LMFDB - Group of Dirichlet characters of modulus 473

Show commands: PariGP / SageMath

sage: H = DirichletGroup(473)

pari: g = idealstar(,473,2)

Character group

sage: G.order() pari: g.no
Order	=	420
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{210}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{473}(431,\cdot)$, $\chi_{473}(89,\cdot)$

First 32 of 420 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$12$
$\chi_{473}(1,\cdot)$	473.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{473}(2,\cdot)$	473.bb	70	yes	$1$	$1$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{5}{14}\right)$
$\chi_{473}(3,\cdot)$	473.be	210	yes	$-1$	$1$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{89}{210}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{167}{210}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{89}{105}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{13}{42}\right)$
$\chi_{473}(4,\cdot)$	473.v	35	yes	$1$	$1$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{5}{7}\right)$
$\chi_{473}(5,\cdot)$	473.be	210	yes	$-1$	$1$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{167}{210}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{101}{210}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{62}{105}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{31}{42}\right)$
$\chi_{473}(6,\cdot)$	473.u	30	yes	$-1$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{473}(7,\cdot)$	473.s	30	yes	$1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{473}(8,\cdot)$	473.bb	70	yes	$1$	$1$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{1}{14}\right)$
$\chi_{473}(9,\cdot)$	473.bc	105	yes	$1$	$1$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{89}{105}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{62}{105}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{73}{105}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{13}{21}\right)$
$\chi_{473}(10,\cdot)$	473.y	42	yes	$-1$	$1$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{2}{21}\right)$
$\chi_{473}(12,\cdot)$	473.x	42	no	$-1$	$1$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{1}{42}\right)$
$\chi_{473}(13,\cdot)$	473.bd	210	yes	$-1$	$1$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{59}{105}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{47}{105}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{13}{105}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{19}{21}\right)$
$\chi_{473}(14,\cdot)$	473.bc	105	yes	$1$	$1$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{92}{105}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{11}{105}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{79}{105}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{4}{21}\right)$
$\chi_{473}(15,\cdot)$	473.bc	105	yes	$1$	$1$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{23}{105}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{29}{105}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{46}{105}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{1}{21}\right)$
$\chi_{473}(16,\cdot)$	473.v	35	yes	$1$	$1$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{3}{7}\right)$
$\chi_{473}(17,\cdot)$	473.bd	210	yes	$-1$	$1$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{11}{105}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{23}{105}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{22}{105}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{16}{21}\right)$
$\chi_{473}(18,\cdot)$	473.bf	210	yes	$1$	$1$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{61}{210}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{13}{210}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{61}{105}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{41}{42}\right)$
$\chi_{473}(19,\cdot)$	473.bf	210	yes	$1$	$1$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{179}{210}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{107}{210}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{74}{105}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{37}{42}\right)$
$\chi_{473}(20,\cdot)$	473.be	210	yes	$-1$	$1$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{143}{210}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{89}{210}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{11}{70}\right)$	$e\left(\frac{38}{105}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{19}{42}\right)$
$\chi_{473}(21,\cdot)$	473.o	14	yes	$-1$	$1$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{3}{7}\right)$	$-1$	$-1$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{1}{7}\right)$
$\chi_{473}(23,\cdot)$	473.r	21	no	$1$	$1$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{20}{21}\right)$
$\chi_{473}(24,\cdot)$	473.bd	210	yes	$-1$	$1$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{79}{105}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{22}{105}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{53}{105}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{8}{21}\right)$
$\chi_{473}(25,\cdot)$	473.bc	105	yes	$1$	$1$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{62}{105}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{101}{105}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{19}{105}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{10}{21}\right)$
$\chi_{473}(26,\cdot)$	473.be	210	yes	$-1$	$1$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{1}{210}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{193}{210}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{1}{105}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{11}{42}\right)$
$\chi_{473}(27,\cdot)$	473.z	70	yes	$-1$	$1$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{13}{14}\right)$
$\chi_{473}(28,\cdot)$	473.bf	210	yes	$1$	$1$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{67}{210}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{121}{210}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{67}{105}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{23}{42}\right)$
$\chi_{473}(29,\cdot)$	473.bf	210	yes	$1$	$1$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{121}{210}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{43}{210}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{16}{105}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{29}{42}\right)$
$\chi_{473}(30,\cdot)$	473.bf	210	yes	$1$	$1$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{139}{210}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{157}{210}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{34}{105}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{17}{42}\right)$
$\chi_{473}(31,\cdot)$	473.bc	105	yes	$1$	$1$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{64}{105}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{67}{105}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{23}{105}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{11}{21}\right)$
$\chi_{473}(32,\cdot)$	473.n	14	yes	$1$	$1$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{5}{14}\right)$	$-1$	$1$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{11}{14}\right)$
$\chi_{473}(34,\cdot)$	473.x	42	no	$-1$	$1$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{5}{42}\right)$
$\chi_{473}(35,\cdot)$	473.ba	70	yes	$-1$	$1$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{4}{7}\right)$

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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	$473$
Structure	\(C_{2}\times C_{210}\)
Order	$420$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(12\)
\(\chi_{473}(1,\cdot)\)	473.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{473}(2,\cdot)\)	473.bb	70	yes	\(1\)	\(1\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{5}{14}\right)\)
\(\chi_{473}(3,\cdot)\)	473.be	210	yes	\(-1\)	\(1\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{89}{210}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{167}{210}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{89}{105}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{13}{42}\right)\)
\(\chi_{473}(4,\cdot)\)	473.v	35	yes	\(1\)	\(1\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{473}(5,\cdot)\)	473.be	210	yes	\(-1\)	\(1\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{167}{210}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{101}{210}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{62}{105}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{31}{42}\right)\)
\(\chi_{473}(6,\cdot)\)	473.u	30	yes	\(-1\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{473}(7,\cdot)\)	473.s	30	yes	\(1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{473}(8,\cdot)\)	473.bb	70	yes	\(1\)	\(1\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{1}{14}\right)\)
\(\chi_{473}(9,\cdot)\)	473.bc	105	yes	\(1\)	\(1\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{89}{105}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{62}{105}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{73}{105}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)
\(\chi_{473}(10,\cdot)\)	473.y	42	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{2}{21}\right)\)
\(\chi_{473}(12,\cdot)\)	473.x	42	no	\(-1\)	\(1\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{1}{42}\right)\)
\(\chi_{473}(13,\cdot)\)	473.bd	210	yes	\(-1\)	\(1\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{59}{105}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{47}{105}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{13}{105}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{19}{21}\right)\)
\(\chi_{473}(14,\cdot)\)	473.bc	105	yes	\(1\)	\(1\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{92}{105}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{11}{105}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{79}{105}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{4}{21}\right)\)
\(\chi_{473}(15,\cdot)\)	473.bc	105	yes	\(1\)	\(1\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{23}{105}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{29}{105}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{46}{105}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{1}{21}\right)\)
\(\chi_{473}(16,\cdot)\)	473.v	35	yes	\(1\)	\(1\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)
\(\chi_{473}(17,\cdot)\)	473.bd	210	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{11}{105}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{23}{105}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{22}{105}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{16}{21}\right)\)
\(\chi_{473}(18,\cdot)\)	473.bf	210	yes	\(1\)	\(1\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{61}{210}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{13}{210}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{61}{105}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{41}{42}\right)\)
\(\chi_{473}(19,\cdot)\)	473.bf	210	yes	\(1\)	\(1\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{179}{210}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{107}{210}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{74}{105}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{37}{42}\right)\)
\(\chi_{473}(20,\cdot)\)	473.be	210	yes	\(-1\)	\(1\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{143}{210}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{89}{210}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{11}{70}\right)\)	\(e\left(\frac{38}{105}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{19}{42}\right)\)
\(\chi_{473}(21,\cdot)\)	473.o	14	yes	\(-1\)	\(1\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)
\(\chi_{473}(23,\cdot)\)	473.r	21	no	\(1\)	\(1\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{20}{21}\right)\)
\(\chi_{473}(24,\cdot)\)	473.bd	210	yes	\(-1\)	\(1\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{79}{105}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{22}{105}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{53}{105}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{8}{21}\right)\)
\(\chi_{473}(25,\cdot)\)	473.bc	105	yes	\(1\)	\(1\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{62}{105}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{101}{105}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{19}{105}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{10}{21}\right)\)
\(\chi_{473}(26,\cdot)\)	473.be	210	yes	\(-1\)	\(1\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{1}{210}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{193}{210}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{1}{105}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{11}{42}\right)\)
\(\chi_{473}(27,\cdot)\)	473.z	70	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)
\(\chi_{473}(28,\cdot)\)	473.bf	210	yes	\(1\)	\(1\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{67}{210}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{121}{210}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{67}{105}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{23}{42}\right)\)
\(\chi_{473}(29,\cdot)\)	473.bf	210	yes	\(1\)	\(1\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{121}{210}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{43}{210}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{16}{105}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{29}{42}\right)\)
\(\chi_{473}(30,\cdot)\)	473.bf	210	yes	\(1\)	\(1\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{139}{210}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{157}{210}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{34}{105}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{17}{42}\right)\)
\(\chi_{473}(31,\cdot)\)	473.bc	105	yes	\(1\)	\(1\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{64}{105}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{67}{105}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{23}{105}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)
\(\chi_{473}(32,\cdot)\)	473.n	14	yes	\(1\)	\(1\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{11}{14}\right)\)
\(\chi_{473}(34,\cdot)\)	473.x	42	no	\(-1\)	\(1\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{5}{42}\right)\)
\(\chi_{473}(35,\cdot)\)	473.ba	70	yes	\(-1\)	\(1\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)

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L-functions

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First 32 of 420 characters

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.