LMFDB - Group of Dirichlet characters of modulus 527

Show commands: PariGP / SageMath

sage: H = DirichletGroup(527)

pari: g = idealstar(,527,2)

Character group

sage: G.order() pari: g.no
Order	=	480
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{240}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{527}(156,\cdot)$, $\chi_{527}(375,\cdot)$

First 32 of 480 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{527}(1,\cdot)$	527.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{527}(2,\cdot)$	527.bd	40	yes	$1$	$1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{21}{40}\right)$
$\chi_{527}(3,\cdot)$	527.bm	240	yes	$1$	$1$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{23}{240}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{149}{240}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{23}{120}\right)$	$e\left(\frac{157}{240}\right)$	$e\left(\frac{49}{240}\right)$
$\chi_{527}(4,\cdot)$	527.v	20	yes	$1$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{4}{5}\right)$	$-i$	$i$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{1}{20}\right)$
$\chi_{527}(5,\cdot)$	527.be	48	yes	$-1$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{47}{48}\right)$	$-i$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{25}{48}\right)$
$\chi_{527}(6,\cdot)$	527.bf	48	yes	$1$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{37}{48}\right)$	$i$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{35}{48}\right)$
$\chi_{527}(7,\cdot)$	527.bn	240	yes	$-1$	$1$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{149}{240}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{167}{240}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{29}{120}\right)$	$e\left(\frac{31}{240}\right)$	$e\left(\frac{67}{240}\right)$
$\chi_{527}(8,\cdot)$	527.bd	40	yes	$1$	$1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{23}{40}\right)$
$\chi_{527}(9,\cdot)$	527.bk	120	yes	$1$	$1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{23}{120}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{29}{120}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{37}{120}\right)$	$e\left(\frac{49}{120}\right)$
$\chi_{527}(10,\cdot)$	527.bn	240	yes	$-1$	$1$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{157}{240}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{31}{240}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{37}{120}\right)$	$e\left(\frac{23}{240}\right)$	$e\left(\frac{11}{240}\right)$
$\chi_{527}(11,\cdot)$	527.bm	240	yes	$1$	$1$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{49}{240}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{67}{240}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{49}{120}\right)$	$e\left(\frac{11}{240}\right)$	$e\left(\frac{167}{240}\right)$
$\chi_{527}(12,\cdot)$	527.bm	240	yes	$1$	$1$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{107}{240}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{161}{240}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{107}{120}\right)$	$e\left(\frac{73}{240}\right)$	$e\left(\frac{61}{240}\right)$
$\chi_{527}(13,\cdot)$	527.bg	60	yes	$-1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{11}{60}\right)$
$\chi_{527}(14,\cdot)$	527.bn	240	yes	$-1$	$1$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{71}{240}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{173}{240}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{71}{120}\right)$	$e\left(\frac{229}{240}\right)$	$e\left(\frac{193}{240}\right)$
$\chi_{527}(15,\cdot)$	527.bc	40	yes	$-1$	$1$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{29}{40}\right)$
$\chi_{527}(16,\cdot)$	527.o	10	yes	$1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{5}\right)$	$-1$	$-1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{527}(18,\cdot)$	527.s	15	no	$1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{14}{15}\right)$
$\chi_{527}(19,\cdot)$	527.bk	120	yes	$1$	$1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{120}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{43}{120}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{59}{120}\right)$	$e\left(\frac{23}{120}\right)$
$\chi_{527}(20,\cdot)$	527.bn	240	yes	$-1$	$1$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{79}{240}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{37}{240}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{79}{120}\right)$	$e\left(\frac{221}{240}\right)$	$e\left(\frac{137}{240}\right)$
$\chi_{527}(21,\cdot)$	527.bg	60	yes	$-1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{29}{60}\right)$
$\chi_{527}(22,\cdot)$	527.bm	240	yes	$1$	$1$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{211}{240}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{73}{240}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{91}{120}\right)$	$e\left(\frac{209}{240}\right)$	$e\left(\frac{53}{240}\right)$
$\chi_{527}(23,\cdot)$	527.bj	80	yes	$1$	$1$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{21}{80}\right)$
$\chi_{527}(24,\cdot)$	527.bm	240	yes	$1$	$1$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{29}{240}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{167}{240}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{29}{120}\right)$	$e\left(\frac{31}{240}\right)$	$e\left(\frac{187}{240}\right)$
$\chi_{527}(25,\cdot)$	527.y	24	yes	$1$	$1$	$-i$	$e\left(\frac{23}{24}\right)$	$-1$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{5}{24}\right)$	$i$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{1}{24}\right)$
$\chi_{527}(26,\cdot)$	527.x	24	yes	$-1$	$1$	$-i$	$e\left(\frac{7}{24}\right)$	$-1$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{1}{24}\right)$	$i$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{17}{24}\right)$
$\chi_{527}(27,\cdot)$	527.bj	80	yes	$1$	$1$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{49}{80}\right)$
$\chi_{527}(28,\cdot)$	527.bn	240	yes	$-1$	$1$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{233}{240}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{179}{240}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{113}{120}\right)$	$e\left(\frac{187}{240}\right)$	$e\left(\frac{79}{240}\right)$
$\chi_{527}(29,\cdot)$	527.bj	80	yes	$1$	$1$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{47}{80}\right)$
$\chi_{527}(30,\cdot)$	527.f	4	yes	$-1$	$1$	$-1$	$-i$	$1$	$i$	$i$	$-i$	$-1$	$-1$	$-i$	$i$
$\chi_{527}(32,\cdot)$	527.l	8	no	$1$	$1$	$i$	$e\left(\frac{3}{8}\right)$	$-1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{8}\right)$	$-i$	$-i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{527}(33,\cdot)$	527.o	10	yes	$1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{2}{5}\right)$	$-1$	$-1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{527}(35,\cdot)$	527.h	5	no	$1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{4}{5}\right)$	$1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$

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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	$527$
Structure	\(C_{2}\times C_{240}\)
Order	$480$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{527}(1,\cdot)\)	527.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{527}(2,\cdot)\)	527.bd	40	yes	\(1\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{21}{40}\right)\)
\(\chi_{527}(3,\cdot)\)	527.bm	240	yes	\(1\)	\(1\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{23}{240}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{149}{240}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{23}{120}\right)\)	\(e\left(\frac{157}{240}\right)\)	\(e\left(\frac{49}{240}\right)\)
\(\chi_{527}(4,\cdot)\)	527.v	20	yes	\(1\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(-i\)	\(i\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)
\(\chi_{527}(5,\cdot)\)	527.be	48	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(-i\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{25}{48}\right)\)
\(\chi_{527}(6,\cdot)\)	527.bf	48	yes	\(1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(i\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{35}{48}\right)\)
\(\chi_{527}(7,\cdot)\)	527.bn	240	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{149}{240}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{167}{240}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{29}{120}\right)\)	\(e\left(\frac{31}{240}\right)\)	\(e\left(\frac{67}{240}\right)\)
\(\chi_{527}(8,\cdot)\)	527.bd	40	yes	\(1\)	\(1\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{23}{40}\right)\)
\(\chi_{527}(9,\cdot)\)	527.bk	120	yes	\(1\)	\(1\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{23}{120}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{29}{120}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{37}{120}\right)\)	\(e\left(\frac{49}{120}\right)\)
\(\chi_{527}(10,\cdot)\)	527.bn	240	yes	\(-1\)	\(1\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{157}{240}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{31}{240}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{37}{120}\right)\)	\(e\left(\frac{23}{240}\right)\)	\(e\left(\frac{11}{240}\right)\)
\(\chi_{527}(11,\cdot)\)	527.bm	240	yes	\(1\)	\(1\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{49}{240}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{67}{240}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{49}{120}\right)\)	\(e\left(\frac{11}{240}\right)\)	\(e\left(\frac{167}{240}\right)\)
\(\chi_{527}(12,\cdot)\)	527.bm	240	yes	\(1\)	\(1\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{107}{240}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{161}{240}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{107}{120}\right)\)	\(e\left(\frac{73}{240}\right)\)	\(e\left(\frac{61}{240}\right)\)
\(\chi_{527}(13,\cdot)\)	527.bg	60	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{11}{60}\right)\)
\(\chi_{527}(14,\cdot)\)	527.bn	240	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{71}{240}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{173}{240}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{71}{120}\right)\)	\(e\left(\frac{229}{240}\right)\)	\(e\left(\frac{193}{240}\right)\)
\(\chi_{527}(15,\cdot)\)	527.bc	40	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{29}{40}\right)\)
\(\chi_{527}(16,\cdot)\)	527.o	10	yes	\(1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{527}(18,\cdot)\)	527.s	15	no	\(1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)
\(\chi_{527}(19,\cdot)\)	527.bk	120	yes	\(1\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{1}{120}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{43}{120}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{59}{120}\right)\)	\(e\left(\frac{23}{120}\right)\)
\(\chi_{527}(20,\cdot)\)	527.bn	240	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{79}{240}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{37}{240}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{79}{120}\right)\)	\(e\left(\frac{221}{240}\right)\)	\(e\left(\frac{137}{240}\right)\)
\(\chi_{527}(21,\cdot)\)	527.bg	60	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{29}{60}\right)\)
\(\chi_{527}(22,\cdot)\)	527.bm	240	yes	\(1\)	\(1\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{211}{240}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{73}{240}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{91}{120}\right)\)	\(e\left(\frac{209}{240}\right)\)	\(e\left(\frac{53}{240}\right)\)
\(\chi_{527}(23,\cdot)\)	527.bj	80	yes	\(1\)	\(1\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{21}{80}\right)\)
\(\chi_{527}(24,\cdot)\)	527.bm	240	yes	\(1\)	\(1\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{29}{240}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{167}{240}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{29}{120}\right)\)	\(e\left(\frac{31}{240}\right)\)	\(e\left(\frac{187}{240}\right)\)
\(\chi_{527}(25,\cdot)\)	527.y	24	yes	\(1\)	\(1\)	\(-i\)	\(e\left(\frac{23}{24}\right)\)	\(-1\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(i\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{1}{24}\right)\)
\(\chi_{527}(26,\cdot)\)	527.x	24	yes	\(-1\)	\(1\)	\(-i\)	\(e\left(\frac{7}{24}\right)\)	\(-1\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(i\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{17}{24}\right)\)
\(\chi_{527}(27,\cdot)\)	527.bj	80	yes	\(1\)	\(1\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{49}{80}\right)\)
\(\chi_{527}(28,\cdot)\)	527.bn	240	yes	\(-1\)	\(1\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{233}{240}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{179}{240}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{113}{120}\right)\)	\(e\left(\frac{187}{240}\right)\)	\(e\left(\frac{79}{240}\right)\)
\(\chi_{527}(29,\cdot)\)	527.bj	80	yes	\(1\)	\(1\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{47}{80}\right)\)
\(\chi_{527}(30,\cdot)\)	527.f	4	yes	\(-1\)	\(1\)	\(-1\)	\(-i\)	\(1\)	\(i\)	\(i\)	\(-i\)	\(-1\)	\(-1\)	\(-i\)	\(i\)
\(\chi_{527}(32,\cdot)\)	527.l	8	no	\(1\)	\(1\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(-1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(-i\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{527}(33,\cdot)\)	527.o	10	yes	\(1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{527}(35,\cdot)\)	527.h	5	no	\(1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)

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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.