LMFDB - Group of Dirichlet characters of modulus 1944

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1944)

pari: g = idealstar(,1944,2)

Character group

sage: G.order() pari: g.no
Order	=	648
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{162}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{1944}(487,\cdot)$, $\chi_{1944}(973,\cdot)$, $\chi_{1944}(1217,\cdot)$

First 32 of 648 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	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$
$\chi_{1944}(1,\cdot)$	1944.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1944}(5,\cdot)$	1944.bn	162	yes	$-1$	$1$	$e\left(\frac{62}{81}\right)$	$e\left(\frac{76}{81}\right)$	$e\left(\frac{55}{81}\right)$	$e\left(\frac{103}{162}\right)$	$e\left(\frac{37}{54}\right)$	$e\left(\frac{35}{54}\right)$	$e\left(\frac{37}{162}\right)$	$e\left(\frac{43}{81}\right)$	$e\left(\frac{61}{81}\right)$	$e\left(\frac{68}{81}\right)$
$\chi_{1944}(7,\cdot)$	1944.bi	162	no	$-1$	$1$	$e\left(\frac{76}{81}\right)$	$e\left(\frac{121}{162}\right)$	$e\left(\frac{127}{162}\right)$	$e\left(\frac{37}{81}\right)$	$e\left(\frac{7}{27}\right)$	$e\left(\frac{49}{54}\right)$	$e\left(\frac{95}{162}\right)$	$e\left(\frac{71}{81}\right)$	$e\left(\frac{80}{81}\right)$	$e\left(\frac{23}{162}\right)$
$\chi_{1944}(11,\cdot)$	1944.bl	162	yes	$1$	$1$	$e\left(\frac{55}{81}\right)$	$e\left(\frac{127}{162}\right)$	$e\left(\frac{61}{162}\right)$	$e\left(\frac{77}{162}\right)$	$e\left(\frac{35}{54}\right)$	$e\left(\frac{14}{27}\right)$	$e\left(\frac{4}{81}\right)$	$e\left(\frac{29}{81}\right)$	$e\left(\frac{11}{81}\right)$	$e\left(\frac{71}{162}\right)$
$\chi_{1944}(13,\cdot)$	1944.bj	162	yes	$1$	$1$	$e\left(\frac{103}{162}\right)$	$e\left(\frac{37}{81}\right)$	$e\left(\frac{77}{162}\right)$	$e\left(\frac{145}{162}\right)$	$e\left(\frac{17}{27}\right)$	$e\left(\frac{11}{54}\right)$	$e\left(\frac{17}{81}\right)$	$e\left(\frac{22}{81}\right)$	$e\left(\frac{53}{162}\right)$	$e\left(\frac{80}{81}\right)$
$\chi_{1944}(17,\cdot)$	1944.bc	54	no	$-1$	$1$	$e\left(\frac{37}{54}\right)$	$e\left(\frac{7}{27}\right)$	$e\left(\frac{35}{54}\right)$	$e\left(\frac{17}{27}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{13}{54}\right)$	$e\left(\frac{10}{27}\right)$	$e\left(\frac{29}{54}\right)$	$e\left(\frac{2}{27}\right)$
$\chi_{1944}(19,\cdot)$	1944.bf	54	no	$-1$	$1$	$e\left(\frac{35}{54}\right)$	$e\left(\frac{49}{54}\right)$	$e\left(\frac{14}{27}\right)$	$e\left(\frac{11}{54}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{5}{54}\right)$	$e\left(\frac{8}{27}\right)$	$e\left(\frac{7}{54}\right)$	$e\left(\frac{41}{54}\right)$
$\chi_{1944}(23,\cdot)$	1944.bm	162	no	$1$	$1$	$e\left(\frac{37}{162}\right)$	$e\left(\frac{95}{162}\right)$	$e\left(\frac{4}{81}\right)$	$e\left(\frac{17}{81}\right)$	$e\left(\frac{13}{54}\right)$	$e\left(\frac{5}{54}\right)$	$e\left(\frac{47}{81}\right)$	$e\left(\frac{37}{81}\right)$	$e\left(\frac{137}{162}\right)$	$e\left(\frac{85}{162}\right)$
$\chi_{1944}(25,\cdot)$	1944.bg	81	no	$1$	$1$	$e\left(\frac{43}{81}\right)$	$e\left(\frac{71}{81}\right)$	$e\left(\frac{29}{81}\right)$	$e\left(\frac{22}{81}\right)$	$e\left(\frac{10}{27}\right)$	$e\left(\frac{8}{27}\right)$	$e\left(\frac{37}{81}\right)$	$e\left(\frac{5}{81}\right)$	$e\left(\frac{41}{81}\right)$	$e\left(\frac{55}{81}\right)$
$\chi_{1944}(29,\cdot)$	1944.bn	162	yes	$-1$	$1$	$e\left(\frac{61}{81}\right)$	$e\left(\frac{80}{81}\right)$	$e\left(\frac{11}{81}\right)$	$e\left(\frac{53}{162}\right)$	$e\left(\frac{29}{54}\right)$	$e\left(\frac{7}{54}\right)$	$e\left(\frac{137}{162}\right)$	$e\left(\frac{41}{81}\right)$	$e\left(\frac{77}{81}\right)$	$e\left(\frac{46}{81}\right)$
$\chi_{1944}(31,\cdot)$	1944.bi	162	no	$-1$	$1$	$e\left(\frac{68}{81}\right)$	$e\left(\frac{23}{162}\right)$	$e\left(\frac{71}{162}\right)$	$e\left(\frac{80}{81}\right)$	$e\left(\frac{2}{27}\right)$	$e\left(\frac{41}{54}\right)$	$e\left(\frac{85}{162}\right)$	$e\left(\frac{55}{81}\right)$	$e\left(\frac{46}{81}\right)$	$e\left(\frac{157}{162}\right)$
$\chi_{1944}(35,\cdot)$	1944.bb	54	no	$1$	$1$	$e\left(\frac{19}{27}\right)$	$e\left(\frac{37}{54}\right)$	$e\left(\frac{25}{54}\right)$	$e\left(\frac{5}{54}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{22}{27}\right)$	$e\left(\frac{11}{27}\right)$	$e\left(\frac{20}{27}\right)$	$e\left(\frac{53}{54}\right)$
$\chi_{1944}(37,\cdot)$	1944.bd	54	no	$1$	$1$	$e\left(\frac{7}{54}\right)$	$e\left(\frac{13}{27}\right)$	$e\left(\frac{11}{54}\right)$	$e\left(\frac{13}{54}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{14}{27}\right)$	$e\left(\frac{7}{27}\right)$	$e\left(\frac{23}{54}\right)$	$e\left(\frac{23}{27}\right)$
$\chi_{1944}(41,\cdot)$	1944.bk	162	no	$-1$	$1$	$e\left(\frac{85}{162}\right)$	$e\left(\frac{73}{81}\right)$	$e\left(\frac{95}{162}\right)$	$e\left(\frac{50}{81}\right)$	$e\left(\frac{43}{54}\right)$	$e\left(\frac{1}{27}\right)$	$e\left(\frac{43}{162}\right)$	$e\left(\frac{4}{81}\right)$	$e\left(\frac{17}{162}\right)$	$e\left(\frac{44}{81}\right)$
$\chi_{1944}(43,\cdot)$	1944.bh	162	yes	$-1$	$1$	$e\left(\frac{155}{162}\right)$	$e\left(\frac{109}{162}\right)$	$e\left(\frac{8}{81}\right)$	$e\left(\frac{149}{162}\right)$	$e\left(\frac{13}{27}\right)$	$e\left(\frac{5}{27}\right)$	$e\left(\frac{107}{162}\right)$	$e\left(\frac{74}{81}\right)$	$e\left(\frac{31}{162}\right)$	$e\left(\frac{89}{162}\right)$
$\chi_{1944}(47,\cdot)$	1944.bm	162	no	$1$	$1$	$e\left(\frac{107}{162}\right)$	$e\left(\frac{139}{162}\right)$	$e\left(\frac{5}{81}\right)$	$e\left(\frac{1}{81}\right)$	$e\left(\frac{23}{54}\right)$	$e\left(\frac{13}{54}\right)$	$e\left(\frac{79}{81}\right)$	$e\left(\frac{26}{81}\right)$	$e\left(\frac{151}{162}\right)$	$e\left(\frac{5}{162}\right)$
$\chi_{1944}(49,\cdot)$	1944.bg	81	no	$1$	$1$	$e\left(\frac{71}{81}\right)$	$e\left(\frac{40}{81}\right)$	$e\left(\frac{46}{81}\right)$	$e\left(\frac{74}{81}\right)$	$e\left(\frac{14}{27}\right)$	$e\left(\frac{22}{27}\right)$	$e\left(\frac{14}{81}\right)$	$e\left(\frac{61}{81}\right)$	$e\left(\frac{79}{81}\right)$	$e\left(\frac{23}{81}\right)$
$\chi_{1944}(53,\cdot)$	1944.x	18	no	$-1$	$1$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{2}{9}\right)$
$\chi_{1944}(55,\cdot)$	1944.s	18	no	$-1$	$1$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{5}{18}\right)$
$\chi_{1944}(59,\cdot)$	1944.bl	162	yes	$1$	$1$	$e\left(\frac{53}{81}\right)$	$e\left(\frac{143}{162}\right)$	$e\left(\frac{47}{162}\right)$	$e\left(\frac{139}{162}\right)$	$e\left(\frac{19}{54}\right)$	$e\left(\frac{13}{27}\right)$	$e\left(\frac{23}{81}\right)$	$e\left(\frac{25}{81}\right)$	$e\left(\frac{43}{81}\right)$	$e\left(\frac{145}{162}\right)$
$\chi_{1944}(61,\cdot)$	1944.bj	162	yes	$1$	$1$	$e\left(\frac{35}{162}\right)$	$e\left(\frac{11}{81}\right)$	$e\left(\frac{1}{162}\right)$	$e\left(\frac{65}{162}\right)$	$e\left(\frac{16}{27}\right)$	$e\left(\frac{31}{54}\right)$	$e\left(\frac{16}{81}\right)$	$e\left(\frac{35}{81}\right)$	$e\left(\frac{7}{162}\right)$	$e\left(\frac{61}{81}\right)$
$\chi_{1944}(65,\cdot)$	1944.bk	162	no	$-1$	$1$	$e\left(\frac{65}{162}\right)$	$e\left(\frac{32}{81}\right)$	$e\left(\frac{25}{162}\right)$	$e\left(\frac{43}{81}\right)$	$e\left(\frac{17}{54}\right)$	$e\left(\frac{23}{27}\right)$	$e\left(\frac{71}{162}\right)$	$e\left(\frac{65}{81}\right)$	$e\left(\frac{13}{162}\right)$	$e\left(\frac{67}{81}\right)$
$\chi_{1944}(67,\cdot)$	1944.bh	162	yes	$-1$	$1$	$e\left(\frac{121}{162}\right)$	$e\left(\frac{83}{162}\right)$	$e\left(\frac{70}{81}\right)$	$e\left(\frac{109}{162}\right)$	$e\left(\frac{26}{27}\right)$	$e\left(\frac{10}{27}\right)$	$e\left(\frac{25}{162}\right)$	$e\left(\frac{40}{81}\right)$	$e\left(\frac{89}{162}\right)$	$e\left(\frac{151}{162}\right)$
$\chi_{1944}(71,\cdot)$	1944.be	54	no	$1$	$1$	$e\left(\frac{13}{54}\right)$	$e\left(\frac{29}{54}\right)$	$e\left(\frac{16}{27}\right)$	$e\left(\frac{14}{27}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{26}{27}\right)$	$e\left(\frac{13}{27}\right)$	$e\left(\frac{35}{54}\right)$	$e\left(\frac{43}{54}\right)$
$\chi_{1944}(73,\cdot)$	1944.y	27	no	$1$	$1$	$e\left(\frac{16}{27}\right)$	$e\left(\frac{17}{27}\right)$	$e\left(\frac{2}{27}\right)$	$e\left(\frac{22}{27}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{10}{27}\right)$	$e\left(\frac{5}{27}\right)$	$e\left(\frac{14}{27}\right)$	$e\left(\frac{1}{27}\right)$
$\chi_{1944}(77,\cdot)$	1944.bn	162	yes	$-1$	$1$	$e\left(\frac{50}{81}\right)$	$e\left(\frac{43}{81}\right)$	$e\left(\frac{13}{81}\right)$	$e\left(\frac{151}{162}\right)$	$e\left(\frac{49}{54}\right)$	$e\left(\frac{23}{54}\right)$	$e\left(\frac{103}{162}\right)$	$e\left(\frac{19}{81}\right)$	$e\left(\frac{10}{81}\right)$	$e\left(\frac{47}{81}\right)$
$\chi_{1944}(79,\cdot)$	1944.bi	162	no	$-1$	$1$	$e\left(\frac{25}{81}\right)$	$e\left(\frac{43}{162}\right)$	$e\left(\frac{13}{162}\right)$	$e\left(\frac{58}{81}\right)$	$e\left(\frac{19}{27}\right)$	$e\left(\frac{25}{54}\right)$	$e\left(\frac{11}{162}\right)$	$e\left(\frac{50}{81}\right)$	$e\left(\frac{5}{81}\right)$	$e\left(\frac{47}{162}\right)$
$\chi_{1944}(83,\cdot)$	1944.bl	162	yes	$1$	$1$	$e\left(\frac{79}{81}\right)$	$e\left(\frac{97}{162}\right)$	$e\left(\frac{67}{162}\right)$	$e\left(\frac{143}{162}\right)$	$e\left(\frac{11}{54}\right)$	$e\left(\frac{26}{27}\right)$	$e\left(\frac{19}{81}\right)$	$e\left(\frac{77}{81}\right)$	$e\left(\frac{32}{81}\right)$	$e\left(\frac{155}{162}\right)$
$\chi_{1944}(85,\cdot)$	1944.bj	162	yes	$1$	$1$	$e\left(\frac{73}{162}\right)$	$e\left(\frac{16}{81}\right)$	$e\left(\frac{53}{162}\right)$	$e\left(\frac{43}{162}\right)$	$e\left(\frac{11}{27}\right)$	$e\left(\frac{23}{54}\right)$	$e\left(\frac{38}{81}\right)$	$e\left(\frac{73}{81}\right)$	$e\left(\frac{47}{162}\right)$	$e\left(\frac{74}{81}\right)$
$\chi_{1944}(89,\cdot)$	1944.bc	54	no	$-1$	$1$	$e\left(\frac{41}{54}\right)$	$e\left(\frac{26}{27}\right)$	$e\left(\frac{49}{54}\right)$	$e\left(\frac{13}{27}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{29}{54}\right)$	$e\left(\frac{14}{27}\right)$	$e\left(\frac{19}{54}\right)$	$e\left(\frac{19}{27}\right)$
$\chi_{1944}(91,\cdot)$	1944.bf	54	no	$-1$	$1$	$e\left(\frac{31}{54}\right)$	$e\left(\frac{11}{54}\right)$	$e\left(\frac{7}{27}\right)$	$e\left(\frac{19}{54}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{43}{54}\right)$	$e\left(\frac{4}{27}\right)$	$e\left(\frac{17}{54}\right)$	$e\left(\frac{7}{54}\right)$
$\chi_{1944}(95,\cdot)$	1944.bm	162	no	$1$	$1$	$e\left(\frac{67}{162}\right)$	$e\left(\frac{137}{162}\right)$	$e\left(\frac{16}{81}\right)$	$e\left(\frac{68}{81}\right)$	$e\left(\frac{25}{54}\right)$	$e\left(\frac{47}{54}\right)$	$e\left(\frac{26}{81}\right)$	$e\left(\frac{67}{81}\right)$	$e\left(\frac{143}{162}\right)$	$e\left(\frac{97}{162}\right)$

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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	$1944$
Structure	\(C_{2}\times C_{2}\times C_{162}\)
Order	$648$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)
\(\chi_{1944}(1,\cdot)\)	1944.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1944}(5,\cdot)\)	1944.bn	162	yes	\(-1\)	\(1\)	\(e\left(\frac{62}{81}\right)\)	\(e\left(\frac{76}{81}\right)\)	\(e\left(\frac{55}{81}\right)\)	\(e\left(\frac{103}{162}\right)\)	\(e\left(\frac{37}{54}\right)\)	\(e\left(\frac{35}{54}\right)\)	\(e\left(\frac{37}{162}\right)\)	\(e\left(\frac{43}{81}\right)\)	\(e\left(\frac{61}{81}\right)\)	\(e\left(\frac{68}{81}\right)\)
\(\chi_{1944}(7,\cdot)\)	1944.bi	162	no	\(-1\)	\(1\)	\(e\left(\frac{76}{81}\right)\)	\(e\left(\frac{121}{162}\right)\)	\(e\left(\frac{127}{162}\right)\)	\(e\left(\frac{37}{81}\right)\)	\(e\left(\frac{7}{27}\right)\)	\(e\left(\frac{49}{54}\right)\)	\(e\left(\frac{95}{162}\right)\)	\(e\left(\frac{71}{81}\right)\)	\(e\left(\frac{80}{81}\right)\)	\(e\left(\frac{23}{162}\right)\)
\(\chi_{1944}(11,\cdot)\)	1944.bl	162	yes	\(1\)	\(1\)	\(e\left(\frac{55}{81}\right)\)	\(e\left(\frac{127}{162}\right)\)	\(e\left(\frac{61}{162}\right)\)	\(e\left(\frac{77}{162}\right)\)	\(e\left(\frac{35}{54}\right)\)	\(e\left(\frac{14}{27}\right)\)	\(e\left(\frac{4}{81}\right)\)	\(e\left(\frac{29}{81}\right)\)	\(e\left(\frac{11}{81}\right)\)	\(e\left(\frac{71}{162}\right)\)
\(\chi_{1944}(13,\cdot)\)	1944.bj	162	yes	\(1\)	\(1\)	\(e\left(\frac{103}{162}\right)\)	\(e\left(\frac{37}{81}\right)\)	\(e\left(\frac{77}{162}\right)\)	\(e\left(\frac{145}{162}\right)\)	\(e\left(\frac{17}{27}\right)\)	\(e\left(\frac{11}{54}\right)\)	\(e\left(\frac{17}{81}\right)\)	\(e\left(\frac{22}{81}\right)\)	\(e\left(\frac{53}{162}\right)\)	\(e\left(\frac{80}{81}\right)\)
\(\chi_{1944}(17,\cdot)\)	1944.bc	54	no	\(-1\)	\(1\)	\(e\left(\frac{37}{54}\right)\)	\(e\left(\frac{7}{27}\right)\)	\(e\left(\frac{35}{54}\right)\)	\(e\left(\frac{17}{27}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{13}{54}\right)\)	\(e\left(\frac{10}{27}\right)\)	\(e\left(\frac{29}{54}\right)\)	\(e\left(\frac{2}{27}\right)\)
\(\chi_{1944}(19,\cdot)\)	1944.bf	54	no	\(-1\)	\(1\)	\(e\left(\frac{35}{54}\right)\)	\(e\left(\frac{49}{54}\right)\)	\(e\left(\frac{14}{27}\right)\)	\(e\left(\frac{11}{54}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{5}{54}\right)\)	\(e\left(\frac{8}{27}\right)\)	\(e\left(\frac{7}{54}\right)\)	\(e\left(\frac{41}{54}\right)\)
\(\chi_{1944}(23,\cdot)\)	1944.bm	162	no	\(1\)	\(1\)	\(e\left(\frac{37}{162}\right)\)	\(e\left(\frac{95}{162}\right)\)	\(e\left(\frac{4}{81}\right)\)	\(e\left(\frac{17}{81}\right)\)	\(e\left(\frac{13}{54}\right)\)	\(e\left(\frac{5}{54}\right)\)	\(e\left(\frac{47}{81}\right)\)	\(e\left(\frac{37}{81}\right)\)	\(e\left(\frac{137}{162}\right)\)	\(e\left(\frac{85}{162}\right)\)
\(\chi_{1944}(25,\cdot)\)	1944.bg	81	no	\(1\)	\(1\)	\(e\left(\frac{43}{81}\right)\)	\(e\left(\frac{71}{81}\right)\)	\(e\left(\frac{29}{81}\right)\)	\(e\left(\frac{22}{81}\right)\)	\(e\left(\frac{10}{27}\right)\)	\(e\left(\frac{8}{27}\right)\)	\(e\left(\frac{37}{81}\right)\)	\(e\left(\frac{5}{81}\right)\)	\(e\left(\frac{41}{81}\right)\)	\(e\left(\frac{55}{81}\right)\)
\(\chi_{1944}(29,\cdot)\)	1944.bn	162	yes	\(-1\)	\(1\)	\(e\left(\frac{61}{81}\right)\)	\(e\left(\frac{80}{81}\right)\)	\(e\left(\frac{11}{81}\right)\)	\(e\left(\frac{53}{162}\right)\)	\(e\left(\frac{29}{54}\right)\)	\(e\left(\frac{7}{54}\right)\)	\(e\left(\frac{137}{162}\right)\)	\(e\left(\frac{41}{81}\right)\)	\(e\left(\frac{77}{81}\right)\)	\(e\left(\frac{46}{81}\right)\)
\(\chi_{1944}(31,\cdot)\)	1944.bi	162	no	\(-1\)	\(1\)	\(e\left(\frac{68}{81}\right)\)	\(e\left(\frac{23}{162}\right)\)	\(e\left(\frac{71}{162}\right)\)	\(e\left(\frac{80}{81}\right)\)	\(e\left(\frac{2}{27}\right)\)	\(e\left(\frac{41}{54}\right)\)	\(e\left(\frac{85}{162}\right)\)	\(e\left(\frac{55}{81}\right)\)	\(e\left(\frac{46}{81}\right)\)	\(e\left(\frac{157}{162}\right)\)
\(\chi_{1944}(35,\cdot)\)	1944.bb	54	no	\(1\)	\(1\)	\(e\left(\frac{19}{27}\right)\)	\(e\left(\frac{37}{54}\right)\)	\(e\left(\frac{25}{54}\right)\)	\(e\left(\frac{5}{54}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{22}{27}\right)\)	\(e\left(\frac{11}{27}\right)\)	\(e\left(\frac{20}{27}\right)\)	\(e\left(\frac{53}{54}\right)\)
\(\chi_{1944}(37,\cdot)\)	1944.bd	54	no	\(1\)	\(1\)	\(e\left(\frac{7}{54}\right)\)	\(e\left(\frac{13}{27}\right)\)	\(e\left(\frac{11}{54}\right)\)	\(e\left(\frac{13}{54}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{14}{27}\right)\)	\(e\left(\frac{7}{27}\right)\)	\(e\left(\frac{23}{54}\right)\)	\(e\left(\frac{23}{27}\right)\)
\(\chi_{1944}(41,\cdot)\)	1944.bk	162	no	\(-1\)	\(1\)	\(e\left(\frac{85}{162}\right)\)	\(e\left(\frac{73}{81}\right)\)	\(e\left(\frac{95}{162}\right)\)	\(e\left(\frac{50}{81}\right)\)	\(e\left(\frac{43}{54}\right)\)	\(e\left(\frac{1}{27}\right)\)	\(e\left(\frac{43}{162}\right)\)	\(e\left(\frac{4}{81}\right)\)	\(e\left(\frac{17}{162}\right)\)	\(e\left(\frac{44}{81}\right)\)
\(\chi_{1944}(43,\cdot)\)	1944.bh	162	yes	\(-1\)	\(1\)	\(e\left(\frac{155}{162}\right)\)	\(e\left(\frac{109}{162}\right)\)	\(e\left(\frac{8}{81}\right)\)	\(e\left(\frac{149}{162}\right)\)	\(e\left(\frac{13}{27}\right)\)	\(e\left(\frac{5}{27}\right)\)	\(e\left(\frac{107}{162}\right)\)	\(e\left(\frac{74}{81}\right)\)	\(e\left(\frac{31}{162}\right)\)	\(e\left(\frac{89}{162}\right)\)
\(\chi_{1944}(47,\cdot)\)	1944.bm	162	no	\(1\)	\(1\)	\(e\left(\frac{107}{162}\right)\)	\(e\left(\frac{139}{162}\right)\)	\(e\left(\frac{5}{81}\right)\)	\(e\left(\frac{1}{81}\right)\)	\(e\left(\frac{23}{54}\right)\)	\(e\left(\frac{13}{54}\right)\)	\(e\left(\frac{79}{81}\right)\)	\(e\left(\frac{26}{81}\right)\)	\(e\left(\frac{151}{162}\right)\)	\(e\left(\frac{5}{162}\right)\)
\(\chi_{1944}(49,\cdot)\)	1944.bg	81	no	\(1\)	\(1\)	\(e\left(\frac{71}{81}\right)\)	\(e\left(\frac{40}{81}\right)\)	\(e\left(\frac{46}{81}\right)\)	\(e\left(\frac{74}{81}\right)\)	\(e\left(\frac{14}{27}\right)\)	\(e\left(\frac{22}{27}\right)\)	\(e\left(\frac{14}{81}\right)\)	\(e\left(\frac{61}{81}\right)\)	\(e\left(\frac{79}{81}\right)\)	\(e\left(\frac{23}{81}\right)\)
\(\chi_{1944}(53,\cdot)\)	1944.x	18	no	\(-1\)	\(1\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)
\(\chi_{1944}(55,\cdot)\)	1944.s	18	no	\(-1\)	\(1\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{5}{18}\right)\)
\(\chi_{1944}(59,\cdot)\)	1944.bl	162	yes	\(1\)	\(1\)	\(e\left(\frac{53}{81}\right)\)	\(e\left(\frac{143}{162}\right)\)	\(e\left(\frac{47}{162}\right)\)	\(e\left(\frac{139}{162}\right)\)	\(e\left(\frac{19}{54}\right)\)	\(e\left(\frac{13}{27}\right)\)	\(e\left(\frac{23}{81}\right)\)	\(e\left(\frac{25}{81}\right)\)	\(e\left(\frac{43}{81}\right)\)	\(e\left(\frac{145}{162}\right)\)
\(\chi_{1944}(61,\cdot)\)	1944.bj	162	yes	\(1\)	\(1\)	\(e\left(\frac{35}{162}\right)\)	\(e\left(\frac{11}{81}\right)\)	\(e\left(\frac{1}{162}\right)\)	\(e\left(\frac{65}{162}\right)\)	\(e\left(\frac{16}{27}\right)\)	\(e\left(\frac{31}{54}\right)\)	\(e\left(\frac{16}{81}\right)\)	\(e\left(\frac{35}{81}\right)\)	\(e\left(\frac{7}{162}\right)\)	\(e\left(\frac{61}{81}\right)\)
\(\chi_{1944}(65,\cdot)\)	1944.bk	162	no	\(-1\)	\(1\)	\(e\left(\frac{65}{162}\right)\)	\(e\left(\frac{32}{81}\right)\)	\(e\left(\frac{25}{162}\right)\)	\(e\left(\frac{43}{81}\right)\)	\(e\left(\frac{17}{54}\right)\)	\(e\left(\frac{23}{27}\right)\)	\(e\left(\frac{71}{162}\right)\)	\(e\left(\frac{65}{81}\right)\)	\(e\left(\frac{13}{162}\right)\)	\(e\left(\frac{67}{81}\right)\)
\(\chi_{1944}(67,\cdot)\)	1944.bh	162	yes	\(-1\)	\(1\)	\(e\left(\frac{121}{162}\right)\)	\(e\left(\frac{83}{162}\right)\)	\(e\left(\frac{70}{81}\right)\)	\(e\left(\frac{109}{162}\right)\)	\(e\left(\frac{26}{27}\right)\)	\(e\left(\frac{10}{27}\right)\)	\(e\left(\frac{25}{162}\right)\)	\(e\left(\frac{40}{81}\right)\)	\(e\left(\frac{89}{162}\right)\)	\(e\left(\frac{151}{162}\right)\)
\(\chi_{1944}(71,\cdot)\)	1944.be	54	no	\(1\)	\(1\)	\(e\left(\frac{13}{54}\right)\)	\(e\left(\frac{29}{54}\right)\)	\(e\left(\frac{16}{27}\right)\)	\(e\left(\frac{14}{27}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{26}{27}\right)\)	\(e\left(\frac{13}{27}\right)\)	\(e\left(\frac{35}{54}\right)\)	\(e\left(\frac{43}{54}\right)\)
\(\chi_{1944}(73,\cdot)\)	1944.y	27	no	\(1\)	\(1\)	\(e\left(\frac{16}{27}\right)\)	\(e\left(\frac{17}{27}\right)\)	\(e\left(\frac{2}{27}\right)\)	\(e\left(\frac{22}{27}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{10}{27}\right)\)	\(e\left(\frac{5}{27}\right)\)	\(e\left(\frac{14}{27}\right)\)	\(e\left(\frac{1}{27}\right)\)
\(\chi_{1944}(77,\cdot)\)	1944.bn	162	yes	\(-1\)	\(1\)	\(e\left(\frac{50}{81}\right)\)	\(e\left(\frac{43}{81}\right)\)	\(e\left(\frac{13}{81}\right)\)	\(e\left(\frac{151}{162}\right)\)	\(e\left(\frac{49}{54}\right)\)	\(e\left(\frac{23}{54}\right)\)	\(e\left(\frac{103}{162}\right)\)	\(e\left(\frac{19}{81}\right)\)	\(e\left(\frac{10}{81}\right)\)	\(e\left(\frac{47}{81}\right)\)
\(\chi_{1944}(79,\cdot)\)	1944.bi	162	no	\(-1\)	\(1\)	\(e\left(\frac{25}{81}\right)\)	\(e\left(\frac{43}{162}\right)\)	\(e\left(\frac{13}{162}\right)\)	\(e\left(\frac{58}{81}\right)\)	\(e\left(\frac{19}{27}\right)\)	\(e\left(\frac{25}{54}\right)\)	\(e\left(\frac{11}{162}\right)\)	\(e\left(\frac{50}{81}\right)\)	\(e\left(\frac{5}{81}\right)\)	\(e\left(\frac{47}{162}\right)\)
\(\chi_{1944}(83,\cdot)\)	1944.bl	162	yes	\(1\)	\(1\)	\(e\left(\frac{79}{81}\right)\)	\(e\left(\frac{97}{162}\right)\)	\(e\left(\frac{67}{162}\right)\)	\(e\left(\frac{143}{162}\right)\)	\(e\left(\frac{11}{54}\right)\)	\(e\left(\frac{26}{27}\right)\)	\(e\left(\frac{19}{81}\right)\)	\(e\left(\frac{77}{81}\right)\)	\(e\left(\frac{32}{81}\right)\)	\(e\left(\frac{155}{162}\right)\)
\(\chi_{1944}(85,\cdot)\)	1944.bj	162	yes	\(1\)	\(1\)	\(e\left(\frac{73}{162}\right)\)	\(e\left(\frac{16}{81}\right)\)	\(e\left(\frac{53}{162}\right)\)	\(e\left(\frac{43}{162}\right)\)	\(e\left(\frac{11}{27}\right)\)	\(e\left(\frac{23}{54}\right)\)	\(e\left(\frac{38}{81}\right)\)	\(e\left(\frac{73}{81}\right)\)	\(e\left(\frac{47}{162}\right)\)	\(e\left(\frac{74}{81}\right)\)
\(\chi_{1944}(89,\cdot)\)	1944.bc	54	no	\(-1\)	\(1\)	\(e\left(\frac{41}{54}\right)\)	\(e\left(\frac{26}{27}\right)\)	\(e\left(\frac{49}{54}\right)\)	\(e\left(\frac{13}{27}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{29}{54}\right)\)	\(e\left(\frac{14}{27}\right)\)	\(e\left(\frac{19}{54}\right)\)	\(e\left(\frac{19}{27}\right)\)
\(\chi_{1944}(91,\cdot)\)	1944.bf	54	no	\(-1\)	\(1\)	\(e\left(\frac{31}{54}\right)\)	\(e\left(\frac{11}{54}\right)\)	\(e\left(\frac{7}{27}\right)\)	\(e\left(\frac{19}{54}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{43}{54}\right)\)	\(e\left(\frac{4}{27}\right)\)	\(e\left(\frac{17}{54}\right)\)	\(e\left(\frac{7}{54}\right)\)
\(\chi_{1944}(95,\cdot)\)	1944.bm	162	no	\(1\)	\(1\)	\(e\left(\frac{67}{162}\right)\)	\(e\left(\frac{137}{162}\right)\)	\(e\left(\frac{16}{81}\right)\)	\(e\left(\frac{68}{81}\right)\)	\(e\left(\frac{25}{54}\right)\)	\(e\left(\frac{47}{54}\right)\)	\(e\left(\frac{26}{81}\right)\)	\(e\left(\frac{67}{81}\right)\)	\(e\left(\frac{143}{162}\right)\)	\(e\left(\frac{97}{162}\right)\)

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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.