LMFDB - Group of Dirichlet characters of modulus 4851

Show commands: PariGP / SageMath

sage: H = DirichletGroup(4851)

pari: g = idealstar(,4851,2)

Character group

sage: G.order() pari: g.no
Order	=	2520
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{6}\times C_{210}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{4851}(4313,\cdot)$, $\chi_{4851}(199,\cdot)$, $\chi_{4851}(442,\cdot)$

First 32 of 2520 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	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$13$	$16$	$17$	$19$	$20$
$\chi_{4851}(1,\cdot)$	4851.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{4851}(2,\cdot)$	4851.fg	210	yes	$1$	$1$	$e\left(\frac{38}{105}\right)$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{181}{210}\right)$	$e\left(\frac{47}{105}\right)$	$e\left(\frac{92}{105}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{191}{210}\right)$
$\chi_{4851}(4,\cdot)$	4851.fa	105	yes	$1$	$1$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{47}{105}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{94}{105}\right)$	$e\left(\frac{79}{105}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{86}{105}\right)$
$\chi_{4851}(5,\cdot)$	4851.fc	210	yes	$1$	$1$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{83}{105}\right)$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{179}{210}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{38}{105}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{17}{105}\right)$
$\chi_{4851}(8,\cdot)$	4851.ew	70	no	$1$	$1$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{51}{70}\right)$
$\chi_{4851}(10,\cdot)$	4851.dx	42	no	$1$	$1$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{14}\right)$
$\chi_{4851}(13,\cdot)$	4851.fw	210	yes	$1$	$1$	$e\left(\frac{181}{210}\right)$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{179}{210}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{73}{105}\right)$	$e\left(\frac{47}{105}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{121}{210}\right)$
$\chi_{4851}(16,\cdot)$	4851.fa	105	yes	$1$	$1$	$e\left(\frac{47}{105}\right)$	$e\left(\frac{94}{105}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{47}{105}\right)$	$e\left(\frac{83}{105}\right)$	$e\left(\frac{53}{105}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{67}{105}\right)$
$\chi_{4851}(17,\cdot)$	4851.fj	210	no	$-1$	$1$	$e\left(\frac{92}{105}\right)$	$e\left(\frac{79}{105}\right)$	$e\left(\frac{38}{105}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{53}{105}\right)$	$e\left(\frac{101}{210}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{4}{35}\right)$
$\chi_{4851}(19,\cdot)$	4851.cs	30	no	$1$	$1$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{4851}(20,\cdot)$	4851.fu	210	yes	$1$	$1$	$e\left(\frac{191}{210}\right)$	$e\left(\frac{86}{105}\right)$	$e\left(\frac{17}{105}\right)$	$e\left(\frac{51}{70}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{121}{210}\right)$	$e\left(\frac{67}{105}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{103}{105}\right)$
$\chi_{4851}(23,\cdot)$	4851.en	42	no	$-1$	$1$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{42}\right)$
$\chi_{4851}(25,\cdot)$	4851.fb	105	yes	$1$	$1$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{61}{105}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{74}{105}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{34}{105}\right)$
$\chi_{4851}(26,\cdot)$	4851.fr	210	no	$1$	$1$	$e\left(\frac{47}{210}\right)$	$e\left(\frac{47}{105}\right)$	$e\left(\frac{4}{105}\right)$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{94}{105}\right)$	$e\left(\frac{44}{105}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{17}{35}\right)$
$\chi_{4851}(29,\cdot)$	4851.fn	210	yes	$1$	$1$	$e\left(\frac{1}{105}\right)$	$e\left(\frac{2}{105}\right)$	$e\left(\frac{13}{210}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{37}{210}\right)$	$e\left(\frac{4}{105}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{17}{210}\right)$
$\chi_{4851}(31,\cdot)$	4851.di	30	no	$-1$	$1$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{13}{30}\right)$
$\chi_{4851}(32,\cdot)$	4851.em	42	yes	$1$	$1$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{23}{42}\right)$
$\chi_{4851}(34,\cdot)$	4851.ei	42	no	$-1$	$1$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{5}{14}\right)$	$-1$	$e\left(\frac{1}{42}\right)$
$\chi_{4851}(37,\cdot)$	4851.ez	105	no	$1$	$1$	$e\left(\frac{1}{105}\right)$	$e\left(\frac{2}{105}\right)$	$e\left(\frac{94}{105}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{4}{105}\right)$	$e\left(\frac{89}{105}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{32}{35}\right)$
$\chi_{4851}(38,\cdot)$	4851.fc	210	yes	$1$	$1$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{58}{105}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{139}{210}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{43}{105}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{22}{105}\right)$
$\chi_{4851}(40,\cdot)$	4851.fe	210	yes	$1$	$1$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{73}{210}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{46}{105}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{104}{105}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{187}{210}\right)$
$\chi_{4851}(41,\cdot)$	4851.fi	210	yes	$-1$	$1$	$e\left(\frac{44}{105}\right)$	$e\left(\frac{88}{105}\right)$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{79}{105}\right)$	$e\left(\frac{71}{105}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{59}{105}\right)$
$\chi_{4851}(43,\cdot)$	4851.eb	42	yes	$-1$	$1$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{1}{14}\right)$	$-1$	$e\left(\frac{5}{21}\right)$
$\chi_{4851}(46,\cdot)$	4851.fs	210	no	$-1$	$1$	$e\left(\frac{151}{210}\right)$	$e\left(\frac{46}{105}\right)$	$e\left(\frac{62}{105}\right)$	$e\left(\frac{11}{70}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{92}{105}\right)$	$e\left(\frac{209}{210}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{35}\right)$
$\chi_{4851}(47,\cdot)$	4851.fz	210	yes	$1$	$1$	$e\left(\frac{13}{210}\right)$	$e\left(\frac{13}{105}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{13}{210}\right)$	$e\left(\frac{26}{105}\right)$	$e\left(\frac{71}{105}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{64}{105}\right)$
$\chi_{4851}(50,\cdot)$	4851.dc	30	no	$1$	$1$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{1}{5}\right)$	$-1$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{30}\right)$
$\chi_{4851}(52,\cdot)$	4851.fe	210	yes	$1$	$1$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{47}{210}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{44}{105}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{31}{105}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{83}{210}\right)$
$\chi_{4851}(53,\cdot)$	4851.fy	210	no	$-1$	$1$	$e\left(\frac{61}{210}\right)$	$e\left(\frac{61}{105}\right)$	$e\left(\frac{169}{210}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{17}{105}\right)$	$e\left(\frac{179}{210}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{27}{70}\right)$
$\chi_{4851}(58,\cdot)$	4851.fb	105	yes	$1$	$1$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{26}{105}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{4}{105}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{41}{105}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{104}{105}\right)$
$\chi_{4851}(59,\cdot)$	4851.fz	210	yes	$1$	$1$	$e\left(\frac{17}{210}\right)$	$e\left(\frac{17}{105}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{17}{70}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{17}{210}\right)$	$e\left(\frac{34}{105}\right)$	$e\left(\frac{4}{105}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{11}{105}\right)$
$\chi_{4851}(61,\cdot)$	4851.fp	210	yes	$1$	$1$	$e\left(\frac{79}{210}\right)$	$e\left(\frac{79}{105}\right)$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{92}{105}\right)$	$e\left(\frac{53}{105}\right)$	$e\left(\frac{68}{105}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{59}{210}\right)$
$\chi_{4851}(62,\cdot)$	4851.ex	70	no	$-1$	$1$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{12}{35}\right)$

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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	$4851$
Structure	\(C_{2}\times C_{6}\times C_{210}\)
Order	$2520$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(8\)	\(10\)	\(13\)	\(16\)	\(17\)	\(19\)	\(20\)
\(\chi_{4851}(1,\cdot)\)	4851.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{4851}(2,\cdot)\)	4851.fg	210	yes	\(1\)	\(1\)	\(e\left(\frac{38}{105}\right)\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{181}{210}\right)\)	\(e\left(\frac{47}{105}\right)\)	\(e\left(\frac{92}{105}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{191}{210}\right)\)
\(\chi_{4851}(4,\cdot)\)	4851.fa	105	yes	\(1\)	\(1\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{47}{105}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{94}{105}\right)\)	\(e\left(\frac{79}{105}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{86}{105}\right)\)
\(\chi_{4851}(5,\cdot)\)	4851.fc	210	yes	\(1\)	\(1\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{83}{105}\right)\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{179}{210}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{38}{105}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{17}{105}\right)\)
\(\chi_{4851}(8,\cdot)\)	4851.ew	70	no	\(1\)	\(1\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{51}{70}\right)\)
\(\chi_{4851}(10,\cdot)\)	4851.dx	42	no	\(1\)	\(1\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{14}\right)\)
\(\chi_{4851}(13,\cdot)\)	4851.fw	210	yes	\(1\)	\(1\)	\(e\left(\frac{181}{210}\right)\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{179}{210}\right)\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{73}{105}\right)\)	\(e\left(\frac{47}{105}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{121}{210}\right)\)
\(\chi_{4851}(16,\cdot)\)	4851.fa	105	yes	\(1\)	\(1\)	\(e\left(\frac{47}{105}\right)\)	\(e\left(\frac{94}{105}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{47}{105}\right)\)	\(e\left(\frac{83}{105}\right)\)	\(e\left(\frac{53}{105}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{67}{105}\right)\)
\(\chi_{4851}(17,\cdot)\)	4851.fj	210	no	\(-1\)	\(1\)	\(e\left(\frac{92}{105}\right)\)	\(e\left(\frac{79}{105}\right)\)	\(e\left(\frac{38}{105}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{53}{105}\right)\)	\(e\left(\frac{101}{210}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{4}{35}\right)\)
\(\chi_{4851}(19,\cdot)\)	4851.cs	30	no	\(1\)	\(1\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{4851}(20,\cdot)\)	4851.fu	210	yes	\(1\)	\(1\)	\(e\left(\frac{191}{210}\right)\)	\(e\left(\frac{86}{105}\right)\)	\(e\left(\frac{17}{105}\right)\)	\(e\left(\frac{51}{70}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{121}{210}\right)\)	\(e\left(\frac{67}{105}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{103}{105}\right)\)
\(\chi_{4851}(23,\cdot)\)	4851.en	42	no	\(-1\)	\(1\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{42}\right)\)
\(\chi_{4851}(25,\cdot)\)	4851.fb	105	yes	\(1\)	\(1\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{61}{105}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{74}{105}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{34}{105}\right)\)
\(\chi_{4851}(26,\cdot)\)	4851.fr	210	no	\(1\)	\(1\)	\(e\left(\frac{47}{210}\right)\)	\(e\left(\frac{47}{105}\right)\)	\(e\left(\frac{4}{105}\right)\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{94}{105}\right)\)	\(e\left(\frac{44}{105}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{17}{35}\right)\)
\(\chi_{4851}(29,\cdot)\)	4851.fn	210	yes	\(1\)	\(1\)	\(e\left(\frac{1}{105}\right)\)	\(e\left(\frac{2}{105}\right)\)	\(e\left(\frac{13}{210}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{37}{210}\right)\)	\(e\left(\frac{4}{105}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{17}{210}\right)\)
\(\chi_{4851}(31,\cdot)\)	4851.di	30	no	\(-1\)	\(1\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{13}{30}\right)\)
\(\chi_{4851}(32,\cdot)\)	4851.em	42	yes	\(1\)	\(1\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{23}{42}\right)\)
\(\chi_{4851}(34,\cdot)\)	4851.ei	42	no	\(-1\)	\(1\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(-1\)	\(e\left(\frac{1}{42}\right)\)
\(\chi_{4851}(37,\cdot)\)	4851.ez	105	no	\(1\)	\(1\)	\(e\left(\frac{1}{105}\right)\)	\(e\left(\frac{2}{105}\right)\)	\(e\left(\frac{94}{105}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{4}{105}\right)\)	\(e\left(\frac{89}{105}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{32}{35}\right)\)
\(\chi_{4851}(38,\cdot)\)	4851.fc	210	yes	\(1\)	\(1\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{58}{105}\right)\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{139}{210}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{43}{105}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{22}{105}\right)\)
\(\chi_{4851}(40,\cdot)\)	4851.fe	210	yes	\(1\)	\(1\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{73}{210}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{46}{105}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{104}{105}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{187}{210}\right)\)
\(\chi_{4851}(41,\cdot)\)	4851.fi	210	yes	\(-1\)	\(1\)	\(e\left(\frac{44}{105}\right)\)	\(e\left(\frac{88}{105}\right)\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{79}{105}\right)\)	\(e\left(\frac{71}{105}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{59}{105}\right)\)
\(\chi_{4851}(43,\cdot)\)	4851.eb	42	yes	\(-1\)	\(1\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(-1\)	\(e\left(\frac{5}{21}\right)\)
\(\chi_{4851}(46,\cdot)\)	4851.fs	210	no	\(-1\)	\(1\)	\(e\left(\frac{151}{210}\right)\)	\(e\left(\frac{46}{105}\right)\)	\(e\left(\frac{62}{105}\right)\)	\(e\left(\frac{11}{70}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{92}{105}\right)\)	\(e\left(\frac{209}{210}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{35}\right)\)
\(\chi_{4851}(47,\cdot)\)	4851.fz	210	yes	\(1\)	\(1\)	\(e\left(\frac{13}{210}\right)\)	\(e\left(\frac{13}{105}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{13}{210}\right)\)	\(e\left(\frac{26}{105}\right)\)	\(e\left(\frac{71}{105}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{64}{105}\right)\)
\(\chi_{4851}(50,\cdot)\)	4851.dc	30	no	\(1\)	\(1\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(-1\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{30}\right)\)
\(\chi_{4851}(52,\cdot)\)	4851.fe	210	yes	\(1\)	\(1\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{47}{210}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{44}{105}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{31}{105}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{83}{210}\right)\)
\(\chi_{4851}(53,\cdot)\)	4851.fy	210	no	\(-1\)	\(1\)	\(e\left(\frac{61}{210}\right)\)	\(e\left(\frac{61}{105}\right)\)	\(e\left(\frac{169}{210}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{17}{105}\right)\)	\(e\left(\frac{179}{210}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{27}{70}\right)\)
\(\chi_{4851}(58,\cdot)\)	4851.fb	105	yes	\(1\)	\(1\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{26}{105}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{4}{105}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{41}{105}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{104}{105}\right)\)
\(\chi_{4851}(59,\cdot)\)	4851.fz	210	yes	\(1\)	\(1\)	\(e\left(\frac{17}{210}\right)\)	\(e\left(\frac{17}{105}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{17}{70}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{17}{210}\right)\)	\(e\left(\frac{34}{105}\right)\)	\(e\left(\frac{4}{105}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{11}{105}\right)\)
\(\chi_{4851}(61,\cdot)\)	4851.fp	210	yes	\(1\)	\(1\)	\(e\left(\frac{79}{210}\right)\)	\(e\left(\frac{79}{105}\right)\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{92}{105}\right)\)	\(e\left(\frac{53}{105}\right)\)	\(e\left(\frac{68}{105}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{59}{210}\right)\)
\(\chi_{4851}(62,\cdot)\)	4851.ex	70	no	\(-1\)	\(1\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{12}{35}\right)\)

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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.