LMFDB - Group of Dirichlet characters of modulus 1296

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1296)

pari: g = idealstar(,1296,2)

Character group

sage: G.order() pari: g.no
Order	=	432
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{108}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{1296}(1135,\cdot)$, $\chi_{1296}(325,\cdot)$, $\chi_{1296}(1217,\cdot)$

First 32 of 432 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	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$
$\chi_{1296}(1,\cdot)$	1296.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1296}(5,\cdot)$	1296.bu	108	yes	$-1$	$1$	$e\left(\frac{5}{108}\right)$	$e\left(\frac{17}{54}\right)$	$e\left(\frac{85}{108}\right)$	$e\left(\frac{17}{108}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{5}{27}\right)$	$e\left(\frac{5}{54}\right)$	$e\left(\frac{55}{108}\right)$	$e\left(\frac{14}{27}\right)$
$\chi_{1296}(7,\cdot)$	1296.br	54	no	$-1$	$1$	$e\left(\frac{17}{54}\right)$	$e\left(\frac{13}{54}\right)$	$e\left(\frac{23}{27}\right)$	$e\left(\frac{47}{54}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{41}{54}\right)$	$e\left(\frac{17}{27}\right)$	$e\left(\frac{25}{54}\right)$	$e\left(\frac{23}{54}\right)$
$\chi_{1296}(11,\cdot)$	1296.bs	108	yes	$1$	$1$	$e\left(\frac{85}{108}\right)$	$e\left(\frac{23}{27}\right)$	$e\left(\frac{95}{108}\right)$	$e\left(\frac{73}{108}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{35}{54}\right)$	$e\left(\frac{31}{54}\right)$	$e\left(\frac{71}{108}\right)$	$e\left(\frac{17}{54}\right)$
$\chi_{1296}(13,\cdot)$	1296.bv	108	yes	$1$	$1$	$e\left(\frac{17}{108}\right)$	$e\left(\frac{47}{54}\right)$	$e\left(\frac{73}{108}\right)$	$e\left(\frac{47}{108}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{7}{54}\right)$	$e\left(\frac{17}{54}\right)$	$e\left(\frac{79}{108}\right)$	$e\left(\frac{26}{27}\right)$
$\chi_{1296}(17,\cdot)$	1296.bc	18	no	$-1$	$1$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{2}{9}\right)$
$\chi_{1296}(19,\cdot)$	1296.bi	36	no	$-1$	$1$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{5}{18}\right)$
$\chi_{1296}(23,\cdot)$	1296.bn	54	no	$1$	$1$	$e\left(\frac{5}{27}\right)$	$e\left(\frac{41}{54}\right)$	$e\left(\frac{35}{54}\right)$	$e\left(\frac{7}{54}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{20}{27}\right)$	$e\left(\frac{10}{27}\right)$	$e\left(\frac{1}{27}\right)$	$e\left(\frac{31}{54}\right)$
$\chi_{1296}(25,\cdot)$	1296.bp	54	no	$1$	$1$	$e\left(\frac{5}{54}\right)$	$e\left(\frac{17}{27}\right)$	$e\left(\frac{31}{54}\right)$	$e\left(\frac{17}{54}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{10}{27}\right)$	$e\left(\frac{5}{27}\right)$	$e\left(\frac{1}{54}\right)$	$e\left(\frac{1}{27}\right)$
$\chi_{1296}(29,\cdot)$	1296.bu	108	yes	$-1$	$1$	$e\left(\frac{55}{108}\right)$	$e\left(\frac{25}{54}\right)$	$e\left(\frac{71}{108}\right)$	$e\left(\frac{79}{108}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{1}{27}\right)$	$e\left(\frac{1}{54}\right)$	$e\left(\frac{65}{108}\right)$	$e\left(\frac{19}{27}\right)$
$\chi_{1296}(31,\cdot)$	1296.bm	54	no	$-1$	$1$	$e\left(\frac{14}{27}\right)$	$e\left(\frac{23}{54}\right)$	$e\left(\frac{17}{54}\right)$	$e\left(\frac{26}{27}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{31}{54}\right)$	$e\left(\frac{1}{27}\right)$	$e\left(\frac{19}{27}\right)$	$e\left(\frac{49}{54}\right)$
$\chi_{1296}(35,\cdot)$	1296.bk	36	no	$1$	$1$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{17}{18}\right)$
$\chi_{1296}(37,\cdot)$	1296.bh	36	no	$1$	$1$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{5}{9}\right)$
$\chi_{1296}(41,\cdot)$	1296.bl	54	no	$-1$	$1$	$e\left(\frac{2}{27}\right)$	$e\left(\frac{19}{27}\right)$	$e\left(\frac{7}{27}\right)$	$e\left(\frac{19}{54}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{43}{54}\right)$	$e\left(\frac{4}{27}\right)$	$e\left(\frac{22}{27}\right)$	$e\left(\frac{17}{27}\right)$
$\chi_{1296}(43,\cdot)$	1296.bt	108	yes	$-1$	$1$	$e\left(\frac{67}{108}\right)$	$e\left(\frac{14}{27}\right)$	$e\left(\frac{5}{108}\right)$	$e\left(\frac{1}{108}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{13}{27}\right)$	$e\left(\frac{13}{54}\right)$	$e\left(\frac{89}{108}\right)$	$e\left(\frac{35}{54}\right)$
$\chi_{1296}(47,\cdot)$	1296.bq	54	no	$1$	$1$	$e\left(\frac{53}{54}\right)$	$e\left(\frac{31}{54}\right)$	$e\left(\frac{5}{27}\right)$	$e\left(\frac{1}{27}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{25}{27}\right)$	$e\left(\frac{26}{27}\right)$	$e\left(\frac{43}{54}\right)$	$e\left(\frac{5}{54}\right)$
$\chi_{1296}(49,\cdot)$	1296.bg	27	no	$1$	$1$	$e\left(\frac{17}{27}\right)$	$e\left(\frac{13}{27}\right)$	$e\left(\frac{19}{27}\right)$	$e\left(\frac{20}{27}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{14}{27}\right)$	$e\left(\frac{7}{27}\right)$	$e\left(\frac{25}{27}\right)$	$e\left(\frac{23}{27}\right)$
$\chi_{1296}(53,\cdot)$	1296.x	12	no	$-1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{12}\right)$	$-1$	$-i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{1296}(55,\cdot)$	1296.t	6	no	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{1296}(59,\cdot)$	1296.bs	108	yes	$1$	$1$	$e\left(\frac{77}{108}\right)$	$e\left(\frac{4}{27}\right)$	$e\left(\frac{67}{108}\right)$	$e\left(\frac{89}{108}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{19}{54}\right)$	$e\left(\frac{23}{54}\right)$	$e\left(\frac{91}{108}\right)$	$e\left(\frac{37}{54}\right)$
$\chi_{1296}(61,\cdot)$	1296.bv	108	yes	$1$	$1$	$e\left(\frac{97}{108}\right)$	$e\left(\frac{49}{54}\right)$	$e\left(\frac{29}{108}\right)$	$e\left(\frac{103}{108}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{5}{54}\right)$	$e\left(\frac{43}{54}\right)$	$e\left(\frac{95}{108}\right)$	$e\left(\frac{7}{27}\right)$
$\chi_{1296}(65,\cdot)$	1296.bo	54	no	$-1$	$1$	$e\left(\frac{11}{54}\right)$	$e\left(\frac{5}{27}\right)$	$e\left(\frac{25}{54}\right)$	$e\left(\frac{16}{27}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{17}{54}\right)$	$e\left(\frac{11}{27}\right)$	$e\left(\frac{13}{54}\right)$	$e\left(\frac{13}{27}\right)$
$\chi_{1296}(67,\cdot)$	1296.bt	108	yes	$-1$	$1$	$e\left(\frac{53}{108}\right)$	$e\left(\frac{1}{27}\right)$	$e\left(\frac{91}{108}\right)$	$e\left(\frac{83}{108}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{26}{27}\right)$	$e\left(\frac{53}{54}\right)$	$e\left(\frac{43}{108}\right)$	$e\left(\frac{43}{54}\right)$
$\chi_{1296}(71,\cdot)$	1296.bd	18	no	$1$	$1$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{7}{18}\right)$
$\chi_{1296}(73,\cdot)$	1296.bb	18	no	$1$	$1$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{1}{9}\right)$
$\chi_{1296}(77,\cdot)$	1296.bu	108	yes	$-1$	$1$	$e\left(\frac{11}{108}\right)$	$e\left(\frac{5}{54}\right)$	$e\left(\frac{79}{108}\right)$	$e\left(\frac{59}{108}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{11}{27}\right)$	$e\left(\frac{11}{54}\right)$	$e\left(\frac{13}{108}\right)$	$e\left(\frac{20}{27}\right)$
$\chi_{1296}(79,\cdot)$	1296.bm	54	no	$-1$	$1$	$e\left(\frac{25}{27}\right)$	$e\left(\frac{43}{54}\right)$	$e\left(\frac{13}{54}\right)$	$e\left(\frac{4}{27}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{11}{54}\right)$	$e\left(\frac{23}{27}\right)$	$e\left(\frac{5}{27}\right)$	$e\left(\frac{47}{54}\right)$
$\chi_{1296}(83,\cdot)$	1296.bs	108	yes	$1$	$1$	$e\left(\frac{19}{108}\right)$	$e\left(\frac{8}{27}\right)$	$e\left(\frac{53}{108}\right)$	$e\left(\frac{43}{108}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{11}{54}\right)$	$e\left(\frac{19}{54}\right)$	$e\left(\frac{101}{108}\right)$	$e\left(\frac{47}{54}\right)$
$\chi_{1296}(85,\cdot)$	1296.bv	108	yes	$1$	$1$	$e\left(\frac{11}{108}\right)$	$e\left(\frac{5}{54}\right)$	$e\left(\frac{79}{108}\right)$	$e\left(\frac{5}{108}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{49}{54}\right)$	$e\left(\frac{11}{54}\right)$	$e\left(\frac{13}{108}\right)$	$e\left(\frac{20}{27}\right)$
$\chi_{1296}(89,\cdot)$	1296.bf	18	no	$-1$	$1$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{9}\right)$
$\chi_{1296}(91,\cdot)$	1296.bi	36	no	$-1$	$1$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{7}{18}\right)$
$\chi_{1296}(95,\cdot)$	1296.bq	54	no	$1$	$1$	$e\left(\frac{13}{54}\right)$	$e\left(\frac{29}{54}\right)$	$e\left(\frac{16}{27}\right)$	$e\left(\frac{14}{27}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{26}{27}\right)$	$e\left(\frac{13}{27}\right)$	$e\left(\frac{35}{54}\right)$	$e\left(\frac{43}{54}\right)$

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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	$1296$
Structure	\(C_{2}\times C_{2}\times C_{108}\)
Order	$432$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)
\(\chi_{1296}(1,\cdot)\)	1296.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1296}(5,\cdot)\)	1296.bu	108	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{108}\right)\)	\(e\left(\frac{17}{54}\right)\)	\(e\left(\frac{85}{108}\right)\)	\(e\left(\frac{17}{108}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{5}{27}\right)\)	\(e\left(\frac{5}{54}\right)\)	\(e\left(\frac{55}{108}\right)\)	\(e\left(\frac{14}{27}\right)\)
\(\chi_{1296}(7,\cdot)\)	1296.br	54	no	\(-1\)	\(1\)	\(e\left(\frac{17}{54}\right)\)	\(e\left(\frac{13}{54}\right)\)	\(e\left(\frac{23}{27}\right)\)	\(e\left(\frac{47}{54}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{41}{54}\right)\)	\(e\left(\frac{17}{27}\right)\)	\(e\left(\frac{25}{54}\right)\)	\(e\left(\frac{23}{54}\right)\)
\(\chi_{1296}(11,\cdot)\)	1296.bs	108	yes	\(1\)	\(1\)	\(e\left(\frac{85}{108}\right)\)	\(e\left(\frac{23}{27}\right)\)	\(e\left(\frac{95}{108}\right)\)	\(e\left(\frac{73}{108}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{35}{54}\right)\)	\(e\left(\frac{31}{54}\right)\)	\(e\left(\frac{71}{108}\right)\)	\(e\left(\frac{17}{54}\right)\)
\(\chi_{1296}(13,\cdot)\)	1296.bv	108	yes	\(1\)	\(1\)	\(e\left(\frac{17}{108}\right)\)	\(e\left(\frac{47}{54}\right)\)	\(e\left(\frac{73}{108}\right)\)	\(e\left(\frac{47}{108}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{7}{54}\right)\)	\(e\left(\frac{17}{54}\right)\)	\(e\left(\frac{79}{108}\right)\)	\(e\left(\frac{26}{27}\right)\)
\(\chi_{1296}(17,\cdot)\)	1296.bc	18	no	\(-1\)	\(1\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)
\(\chi_{1296}(19,\cdot)\)	1296.bi	36	no	\(-1\)	\(1\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{5}{18}\right)\)
\(\chi_{1296}(23,\cdot)\)	1296.bn	54	no	\(1\)	\(1\)	\(e\left(\frac{5}{27}\right)\)	\(e\left(\frac{41}{54}\right)\)	\(e\left(\frac{35}{54}\right)\)	\(e\left(\frac{7}{54}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{20}{27}\right)\)	\(e\left(\frac{10}{27}\right)\)	\(e\left(\frac{1}{27}\right)\)	\(e\left(\frac{31}{54}\right)\)
\(\chi_{1296}(25,\cdot)\)	1296.bp	54	no	\(1\)	\(1\)	\(e\left(\frac{5}{54}\right)\)	\(e\left(\frac{17}{27}\right)\)	\(e\left(\frac{31}{54}\right)\)	\(e\left(\frac{17}{54}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{10}{27}\right)\)	\(e\left(\frac{5}{27}\right)\)	\(e\left(\frac{1}{54}\right)\)	\(e\left(\frac{1}{27}\right)\)
\(\chi_{1296}(29,\cdot)\)	1296.bu	108	yes	\(-1\)	\(1\)	\(e\left(\frac{55}{108}\right)\)	\(e\left(\frac{25}{54}\right)\)	\(e\left(\frac{71}{108}\right)\)	\(e\left(\frac{79}{108}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{1}{27}\right)\)	\(e\left(\frac{1}{54}\right)\)	\(e\left(\frac{65}{108}\right)\)	\(e\left(\frac{19}{27}\right)\)
\(\chi_{1296}(31,\cdot)\)	1296.bm	54	no	\(-1\)	\(1\)	\(e\left(\frac{14}{27}\right)\)	\(e\left(\frac{23}{54}\right)\)	\(e\left(\frac{17}{54}\right)\)	\(e\left(\frac{26}{27}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{31}{54}\right)\)	\(e\left(\frac{1}{27}\right)\)	\(e\left(\frac{19}{27}\right)\)	\(e\left(\frac{49}{54}\right)\)
\(\chi_{1296}(35,\cdot)\)	1296.bk	36	no	\(1\)	\(1\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{17}{18}\right)\)
\(\chi_{1296}(37,\cdot)\)	1296.bh	36	no	\(1\)	\(1\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{5}{9}\right)\)
\(\chi_{1296}(41,\cdot)\)	1296.bl	54	no	\(-1\)	\(1\)	\(e\left(\frac{2}{27}\right)\)	\(e\left(\frac{19}{27}\right)\)	\(e\left(\frac{7}{27}\right)\)	\(e\left(\frac{19}{54}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{43}{54}\right)\)	\(e\left(\frac{4}{27}\right)\)	\(e\left(\frac{22}{27}\right)\)	\(e\left(\frac{17}{27}\right)\)
\(\chi_{1296}(43,\cdot)\)	1296.bt	108	yes	\(-1\)	\(1\)	\(e\left(\frac{67}{108}\right)\)	\(e\left(\frac{14}{27}\right)\)	\(e\left(\frac{5}{108}\right)\)	\(e\left(\frac{1}{108}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{13}{27}\right)\)	\(e\left(\frac{13}{54}\right)\)	\(e\left(\frac{89}{108}\right)\)	\(e\left(\frac{35}{54}\right)\)
\(\chi_{1296}(47,\cdot)\)	1296.bq	54	no	\(1\)	\(1\)	\(e\left(\frac{53}{54}\right)\)	\(e\left(\frac{31}{54}\right)\)	\(e\left(\frac{5}{27}\right)\)	\(e\left(\frac{1}{27}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{25}{27}\right)\)	\(e\left(\frac{26}{27}\right)\)	\(e\left(\frac{43}{54}\right)\)	\(e\left(\frac{5}{54}\right)\)
\(\chi_{1296}(49,\cdot)\)	1296.bg	27	no	\(1\)	\(1\)	\(e\left(\frac{17}{27}\right)\)	\(e\left(\frac{13}{27}\right)\)	\(e\left(\frac{19}{27}\right)\)	\(e\left(\frac{20}{27}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{14}{27}\right)\)	\(e\left(\frac{7}{27}\right)\)	\(e\left(\frac{25}{27}\right)\)	\(e\left(\frac{23}{27}\right)\)
\(\chi_{1296}(53,\cdot)\)	1296.x	12	no	\(-1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(-1\)	\(-i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{1296}(55,\cdot)\)	1296.t	6	no	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{1296}(59,\cdot)\)	1296.bs	108	yes	\(1\)	\(1\)	\(e\left(\frac{77}{108}\right)\)	\(e\left(\frac{4}{27}\right)\)	\(e\left(\frac{67}{108}\right)\)	\(e\left(\frac{89}{108}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{19}{54}\right)\)	\(e\left(\frac{23}{54}\right)\)	\(e\left(\frac{91}{108}\right)\)	\(e\left(\frac{37}{54}\right)\)
\(\chi_{1296}(61,\cdot)\)	1296.bv	108	yes	\(1\)	\(1\)	\(e\left(\frac{97}{108}\right)\)	\(e\left(\frac{49}{54}\right)\)	\(e\left(\frac{29}{108}\right)\)	\(e\left(\frac{103}{108}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{5}{54}\right)\)	\(e\left(\frac{43}{54}\right)\)	\(e\left(\frac{95}{108}\right)\)	\(e\left(\frac{7}{27}\right)\)
\(\chi_{1296}(65,\cdot)\)	1296.bo	54	no	\(-1\)	\(1\)	\(e\left(\frac{11}{54}\right)\)	\(e\left(\frac{5}{27}\right)\)	\(e\left(\frac{25}{54}\right)\)	\(e\left(\frac{16}{27}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{17}{54}\right)\)	\(e\left(\frac{11}{27}\right)\)	\(e\left(\frac{13}{54}\right)\)	\(e\left(\frac{13}{27}\right)\)
\(\chi_{1296}(67,\cdot)\)	1296.bt	108	yes	\(-1\)	\(1\)	\(e\left(\frac{53}{108}\right)\)	\(e\left(\frac{1}{27}\right)\)	\(e\left(\frac{91}{108}\right)\)	\(e\left(\frac{83}{108}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{26}{27}\right)\)	\(e\left(\frac{53}{54}\right)\)	\(e\left(\frac{43}{108}\right)\)	\(e\left(\frac{43}{54}\right)\)
\(\chi_{1296}(71,\cdot)\)	1296.bd	18	no	\(1\)	\(1\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{7}{18}\right)\)
\(\chi_{1296}(73,\cdot)\)	1296.bb	18	no	\(1\)	\(1\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)
\(\chi_{1296}(77,\cdot)\)	1296.bu	108	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{108}\right)\)	\(e\left(\frac{5}{54}\right)\)	\(e\left(\frac{79}{108}\right)\)	\(e\left(\frac{59}{108}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{11}{27}\right)\)	\(e\left(\frac{11}{54}\right)\)	\(e\left(\frac{13}{108}\right)\)	\(e\left(\frac{20}{27}\right)\)
\(\chi_{1296}(79,\cdot)\)	1296.bm	54	no	\(-1\)	\(1\)	\(e\left(\frac{25}{27}\right)\)	\(e\left(\frac{43}{54}\right)\)	\(e\left(\frac{13}{54}\right)\)	\(e\left(\frac{4}{27}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{11}{54}\right)\)	\(e\left(\frac{23}{27}\right)\)	\(e\left(\frac{5}{27}\right)\)	\(e\left(\frac{47}{54}\right)\)
\(\chi_{1296}(83,\cdot)\)	1296.bs	108	yes	\(1\)	\(1\)	\(e\left(\frac{19}{108}\right)\)	\(e\left(\frac{8}{27}\right)\)	\(e\left(\frac{53}{108}\right)\)	\(e\left(\frac{43}{108}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{11}{54}\right)\)	\(e\left(\frac{19}{54}\right)\)	\(e\left(\frac{101}{108}\right)\)	\(e\left(\frac{47}{54}\right)\)
\(\chi_{1296}(85,\cdot)\)	1296.bv	108	yes	\(1\)	\(1\)	\(e\left(\frac{11}{108}\right)\)	\(e\left(\frac{5}{54}\right)\)	\(e\left(\frac{79}{108}\right)\)	\(e\left(\frac{5}{108}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{49}{54}\right)\)	\(e\left(\frac{11}{54}\right)\)	\(e\left(\frac{13}{108}\right)\)	\(e\left(\frac{20}{27}\right)\)
\(\chi_{1296}(89,\cdot)\)	1296.bf	18	no	\(-1\)	\(1\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)
\(\chi_{1296}(91,\cdot)\)	1296.bi	36	no	\(-1\)	\(1\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{7}{18}\right)\)
\(\chi_{1296}(95,\cdot)\)	1296.bq	54	no	\(1\)	\(1\)	\(e\left(\frac{13}{54}\right)\)	\(e\left(\frac{29}{54}\right)\)	\(e\left(\frac{16}{27}\right)\)	\(e\left(\frac{14}{27}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{26}{27}\right)\)	\(e\left(\frac{13}{27}\right)\)	\(e\left(\frac{35}{54}\right)\)	\(e\left(\frac{43}{54}\right)\)

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L-functions

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First 32 of 432 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.