LMFDB - Group of Dirichlet characters of modulus 8034

Show commands: PariGP / SageMath

sage: H = DirichletGroup(8034)

pari: g = idealstar(,8034,2)

Character group

sage: G.order() pari: g.no
Order	=	2448
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{6}\times C_{204}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{8034}(5357,\cdot)$, $\chi_{8034}(1237,\cdot)$, $\chi_{8034}(5773,\cdot)$

First 32 of 2448 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	$-1$	$1$	$5$	$7$	$11$	$17$	$19$	$23$	$25$	$29$	$31$	$35$
$\chi_{8034}(1,\cdot)$	8034.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{8034}(5,\cdot)$	8034.ej	204	no	$-1$	$1$	$e\left(\frac{53}{204}\right)$	$e\left(\frac{59}{204}\right)$	$e\left(\frac{71}{204}\right)$	$e\left(\frac{35}{51}\right)$	$e\left(\frac{109}{204}\right)$	$e\left(\frac{4}{17}\right)$	$e\left(\frac{53}{102}\right)$	$e\left(\frac{35}{102}\right)$	$e\left(\frac{21}{68}\right)$	$e\left(\frac{28}{51}\right)$
$\chi_{8034}(7,\cdot)$	8034.ec	204	no	$-1$	$1$	$e\left(\frac{59}{204}\right)$	$e\left(\frac{49}{204}\right)$	$e\left(\frac{55}{68}\right)$	$e\left(\frac{59}{102}\right)$	$e\left(\frac{49}{68}\right)$	$e\left(\frac{11}{102}\right)$	$e\left(\frac{59}{102}\right)$	$e\left(\frac{2}{51}\right)$	$e\left(\frac{33}{68}\right)$	$e\left(\frac{9}{17}\right)$
$\chi_{8034}(11,\cdot)$	8034.eb	204	no	$-1$	$1$	$e\left(\frac{71}{204}\right)$	$e\left(\frac{55}{68}\right)$	$e\left(\frac{13}{204}\right)$	$e\left(\frac{9}{17}\right)$	$e\left(\frac{155}{204}\right)$	$e\left(\frac{35}{51}\right)$	$e\left(\frac{71}{102}\right)$	$e\left(\frac{9}{34}\right)$	$e\left(\frac{23}{68}\right)$	$e\left(\frac{8}{51}\right)$
$\chi_{8034}(17,\cdot)$	8034.do	102	no	$-1$	$1$	$e\left(\frac{35}{51}\right)$	$e\left(\frac{59}{102}\right)$	$e\left(\frac{9}{17}\right)$	$e\left(\frac{89}{102}\right)$	$e\left(\frac{25}{34}\right)$	$e\left(\frac{65}{102}\right)$	$e\left(\frac{19}{51}\right)$	$e\left(\frac{19}{102}\right)$	$e\left(\frac{21}{34}\right)$	$e\left(\frac{9}{34}\right)$
$\chi_{8034}(19,\cdot)$	8034.ep	204	no	$-1$	$1$	$e\left(\frac{109}{204}\right)$	$e\left(\frac{49}{68}\right)$	$e\left(\frac{155}{204}\right)$	$e\left(\frac{25}{34}\right)$	$e\left(\frac{169}{204}\right)$	$e\left(\frac{101}{102}\right)$	$e\left(\frac{7}{102}\right)$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{31}{68}\right)$	$e\left(\frac{13}{51}\right)$
$\chi_{8034}(23,\cdot)$	8034.cy	102	no	$-1$	$1$	$e\left(\frac{4}{17}\right)$	$e\left(\frac{11}{102}\right)$	$e\left(\frac{35}{51}\right)$	$e\left(\frac{65}{102}\right)$	$e\left(\frac{101}{102}\right)$	$e\left(\frac{49}{102}\right)$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{7}{102}\right)$	$e\left(\frac{31}{34}\right)$	$e\left(\frac{35}{102}\right)$
$\chi_{8034}(25,\cdot)$	8034.de	102	no	$1$	$1$	$e\left(\frac{53}{102}\right)$	$e\left(\frac{59}{102}\right)$	$e\left(\frac{71}{102}\right)$	$e\left(\frac{19}{51}\right)$	$e\left(\frac{7}{102}\right)$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{2}{51}\right)$	$e\left(\frac{35}{51}\right)$	$e\left(\frac{21}{34}\right)$	$e\left(\frac{5}{51}\right)$
$\chi_{8034}(29,\cdot)$	8034.dj	102	no	$-1$	$1$	$e\left(\frac{35}{102}\right)$	$e\left(\frac{2}{51}\right)$	$e\left(\frac{9}{34}\right)$	$e\left(\frac{19}{102}\right)$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{7}{102}\right)$	$e\left(\frac{35}{51}\right)$	$e\left(\frac{35}{102}\right)$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{13}{34}\right)$
$\chi_{8034}(31,\cdot)$	8034.cx	68	no	$1$	$1$	$e\left(\frac{21}{68}\right)$	$e\left(\frac{33}{68}\right)$	$e\left(\frac{23}{68}\right)$	$e\left(\frac{21}{34}\right)$	$e\left(\frac{31}{68}\right)$	$e\left(\frac{31}{34}\right)$	$e\left(\frac{21}{34}\right)$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{41}{68}\right)$	$e\left(\frac{27}{34}\right)$
$\chi_{8034}(35,\cdot)$	8034.dn	102	no	$1$	$1$	$e\left(\frac{28}{51}\right)$	$e\left(\frac{9}{17}\right)$	$e\left(\frac{8}{51}\right)$	$e\left(\frac{9}{34}\right)$	$e\left(\frac{13}{51}\right)$	$e\left(\frac{35}{102}\right)$	$e\left(\frac{5}{51}\right)$	$e\left(\frac{13}{34}\right)$	$e\left(\frac{27}{34}\right)$	$e\left(\frac{4}{51}\right)$
$\chi_{8034}(37,\cdot)$	8034.ee	204	no	$1$	$1$	$e\left(\frac{11}{68}\right)$	$e\left(\frac{13}{204}\right)$	$e\left(\frac{143}{204}\right)$	$e\left(\frac{101}{102}\right)$	$e\left(\frac{175}{204}\right)$	$e\left(\frac{73}{102}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{38}{51}\right)$	$e\left(\frac{15}{68}\right)$	$e\left(\frac{23}{102}\right)$
$\chi_{8034}(41,\cdot)$	8034.el	204	no	$1$	$1$	$e\left(\frac{151}{204}\right)$	$e\left(\frac{179}{204}\right)$	$e\left(\frac{67}{68}\right)$	$e\left(\frac{50}{51}\right)$	$e\left(\frac{43}{68}\right)$	$e\left(\frac{5}{51}\right)$	$e\left(\frac{49}{102}\right)$	$e\left(\frac{101}{102}\right)$	$e\left(\frac{47}{68}\right)$	$e\left(\frac{21}{34}\right)$
$\chi_{8034}(43,\cdot)$	8034.du	102	no	$-1$	$1$	$e\left(\frac{13}{51}\right)$	$e\left(\frac{29}{34}\right)$	$e\left(\frac{11}{51}\right)$	$e\left(\frac{3}{17}\right)$	$e\left(\frac{23}{102}\right)$	$e\left(\frac{40}{51}\right)$	$e\left(\frac{26}{51}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{9}{17}\right)$	$e\left(\frac{11}{102}\right)$
$\chi_{8034}(47,\cdot)$	8034.by	12	no	$-1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$-i$	$e\left(\frac{2}{3}\right)$
$\chi_{8034}(49,\cdot)$	8034.dg	102	no	$1$	$1$	$e\left(\frac{59}{102}\right)$	$e\left(\frac{49}{102}\right)$	$e\left(\frac{21}{34}\right)$	$e\left(\frac{8}{51}\right)$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{11}{51}\right)$	$e\left(\frac{8}{51}\right)$	$e\left(\frac{4}{51}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{1}{17}\right)$
$\chi_{8034}(53,\cdot)$	8034.dt	102	no	$1$	$1$	$e\left(\frac{23}{51}\right)$	$e\left(\frac{41}{51}\right)$	$e\left(\frac{26}{51}\right)$	$e\left(\frac{7}{102}\right)$	$e\left(\frac{4}{51}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{46}{51}\right)$	$e\left(\frac{29}{102}\right)$	$e\left(\frac{7}{34}\right)$	$e\left(\frac{13}{51}\right)$
$\chi_{8034}(55,\cdot)$	8034.cs	51	no	$1$	$1$	$e\left(\frac{31}{51}\right)$	$e\left(\frac{5}{51}\right)$	$e\left(\frac{7}{17}\right)$	$e\left(\frac{11}{51}\right)$	$e\left(\frac{5}{17}\right)$	$e\left(\frac{47}{51}\right)$	$e\left(\frac{11}{51}\right)$	$e\left(\frac{31}{51}\right)$	$e\left(\frac{11}{17}\right)$	$e\left(\frac{12}{17}\right)$
$\chi_{8034}(59,\cdot)$	8034.ea	204	no	$1$	$1$	$e\left(\frac{145}{204}\right)$	$e\left(\frac{63}{68}\right)$	$e\left(\frac{107}{204}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{91}{204}\right)$	$e\left(\frac{37}{51}\right)$	$e\left(\frac{43}{102}\right)$	$e\left(\frac{27}{34}\right)$	$e\left(\frac{1}{68}\right)$	$e\left(\frac{65}{102}\right)$
$\chi_{8034}(61,\cdot)$	8034.cq	51	no	$1$	$1$	$e\left(\frac{6}{17}\right)$	$e\left(\frac{38}{51}\right)$	$e\left(\frac{10}{51}\right)$	$e\left(\frac{2}{51}\right)$	$e\left(\frac{29}{51}\right)$	$e\left(\frac{7}{51}\right)$	$e\left(\frac{12}{17}\right)$	$e\left(\frac{1}{51}\right)$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{5}{51}\right)$
$\chi_{8034}(67,\cdot)$	8034.eo	204	no	$1$	$1$	$e\left(\frac{179}{204}\right)$	$e\left(\frac{29}{68}\right)$	$e\left(\frac{73}{204}\right)$	$e\left(\frac{3}{34}\right)$	$e\left(\frac{125}{204}\right)$	$e\left(\frac{91}{102}\right)$	$e\left(\frac{77}{102}\right)$	$e\left(\frac{5}{17}\right)$	$e\left(\frac{1}{68}\right)$	$e\left(\frac{31}{102}\right)$
$\chi_{8034}(71,\cdot)$	8034.ek	204	no	$-1$	$1$	$e\left(\frac{185}{204}\right)$	$e\left(\frac{43}{204}\right)$	$e\left(\frac{33}{68}\right)$	$e\left(\frac{16}{51}\right)$	$e\left(\frac{43}{68}\right)$	$e\left(\frac{22}{51}\right)$	$e\left(\frac{83}{102}\right)$	$e\left(\frac{67}{102}\right)$	$e\left(\frac{13}{68}\right)$	$e\left(\frac{2}{17}\right)$
$\chi_{8034}(73,\cdot)$	8034.cx	68	no	$1$	$1$	$e\left(\frac{39}{68}\right)$	$e\left(\frac{3}{68}\right)$	$e\left(\frac{33}{68}\right)$	$e\left(\frac{5}{34}\right)$	$e\left(\frac{9}{68}\right)$	$e\left(\frac{9}{34}\right)$	$e\left(\frac{5}{34}\right)$	$e\left(\frac{14}{17}\right)$	$e\left(\frac{47}{68}\right)$	$e\left(\frac{21}{34}\right)$
$\chi_{8034}(77,\cdot)$	8034.dd	102	no	$1$	$1$	$e\left(\frac{65}{102}\right)$	$e\left(\frac{5}{102}\right)$	$e\left(\frac{89}{102}\right)$	$e\left(\frac{11}{102}\right)$	$e\left(\frac{49}{102}\right)$	$e\left(\frac{27}{34}\right)$	$e\left(\frac{14}{51}\right)$	$e\left(\frac{31}{102}\right)$	$e\left(\frac{14}{17}\right)$	$e\left(\frac{35}{51}\right)$
$\chi_{8034}(79,\cdot)$	8034.ci	17	no	$1$	$1$	$e\left(\frac{3}{17}\right)$	$e\left(\frac{12}{17}\right)$	$e\left(\frac{13}{17}\right)$	$e\left(\frac{6}{17}\right)$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{4}{17}\right)$	$e\left(\frac{6}{17}\right)$	$e\left(\frac{3}{17}\right)$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{15}{17}\right)$
$\chi_{8034}(83,\cdot)$	8034.ei	204	no	$1$	$1$	$e\left(\frac{127}{204}\right)$	$e\left(\frac{151}{204}\right)$	$e\left(\frac{97}{204}\right)$	$e\left(\frac{4}{51}\right)$	$e\left(\frac{113}{204}\right)$	$e\left(\frac{16}{17}\right)$	$e\left(\frac{25}{102}\right)$	$e\left(\frac{55}{102}\right)$	$e\left(\frac{67}{68}\right)$	$e\left(\frac{37}{102}\right)$
$\chi_{8034}(85,\cdot)$	8034.eo	204	no	$1$	$1$	$e\left(\frac{193}{204}\right)$	$e\left(\frac{59}{68}\right)$	$e\left(\frac{179}{204}\right)$	$e\left(\frac{19}{34}\right)$	$e\left(\frac{55}{204}\right)$	$e\left(\frac{89}{102}\right)$	$e\left(\frac{91}{102}\right)$	$e\left(\frac{9}{17}\right)$	$e\left(\frac{63}{68}\right)$	$e\left(\frac{83}{102}\right)$
$\chi_{8034}(89,\cdot)$	8034.en	204	no	$-1$	$1$	$e\left(\frac{49}{68}\right)$	$e\left(\frac{61}{204}\right)$	$e\left(\frac{161}{204}\right)$	$e\left(\frac{31}{51}\right)$	$e\left(\frac{115}{204}\right)$	$e\left(\frac{32}{51}\right)$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{31}{102}\right)$	$e\left(\frac{39}{68}\right)$	$e\left(\frac{1}{51}\right)$
$\chi_{8034}(95,\cdot)$	8034.dw	102	no	$1$	$1$	$e\left(\frac{27}{34}\right)$	$e\left(\frac{1}{102}\right)$	$e\left(\frac{11}{102}\right)$	$e\left(\frac{43}{102}\right)$	$e\left(\frac{37}{102}\right)$	$e\left(\frac{23}{102}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{47}{102}\right)$	$e\left(\frac{13}{17}\right)$	$e\left(\frac{41}{51}\right)$
$\chi_{8034}(97,\cdot)$	8034.ep	204	no	$-1$	$1$	$e\left(\frac{13}{204}\right)$	$e\left(\frac{57}{68}\right)$	$e\left(\frac{11}{204}\right)$	$e\left(\frac{27}{34}\right)$	$e\left(\frac{37}{204}\right)$	$e\left(\frac{71}{102}\right)$	$e\left(\frac{13}{102}\right)$	$e\left(\frac{11}{17}\right)$	$e\left(\frac{43}{68}\right)$	$e\left(\frac{46}{51}\right)$
$\chi_{8034}(101,\cdot)$	8034.df	102	no	$1$	$1$	$e\left(\frac{95}{102}\right)$	$e\left(\frac{91}{102}\right)$	$e\left(\frac{5}{34}\right)$	$e\left(\frac{37}{102}\right)$	$e\left(\frac{23}{34}\right)$	$e\left(\frac{19}{102}\right)$	$e\left(\frac{44}{51}\right)$	$e\left(\frac{95}{102}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{14}{17}\right)$
$\chi_{8034}(107,\cdot)$	8034.dc	102	no	$-1$	$1$	$e\left(\frac{37}{102}\right)$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{47}{102}\right)$	$e\left(\frac{19}{34}\right)$	$e\left(\frac{35}{51}\right)$	$e\left(\frac{55}{102}\right)$	$e\left(\frac{37}{51}\right)$	$e\left(\frac{1}{34}\right)$	$e\left(\frac{3}{17}\right)$	$e\left(\frac{49}{102}\right)$

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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	$8034$
Structure	\(C_{2}\times C_{6}\times C_{204}\)
Order	$2448$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(35\)
\(\chi_{8034}(1,\cdot)\)	8034.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{8034}(5,\cdot)\)	8034.ej	204	no	\(-1\)	\(1\)	\(e\left(\frac{53}{204}\right)\)	\(e\left(\frac{59}{204}\right)\)	\(e\left(\frac{71}{204}\right)\)	\(e\left(\frac{35}{51}\right)\)	\(e\left(\frac{109}{204}\right)\)	\(e\left(\frac{4}{17}\right)\)	\(e\left(\frac{53}{102}\right)\)	\(e\left(\frac{35}{102}\right)\)	\(e\left(\frac{21}{68}\right)\)	\(e\left(\frac{28}{51}\right)\)
\(\chi_{8034}(7,\cdot)\)	8034.ec	204	no	\(-1\)	\(1\)	\(e\left(\frac{59}{204}\right)\)	\(e\left(\frac{49}{204}\right)\)	\(e\left(\frac{55}{68}\right)\)	\(e\left(\frac{59}{102}\right)\)	\(e\left(\frac{49}{68}\right)\)	\(e\left(\frac{11}{102}\right)\)	\(e\left(\frac{59}{102}\right)\)	\(e\left(\frac{2}{51}\right)\)	\(e\left(\frac{33}{68}\right)\)	\(e\left(\frac{9}{17}\right)\)
\(\chi_{8034}(11,\cdot)\)	8034.eb	204	no	\(-1\)	\(1\)	\(e\left(\frac{71}{204}\right)\)	\(e\left(\frac{55}{68}\right)\)	\(e\left(\frac{13}{204}\right)\)	\(e\left(\frac{9}{17}\right)\)	\(e\left(\frac{155}{204}\right)\)	\(e\left(\frac{35}{51}\right)\)	\(e\left(\frac{71}{102}\right)\)	\(e\left(\frac{9}{34}\right)\)	\(e\left(\frac{23}{68}\right)\)	\(e\left(\frac{8}{51}\right)\)
\(\chi_{8034}(17,\cdot)\)	8034.do	102	no	\(-1\)	\(1\)	\(e\left(\frac{35}{51}\right)\)	\(e\left(\frac{59}{102}\right)\)	\(e\left(\frac{9}{17}\right)\)	\(e\left(\frac{89}{102}\right)\)	\(e\left(\frac{25}{34}\right)\)	\(e\left(\frac{65}{102}\right)\)	\(e\left(\frac{19}{51}\right)\)	\(e\left(\frac{19}{102}\right)\)	\(e\left(\frac{21}{34}\right)\)	\(e\left(\frac{9}{34}\right)\)
\(\chi_{8034}(19,\cdot)\)	8034.ep	204	no	\(-1\)	\(1\)	\(e\left(\frac{109}{204}\right)\)	\(e\left(\frac{49}{68}\right)\)	\(e\left(\frac{155}{204}\right)\)	\(e\left(\frac{25}{34}\right)\)	\(e\left(\frac{169}{204}\right)\)	\(e\left(\frac{101}{102}\right)\)	\(e\left(\frac{7}{102}\right)\)	\(e\left(\frac{2}{17}\right)\)	\(e\left(\frac{31}{68}\right)\)	\(e\left(\frac{13}{51}\right)\)
\(\chi_{8034}(23,\cdot)\)	8034.cy	102	no	\(-1\)	\(1\)	\(e\left(\frac{4}{17}\right)\)	\(e\left(\frac{11}{102}\right)\)	\(e\left(\frac{35}{51}\right)\)	\(e\left(\frac{65}{102}\right)\)	\(e\left(\frac{101}{102}\right)\)	\(e\left(\frac{49}{102}\right)\)	\(e\left(\frac{8}{17}\right)\)	\(e\left(\frac{7}{102}\right)\)	\(e\left(\frac{31}{34}\right)\)	\(e\left(\frac{35}{102}\right)\)
\(\chi_{8034}(25,\cdot)\)	8034.de	102	no	\(1\)	\(1\)	\(e\left(\frac{53}{102}\right)\)	\(e\left(\frac{59}{102}\right)\)	\(e\left(\frac{71}{102}\right)\)	\(e\left(\frac{19}{51}\right)\)	\(e\left(\frac{7}{102}\right)\)	\(e\left(\frac{8}{17}\right)\)	\(e\left(\frac{2}{51}\right)\)	\(e\left(\frac{35}{51}\right)\)	\(e\left(\frac{21}{34}\right)\)	\(e\left(\frac{5}{51}\right)\)
\(\chi_{8034}(29,\cdot)\)	8034.dj	102	no	\(-1\)	\(1\)	\(e\left(\frac{35}{102}\right)\)	\(e\left(\frac{2}{51}\right)\)	\(e\left(\frac{9}{34}\right)\)	\(e\left(\frac{19}{102}\right)\)	\(e\left(\frac{2}{17}\right)\)	\(e\left(\frac{7}{102}\right)\)	\(e\left(\frac{35}{51}\right)\)	\(e\left(\frac{35}{102}\right)\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{13}{34}\right)\)
\(\chi_{8034}(31,\cdot)\)	8034.cx	68	no	\(1\)	\(1\)	\(e\left(\frac{21}{68}\right)\)	\(e\left(\frac{33}{68}\right)\)	\(e\left(\frac{23}{68}\right)\)	\(e\left(\frac{21}{34}\right)\)	\(e\left(\frac{31}{68}\right)\)	\(e\left(\frac{31}{34}\right)\)	\(e\left(\frac{21}{34}\right)\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{41}{68}\right)\)	\(e\left(\frac{27}{34}\right)\)
\(\chi_{8034}(35,\cdot)\)	8034.dn	102	no	\(1\)	\(1\)	\(e\left(\frac{28}{51}\right)\)	\(e\left(\frac{9}{17}\right)\)	\(e\left(\frac{8}{51}\right)\)	\(e\left(\frac{9}{34}\right)\)	\(e\left(\frac{13}{51}\right)\)	\(e\left(\frac{35}{102}\right)\)	\(e\left(\frac{5}{51}\right)\)	\(e\left(\frac{13}{34}\right)\)	\(e\left(\frac{27}{34}\right)\)	\(e\left(\frac{4}{51}\right)\)
\(\chi_{8034}(37,\cdot)\)	8034.ee	204	no	\(1\)	\(1\)	\(e\left(\frac{11}{68}\right)\)	\(e\left(\frac{13}{204}\right)\)	\(e\left(\frac{143}{204}\right)\)	\(e\left(\frac{101}{102}\right)\)	\(e\left(\frac{175}{204}\right)\)	\(e\left(\frac{73}{102}\right)\)	\(e\left(\frac{11}{34}\right)\)	\(e\left(\frac{38}{51}\right)\)	\(e\left(\frac{15}{68}\right)\)	\(e\left(\frac{23}{102}\right)\)
\(\chi_{8034}(41,\cdot)\)	8034.el	204	no	\(1\)	\(1\)	\(e\left(\frac{151}{204}\right)\)	\(e\left(\frac{179}{204}\right)\)	\(e\left(\frac{67}{68}\right)\)	\(e\left(\frac{50}{51}\right)\)	\(e\left(\frac{43}{68}\right)\)	\(e\left(\frac{5}{51}\right)\)	\(e\left(\frac{49}{102}\right)\)	\(e\left(\frac{101}{102}\right)\)	\(e\left(\frac{47}{68}\right)\)	\(e\left(\frac{21}{34}\right)\)
\(\chi_{8034}(43,\cdot)\)	8034.du	102	no	\(-1\)	\(1\)	\(e\left(\frac{13}{51}\right)\)	\(e\left(\frac{29}{34}\right)\)	\(e\left(\frac{11}{51}\right)\)	\(e\left(\frac{3}{17}\right)\)	\(e\left(\frac{23}{102}\right)\)	\(e\left(\frac{40}{51}\right)\)	\(e\left(\frac{26}{51}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{9}{17}\right)\)	\(e\left(\frac{11}{102}\right)\)
\(\chi_{8034}(47,\cdot)\)	8034.by	12	no	\(-1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-i\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{8034}(49,\cdot)\)	8034.dg	102	no	\(1\)	\(1\)	\(e\left(\frac{59}{102}\right)\)	\(e\left(\frac{49}{102}\right)\)	\(e\left(\frac{21}{34}\right)\)	\(e\left(\frac{8}{51}\right)\)	\(e\left(\frac{15}{34}\right)\)	\(e\left(\frac{11}{51}\right)\)	\(e\left(\frac{8}{51}\right)\)	\(e\left(\frac{4}{51}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{1}{17}\right)\)
\(\chi_{8034}(53,\cdot)\)	8034.dt	102	no	\(1\)	\(1\)	\(e\left(\frac{23}{51}\right)\)	\(e\left(\frac{41}{51}\right)\)	\(e\left(\frac{26}{51}\right)\)	\(e\left(\frac{7}{102}\right)\)	\(e\left(\frac{4}{51}\right)\)	\(e\left(\frac{11}{34}\right)\)	\(e\left(\frac{46}{51}\right)\)	\(e\left(\frac{29}{102}\right)\)	\(e\left(\frac{7}{34}\right)\)	\(e\left(\frac{13}{51}\right)\)
\(\chi_{8034}(55,\cdot)\)	8034.cs	51	no	\(1\)	\(1\)	\(e\left(\frac{31}{51}\right)\)	\(e\left(\frac{5}{51}\right)\)	\(e\left(\frac{7}{17}\right)\)	\(e\left(\frac{11}{51}\right)\)	\(e\left(\frac{5}{17}\right)\)	\(e\left(\frac{47}{51}\right)\)	\(e\left(\frac{11}{51}\right)\)	\(e\left(\frac{31}{51}\right)\)	\(e\left(\frac{11}{17}\right)\)	\(e\left(\frac{12}{17}\right)\)
\(\chi_{8034}(59,\cdot)\)	8034.ea	204	no	\(1\)	\(1\)	\(e\left(\frac{145}{204}\right)\)	\(e\left(\frac{63}{68}\right)\)	\(e\left(\frac{107}{204}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{91}{204}\right)\)	\(e\left(\frac{37}{51}\right)\)	\(e\left(\frac{43}{102}\right)\)	\(e\left(\frac{27}{34}\right)\)	\(e\left(\frac{1}{68}\right)\)	\(e\left(\frac{65}{102}\right)\)
\(\chi_{8034}(61,\cdot)\)	8034.cq	51	no	\(1\)	\(1\)	\(e\left(\frac{6}{17}\right)\)	\(e\left(\frac{38}{51}\right)\)	\(e\left(\frac{10}{51}\right)\)	\(e\left(\frac{2}{51}\right)\)	\(e\left(\frac{29}{51}\right)\)	\(e\left(\frac{7}{51}\right)\)	\(e\left(\frac{12}{17}\right)\)	\(e\left(\frac{1}{51}\right)\)	\(e\left(\frac{2}{17}\right)\)	\(e\left(\frac{5}{51}\right)\)
\(\chi_{8034}(67,\cdot)\)	8034.eo	204	no	\(1\)	\(1\)	\(e\left(\frac{179}{204}\right)\)	\(e\left(\frac{29}{68}\right)\)	\(e\left(\frac{73}{204}\right)\)	\(e\left(\frac{3}{34}\right)\)	\(e\left(\frac{125}{204}\right)\)	\(e\left(\frac{91}{102}\right)\)	\(e\left(\frac{77}{102}\right)\)	\(e\left(\frac{5}{17}\right)\)	\(e\left(\frac{1}{68}\right)\)	\(e\left(\frac{31}{102}\right)\)
\(\chi_{8034}(71,\cdot)\)	8034.ek	204	no	\(-1\)	\(1\)	\(e\left(\frac{185}{204}\right)\)	\(e\left(\frac{43}{204}\right)\)	\(e\left(\frac{33}{68}\right)\)	\(e\left(\frac{16}{51}\right)\)	\(e\left(\frac{43}{68}\right)\)	\(e\left(\frac{22}{51}\right)\)	\(e\left(\frac{83}{102}\right)\)	\(e\left(\frac{67}{102}\right)\)	\(e\left(\frac{13}{68}\right)\)	\(e\left(\frac{2}{17}\right)\)
\(\chi_{8034}(73,\cdot)\)	8034.cx	68	no	\(1\)	\(1\)	\(e\left(\frac{39}{68}\right)\)	\(e\left(\frac{3}{68}\right)\)	\(e\left(\frac{33}{68}\right)\)	\(e\left(\frac{5}{34}\right)\)	\(e\left(\frac{9}{68}\right)\)	\(e\left(\frac{9}{34}\right)\)	\(e\left(\frac{5}{34}\right)\)	\(e\left(\frac{14}{17}\right)\)	\(e\left(\frac{47}{68}\right)\)	\(e\left(\frac{21}{34}\right)\)
\(\chi_{8034}(77,\cdot)\)	8034.dd	102	no	\(1\)	\(1\)	\(e\left(\frac{65}{102}\right)\)	\(e\left(\frac{5}{102}\right)\)	\(e\left(\frac{89}{102}\right)\)	\(e\left(\frac{11}{102}\right)\)	\(e\left(\frac{49}{102}\right)\)	\(e\left(\frac{27}{34}\right)\)	\(e\left(\frac{14}{51}\right)\)	\(e\left(\frac{31}{102}\right)\)	\(e\left(\frac{14}{17}\right)\)	\(e\left(\frac{35}{51}\right)\)
\(\chi_{8034}(79,\cdot)\)	8034.ci	17	no	\(1\)	\(1\)	\(e\left(\frac{3}{17}\right)\)	\(e\left(\frac{12}{17}\right)\)	\(e\left(\frac{13}{17}\right)\)	\(e\left(\frac{6}{17}\right)\)	\(e\left(\frac{2}{17}\right)\)	\(e\left(\frac{4}{17}\right)\)	\(e\left(\frac{6}{17}\right)\)	\(e\left(\frac{3}{17}\right)\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{15}{17}\right)\)
\(\chi_{8034}(83,\cdot)\)	8034.ei	204	no	\(1\)	\(1\)	\(e\left(\frac{127}{204}\right)\)	\(e\left(\frac{151}{204}\right)\)	\(e\left(\frac{97}{204}\right)\)	\(e\left(\frac{4}{51}\right)\)	\(e\left(\frac{113}{204}\right)\)	\(e\left(\frac{16}{17}\right)\)	\(e\left(\frac{25}{102}\right)\)	\(e\left(\frac{55}{102}\right)\)	\(e\left(\frac{67}{68}\right)\)	\(e\left(\frac{37}{102}\right)\)
\(\chi_{8034}(85,\cdot)\)	8034.eo	204	no	\(1\)	\(1\)	\(e\left(\frac{193}{204}\right)\)	\(e\left(\frac{59}{68}\right)\)	\(e\left(\frac{179}{204}\right)\)	\(e\left(\frac{19}{34}\right)\)	\(e\left(\frac{55}{204}\right)\)	\(e\left(\frac{89}{102}\right)\)	\(e\left(\frac{91}{102}\right)\)	\(e\left(\frac{9}{17}\right)\)	\(e\left(\frac{63}{68}\right)\)	\(e\left(\frac{83}{102}\right)\)
\(\chi_{8034}(89,\cdot)\)	8034.en	204	no	\(-1\)	\(1\)	\(e\left(\frac{49}{68}\right)\)	\(e\left(\frac{61}{204}\right)\)	\(e\left(\frac{161}{204}\right)\)	\(e\left(\frac{31}{51}\right)\)	\(e\left(\frac{115}{204}\right)\)	\(e\left(\frac{32}{51}\right)\)	\(e\left(\frac{15}{34}\right)\)	\(e\left(\frac{31}{102}\right)\)	\(e\left(\frac{39}{68}\right)\)	\(e\left(\frac{1}{51}\right)\)
\(\chi_{8034}(95,\cdot)\)	8034.dw	102	no	\(1\)	\(1\)	\(e\left(\frac{27}{34}\right)\)	\(e\left(\frac{1}{102}\right)\)	\(e\left(\frac{11}{102}\right)\)	\(e\left(\frac{43}{102}\right)\)	\(e\left(\frac{37}{102}\right)\)	\(e\left(\frac{23}{102}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{47}{102}\right)\)	\(e\left(\frac{13}{17}\right)\)	\(e\left(\frac{41}{51}\right)\)
\(\chi_{8034}(97,\cdot)\)	8034.ep	204	no	\(-1\)	\(1\)	\(e\left(\frac{13}{204}\right)\)	\(e\left(\frac{57}{68}\right)\)	\(e\left(\frac{11}{204}\right)\)	\(e\left(\frac{27}{34}\right)\)	\(e\left(\frac{37}{204}\right)\)	\(e\left(\frac{71}{102}\right)\)	\(e\left(\frac{13}{102}\right)\)	\(e\left(\frac{11}{17}\right)\)	\(e\left(\frac{43}{68}\right)\)	\(e\left(\frac{46}{51}\right)\)
\(\chi_{8034}(101,\cdot)\)	8034.df	102	no	\(1\)	\(1\)	\(e\left(\frac{95}{102}\right)\)	\(e\left(\frac{91}{102}\right)\)	\(e\left(\frac{5}{34}\right)\)	\(e\left(\frac{37}{102}\right)\)	\(e\left(\frac{23}{34}\right)\)	\(e\left(\frac{19}{102}\right)\)	\(e\left(\frac{44}{51}\right)\)	\(e\left(\frac{95}{102}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{14}{17}\right)\)
\(\chi_{8034}(107,\cdot)\)	8034.dc	102	no	\(-1\)	\(1\)	\(e\left(\frac{37}{102}\right)\)	\(e\left(\frac{2}{17}\right)\)	\(e\left(\frac{47}{102}\right)\)	\(e\left(\frac{19}{34}\right)\)	\(e\left(\frac{35}{51}\right)\)	\(e\left(\frac{55}{102}\right)\)	\(e\left(\frac{37}{51}\right)\)	\(e\left(\frac{1}{34}\right)\)	\(e\left(\frac{3}{17}\right)\)	\(e\left(\frac{49}{102}\right)\)

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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.