LMFDB - Group of Dirichlet characters of modulus 3520

Show commands: PariGP / SageMath

sage: H = DirichletGroup(3520)

pari: g = idealstar(,3520,2)

Character group

sage: G.order() pari: g.no
Order	=	1280
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{4}\times C_{80}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{3520}(2751,\cdot)$, $\chi_{3520}(1541,\cdot)$, $\chi_{3520}(2817,\cdot)$, $\chi_{3520}(321,\cdot)$

First 32 of 1280 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	$-1$	$1$	$3$	$7$	$9$	$13$	$17$	$19$	$21$	$23$	$27$	$29$
$\chi_{3520}(1,\cdot)$	3520.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{3520}(3,\cdot)$	3520.ez	80	yes	$1$	$1$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{13}{80}\right)$
$\chi_{3520}(7,\cdot)$	3520.ex	40	no	$-1$	$1$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{5}{8}\right)$	$1$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{11}{40}\right)$
$\chi_{3520}(9,\cdot)$	3520.em	40	no	$1$	$1$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{7}{8}\right)$	$-i$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{13}{40}\right)$
$\chi_{3520}(13,\cdot)$	3520.fm	80	yes	$1$	$1$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{41}{80}\right)$
$\chi_{3520}(17,\cdot)$	3520.dm	20	no	$1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{9}{20}\right)$	$i$	$i$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{20}\right)$
$\chi_{3520}(19,\cdot)$	3520.fe	80	yes	$1$	$1$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{73}{80}\right)$
$\chi_{3520}(21,\cdot)$	3520.cy	16	no	$-1$	$1$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{11}{16}\right)$	$i$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{7}{16}\right)$
$\chi_{3520}(23,\cdot)$	3520.cd	8	no	$1$	$1$	$e\left(\frac{3}{8}\right)$	$1$	$-i$	$e\left(\frac{3}{8}\right)$	$i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{8}\right)$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{3520}(27,\cdot)$	3520.ez	80	yes	$1$	$1$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{39}{80}\right)$
$\chi_{3520}(29,\cdot)$	3520.fg	80	yes	$-1$	$1$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{37}{80}\right)$
$\chi_{3520}(31,\cdot)$	3520.ck	10	no	$-1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$-1$	$-1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{3520}(37,\cdot)$	3520.fa	80	yes	$-1$	$1$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{7}{80}\right)$
$\chi_{3520}(39,\cdot)$	3520.et	40	no	$1$	$1$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{1}{8}\right)$	$-i$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{27}{40}\right)$
$\chi_{3520}(41,\cdot)$	3520.en	40	no	$-1$	$1$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{7}{8}\right)$	$i$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{29}{40}\right)$
$\chi_{3520}(43,\cdot)$	3520.dj	16	yes	$-1$	$1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{15}{16}\right)$	$1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{15}{16}\right)$
$\chi_{3520}(47,\cdot)$	3520.ef	20	no	$1$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{13}{20}\right)$	$-i$	$-i$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{20}\right)$
$\chi_{3520}(49,\cdot)$	3520.dr	20	no	$1$	$1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{19}{20}\right)$	$i$	$1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{11}{20}\right)$
$\chi_{3520}(51,\cdot)$	3520.fd	80	no	$1$	$1$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{17}{80}\right)$
$\chi_{3520}(53,\cdot)$	3520.fn	80	yes	$-1$	$1$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{11}{80}\right)$
$\chi_{3520}(57,\cdot)$	3520.ei	40	no	$1$	$1$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{5}{8}\right)$	$-1$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{3}{40}\right)$
$\chi_{3520}(59,\cdot)$	3520.fc	80	yes	$-1$	$1$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{7}{80}\right)$
$\chi_{3520}(61,\cdot)$	3520.fj	80	no	$-1$	$1$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{29}{80}\right)$
$\chi_{3520}(63,\cdot)$	3520.dx	20	no	$-1$	$1$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{9}{10}\right)$	$-1$	$-i$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{3520}(67,\cdot)$	3520.cx	16	no	$1$	$1$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{9}{16}\right)$	$-1$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{9}{16}\right)$
$\chi_{3520}(69,\cdot)$	3520.fi	80	yes	$1$	$1$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{23}{80}\right)$
$\chi_{3520}(71,\cdot)$	3520.es	40	no	$-1$	$1$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{1}{8}\right)$	$i$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{27}{40}\right)$
$\chi_{3520}(73,\cdot)$	3520.ei	40	no	$1$	$1$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{3}{8}\right)$	$-1$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{21}{40}\right)$
$\chi_{3520}(79,\cdot)$	3520.do	20	no	$1$	$1$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{11}{20}\right)$	$-i$	$-1$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{9}{20}\right)$
$\chi_{3520}(81,\cdot)$	3520.ea	20	no	$1$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{17}{20}\right)$	$-i$	$-1$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{13}{20}\right)$
$\chi_{3520}(83,\cdot)$	3520.fl	80	yes	$-1$	$1$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{49}{80}\right)$
$\chi_{3520}(87,\cdot)$	3520.cb	8	no	$-1$	$1$	$e\left(\frac{7}{8}\right)$	$1$	$-i$	$e\left(\frac{3}{8}\right)$	$i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{8}\right)$	$-1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{8}\right)$

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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	$3520$
Structure	\(C_{2}\times C_{2}\times C_{4}\times C_{80}\)
Order	$1280$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(13\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)	\(29\)
\(\chi_{3520}(1,\cdot)\)	3520.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{3520}(3,\cdot)\)	3520.ez	80	yes	\(1\)	\(1\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{13}{80}\right)\)
\(\chi_{3520}(7,\cdot)\)	3520.ex	40	no	\(-1\)	\(1\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(1\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{11}{40}\right)\)
\(\chi_{3520}(9,\cdot)\)	3520.em	40	no	\(1\)	\(1\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(-i\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{13}{40}\right)\)
\(\chi_{3520}(13,\cdot)\)	3520.fm	80	yes	\(1\)	\(1\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{41}{80}\right)\)
\(\chi_{3520}(17,\cdot)\)	3520.dm	20	no	\(1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(i\)	\(i\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{20}\right)\)
\(\chi_{3520}(19,\cdot)\)	3520.fe	80	yes	\(1\)	\(1\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{73}{80}\right)\)
\(\chi_{3520}(21,\cdot)\)	3520.cy	16	no	\(-1\)	\(1\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(i\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)
\(\chi_{3520}(23,\cdot)\)	3520.cd	8	no	\(1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(1\)	\(-i\)	\(e\left(\frac{3}{8}\right)\)	\(i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{3520}(27,\cdot)\)	3520.ez	80	yes	\(1\)	\(1\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{39}{80}\right)\)
\(\chi_{3520}(29,\cdot)\)	3520.fg	80	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{37}{80}\right)\)
\(\chi_{3520}(31,\cdot)\)	3520.ck	10	no	\(-1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{3520}(37,\cdot)\)	3520.fa	80	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{7}{80}\right)\)
\(\chi_{3520}(39,\cdot)\)	3520.et	40	no	\(1\)	\(1\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(-i\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{27}{40}\right)\)
\(\chi_{3520}(41,\cdot)\)	3520.en	40	no	\(-1\)	\(1\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(i\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{29}{40}\right)\)
\(\chi_{3520}(43,\cdot)\)	3520.dj	16	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(1\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)
\(\chi_{3520}(47,\cdot)\)	3520.ef	20	no	\(1\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(-i\)	\(-i\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)
\(\chi_{3520}(49,\cdot)\)	3520.dr	20	no	\(1\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(i\)	\(1\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)
\(\chi_{3520}(51,\cdot)\)	3520.fd	80	no	\(1\)	\(1\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{17}{80}\right)\)
\(\chi_{3520}(53,\cdot)\)	3520.fn	80	yes	\(-1\)	\(1\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{11}{80}\right)\)
\(\chi_{3520}(57,\cdot)\)	3520.ei	40	no	\(1\)	\(1\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(-1\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{3}{40}\right)\)
\(\chi_{3520}(59,\cdot)\)	3520.fc	80	yes	\(-1\)	\(1\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{7}{80}\right)\)
\(\chi_{3520}(61,\cdot)\)	3520.fj	80	no	\(-1\)	\(1\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{29}{80}\right)\)
\(\chi_{3520}(63,\cdot)\)	3520.dx	20	no	\(-1\)	\(1\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(-1\)	\(-i\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{3520}(67,\cdot)\)	3520.cx	16	no	\(1\)	\(1\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(-1\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)
\(\chi_{3520}(69,\cdot)\)	3520.fi	80	yes	\(1\)	\(1\)	\(e\left(\frac{7}{80}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{21}{80}\right)\)	\(e\left(\frac{23}{80}\right)\)
\(\chi_{3520}(71,\cdot)\)	3520.es	40	no	\(-1\)	\(1\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(i\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{27}{40}\right)\)
\(\chi_{3520}(73,\cdot)\)	3520.ei	40	no	\(1\)	\(1\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(-1\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{21}{40}\right)\)
\(\chi_{3520}(79,\cdot)\)	3520.do	20	no	\(1\)	\(1\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)
\(\chi_{3520}(81,\cdot)\)	3520.ea	20	no	\(1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)
\(\chi_{3520}(83,\cdot)\)	3520.fl	80	yes	\(-1\)	\(1\)	\(e\left(\frac{21}{80}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{49}{80}\right)\)
\(\chi_{3520}(87,\cdot)\)	3520.cb	8	no	\(-1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(1\)	\(-i\)	\(e\left(\frac{3}{8}\right)\)	\(i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(-1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)

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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.