LMFDB - Group of Dirichlet characters of modulus 3528

Show commands: PariGP / SageMath

sage: H = DirichletGroup(3528)

pari: g = idealstar(,3528,2)

Character group

sage: G.order() pari: g.no
Order	=	1008
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{6}\times C_{42}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{3528}(2647,\cdot)$, $\chi_{3528}(1765,\cdot)$, $\chi_{3528}(785,\cdot)$, $\chi_{3528}(1081,\cdot)$

First 32 of 1008 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	$-1$	$1$	$5$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$	$37$
$\chi_{3528}(1,\cdot)$	3528.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{3528}(5,\cdot)$	3528.ex	42	yes	$1$	$1$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{16}{21}\right)$	$-1$	$e\left(\frac{25}{42}\right)$
$\chi_{3528}(11,\cdot)$	3528.fe	42	yes	$1$	$1$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{17}{21}\right)$	$-1$	$e\left(\frac{41}{42}\right)$
$\chi_{3528}(13,\cdot)$	3528.fk	42	yes	$-1$	$1$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{9}{14}\right)$	$1$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{9}{14}\right)$
$\chi_{3528}(17,\cdot)$	3528.fm	42	no	$1$	$1$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{21}\right)$
$\chi_{3528}(19,\cdot)$	3528.bk	6	no	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{3528}(23,\cdot)$	3528.ew	42	no	$1$	$1$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{5}{42}\right)$	$-1$	$e\left(\frac{20}{21}\right)$
$\chi_{3528}(25,\cdot)$	3528.dv	21	no	$1$	$1$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{11}{21}\right)$	$1$	$e\left(\frac{4}{21}\right)$
$\chi_{3528}(29,\cdot)$	3528.fr	42	yes	$-1$	$1$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{3}{14}\right)$	$-1$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{14}\right)$
$\chi_{3528}(31,\cdot)$	3528.x	6	no	$1$	$1$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{3528}(37,\cdot)$	3528.eo	42	no	$1$	$1$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{37}{42}\right)$
$\chi_{3528}(41,\cdot)$	3528.fd	42	no	$1$	$1$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{3}{7}\right)$	$-1$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{7}\right)$
$\chi_{3528}(43,\cdot)$	3528.er	42	yes	$-1$	$1$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{4}{7}\right)$	$1$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{14}\right)$
$\chi_{3528}(47,\cdot)$	3528.dx	42	no	$-1$	$1$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{17}{21}\right)$
$\chi_{3528}(53,\cdot)$	3528.fu	42	no	$-1$	$1$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{42}\right)$
$\chi_{3528}(55,\cdot)$	3528.dr	14	no	$1$	$1$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{1}{14}\right)$	$1$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{4}{7}\right)$	$1$	$e\left(\frac{4}{7}\right)$
$\chi_{3528}(59,\cdot)$	3528.gd	42	yes	$-1$	$1$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{17}{42}\right)$
$\chi_{3528}(61,\cdot)$	3528.eb	42	yes	$-1$	$1$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{37}{42}\right)$
$\chi_{3528}(65,\cdot)$	3528.gc	42	no	$-1$	$1$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{21}\right)$
$\chi_{3528}(67,\cdot)$	3528.ba	6	no	$-1$	$1$	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{3528}(71,\cdot)$	3528.dl	14	no	$1$	$1$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{11}{14}\right)$	$-1$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{11}{14}\right)$	$-1$	$e\left(\frac{2}{7}\right)$
$\chi_{3528}(73,\cdot)$	3528.ez	42	no	$-1$	$1$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{4}{21}\right)$
$\chi_{3528}(79,\cdot)$	3528.cv	6	no	$-1$	$1$	$1$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{3528}(83,\cdot)$	3528.ej	42	yes	$-1$	$1$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{6}{7}\right)$	$-1$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{14}\right)$
$\chi_{3528}(85,\cdot)$	3528.ef	42	yes	$1$	$1$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{1}{7}\right)$	$-1$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{9}{14}\right)$
$\chi_{3528}(89,\cdot)$	3528.fm	42	no	$1$	$1$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{21}\right)$
$\chi_{3528}(95,\cdot)$	3528.fy	42	no	$1$	$1$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{16}{21}\right)$
$\chi_{3528}(97,\cdot)$	3528.cd	6	no	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$1$
$\chi_{3528}(101,\cdot)$	3528.ex	42	yes	$1$	$1$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{2}{21}\right)$	$-1$	$e\left(\frac{11}{42}\right)$
$\chi_{3528}(103,\cdot)$	3528.eg	42	no	$1$	$1$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{16}{21}\right)$	$1$	$e\left(\frac{2}{21}\right)$
$\chi_{3528}(107,\cdot)$	3528.fl	42	no	$1$	$1$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{42}\right)$
$\chi_{3528}(109,\cdot)$	3528.eo	42	no	$1$	$1$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{41}{42}\right)$

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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	$3528$
Structure	\(C_{2}\times C_{2}\times C_{6}\times C_{42}\)
Order	$1008$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(37\)
\(\chi_{3528}(1,\cdot)\)	3528.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{3528}(5,\cdot)\)	3528.ex	42	yes	\(1\)	\(1\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(-1\)	\(e\left(\frac{25}{42}\right)\)
\(\chi_{3528}(11,\cdot)\)	3528.fe	42	yes	\(1\)	\(1\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(-1\)	\(e\left(\frac{41}{42}\right)\)
\(\chi_{3528}(13,\cdot)\)	3528.fk	42	yes	\(-1\)	\(1\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(1\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{9}{14}\right)\)
\(\chi_{3528}(17,\cdot)\)	3528.fm	42	no	\(1\)	\(1\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{21}\right)\)
\(\chi_{3528}(19,\cdot)\)	3528.bk	6	no	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{3528}(23,\cdot)\)	3528.ew	42	no	\(1\)	\(1\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(-1\)	\(e\left(\frac{20}{21}\right)\)
\(\chi_{3528}(25,\cdot)\)	3528.dv	21	no	\(1\)	\(1\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(1\)	\(e\left(\frac{4}{21}\right)\)
\(\chi_{3528}(29,\cdot)\)	3528.fr	42	yes	\(-1\)	\(1\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(-1\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{3}{14}\right)\)
\(\chi_{3528}(31,\cdot)\)	3528.x	6	no	\(1\)	\(1\)	\(-1\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{3528}(37,\cdot)\)	3528.eo	42	no	\(1\)	\(1\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{37}{42}\right)\)
\(\chi_{3528}(41,\cdot)\)	3528.fd	42	no	\(1\)	\(1\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(-1\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{3}{7}\right)\)
\(\chi_{3528}(43,\cdot)\)	3528.er	42	yes	\(-1\)	\(1\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(1\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{14}\right)\)
\(\chi_{3528}(47,\cdot)\)	3528.dx	42	no	\(-1\)	\(1\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{17}{21}\right)\)
\(\chi_{3528}(53,\cdot)\)	3528.fu	42	no	\(-1\)	\(1\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{42}\right)\)
\(\chi_{3528}(55,\cdot)\)	3528.dr	14	no	\(1\)	\(1\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(1\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(1\)	\(e\left(\frac{4}{7}\right)\)
\(\chi_{3528}(59,\cdot)\)	3528.gd	42	yes	\(-1\)	\(1\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{17}{42}\right)\)
\(\chi_{3528}(61,\cdot)\)	3528.eb	42	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{37}{42}\right)\)
\(\chi_{3528}(65,\cdot)\)	3528.gc	42	no	\(-1\)	\(1\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{21}\right)\)
\(\chi_{3528}(67,\cdot)\)	3528.ba	6	no	\(-1\)	\(1\)	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{3528}(71,\cdot)\)	3528.dl	14	no	\(1\)	\(1\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(-1\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(-1\)	\(e\left(\frac{2}{7}\right)\)
\(\chi_{3528}(73,\cdot)\)	3528.ez	42	no	\(-1\)	\(1\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{4}{21}\right)\)
\(\chi_{3528}(79,\cdot)\)	3528.cv	6	no	\(-1\)	\(1\)	\(1\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{3528}(83,\cdot)\)	3528.ej	42	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(-1\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{14}\right)\)
\(\chi_{3528}(85,\cdot)\)	3528.ef	42	yes	\(1\)	\(1\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(-1\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{9}{14}\right)\)
\(\chi_{3528}(89,\cdot)\)	3528.fm	42	no	\(1\)	\(1\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{21}\right)\)
\(\chi_{3528}(95,\cdot)\)	3528.fy	42	no	\(1\)	\(1\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{16}{21}\right)\)
\(\chi_{3528}(97,\cdot)\)	3528.cd	6	no	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)
\(\chi_{3528}(101,\cdot)\)	3528.ex	42	yes	\(1\)	\(1\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(-1\)	\(e\left(\frac{11}{42}\right)\)
\(\chi_{3528}(103,\cdot)\)	3528.eg	42	no	\(1\)	\(1\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(1\)	\(e\left(\frac{2}{21}\right)\)
\(\chi_{3528}(107,\cdot)\)	3528.fl	42	no	\(1\)	\(1\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{42}\right)\)
\(\chi_{3528}(109,\cdot)\)	3528.eo	42	no	\(1\)	\(1\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{41}{42}\right)\)

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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.