LMFDB - Group of Dirichlet characters of modulus 810

Show commands: PariGP / SageMath

sage: H = DirichletGroup(810)

pari: g = idealstar(,810,2)

Character group

sage: G.order() pari: g.no
Order	=	216
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{108}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{810}(731,\cdot)$, $\chi_{810}(487,\cdot)$

First 32 of 216 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	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{810}(1,\cdot)$	810.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{810}(7,\cdot)$	810.x	108	no	$-1$	$1$	$e\left(\frac{107}{108}\right)$	$e\left(\frac{23}{27}\right)$	$e\left(\frac{13}{108}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{108}\right)$	$e\left(\frac{25}{54}\right)$	$e\left(\frac{25}{27}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{19}{27}\right)$
$\chi_{810}(11,\cdot)$	810.u	54	no	$-1$	$1$	$e\left(\frac{23}{27}\right)$	$e\left(\frac{7}{54}\right)$	$e\left(\frac{25}{27}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{35}{54}\right)$	$e\left(\frac{49}{54}\right)$	$e\left(\frac{22}{27}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{41}{54}\right)$
$\chi_{810}(13,\cdot)$	810.x	108	no	$-1$	$1$	$e\left(\frac{13}{108}\right)$	$e\left(\frac{25}{27}\right)$	$e\left(\frac{47}{108}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{95}{108}\right)$	$e\left(\frac{53}{54}\right)$	$e\left(\frac{26}{27}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{23}{27}\right)$
$\chi_{810}(17,\cdot)$	810.s	36	no	$1$	$1$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{18}\right)$
$\chi_{810}(19,\cdot)$	810.p	18	no	$1$	$1$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{9}\right)$
$\chi_{810}(23,\cdot)$	810.w	108	no	$1$	$1$	$e\left(\frac{1}{108}\right)$	$e\left(\frac{35}{54}\right)$	$e\left(\frac{95}{108}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{53}{108}\right)$	$e\left(\frac{1}{27}\right)$	$e\left(\frac{2}{27}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{43}{54}\right)$
$\chi_{810}(29,\cdot)$	810.t	54	no	$-1$	$1$	$e\left(\frac{25}{54}\right)$	$e\left(\frac{49}{54}\right)$	$e\left(\frac{53}{54}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{27}\right)$	$e\left(\frac{19}{54}\right)$	$e\left(\frac{19}{27}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{17}{54}\right)$
$\chi_{810}(31,\cdot)$	810.q	27	no	$1$	$1$	$e\left(\frac{25}{27}\right)$	$e\left(\frac{22}{27}\right)$	$e\left(\frac{26}{27}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{2}{27}\right)$	$e\left(\frac{19}{27}\right)$	$e\left(\frac{11}{27}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{17}{27}\right)$
$\chi_{810}(37,\cdot)$	810.r	36	no	$-1$	$1$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{2}{9}\right)$
$\chi_{810}(41,\cdot)$	810.u	54	no	$-1$	$1$	$e\left(\frac{19}{27}\right)$	$e\left(\frac{41}{54}\right)$	$e\left(\frac{23}{27}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{43}{54}\right)$	$e\left(\frac{17}{54}\right)$	$e\left(\frac{17}{27}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{54}\right)$
$\chi_{810}(43,\cdot)$	810.x	108	no	$-1$	$1$	$e\left(\frac{29}{108}\right)$	$e\left(\frac{8}{27}\right)$	$e\left(\frac{55}{108}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{79}{108}\right)$	$e\left(\frac{31}{54}\right)$	$e\left(\frac{4}{27}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{16}{27}\right)$
$\chi_{810}(47,\cdot)$	810.w	108	no	$1$	$1$	$e\left(\frac{35}{108}\right)$	$e\left(\frac{37}{54}\right)$	$e\left(\frac{85}{108}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{19}{108}\right)$	$e\left(\frac{8}{27}\right)$	$e\left(\frac{16}{27}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{47}{54}\right)$
$\chi_{810}(49,\cdot)$	810.v	54	no	$1$	$1$	$e\left(\frac{53}{54}\right)$	$e\left(\frac{19}{27}\right)$	$e\left(\frac{13}{54}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{54}\right)$	$e\left(\frac{25}{27}\right)$	$e\left(\frac{23}{27}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{11}{27}\right)$
$\chi_{810}(53,\cdot)$	810.m	12	no	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{12}\right)$	$i$	$-1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-i$	$e\left(\frac{1}{6}\right)$
$\chi_{810}(59,\cdot)$	810.t	54	no	$-1$	$1$	$e\left(\frac{35}{54}\right)$	$e\left(\frac{47}{54}\right)$	$e\left(\frac{31}{54}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{23}{27}\right)$	$e\left(\frac{5}{54}\right)$	$e\left(\frac{5}{27}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{13}{54}\right)$
$\chi_{810}(61,\cdot)$	810.q	27	no	$1$	$1$	$e\left(\frac{11}{27}\right)$	$e\left(\frac{14}{27}\right)$	$e\left(\frac{19}{27}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{16}{27}\right)$	$e\left(\frac{17}{27}\right)$	$e\left(\frac{7}{27}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{27}\right)$
$\chi_{810}(67,\cdot)$	810.x	108	no	$-1$	$1$	$e\left(\frac{31}{108}\right)$	$e\left(\frac{16}{27}\right)$	$e\left(\frac{29}{108}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{77}{108}\right)$	$e\left(\frac{35}{54}\right)$	$e\left(\frac{8}{27}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{5}{27}\right)$
$\chi_{810}(71,\cdot)$	810.o	18	no	$-1$	$1$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{18}\right)$
$\chi_{810}(73,\cdot)$	810.r	36	no	$-1$	$1$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{4}{9}\right)$
$\chi_{810}(77,\cdot)$	810.w	108	no	$1$	$1$	$e\left(\frac{91}{108}\right)$	$e\left(\frac{53}{54}\right)$	$e\left(\frac{5}{108}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{71}{108}\right)$	$e\left(\frac{10}{27}\right)$	$e\left(\frac{20}{27}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{25}{54}\right)$
$\chi_{810}(79,\cdot)$	810.v	54	no	$1$	$1$	$e\left(\frac{43}{54}\right)$	$e\left(\frac{20}{27}\right)$	$e\left(\frac{35}{54}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{11}{54}\right)$	$e\left(\frac{5}{27}\right)$	$e\left(\frac{10}{27}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{13}{27}\right)$
$\chi_{810}(83,\cdot)$	810.w	108	no	$1$	$1$	$e\left(\frac{5}{108}\right)$	$e\left(\frac{13}{54}\right)$	$e\left(\frac{43}{108}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{49}{108}\right)$	$e\left(\frac{5}{27}\right)$	$e\left(\frac{10}{27}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{53}{54}\right)$
$\chi_{810}(89,\cdot)$	810.n	18	no	$-1$	$1$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{17}{18}\right)$
$\chi_{810}(91,\cdot)$	810.k	9	no	$1$	$1$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{9}\right)$
$\chi_{810}(97,\cdot)$	810.x	108	no	$-1$	$1$	$e\left(\frac{47}{108}\right)$	$e\left(\frac{26}{27}\right)$	$e\left(\frac{37}{108}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{61}{108}\right)$	$e\left(\frac{13}{54}\right)$	$e\left(\frac{13}{27}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{25}{27}\right)$
$\chi_{810}(101,\cdot)$	810.u	54	no	$-1$	$1$	$e\left(\frac{11}{27}\right)$	$e\left(\frac{1}{54}\right)$	$e\left(\frac{19}{27}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{5}{54}\right)$	$e\left(\frac{7}{54}\right)$	$e\left(\frac{7}{27}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{29}{54}\right)$
$\chi_{810}(103,\cdot)$	810.x	108	no	$-1$	$1$	$e\left(\frac{97}{108}\right)$	$e\left(\frac{10}{27}\right)$	$e\left(\frac{35}{108}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{11}{108}\right)$	$e\left(\frac{5}{54}\right)$	$e\left(\frac{5}{27}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{20}{27}\right)$
$\chi_{810}(107,\cdot)$	810.m	12	no	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{12}\right)$	$-i$	$-1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$i$	$e\left(\frac{5}{6}\right)$
$\chi_{810}(109,\cdot)$	810.i	6	no	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{2}{3}\right)$
$\chi_{810}(113,\cdot)$	810.w	108	no	$1$	$1$	$e\left(\frac{25}{108}\right)$	$e\left(\frac{11}{54}\right)$	$e\left(\frac{107}{108}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{29}{108}\right)$	$e\left(\frac{25}{27}\right)$	$e\left(\frac{23}{27}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{49}{54}\right)$
$\chi_{810}(119,\cdot)$	810.t	54	no	$-1$	$1$	$e\left(\frac{1}{54}\right)$	$e\left(\frac{43}{54}\right)$	$e\left(\frac{41}{54}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{13}{27}\right)$	$e\left(\frac{31}{54}\right)$	$e\left(\frac{4}{27}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{5}{54}\right)$

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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	$810$
Structure	\(C_{2}\times C_{108}\)
Order	$216$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{810}(1,\cdot)\)	810.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{810}(7,\cdot)\)	810.x	108	no	\(-1\)	\(1\)	\(e\left(\frac{107}{108}\right)\)	\(e\left(\frac{23}{27}\right)\)	\(e\left(\frac{13}{108}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{1}{108}\right)\)	\(e\left(\frac{25}{54}\right)\)	\(e\left(\frac{25}{27}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{19}{27}\right)\)
\(\chi_{810}(11,\cdot)\)	810.u	54	no	\(-1\)	\(1\)	\(e\left(\frac{23}{27}\right)\)	\(e\left(\frac{7}{54}\right)\)	\(e\left(\frac{25}{27}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{35}{54}\right)\)	\(e\left(\frac{49}{54}\right)\)	\(e\left(\frac{22}{27}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{41}{54}\right)\)
\(\chi_{810}(13,\cdot)\)	810.x	108	no	\(-1\)	\(1\)	\(e\left(\frac{13}{108}\right)\)	\(e\left(\frac{25}{27}\right)\)	\(e\left(\frac{47}{108}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{95}{108}\right)\)	\(e\left(\frac{53}{54}\right)\)	\(e\left(\frac{26}{27}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{23}{27}\right)\)
\(\chi_{810}(17,\cdot)\)	810.s	36	no	\(1\)	\(1\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{18}\right)\)
\(\chi_{810}(19,\cdot)\)	810.p	18	no	\(1\)	\(1\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{9}\right)\)
\(\chi_{810}(23,\cdot)\)	810.w	108	no	\(1\)	\(1\)	\(e\left(\frac{1}{108}\right)\)	\(e\left(\frac{35}{54}\right)\)	\(e\left(\frac{95}{108}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{53}{108}\right)\)	\(e\left(\frac{1}{27}\right)\)	\(e\left(\frac{2}{27}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{43}{54}\right)\)
\(\chi_{810}(29,\cdot)\)	810.t	54	no	\(-1\)	\(1\)	\(e\left(\frac{25}{54}\right)\)	\(e\left(\frac{49}{54}\right)\)	\(e\left(\frac{53}{54}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{27}\right)\)	\(e\left(\frac{19}{54}\right)\)	\(e\left(\frac{19}{27}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{17}{54}\right)\)
\(\chi_{810}(31,\cdot)\)	810.q	27	no	\(1\)	\(1\)	\(e\left(\frac{25}{27}\right)\)	\(e\left(\frac{22}{27}\right)\)	\(e\left(\frac{26}{27}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{2}{27}\right)\)	\(e\left(\frac{19}{27}\right)\)	\(e\left(\frac{11}{27}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{17}{27}\right)\)
\(\chi_{810}(37,\cdot)\)	810.r	36	no	\(-1\)	\(1\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{2}{9}\right)\)
\(\chi_{810}(41,\cdot)\)	810.u	54	no	\(-1\)	\(1\)	\(e\left(\frac{19}{27}\right)\)	\(e\left(\frac{41}{54}\right)\)	\(e\left(\frac{23}{27}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{43}{54}\right)\)	\(e\left(\frac{17}{54}\right)\)	\(e\left(\frac{17}{27}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{54}\right)\)
\(\chi_{810}(43,\cdot)\)	810.x	108	no	\(-1\)	\(1\)	\(e\left(\frac{29}{108}\right)\)	\(e\left(\frac{8}{27}\right)\)	\(e\left(\frac{55}{108}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{79}{108}\right)\)	\(e\left(\frac{31}{54}\right)\)	\(e\left(\frac{4}{27}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{16}{27}\right)\)
\(\chi_{810}(47,\cdot)\)	810.w	108	no	\(1\)	\(1\)	\(e\left(\frac{35}{108}\right)\)	\(e\left(\frac{37}{54}\right)\)	\(e\left(\frac{85}{108}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{19}{108}\right)\)	\(e\left(\frac{8}{27}\right)\)	\(e\left(\frac{16}{27}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{47}{54}\right)\)
\(\chi_{810}(49,\cdot)\)	810.v	54	no	\(1\)	\(1\)	\(e\left(\frac{53}{54}\right)\)	\(e\left(\frac{19}{27}\right)\)	\(e\left(\frac{13}{54}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{1}{54}\right)\)	\(e\left(\frac{25}{27}\right)\)	\(e\left(\frac{23}{27}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{11}{27}\right)\)
\(\chi_{810}(53,\cdot)\)	810.m	12	no	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-i\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{810}(59,\cdot)\)	810.t	54	no	\(-1\)	\(1\)	\(e\left(\frac{35}{54}\right)\)	\(e\left(\frac{47}{54}\right)\)	\(e\left(\frac{31}{54}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{23}{27}\right)\)	\(e\left(\frac{5}{54}\right)\)	\(e\left(\frac{5}{27}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{13}{54}\right)\)
\(\chi_{810}(61,\cdot)\)	810.q	27	no	\(1\)	\(1\)	\(e\left(\frac{11}{27}\right)\)	\(e\left(\frac{14}{27}\right)\)	\(e\left(\frac{19}{27}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{16}{27}\right)\)	\(e\left(\frac{17}{27}\right)\)	\(e\left(\frac{7}{27}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{1}{27}\right)\)
\(\chi_{810}(67,\cdot)\)	810.x	108	no	\(-1\)	\(1\)	\(e\left(\frac{31}{108}\right)\)	\(e\left(\frac{16}{27}\right)\)	\(e\left(\frac{29}{108}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{77}{108}\right)\)	\(e\left(\frac{35}{54}\right)\)	\(e\left(\frac{8}{27}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{5}{27}\right)\)
\(\chi_{810}(71,\cdot)\)	810.o	18	no	\(-1\)	\(1\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{18}\right)\)
\(\chi_{810}(73,\cdot)\)	810.r	36	no	\(-1\)	\(1\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{4}{9}\right)\)
\(\chi_{810}(77,\cdot)\)	810.w	108	no	\(1\)	\(1\)	\(e\left(\frac{91}{108}\right)\)	\(e\left(\frac{53}{54}\right)\)	\(e\left(\frac{5}{108}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{71}{108}\right)\)	\(e\left(\frac{10}{27}\right)\)	\(e\left(\frac{20}{27}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{25}{54}\right)\)
\(\chi_{810}(79,\cdot)\)	810.v	54	no	\(1\)	\(1\)	\(e\left(\frac{43}{54}\right)\)	\(e\left(\frac{20}{27}\right)\)	\(e\left(\frac{35}{54}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{11}{54}\right)\)	\(e\left(\frac{5}{27}\right)\)	\(e\left(\frac{10}{27}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{13}{27}\right)\)
\(\chi_{810}(83,\cdot)\)	810.w	108	no	\(1\)	\(1\)	\(e\left(\frac{5}{108}\right)\)	\(e\left(\frac{13}{54}\right)\)	\(e\left(\frac{43}{108}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{49}{108}\right)\)	\(e\left(\frac{5}{27}\right)\)	\(e\left(\frac{10}{27}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{53}{54}\right)\)
\(\chi_{810}(89,\cdot)\)	810.n	18	no	\(-1\)	\(1\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{17}{18}\right)\)
\(\chi_{810}(91,\cdot)\)	810.k	9	no	\(1\)	\(1\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{9}\right)\)
\(\chi_{810}(97,\cdot)\)	810.x	108	no	\(-1\)	\(1\)	\(e\left(\frac{47}{108}\right)\)	\(e\left(\frac{26}{27}\right)\)	\(e\left(\frac{37}{108}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{61}{108}\right)\)	\(e\left(\frac{13}{54}\right)\)	\(e\left(\frac{13}{27}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{25}{27}\right)\)
\(\chi_{810}(101,\cdot)\)	810.u	54	no	\(-1\)	\(1\)	\(e\left(\frac{11}{27}\right)\)	\(e\left(\frac{1}{54}\right)\)	\(e\left(\frac{19}{27}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{5}{54}\right)\)	\(e\left(\frac{7}{54}\right)\)	\(e\left(\frac{7}{27}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{29}{54}\right)\)
\(\chi_{810}(103,\cdot)\)	810.x	108	no	\(-1\)	\(1\)	\(e\left(\frac{97}{108}\right)\)	\(e\left(\frac{10}{27}\right)\)	\(e\left(\frac{35}{108}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{11}{108}\right)\)	\(e\left(\frac{5}{54}\right)\)	\(e\left(\frac{5}{27}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{20}{27}\right)\)
\(\chi_{810}(107,\cdot)\)	810.m	12	no	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(i\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{810}(109,\cdot)\)	810.i	6	no	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{810}(113,\cdot)\)	810.w	108	no	\(1\)	\(1\)	\(e\left(\frac{25}{108}\right)\)	\(e\left(\frac{11}{54}\right)\)	\(e\left(\frac{107}{108}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{29}{108}\right)\)	\(e\left(\frac{25}{27}\right)\)	\(e\left(\frac{23}{27}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{49}{54}\right)\)
\(\chi_{810}(119,\cdot)\)	810.t	54	no	\(-1\)	\(1\)	\(e\left(\frac{1}{54}\right)\)	\(e\left(\frac{43}{54}\right)\)	\(e\left(\frac{41}{54}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{13}{27}\right)\)	\(e\left(\frac{31}{54}\right)\)	\(e\left(\frac{4}{27}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{5}{54}\right)\)

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L-functions

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First 32 of 216 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.