LMFDB - Group of Dirichlet characters of modulus 629

Show commands: PariGP / SageMath

sage: H = DirichletGroup(629)

pari: g = idealstar(,629,2)

Character group

sage: G.order() pari: g.no
Order	=	576
sage: H.invariants() pari: g.cyc
Structure	=	$C_{4}\times C_{144}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{629}(445,\cdot)$, $\chi_{629}(409,\cdot)$

First 32 of 576 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{629}(1,\cdot)$	629.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{629}(2,\cdot)$	629.bx	72	yes	$-1$	$1$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{72}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{23}{24}\right)$
$\chi_{629}(3,\cdot)$	629.cb	144	yes	$-1$	$1$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{121}{144}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{133}{144}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{115}{144}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{49}{72}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{5}{48}\right)$
$\chi_{629}(4,\cdot)$	629.bl	36	yes	$1$	$1$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{36}\right)$	$-i$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{629}(5,\cdot)$	629.bz	144	yes	$1$	$1$	$e\left(\frac{1}{72}\right)$	$e\left(\frac{133}{144}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{37}{144}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{127}{144}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{17}{48}\right)$
$\chi_{629}(6,\cdot)$	629.bc	16	yes	$1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{16}\right)$	$-i$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{1}{16}\right)$
$\chi_{629}(7,\cdot)$	629.ca	144	yes	$-1$	$1$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{115}{144}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{127}{144}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{1}{144}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{23}{48}\right)$
$\chi_{629}(8,\cdot)$	629.bj	24	yes	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{13}{24}\right)$	$-1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{629}(9,\cdot)$	629.bv	72	yes	$1$	$1$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{49}{72}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{5}{24}\right)$
$\chi_{629}(10,\cdot)$	629.br	48	yes	$-1$	$1$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{5}{16}\right)$
$\chi_{629}(11,\cdot)$	629.bs	48	yes	$-1$	$1$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{1}{16}\right)$
$\chi_{629}(12,\cdot)$	629.ca	144	yes	$-1$	$1$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{5}{144}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{137}{144}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{119}{144}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{5}{72}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{1}{48}\right)$
$\chi_{629}(13,\cdot)$	629.bp	36	yes	$-1$	$1$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{5}{18}\right)$	$1$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{629}(14,\cdot)$	629.bq	48	yes	$1$	$1$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{7}{16}\right)$
$\chi_{629}(15,\cdot)$	629.bx	72	yes	$-1$	$1$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{55}{72}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{13}{72}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{49}{72}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{11}{24}\right)$
$\chi_{629}(16,\cdot)$	629.bd	18	yes	$1$	$1$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{18}\right)$	$-1$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{629}(18,\cdot)$	629.bm	36	no	$-1$	$1$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{31}{36}\right)$	$-i$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{629}(19,\cdot)$	629.bu	72	yes	$-1$	$1$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{53}{72}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{53}{72}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{7}{24}\right)$
$\chi_{629}(20,\cdot)$	629.by	144	yes	$1$	$1$	$e\left(\frac{41}{72}\right)$	$e\left(\frac{17}{144}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{41}{144}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{131}{144}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{17}{72}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{13}{48}\right)$
$\chi_{629}(21,\cdot)$	629.bl	36	yes	$1$	$1$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{29}{36}\right)$	$-i$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{629}(22,\cdot)$	629.bz	144	yes	$1$	$1$	$e\left(\frac{17}{72}\right)$	$e\left(\frac{101}{144}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{53}{144}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{143}{144}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{29}{72}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{1}{48}\right)$
$\chi_{629}(23,\cdot)$	629.bq	48	yes	$1$	$1$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{1}{16}\right)$
$\chi_{629}(24,\cdot)$	629.bz	144	yes	$1$	$1$	$e\left(\frac{31}{72}\right)$	$e\left(\frac{91}{144}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{139}{144}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{49}{144}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{19}{72}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{47}{48}\right)$
$\chi_{629}(25,\cdot)$	629.bw	72	yes	$1$	$1$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{55}{72}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{17}{24}\right)$
$\chi_{629}(26,\cdot)$	629.bi	24	yes	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{24}\right)$	$i$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{629}(27,\cdot)$	629.bs	48	yes	$-1$	$1$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{5}{16}\right)$
$\chi_{629}(28,\cdot)$	629.cb	144	yes	$-1$	$1$	$e\left(\frac{5}{72}\right)$	$e\left(\frac{143}{144}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{131}{144}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{5}{144}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{71}{72}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{19}{48}\right)$
$\chi_{629}(29,\cdot)$	629.bq	48	yes	$1$	$1$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{3}{16}\right)$
$\chi_{629}(30,\cdot)$	629.bl	36	yes	$1$	$1$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{7}{36}\right)$	$i$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{629}(31,\cdot)$	629.bc	16	yes	$1$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{16}\right)$	$i$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{7}{16}\right)$
$\chi_{629}(32,\cdot)$	629.bx	72	yes	$-1$	$1$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{71}{72}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{72}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{41}{72}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{19}{24}\right)$
$\chi_{629}(33,\cdot)$	629.bd	18	yes	$1$	$1$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{5}{18}\right)$	$-1$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

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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	$629$
Structure	\(C_{4}\times C_{144}\)
Order	$576$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{629}(1,\cdot)\)	629.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{629}(2,\cdot)\)	629.bx	72	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{72}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{23}{24}\right)\)
\(\chi_{629}(3,\cdot)\)	629.cb	144	yes	\(-1\)	\(1\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{121}{144}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{133}{144}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{115}{144}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{49}{72}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{5}{48}\right)\)
\(\chi_{629}(4,\cdot)\)	629.bl	36	yes	\(1\)	\(1\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(-i\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{629}(5,\cdot)\)	629.bz	144	yes	\(1\)	\(1\)	\(e\left(\frac{1}{72}\right)\)	\(e\left(\frac{133}{144}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{37}{144}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{127}{144}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{61}{72}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{17}{48}\right)\)
\(\chi_{629}(6,\cdot)\)	629.bc	16	yes	\(1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(-i\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)
\(\chi_{629}(7,\cdot)\)	629.ca	144	yes	\(-1\)	\(1\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{115}{144}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{127}{144}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{1}{144}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{23}{48}\right)\)
\(\chi_{629}(8,\cdot)\)	629.bj	24	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(-1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{629}(9,\cdot)\)	629.bv	72	yes	\(1\)	\(1\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{49}{72}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{61}{72}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{5}{24}\right)\)
\(\chi_{629}(10,\cdot)\)	629.br	48	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)
\(\chi_{629}(11,\cdot)\)	629.bs	48	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)
\(\chi_{629}(12,\cdot)\)	629.ca	144	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{5}{144}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{137}{144}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{119}{144}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{5}{72}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{1}{48}\right)\)
\(\chi_{629}(13,\cdot)\)	629.bp	36	yes	\(-1\)	\(1\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(1\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{629}(14,\cdot)\)	629.bq	48	yes	\(1\)	\(1\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)
\(\chi_{629}(15,\cdot)\)	629.bx	72	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{55}{72}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{13}{72}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{49}{72}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{11}{24}\right)\)
\(\chi_{629}(16,\cdot)\)	629.bd	18	yes	\(1\)	\(1\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(-1\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{629}(18,\cdot)\)	629.bm	36	no	\(-1\)	\(1\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(-i\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{629}(19,\cdot)\)	629.bu	72	yes	\(-1\)	\(1\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{53}{72}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{53}{72}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{7}{24}\right)\)
\(\chi_{629}(20,\cdot)\)	629.by	144	yes	\(1\)	\(1\)	\(e\left(\frac{41}{72}\right)\)	\(e\left(\frac{17}{144}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{41}{144}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{131}{144}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{17}{72}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{13}{48}\right)\)
\(\chi_{629}(21,\cdot)\)	629.bl	36	yes	\(1\)	\(1\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(-i\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{629}(22,\cdot)\)	629.bz	144	yes	\(1\)	\(1\)	\(e\left(\frac{17}{72}\right)\)	\(e\left(\frac{101}{144}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{53}{144}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{143}{144}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{29}{72}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{1}{48}\right)\)
\(\chi_{629}(23,\cdot)\)	629.bq	48	yes	\(1\)	\(1\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)
\(\chi_{629}(24,\cdot)\)	629.bz	144	yes	\(1\)	\(1\)	\(e\left(\frac{31}{72}\right)\)	\(e\left(\frac{91}{144}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{139}{144}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{49}{144}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{19}{72}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{47}{48}\right)\)
\(\chi_{629}(25,\cdot)\)	629.bw	72	yes	\(1\)	\(1\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{61}{72}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{55}{72}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{17}{24}\right)\)
\(\chi_{629}(26,\cdot)\)	629.bi	24	yes	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(i\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{629}(27,\cdot)\)	629.bs	48	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)
\(\chi_{629}(28,\cdot)\)	629.cb	144	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{72}\right)\)	\(e\left(\frac{143}{144}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{131}{144}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{5}{144}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{71}{72}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{19}{48}\right)\)
\(\chi_{629}(29,\cdot)\)	629.bq	48	yes	\(1\)	\(1\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)
\(\chi_{629}(30,\cdot)\)	629.bl	36	yes	\(1\)	\(1\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(i\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{629}(31,\cdot)\)	629.bc	16	yes	\(1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(i\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)
\(\chi_{629}(32,\cdot)\)	629.bx	72	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{71}{72}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{5}{72}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{41}{72}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{19}{24}\right)\)
\(\chi_{629}(33,\cdot)\)	629.bd	18	yes	\(1\)	\(1\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(-1\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)

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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.