}{276}\right)$	$e\left(\frac{53}{92}\right)$	$e\left(\frac{32}{69}\right)$	$e\left(\frac{211}{276}\right)$	$e\left(\frac{18}{23}\right)$	$e\left(\frac{21}{23}\right)$
$\chi_{3055}(21,\cdot)$	3055.bz	92	no	$-1$	$1$	$e\left(\frac{55}{92}\right)$	$e\left(\frac{14}{23}\right)$	$e\left(\frac{9}{46}\right)$	$e\left(\frac{19}{92}\right)$	$e\left(\frac{85}{92}\right)$	$e\left(\frac{73}{92}\right)$	$e\left(\frac{5}{23}\right)$	$e\left(\frac{61}{92}\right)$	$e\left(\frac{37}{46}\right)$	$e\left(\frac{12}{23}\right)$
$\chi_{3055}(22,\cdot)$	3055.cw	276	yes	$1$	$1$	$e\left(\frac{193}{276}\right)$	$e\left(\frac{79}{276}\right)$	$e\left(\frac{55}{138}\right)$	$e\left(\frac{68}{69}\right)$	$e\left(\frac{269}{276}\right)$	$e\left(\frac{9}{92}\right)$	$e\left(\frac{79}{138}\right)$	$e\left(\frac{65}{138}\right)$	$e\left(\frac{63}{92}\right)$	$e\left(\frac{31}{46}\right)$
$\chi_{3055}(23,\cdot)$	3055.cv	276	yes	$1$	$1$	$e\left(\frac{149}{276}\right)$	$e\left(\frac{209}{276}\right)$	$e\left(\frac{11}{138}\right)$	$e\left(\frac{41}{138}\right)$	$e\left(\frac{109}{276}\right)$	$e\left(\frac{57}{92}\right)$	$e\left(\frac{71}{138}\right)$	$e\left(\frac{41}{69}\right)$	$e\left(\frac{77}{92}\right)$	$e\left(\frac{43}{46}\right)$
$\chi_{3055}(24,\cdot)$	3055.cs	276	yes	$-1$	$1$	$e\left(\frac{11}{276}\right)$	$e\left(\frac{1}{138}\right)$	$e\left(\frac{11}{138}\right)$	$e\left(\frac{13}{276}\right)$	$e\left(\frac{109}{276}\right)$	$e\left(\frac{11}{92}\right)$	$e\left(\frac{1}{69}\right)$	$e\left(\frac{95}{276}\right)$	$e\left(\frac{2}{23}\right)$	$e\left(\frac{10}{23}\right)$
$\chi_{3055}(27,\cdot)$	3055.cb	92	no	$-1$	$1$	$e\left(\frac{67}{92}\right)$	$e\left(\frac{77}{92}\right)$	$e\left(\frac{21}{46}\right)$	$e\left(\frac{13}{23}\right)$	$e\left(\frac{91}{92}\right)$	$e\left(\frac{17}{92}\right)$	$e\left(\frac{31}{46}\right)$	$e\left(\frac{3}{23}\right)$	$e\left(\frac{27}{92}\right)$	$e\left(\frac{33}{46}\right)$
$\chi_{3055}(28,\cdot)$	3055.cq	276	yes	$1$	$1$	$e\left(\frac{61}{138}\right)$	$e\left(\frac{41}{276}\right)$	$e\left(\frac{61}{69}\right)$	$e\left(\frac{163}{276}\right)$	$e\left(\frac{67}{69}\right)$	$e\left(\frac{15}{46}\right)$	$e\left(\frac{41}{138}\right)$	$e\left(\frac{257}{276}\right)$	$e\left(\frac{3}{92}\right)$	$e\left(\frac{19}{46}\right)$
$\chi_{3055}(29,\cdot)$	3055.cj	138	yes	$-1$	$1$	$e\left(\frac{73}{138}\right)$	$e\left(\frac{7}{138}\right)$	$e\left(\frac{4}{69}\right)$	$e\left(\frac{40}{69}\right)$	$e\left(\frac{71}{138}\right)$	$e\left(\frac{27}{46}\right)$	$e\left(\frac{7}{69}\right)$	$e\left(\frac{91}{138}\right)$	$e\left(\frac{5}{46}\right)$	$e\left(\frac{1}{23}\right)$
$\chi_{3055}(31,\cdot)$	3055.ca	92	no	$1$	$1$	$e\left(\frac{85}{92}\right)$	$e\left(\frac{7}{23}\right)$	$e\left(\frac{39}{46}\right)$	$e\left(\frac{21}{92}\right)$	$e\left(\frac{31}{92}\right)$	$e\left(\frac{71}{92}\right)$	$e\left(\frac{14}{23}\right)$	$e\left(\frac{65}{92}\right)$	$e\left(\frac{7}{46}\right)$	$e\left(\frac{6}{23}\right)$
$\chi_{3055}(32,\cdot)$	3055.da	276	yes	$1$	$1$	$e\left(\frac{61}{69}\right)$	$e\left(\frac{151}{276}\right)$	$e\left(\frac{53}{69}\right)$	$e\left(\frac{119}{276}\right)$	$e\left(\frac{61}{138}\right)$	$e\left(\frac{15}{23}\right)$	$e\left(\frac{13}{138}\right)$	$e\left(\frac{169}{276}\right)$	$e\left(\frac{29}{92}\right)$	$e\left(\frac{15}{46}\right)$
$\chi_{3055}(33,\cdot)$	3055.db	276	yes	$-1$	$1$	$e\left(\frac{16}{69}\right)$	$e\left(\frac{181}{276}\right)$	$e\left(\frac{32}{69}\right)$	$e\left(\frac{245}{276}\right)$	$e\left(\frac{85}{138}\right)$	$e\left(\frac{16}{23}\right)$	$e\left(\frac{43}{138}\right)$	$e\left(\frac{145}{276}\right)$	$e\left(\frac{11}{92}\right)$	$e\left(\frac{39}{46}\right)$
$\chi_{3055}(34,\cdot)$	3055.cg	92	yes	$-1$	$1$	$e\left(\frac{5}{92}\right)$	$e\left(\frac{13}{46}\right)$	$e\left(\frac{5}{46}\right)$	$e\left(\frac{31}{92}\right)$	$e\left(\frac{83}{92}\right)$	$e\left(\frac{15}{92}\right)$	$e\left(\frac{13}{23}\right)$	$e\left(\frac{85}{92}\right)$	$e\left(\frac{9}{23}\right)$	$e\left(\frac{22}{23}\right)$
$\chi_{3055}(36,\cdot)$	3055.cl	138	no	$1$	$1$	$e\left(\frac{79}{138}\right)$	$e\left(\frac{26}{69}\right)$	$e\left(\frac{10}{69}\right)$	$e\left(\frac{131}{138}\right)$	$e\left(\frac{5}{138}\right)$	$e\left(\frac{33}{46}\right)$	$e\left(\frac{52}{69}\right)$	$e\left(\frac{55}{138}\right)$	$e\left(\frac{12}{23}\right)$	$e\left(\frac{14}{23}\right)$
$\chi_{3055}(37,\cdot)$	3055.cq	276	yes	$1$	$1$	$e\left(\frac{37}{138}\right)$	$e\left(\frac{95}{276}\right)$	$e\left(\frac{37}{69}\right)$	$e\left(\frac{169}{276}\right)$	$e\left(\frac{61}{69}\right)$	$e\left(\frac{37}{46}\right)$	$e\left(\frac{95}{138}\right)$	$e\left(\frac{131}{276}\right)$	$e\left(\frac{81}{92}\right)$	$e\left(\frac{7}{46}\right)$
$\chi_{3055}(38,\cdot)$	3055.cd	92	yes	$1$	$1$	$e\left(\frac{83}{92}\right)$	$e\left(\frac{59}{92}\right)$	$e\left(\frac{37}{46}\right)$	$e\left(\frac{25}{46}\right)$	$e\left(\frac{7}{92}\right)$	$e\left(\frac{65}{92}\right)$	$e\left(\frac{13}{46}\right)$	$e\left(\frac{2}{23}\right)$	$e\left(\frac{41}{92}\right)$	$e\left(\frac{45}{46}\right)$
$\chi_{3055}(41,\cdot)$	3055.cy	276	no	$1$	$1$	$e\left(\frac{263}{276}\right)$	$e\left(\frac{59}{69}\right)$	$e\left(\frac{125}{138}\right)$	$e\left(\frac{223}{276}\right)$	$e\left(\frac{97}{276}\right)$	$e\left(\frac{79}{92}\right)$	$e\left(\frac{49}{69}\right)$	$e\left(\frac{239}{276}\right)$	$e\left(\frac{35}{46}\right)$	$e\left(\frac{7}{23}\right)$
$\chi_{3055}(42,\cdot)$	3055.cx	276	yes	$-1$	$1$	$e\left(\frac{269}{276}\right)$	$e\left(\frac{143}{276}\right)$	$e\left(\frac{131}{138}\right)$	$e\left(\frac{34}{69}\right)$	$e\left(\frac{169}{276}\right)$	$e\left(\frac{85}{92}\right)$	$e\left(\frac{5}{138}\right)$	$e\left(\frac{68}{69}\right)$	$e\left(\frac{43}{92}\right)$	$e\left(\frac{27}{46}\right)$
$\chi_{3055}(43,\cdot)$	3055.cv	276	yes	$1$	$1$	$e\left(\frac{1}{276}\right)$	$e\left(\frac{157}{276}\right)$	$e\left(\frac{1}{138}\right)$	$e\left(\frac{79}{138}\right)$	$e\left(\frac{173}{276}\right)$	$e\left(\frac{1}{92}\right)$	$e\left(\frac{19}{138}\right)$	$e\left(\frac{10}{69}\right)$	$e\left(\frac{53}{92}\right)$	$e\left(\frac{29}{46}\right)$

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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	$3055$
Structure	\(C_{2}\times C_{4}\times C_{276}\)
Order	$2208$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(7\)	\(8\)	\(9\)	\(11\)	\(12\)	\(14\)
\(\chi_{3055}(1,\cdot)\)	3055.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{3055}(2,\cdot)\)	3055.da	276	yes	\(1\)	\(1\)	\(e\left(\frac{26}{69}\right)\)	\(e\left(\frac{251}{276}\right)\)	\(e\left(\frac{52}{69}\right)\)	\(e\left(\frac{79}{276}\right)\)	\(e\left(\frac{95}{138}\right)\)	\(e\left(\frac{3}{23}\right)\)	\(e\left(\frac{113}{138}\right)\)	\(e\left(\frac{89}{276}\right)\)	\(e\left(\frac{61}{92}\right)\)	\(e\left(\frac{3}{46}\right)\)
\(\chi_{3055}(3,\cdot)\)	3055.cx	276	yes	\(-1\)	\(1\)	\(e\left(\frac{251}{276}\right)\)	\(e\left(\frac{77}{276}\right)\)	\(e\left(\frac{113}{138}\right)\)	\(e\left(\frac{13}{69}\right)\)	\(e\left(\frac{91}{276}\right)\)	\(e\left(\frac{67}{92}\right)\)	\(e\left(\frac{77}{138}\right)\)	\(e\left(\frac{26}{69}\right)\)	\(e\left(\frac{9}{92}\right)\)	\(e\left(\frac{11}{46}\right)\)
\(\chi_{3055}(4,\cdot)\)	3055.cn	138	yes	\(1\)	\(1\)	\(e\left(\frac{52}{69}\right)\)	\(e\left(\frac{113}{138}\right)\)	\(e\left(\frac{35}{69}\right)\)	\(e\left(\frac{79}{138}\right)\)	\(e\left(\frac{26}{69}\right)\)	\(e\left(\frac{6}{23}\right)\)	\(e\left(\frac{44}{69}\right)\)	\(e\left(\frac{89}{138}\right)\)	\(e\left(\frac{15}{46}\right)\)	\(e\left(\frac{3}{23}\right)\)
\(\chi_{3055}(6,\cdot)\)	3055.cz	276	no	\(-1\)	\(1\)	\(e\left(\frac{79}{276}\right)\)	\(e\left(\frac{13}{69}\right)\)	\(e\left(\frac{79}{138}\right)\)	\(e\left(\frac{131}{276}\right)\)	\(e\left(\frac{5}{276}\right)\)	\(e\left(\frac{79}{92}\right)\)	\(e\left(\frac{26}{69}\right)\)	\(e\left(\frac{193}{276}\right)\)	\(e\left(\frac{35}{46}\right)\)	\(e\left(\frac{7}{23}\right)\)
\(\chi_{3055}(7,\cdot)\)	3055.cq	276	yes	\(1\)	\(1\)	\(e\left(\frac{95}{138}\right)\)	\(e\left(\frac{91}{276}\right)\)	\(e\left(\frac{26}{69}\right)\)	\(e\left(\frac{5}{276}\right)\)	\(e\left(\frac{41}{69}\right)\)	\(e\left(\frac{3}{46}\right)\)	\(e\left(\frac{91}{138}\right)\)	\(e\left(\frac{79}{276}\right)\)	\(e\left(\frac{65}{92}\right)\)	\(e\left(\frac{13}{46}\right)\)
\(\chi_{3055}(8,\cdot)\)	3055.by	92	yes	\(1\)	\(1\)	\(e\left(\frac{3}{23}\right)\)	\(e\left(\frac{67}{92}\right)\)	\(e\left(\frac{6}{23}\right)\)	\(e\left(\frac{79}{92}\right)\)	\(e\left(\frac{3}{46}\right)\)	\(e\left(\frac{9}{23}\right)\)	\(e\left(\frac{21}{46}\right)\)	\(e\left(\frac{89}{92}\right)\)	\(e\left(\frac{91}{92}\right)\)	\(e\left(\frac{9}{46}\right)\)
\(\chi_{3055}(9,\cdot)\)	3055.ck	138	yes	\(1\)	\(1\)	\(e\left(\frac{113}{138}\right)\)	\(e\left(\frac{77}{138}\right)\)	\(e\left(\frac{44}{69}\right)\)	\(e\left(\frac{26}{69}\right)\)	\(e\left(\frac{91}{138}\right)\)	\(e\left(\frac{21}{46}\right)\)	\(e\left(\frac{8}{69}\right)\)	\(e\left(\frac{52}{69}\right)\)	\(e\left(\frac{9}{46}\right)\)	\(e\left(\frac{11}{23}\right)\)
\(\chi_{3055}(11,\cdot)\)	3055.cy	276	no	\(1\)	\(1\)	\(e\left(\frac{89}{276}\right)\)	\(e\left(\frac{26}{69}\right)\)	\(e\left(\frac{89}{138}\right)\)	\(e\left(\frac{193}{276}\right)\)	\(e\left(\frac{79}{276}\right)\)	\(e\left(\frac{89}{92}\right)\)	\(e\left(\frac{52}{69}\right)\)	\(e\left(\frac{41}{276}\right)\)	\(e\left(\frac{1}{46}\right)\)	\(e\left(\frac{14}{23}\right)\)
\(\chi_{3055}(12,\cdot)\)	3055.ce	92	yes	\(-1\)	\(1\)	\(e\left(\frac{61}{92}\right)\)	\(e\left(\frac{9}{92}\right)\)	\(e\left(\frac{15}{46}\right)\)	\(e\left(\frac{35}{46}\right)\)	\(e\left(\frac{65}{92}\right)\)	\(e\left(\frac{91}{92}\right)\)	\(e\left(\frac{9}{46}\right)\)	\(e\left(\frac{1}{46}\right)\)	\(e\left(\frac{39}{92}\right)\)	\(e\left(\frac{17}{46}\right)\)
\(\chi_{3055}(14,\cdot)\)	3055.bu	46	no	\(1\)	\(1\)	\(e\left(\frac{3}{46}\right)\)	\(e\left(\frac{11}{46}\right)\)	\(e\left(\frac{3}{23}\right)\)	\(e\left(\frac{7}{23}\right)\)	\(e\left(\frac{13}{46}\right)\)	\(e\left(\frac{9}{46}\right)\)	\(e\left(\frac{11}{23}\right)\)	\(e\left(\frac{14}{23}\right)\)	\(e\left(\frac{17}{46}\right)\)	\(e\left(\frac{8}{23}\right)\)
\(\chi_{3055}(16,\cdot)\)	3055.bw	69	no	\(1\)	\(1\)	\(e\left(\frac{35}{69}\right)\)	\(e\left(\frac{44}{69}\right)\)	\(e\left(\frac{1}{69}\right)\)	\(e\left(\frac{10}{69}\right)\)	\(e\left(\frac{52}{69}\right)\)	\(e\left(\frac{12}{23}\right)\)	\(e\left(\frac{19}{69}\right)\)	\(e\left(\frac{20}{69}\right)\)	\(e\left(\frac{15}{23}\right)\)	\(e\left(\frac{6}{23}\right)\)
\(\chi_{3055}(17,\cdot)\)	3055.cu	276	yes	\(-1\)	\(1\)	\(e\left(\frac{187}{276}\right)\)	\(e\left(\frac{103}{276}\right)\)	\(e\left(\frac{49}{138}\right)\)	\(e\left(\frac{7}{138}\right)\)	\(e\left(\frac{59}{276}\right)\)	\(e\left(\frac{3}{92}\right)\)	\(e\left(\frac{103}{138}\right)\)	\(e\left(\frac{83}{138}\right)\)	\(e\left(\frac{67}{92}\right)\)	\(e\left(\frac{41}{46}\right)\)
\(\chi_{3055}(18,\cdot)\)	3055.ci	92	yes	\(1\)	\(1\)	\(e\left(\frac{9}{46}\right)\)	\(e\left(\frac{43}{92}\right)\)	\(e\left(\frac{9}{23}\right)\)	\(e\left(\frac{61}{92}\right)\)	\(e\left(\frac{8}{23}\right)\)	\(e\left(\frac{27}{46}\right)\)	\(e\left(\frac{43}{46}\right)\)	\(e\left(\frac{7}{92}\right)\)	\(e\left(\frac{79}{92}\right)\)	\(e\left(\frac{25}{46}\right)\)
\(\chi_{3055}(19,\cdot)\)	3055.ct	276	yes	\(1\)	\(1\)	\(e\left(\frac{145}{276}\right)\)	\(e\left(\frac{101}{138}\right)\)	\(e\left(\frac{7}{138}\right)\)	\(e\left(\frac{71}{276}\right)\)	\(e\left(\frac{107}{276}\right)\)	\(e\left(\frac{53}{92}\right)\)	\(e\left(\frac{32}{69}\right)\)	\(e\left(\frac{211}{276}\right)\)	\(e\left(\frac{18}{23}\right)\)	\(e\left(\frac{21}{23}\right)\)
\(\chi_{3055}(21,\cdot)\)	3055.bz	92	no	\(-1\)	\(1\)	\(e\left(\frac{55}{92}\right)\)	\(e\left(\frac{14}{23}\right)\)	\(e\left(\frac{9}{46}\right)\)	\(e\left(\frac{19}{92}\right)\)	\(e\left(\frac{85}{92}\right)\)	\(e\left(\frac{73}{92}\right)\)	\(e\left(\frac{5}{23}\right)\)	\(e\left(\frac{61}{92}\right)\)	\(e\left(\frac{37}{46}\right)\)	\(e\left(\frac{12}{23}\right)\)
\(\chi_{3055}(22,\cdot)\)	3055.cw	276	yes	\(1\)	\(1\)	\(e\left(\frac{193}{276}\right)\)	\(e\left(\frac{79}{276}\right)\)	\(e\left(\frac{55}{138}\right)\)	\(e\left(\frac{68}{69}\right)\)	\(e\left(\frac{269}{276}\right)\)	\(e\left(\frac{9}{92}\right)\)	\(e\left(\frac{79}{138}\right)\)	\(e\left(\frac{65}{138}\right)\)	\(e\left(\frac{63}{92}\right)\)	\(e\left(\frac{31}{46}\right)\)
\(\chi_{3055}(23,\cdot)\)	3055.cv	276	yes	\(1\)	\(1\)	\(e\left(\frac{149}{276}\right)\)	\(e\left(\frac{209}{276}\right)\)	\(e\left(\frac{11}{138}\right)\)	\(e\left(\frac{41}{138}\right)\)	\(e\left(\frac{109}{276}\right)\)	\(e\left(\frac{57}{92}\right)\)	\(e\left(\frac{71}{138}\right)\)	\(e\left(\frac{41}{69}\right)\)	\(e\left(\frac{77}{92}\right)\)	\(e\left(\frac{43}{46}\right)\)
\(\chi_{3055}(24,\cdot)\)	3055.cs	276	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{276}\right)\)	\(e\left(\frac{1}{138}\right)\)	\(e\left(\frac{11}{138}\right)\)	\(e\left(\frac{13}{276}\right)\)	\(e\left(\frac{109}{276}\right)\)	\(e\left(\frac{11}{92}\right)\)	\(e\left(\frac{1}{69}\right)\)	\(e\left(\frac{95}{276}\right)\)	\(e\left(\frac{2}{23}\right)\)	\(e\left(\frac{10}{23}\right)\)
\(\chi_{3055}(27,\cdot)\)	3055.cb	92	no	\(-1\)	\(1\)	\(e\left(\frac{67}{92}\right)\)	\(e\left(\frac{77}{92}\right)\)	\(e\left(\frac{21}{46}\right)\)	\(e\left(\frac{13}{23}\right)\)	\(e\left(\frac{91}{92}\right)\)	\(e\left(\frac{17}{92}\right)\)	\(e\left(\frac{31}{46}\right)\)	\(e\left(\frac{3}{23}\right)\)	\(e\left(\frac{27}{92}\right)\)	\(e\left(\frac{33}{46}\right)\)
\(\chi_{3055}(28,\cdot)\)	3055.cq	276	yes	\(1\)	\(1\)	\(e\left(\frac{61}{138}\right)\)	\(e\left(\frac{41}{276}\right)\)	\(e\left(\frac{61}{69}\right)\)	\(e\left(\frac{163}{276}\right)\)	\(e\left(\frac{67}{69}\right)\)	\(e\left(\frac{15}{46}\right)\)	\(e\left(\frac{41}{138}\right)\)	\(e\left(\frac{257}{276}\right)\)	\(e\left(\frac{3}{92}\right)\)	\(e\left(\frac{19}{46}\right)\)
\(\chi_{3055}(29,\cdot)\)	3055.cj	138	yes	\(-1\)	\(1\)	\(e\left(\frac{73}{138}\right)\)	\(e\left(\frac{7}{138}\right)\)	\(e\left(\frac{4}{69}\right)\)	\(e\left(\frac{40}{69}\right)\)	\(e\left(\frac{71}{138}\right)\)	\(e\left(\frac{27}{46}\right)\)	\(e\left(\frac{7}{69}\right)\)	\(e\left(\frac{91}{138}\right)\)	\(e\left(\frac{5}{46}\right)\)	\(e\left(\frac{1}{23}\right)\)
\(\chi_{3055}(31,\cdot)\)	3055.ca	92	no	\(1\)	\(1\)	\(e\left(\frac{85}{92}\right)\)	\(e\left(\frac{7}{23}\right)\)	\(e\left(\frac{39}{46}\right)\)	\(e\left(\frac{21}{92}\right)\)	\(e\left(\frac{31}{92}\right)\)	\(e\left(\frac{71}{92}\right)\)	\(e\left(\frac{14}{23}\right)\)	\(e\left(\frac{65}{92}\right)\)	\(e\left(\frac{7}{46}\right)\)	\(e\left(\frac{6}{23}\right)\)
\(\chi_{3055}(32,\cdot)\)	3055.da	276	yes	\(1\)	\(1\)	\(e\left(\frac{61}{69}\right)\)	\(e\left(\frac{151}{276}\right)\)	\(e\left(\frac{53}{69}\right)\)	\(e\left(\frac{119}{276}\right)\)	\(e\left(\frac{61}{138}\right)\)	\(e\left(\frac{15}{23}\right)\)	\(e\left(\frac{13}{138}\right)\)	\(e\left(\frac{169}{276}\right)\)	\(e\left(\frac{29}{92}\right)\)	\(e\left(\frac{15}{46}\right)\)
\(\chi_{3055}(33,\cdot)\)	3055.db	276	yes	\(-1\)	\(1\)	\(e\left(\frac{16}{69}\right)\)	\(e\left(\frac{181}{276}\right)\)	\(e\left(\frac{32}{69}\right)\)	\(e\left(\frac{245}{276}\right)\)	\(e\left(\frac{85}{138}\right)\)	\(e\left(\frac{16}{23}\right)\)	\(e\left(\frac{43}{138}\right)\)	\(e\left(\frac{145}{276}\right)\)	\(e\left(\frac{11}{92}\right)\)	\(e\left(\frac{39}{46}\right)\)
\(\chi_{3055}(34,\cdot)\)	3055.cg	92	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{92}\right)\)	\(e\left(\frac{13}{46}\right)\)	\(e\left(\frac{5}{46}\right)\)	\(e\left(\frac{31}{92}\right)\)	\(e\left(\frac{83}{92}\right)\)	\(e\left(\frac{15}{92}\right)\)	\(e\left(\frac{13}{23}\right)\)	\(e\left(\frac{85}{92}\right)\)	\(e\left(\frac{9}{23}\right)\)	\(e\left(\frac{22}{23}\right)\)
\(\chi_{3055}(36,\cdot)\)	3055.cl	138	no	\(1\)	\(1\)	\(e\left(\frac{79}{138}\right)\)	\(e\left(\frac{26}{69}\right)\)	\(e\left(\frac{10}{69}\right)\)	\(e\left(\frac{131}{138}\right)\)	\(e\left(\frac{5}{138}\right)\)	\(e\left(\frac{33}{46}\right)\)	\(e\left(\frac{52}{69}\right)\)	\(e\left(\frac{55}{138}\right)\)	\(e\left(\frac{12}{23}\right)\)	\(e\left(\frac{14}{23}\right)\)
\(\chi_{3055}(37,\cdot)\)	3055.cq	276	yes	\(1\)	\(1\)	\(e\left(\frac{37}{138}\right)\)	\(e\left(\frac{95}{276}\right)\)	\(e\left(\frac{37}{69}\right)\)	\(e\left(\frac{169}{276}\right)\)	\(e\left(\frac{61}{69}\right)\)	\(e\left(\frac{37}{46}\right)\)	\(e\left(\frac{95}{138}\right)\)	\(e\left(\frac{131}{276}\right)\)	\(e\left(\frac{81}{92}\right)\)	\(e\left(\frac{7}{46}\right)\)
\(\chi_{3055}(38,\cdot)\)	3055.cd	92	yes	\(1\)	\(1\)	\(e\left(\frac{83}{92}\right)\)	\(e\left(\frac{59}{92}\right)\)	\(e\left(\frac{37}{46}\right)\)	\(e\left(\frac{25}{46}\right)\)	\(e\left(\frac{7}{92}\right)\)	\(e\left(\frac{65}{92}\right)\)	\(e\left(\frac{13}{46}\right)\)	\(e\left(\frac{2}{23}\right)\)	\(e\left(\frac{41}{92}\right)\)	\(e\left(\frac{45}{46}\right)\)
\(\chi_{3055}(41,\cdot)\)	3055.cy	276	no	\(1\)	\(1\)	\(e\left(\frac{263}{276}\right)\)	\(e\left(\frac{59}{69}\right)\)	\(e\left(\frac{125}{138}\right)\)	\(e\left(\frac{223}{276}\right)\)	\(e\left(\frac{97}{276}\right)\)	\(e\left(\frac{79}{92}\right)\)	\(e\left(\frac{49}{69}\right)\)	\(e\left(\frac{239}{276}\right)\)	\(e\left(\frac{35}{46}\right)\)	\(e\left(\frac{7}{23}\right)\)
\(\chi_{3055}(42,\cdot)\)	3055.cx	276	yes	\(-1\)	\(1\)	\(e\left(\frac{269}{276}\right)\)	\(e\left(\frac{143}{276}\right)\)	\(e\left(\frac{131}{138}\right)\)	\(e\left(\frac{34}{69}\right)\)	\(e\left(\frac{169}{276}\right)\)	\(e\left(\frac{85}{92}\right)\)	\(e\left(\frac{5}{138}\right)\)	\(e\left(\frac{68}{69}\right)\)	\(e\left(\frac{43}{92}\right)\)	\(e\left(\frac{27}{46}\right)\)
\(\chi_{3055}(43,\cdot)\)	3055.cv	276	yes	\(1\)	\(1\)	\(e\left(\frac{1}{276}\right)\)	\(e\left(\frac{157}{276}\right)\)	\(e\left(\frac{1}{138}\right)\)	\(e\left(\frac{79}{138}\right)\)	\(e\left(\frac{173}{276}\right)\)	\(e\left(\frac{1}{92}\right)\)	\(e\left(\frac{19}{138}\right)\)	\(e\left(\frac{10}{69}\right)\)	\(e\left(\frac{53}{92}\right)\)	\(e\left(\frac{29}{46}\right)\)

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L-functions

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First 32 of 2208 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.