LMFDB - Group of Dirichlet characters of modulus 8085

Show commands: PariGP / SageMath

sage: H = DirichletGroup(8085)

pari: g = idealstar(,8085,2)

Character group

sage: G.order() pari: g.no
Order	=	3360
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{420}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{8085}(2696,\cdot)$, $\chi_{8085}(4852,\cdot)$, $\chi_{8085}(1816,\cdot)$, $\chi_{8085}(3676,\cdot)$

First 32 of 3360 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	$-1$	$1$	$2$	$4$	$8$	$13$	$16$	$17$	$19$	$23$	$26$	$29$
$\chi_{8085}(1,\cdot)$	8085.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{8085}(2,\cdot)$	8085.hj	420	yes	$-1$	$1$	$e\left(\frac{397}{420}\right)$	$e\left(\frac{187}{210}\right)$	$e\left(\frac{117}{140}\right)$	$e\left(\frac{39}{140}\right)$	$e\left(\frac{82}{105}\right)$	$e\left(\frac{53}{420}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{47}{210}\right)$	$e\left(\frac{59}{70}\right)$
$\chi_{8085}(4,\cdot)$	8085.gx	210	no	$1$	$1$	$e\left(\frac{187}{210}\right)$	$e\left(\frac{82}{105}\right)$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{59}{105}\right)$	$e\left(\frac{53}{210}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{47}{105}\right)$	$e\left(\frac{24}{35}\right)$
$\chi_{8085}(8,\cdot)$	8085.gf	140	yes	$-1$	$1$	$e\left(\frac{117}{140}\right)$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{71}{140}\right)$	$e\left(\frac{117}{140}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{53}{140}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{37}{70}\right)$
$\chi_{8085}(13,\cdot)$	8085.gk	140	no	$-1$	$1$	$e\left(\frac{39}{140}\right)$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{117}{140}\right)$	$e\left(\frac{39}{140}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{41}{140}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{12}{35}\right)$
$\chi_{8085}(16,\cdot)$	8085.ge	105	no	$1$	$1$	$e\left(\frac{82}{105}\right)$	$e\left(\frac{59}{105}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{13}{105}\right)$	$e\left(\frac{53}{105}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{94}{105}\right)$	$e\left(\frac{13}{35}\right)$
$\chi_{8085}(17,\cdot)$	8085.hc	420	yes	$1$	$1$	$e\left(\frac{53}{420}\right)$	$e\left(\frac{53}{210}\right)$	$e\left(\frac{53}{140}\right)$	$e\left(\frac{41}{140}\right)$	$e\left(\frac{53}{105}\right)$	$e\left(\frac{307}{420}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{44}{105}\right)$	$e\left(\frac{1}{70}\right)$
$\chi_{8085}(19,\cdot)$	8085.eg	30	no	$1$	$1$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{8085}(23,\cdot)$	8085.ga	84	no	$1$	$1$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{2}{7}\right)$
$\chi_{8085}(26,\cdot)$	8085.gu	210	no	$1$	$1$	$e\left(\frac{47}{210}\right)$	$e\left(\frac{47}{105}\right)$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{94}{105}\right)$	$e\left(\frac{44}{105}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{82}{105}\right)$	$e\left(\frac{13}{70}\right)$
$\chi_{8085}(29,\cdot)$	8085.fm	70	yes	$1$	$1$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{4}{35}\right)$
$\chi_{8085}(31,\cdot)$	8085.ef	30	no	$-1$	$1$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{8085}(32,\cdot)$	8085.fw	84	yes	$-1$	$1$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{3}{14}\right)$
$\chi_{8085}(34,\cdot)$	8085.cu	14	no	$-1$	$1$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{6}{7}\right)$	$-1$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{6}{7}\right)$
$\chi_{8085}(37,\cdot)$	8085.hd	420	no	$-1$	$1$	$e\left(\frac{109}{420}\right)$	$e\left(\frac{109}{210}\right)$	$e\left(\frac{109}{140}\right)$	$e\left(\frac{13}{140}\right)$	$e\left(\frac{4}{105}\right)$	$e\left(\frac{41}{420}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{37}{105}\right)$	$e\left(\frac{43}{70}\right)$
$\chi_{8085}(38,\cdot)$	8085.hg	420	yes	$-1$	$1$	$e\left(\frac{173}{420}\right)$	$e\left(\frac{173}{210}\right)$	$e\left(\frac{33}{140}\right)$	$e\left(\frac{81}{140}\right)$	$e\left(\frac{68}{105}\right)$	$e\left(\frac{67}{420}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{104}{105}\right)$	$e\left(\frac{33}{35}\right)$
$\chi_{8085}(41,\cdot)$	8085.ft	70	no	$-1$	$1$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{1}{35}\right)$
$\chi_{8085}(43,\cdot)$	8085.dr	28	no	$1$	$1$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{23}{28}\right)$	$1$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{4}{7}\right)$
$\chi_{8085}(46,\cdot)$	8085.gw	210	no	$-1$	$1$	$e\left(\frac{151}{210}\right)$	$e\left(\frac{46}{105}\right)$	$e\left(\frac{11}{70}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{92}{105}\right)$	$e\left(\frac{209}{210}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{11}{105}\right)$	$e\left(\frac{9}{70}\right)$
$\chi_{8085}(47,\cdot)$	8085.hg	420	yes	$-1$	$1$	$e\left(\frac{271}{420}\right)$	$e\left(\frac{61}{210}\right)$	$e\left(\frac{131}{140}\right)$	$e\left(\frac{67}{140}\right)$	$e\left(\frac{61}{105}\right)$	$e\left(\frac{389}{420}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{13}{105}\right)$	$e\left(\frac{26}{35}\right)$
$\chi_{8085}(52,\cdot)$	8085.he	420	no	$-1$	$1$	$e\left(\frac{71}{420}\right)$	$e\left(\frac{71}{210}\right)$	$e\left(\frac{71}{140}\right)$	$e\left(\frac{117}{140}\right)$	$e\left(\frac{71}{105}\right)$	$e\left(\frac{229}{420}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{1}{210}\right)$	$e\left(\frac{1}{35}\right)$
$\chi_{8085}(53,\cdot)$	8085.hf	420	yes	$1$	$1$	$e\left(\frac{17}{420}\right)$	$e\left(\frac{17}{210}\right)$	$e\left(\frac{17}{140}\right)$	$e\left(\frac{99}{140}\right)$	$e\left(\frac{17}{105}\right)$	$e\left(\frac{253}{420}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{157}{210}\right)$	$e\left(\frac{17}{35}\right)$
$\chi_{8085}(58,\cdot)$	8085.hd	420	no	$-1$	$1$	$e\left(\frac{331}{420}\right)$	$e\left(\frac{121}{210}\right)$	$e\left(\frac{51}{140}\right)$	$e\left(\frac{87}{140}\right)$	$e\left(\frac{16}{105}\right)$	$e\left(\frac{59}{420}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{43}{105}\right)$	$e\left(\frac{67}{70}\right)$
$\chi_{8085}(59,\cdot)$	8085.gs	210	yes	$1$	$1$	$e\left(\frac{26}{105}\right)$	$e\left(\frac{52}{105}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{104}{105}\right)$	$e\left(\frac{113}{210}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{17}{105}\right)$	$e\left(\frac{33}{70}\right)$
$\chi_{8085}(61,\cdot)$	8085.gz	210	no	$1$	$1$	$e\left(\frac{149}{210}\right)$	$e\left(\frac{44}{105}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{88}{105}\right)$	$e\left(\frac{68}{105}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{53}{210}\right)$	$e\left(\frac{1}{70}\right)$
$\chi_{8085}(62,\cdot)$	8085.gm	140	yes	$1$	$1$	$e\left(\frac{123}{140}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{89}{140}\right)$	$e\left(\frac{53}{140}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{97}{140}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{3}{70}\right)$
$\chi_{8085}(64,\cdot)$	8085.fh	70	no	$1$	$1$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{2}{35}\right)$
$\chi_{8085}(67,\cdot)$	8085.cj	12	no	$-1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$-i$	$-i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{3}\right)$	$-1$
$\chi_{8085}(68,\cdot)$	8085.fb	60	no	$1$	$1$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{8085}(71,\cdot)$	8085.fl	70	no	$-1$	$1$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{41}{70}\right)$
$\chi_{8085}(73,\cdot)$	8085.he	420	no	$-1$	$1$	$e\left(\frac{149}{420}\right)$	$e\left(\frac{149}{210}\right)$	$e\left(\frac{9}{140}\right)$	$e\left(\frac{3}{140}\right)$	$e\left(\frac{44}{105}\right)$	$e\left(\frac{31}{420}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{79}{210}\right)$	$e\left(\frac{9}{35}\right)$
$\chi_{8085}(74,\cdot)$	8085.ha	210	yes	$1$	$1$	$e\left(\frac{43}{210}\right)$	$e\left(\frac{43}{105}\right)$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{86}{105}\right)$	$e\left(\frac{47}{210}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{121}{210}\right)$	$e\left(\frac{16}{35}\right)$

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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	$8085$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{420}\)
Order	$3360$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(8\)	\(13\)	\(16\)	\(17\)	\(19\)	\(23\)	\(26\)	\(29\)
\(\chi_{8085}(1,\cdot)\)	8085.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{8085}(2,\cdot)\)	8085.hj	420	yes	\(-1\)	\(1\)	\(e\left(\frac{397}{420}\right)\)	\(e\left(\frac{187}{210}\right)\)	\(e\left(\frac{117}{140}\right)\)	\(e\left(\frac{39}{140}\right)\)	\(e\left(\frac{82}{105}\right)\)	\(e\left(\frac{53}{420}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{47}{210}\right)\)	\(e\left(\frac{59}{70}\right)\)
\(\chi_{8085}(4,\cdot)\)	8085.gx	210	no	\(1\)	\(1\)	\(e\left(\frac{187}{210}\right)\)	\(e\left(\frac{82}{105}\right)\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{59}{105}\right)\)	\(e\left(\frac{53}{210}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{47}{105}\right)\)	\(e\left(\frac{24}{35}\right)\)
\(\chi_{8085}(8,\cdot)\)	8085.gf	140	yes	\(-1\)	\(1\)	\(e\left(\frac{117}{140}\right)\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{71}{140}\right)\)	\(e\left(\frac{117}{140}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{53}{140}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{37}{70}\right)\)
\(\chi_{8085}(13,\cdot)\)	8085.gk	140	no	\(-1\)	\(1\)	\(e\left(\frac{39}{140}\right)\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{117}{140}\right)\)	\(e\left(\frac{39}{140}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{41}{140}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{12}{35}\right)\)
\(\chi_{8085}(16,\cdot)\)	8085.ge	105	no	\(1\)	\(1\)	\(e\left(\frac{82}{105}\right)\)	\(e\left(\frac{59}{105}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{13}{105}\right)\)	\(e\left(\frac{53}{105}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{94}{105}\right)\)	\(e\left(\frac{13}{35}\right)\)
\(\chi_{8085}(17,\cdot)\)	8085.hc	420	yes	\(1\)	\(1\)	\(e\left(\frac{53}{420}\right)\)	\(e\left(\frac{53}{210}\right)\)	\(e\left(\frac{53}{140}\right)\)	\(e\left(\frac{41}{140}\right)\)	\(e\left(\frac{53}{105}\right)\)	\(e\left(\frac{307}{420}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{44}{105}\right)\)	\(e\left(\frac{1}{70}\right)\)
\(\chi_{8085}(19,\cdot)\)	8085.eg	30	no	\(1\)	\(1\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{8085}(23,\cdot)\)	8085.ga	84	no	\(1\)	\(1\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{2}{7}\right)\)
\(\chi_{8085}(26,\cdot)\)	8085.gu	210	no	\(1\)	\(1\)	\(e\left(\frac{47}{210}\right)\)	\(e\left(\frac{47}{105}\right)\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{94}{105}\right)\)	\(e\left(\frac{44}{105}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{82}{105}\right)\)	\(e\left(\frac{13}{70}\right)\)
\(\chi_{8085}(29,\cdot)\)	8085.fm	70	yes	\(1\)	\(1\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{4}{35}\right)\)
\(\chi_{8085}(31,\cdot)\)	8085.ef	30	no	\(-1\)	\(1\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{8085}(32,\cdot)\)	8085.fw	84	yes	\(-1\)	\(1\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{3}{14}\right)\)
\(\chi_{8085}(34,\cdot)\)	8085.cu	14	no	\(-1\)	\(1\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(-1\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)
\(\chi_{8085}(37,\cdot)\)	8085.hd	420	no	\(-1\)	\(1\)	\(e\left(\frac{109}{420}\right)\)	\(e\left(\frac{109}{210}\right)\)	\(e\left(\frac{109}{140}\right)\)	\(e\left(\frac{13}{140}\right)\)	\(e\left(\frac{4}{105}\right)\)	\(e\left(\frac{41}{420}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{37}{105}\right)\)	\(e\left(\frac{43}{70}\right)\)
\(\chi_{8085}(38,\cdot)\)	8085.hg	420	yes	\(-1\)	\(1\)	\(e\left(\frac{173}{420}\right)\)	\(e\left(\frac{173}{210}\right)\)	\(e\left(\frac{33}{140}\right)\)	\(e\left(\frac{81}{140}\right)\)	\(e\left(\frac{68}{105}\right)\)	\(e\left(\frac{67}{420}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{104}{105}\right)\)	\(e\left(\frac{33}{35}\right)\)
\(\chi_{8085}(41,\cdot)\)	8085.ft	70	no	\(-1\)	\(1\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{1}{35}\right)\)
\(\chi_{8085}(43,\cdot)\)	8085.dr	28	no	\(1\)	\(1\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(1\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)
\(\chi_{8085}(46,\cdot)\)	8085.gw	210	no	\(-1\)	\(1\)	\(e\left(\frac{151}{210}\right)\)	\(e\left(\frac{46}{105}\right)\)	\(e\left(\frac{11}{70}\right)\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{92}{105}\right)\)	\(e\left(\frac{209}{210}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{11}{105}\right)\)	\(e\left(\frac{9}{70}\right)\)
\(\chi_{8085}(47,\cdot)\)	8085.hg	420	yes	\(-1\)	\(1\)	\(e\left(\frac{271}{420}\right)\)	\(e\left(\frac{61}{210}\right)\)	\(e\left(\frac{131}{140}\right)\)	\(e\left(\frac{67}{140}\right)\)	\(e\left(\frac{61}{105}\right)\)	\(e\left(\frac{389}{420}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{13}{105}\right)\)	\(e\left(\frac{26}{35}\right)\)
\(\chi_{8085}(52,\cdot)\)	8085.he	420	no	\(-1\)	\(1\)	\(e\left(\frac{71}{420}\right)\)	\(e\left(\frac{71}{210}\right)\)	\(e\left(\frac{71}{140}\right)\)	\(e\left(\frac{117}{140}\right)\)	\(e\left(\frac{71}{105}\right)\)	\(e\left(\frac{229}{420}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{1}{210}\right)\)	\(e\left(\frac{1}{35}\right)\)
\(\chi_{8085}(53,\cdot)\)	8085.hf	420	yes	\(1\)	\(1\)	\(e\left(\frac{17}{420}\right)\)	\(e\left(\frac{17}{210}\right)\)	\(e\left(\frac{17}{140}\right)\)	\(e\left(\frac{99}{140}\right)\)	\(e\left(\frac{17}{105}\right)\)	\(e\left(\frac{253}{420}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{157}{210}\right)\)	\(e\left(\frac{17}{35}\right)\)
\(\chi_{8085}(58,\cdot)\)	8085.hd	420	no	\(-1\)	\(1\)	\(e\left(\frac{331}{420}\right)\)	\(e\left(\frac{121}{210}\right)\)	\(e\left(\frac{51}{140}\right)\)	\(e\left(\frac{87}{140}\right)\)	\(e\left(\frac{16}{105}\right)\)	\(e\left(\frac{59}{420}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{43}{105}\right)\)	\(e\left(\frac{67}{70}\right)\)
\(\chi_{8085}(59,\cdot)\)	8085.gs	210	yes	\(1\)	\(1\)	\(e\left(\frac{26}{105}\right)\)	\(e\left(\frac{52}{105}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{104}{105}\right)\)	\(e\left(\frac{113}{210}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{17}{105}\right)\)	\(e\left(\frac{33}{70}\right)\)
\(\chi_{8085}(61,\cdot)\)	8085.gz	210	no	\(1\)	\(1\)	\(e\left(\frac{149}{210}\right)\)	\(e\left(\frac{44}{105}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{88}{105}\right)\)	\(e\left(\frac{68}{105}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{53}{210}\right)\)	\(e\left(\frac{1}{70}\right)\)
\(\chi_{8085}(62,\cdot)\)	8085.gm	140	yes	\(1\)	\(1\)	\(e\left(\frac{123}{140}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{89}{140}\right)\)	\(e\left(\frac{53}{140}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{97}{140}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{3}{70}\right)\)
\(\chi_{8085}(64,\cdot)\)	8085.fh	70	no	\(1\)	\(1\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{2}{35}\right)\)
\(\chi_{8085}(67,\cdot)\)	8085.cj	12	no	\(-1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-i\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)
\(\chi_{8085}(68,\cdot)\)	8085.fb	60	no	\(1\)	\(1\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{8085}(71,\cdot)\)	8085.fl	70	no	\(-1\)	\(1\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{41}{70}\right)\)
\(\chi_{8085}(73,\cdot)\)	8085.he	420	no	\(-1\)	\(1\)	\(e\left(\frac{149}{420}\right)\)	\(e\left(\frac{149}{210}\right)\)	\(e\left(\frac{9}{140}\right)\)	\(e\left(\frac{3}{140}\right)\)	\(e\left(\frac{44}{105}\right)\)	\(e\left(\frac{31}{420}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{79}{210}\right)\)	\(e\left(\frac{9}{35}\right)\)
\(\chi_{8085}(74,\cdot)\)	8085.ha	210	yes	\(1\)	\(1\)	\(e\left(\frac{43}{210}\right)\)	\(e\left(\frac{43}{105}\right)\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{86}{105}\right)\)	\(e\left(\frac{47}{210}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{121}{210}\right)\)	\(e\left(\frac{16}{35}\right)\)

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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.