LMFDB - Group of Dirichlet characters of modulus 421

Show commands: PariGP / SageMath

sage: H = DirichletGroup(421)

pari: g = idealstar(,421,2)

Character group

sage: G.order() pari: g.no
Order	=	420
sage: H.invariants() pari: g.cyc
Structure	=	$C_{420}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{421}(2,\cdot)$

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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{421}(1,\cdot)$	421.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{421}(2,\cdot)$	421.x	420	yes	$-1$	$1$	$e\left(\frac{1}{420}\right)$	$e\left(\frac{101}{105}\right)$	$e\left(\frac{1}{210}\right)$	$e\left(\frac{139}{210}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{1}{140}\right)$	$e\left(\frac{97}{105}\right)$	$e\left(\frac{93}{140}\right)$	$e\left(\frac{94}{105}\right)$
$\chi_{421}(3,\cdot)$	421.u	105	yes	$1$	$1$	$e\left(\frac{101}{105}\right)$	$e\left(\frac{64}{105}\right)$	$e\left(\frac{97}{105}\right)$	$e\left(\frac{43}{105}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{23}{105}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{71}{105}\right)$
$\chi_{421}(4,\cdot)$	421.w	210	yes	$1$	$1$	$e\left(\frac{1}{210}\right)$	$e\left(\frac{97}{105}\right)$	$e\left(\frac{1}{105}\right)$	$e\left(\frac{34}{105}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{89}{105}\right)$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{83}{105}\right)$
$\chi_{421}(5,\cdot)$	421.w	210	yes	$1$	$1$	$e\left(\frac{139}{210}\right)$	$e\left(\frac{43}{105}\right)$	$e\left(\frac{34}{105}\right)$	$e\left(\frac{1}{105}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{86}{105}\right)$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{92}{105}\right)$
$\chi_{421}(6,\cdot)$	421.n	28	yes	$-1$	$1$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{4}{7}\right)$
$\chi_{421}(7,\cdot)$	421.s	70	yes	$1$	$1$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{23}{35}\right)$
$\chi_{421}(8,\cdot)$	421.v	140	yes	$-1$	$1$	$e\left(\frac{1}{140}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{3}{140}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{139}{140}\right)$	$e\left(\frac{24}{35}\right)$
$\chi_{421}(9,\cdot)$	421.u	105	yes	$1$	$1$	$e\left(\frac{97}{105}\right)$	$e\left(\frac{23}{105}\right)$	$e\left(\frac{89}{105}\right)$	$e\left(\frac{86}{105}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{46}{105}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{37}{105}\right)$
$\chi_{421}(10,\cdot)$	421.v	140	yes	$-1$	$1$	$e\left(\frac{93}{140}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{139}{140}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{47}{140}\right)$	$e\left(\frac{27}{35}\right)$
$\chi_{421}(11,\cdot)$	421.u	105	yes	$1$	$1$	$e\left(\frac{94}{105}\right)$	$e\left(\frac{71}{105}\right)$	$e\left(\frac{83}{105}\right)$	$e\left(\frac{92}{105}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{37}{105}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{64}{105}\right)$
$\chi_{421}(12,\cdot)$	421.o	30	yes	$1$	$1$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{11}{15}\right)$	$-1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{15}\right)$
$\chi_{421}(13,\cdot)$	421.l	20	yes	$-1$	$1$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{10}\right)$	$-i$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{421}(14,\cdot)$	421.x	420	yes	$-1$	$1$	$e\left(\frac{367}{420}\right)$	$e\left(\frac{2}{105}\right)$	$e\left(\frac{157}{210}\right)$	$e\left(\frac{193}{210}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{87}{140}\right)$	$e\left(\frac{4}{105}\right)$	$e\left(\frac{111}{140}\right)$	$e\left(\frac{58}{105}\right)$
$\chi_{421}(15,\cdot)$	421.w	210	yes	$1$	$1$	$e\left(\frac{131}{210}\right)$	$e\left(\frac{2}{105}\right)$	$e\left(\frac{26}{105}\right)$	$e\left(\frac{44}{105}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{4}{105}\right)$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{58}{105}\right)$
$\chi_{421}(16,\cdot)$	421.u	105	yes	$1$	$1$	$e\left(\frac{1}{105}\right)$	$e\left(\frac{89}{105}\right)$	$e\left(\frac{2}{105}\right)$	$e\left(\frac{68}{105}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{73}{105}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{61}{105}\right)$
$\chi_{421}(17,\cdot)$	421.w	210	yes	$1$	$1$	$e\left(\frac{143}{210}\right)$	$e\left(\frac{11}{105}\right)$	$e\left(\frac{38}{105}\right)$	$e\left(\frac{32}{105}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{22}{105}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{4}{105}\right)$
$\chi_{421}(18,\cdot)$	421.x	420	yes	$-1$	$1$	$e\left(\frac{389}{420}\right)$	$e\left(\frac{19}{105}\right)$	$e\left(\frac{179}{210}\right)$	$e\left(\frac{101}{210}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{109}{140}\right)$	$e\left(\frac{38}{105}\right)$	$e\left(\frac{57}{140}\right)$	$e\left(\frac{26}{105}\right)$
$\chi_{421}(19,\cdot)$	421.v	140	yes	$-1$	$1$	$e\left(\frac{79}{140}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{97}{140}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{61}{140}\right)$	$e\left(\frac{6}{35}\right)$
$\chi_{421}(20,\cdot)$	421.c	3	yes	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$
$\chi_{421}(21,\cdot)$	421.f	6	yes	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$1$	$-1$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{1}{3}\right)$
$\chi_{421}(22,\cdot)$	421.x	420	yes	$-1$	$1$	$e\left(\frac{377}{420}\right)$	$e\left(\frac{67}{105}\right)$	$e\left(\frac{167}{210}\right)$	$e\left(\frac{113}{210}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{97}{140}\right)$	$e\left(\frac{29}{105}\right)$	$e\left(\frac{61}{140}\right)$	$e\left(\frac{53}{105}\right)$
$\chi_{421}(23,\cdot)$	421.x	420	yes	$-1$	$1$	$e\left(\frac{187}{420}\right)$	$e\left(\frac{92}{105}\right)$	$e\left(\frac{187}{210}\right)$	$e\left(\frac{163}{210}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{47}{140}\right)$	$e\left(\frac{79}{105}\right)$	$e\left(\frac{31}{140}\right)$	$e\left(\frac{43}{105}\right)$
$\chi_{421}(24,\cdot)$	421.x	420	yes	$-1$	$1$	$e\left(\frac{407}{420}\right)$	$e\left(\frac{52}{105}\right)$	$e\left(\frac{197}{210}\right)$	$e\left(\frac{83}{210}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{127}{140}\right)$	$e\left(\frac{104}{105}\right)$	$e\left(\frac{51}{140}\right)$	$e\left(\frac{38}{105}\right)$
$\chi_{421}(25,\cdot)$	421.u	105	yes	$1$	$1$	$e\left(\frac{34}{105}\right)$	$e\left(\frac{86}{105}\right)$	$e\left(\frac{68}{105}\right)$	$e\left(\frac{2}{105}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{67}{105}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{79}{105}\right)$
$\chi_{421}(26,\cdot)$	421.u	105	yes	$1$	$1$	$e\left(\frac{16}{105}\right)$	$e\left(\frac{59}{105}\right)$	$e\left(\frac{32}{105}\right)$	$e\left(\frac{38}{105}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{13}{105}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{31}{105}\right)$
$\chi_{421}(27,\cdot)$	421.p	35	yes	$1$	$1$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{1}{35}\right)$
$\chi_{421}(28,\cdot)$	421.u	105	yes	$1$	$1$	$e\left(\frac{92}{105}\right)$	$e\left(\frac{103}{105}\right)$	$e\left(\frac{79}{105}\right)$	$e\left(\frac{61}{105}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{101}{105}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{47}{105}\right)$
$\chi_{421}(29,\cdot)$	421.d	4	yes	$-1$	$1$	$i$	$1$	$-1$	$-1$	$i$	$-1$	$-i$	$1$	$-i$	$1$
$\chi_{421}(30,\cdot)$	421.x	420	yes	$-1$	$1$	$e\left(\frac{263}{420}\right)$	$e\left(\frac{103}{105}\right)$	$e\left(\frac{53}{210}\right)$	$e\left(\frac{17}{210}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{123}{140}\right)$	$e\left(\frac{101}{105}\right)$	$e\left(\frac{99}{140}\right)$	$e\left(\frac{47}{105}\right)$
$\chi_{421}(31,\cdot)$	421.u	105	yes	$1$	$1$	$e\left(\frac{29}{105}\right)$	$e\left(\frac{61}{105}\right)$	$e\left(\frac{58}{105}\right)$	$e\left(\frac{82}{105}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{17}{105}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{89}{105}\right)$
$\chi_{421}(32,\cdot)$	421.t	84	yes	$-1$	$1$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{10}{21}\right)$

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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	$421$
Structure	\(C_{420}\)
Order	$420$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{421}(1,\cdot)\)	421.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{421}(2,\cdot)\)	421.x	420	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{420}\right)\)	\(e\left(\frac{101}{105}\right)\)	\(e\left(\frac{1}{210}\right)\)	\(e\left(\frac{139}{210}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{1}{140}\right)\)	\(e\left(\frac{97}{105}\right)\)	\(e\left(\frac{93}{140}\right)\)	\(e\left(\frac{94}{105}\right)\)
\(\chi_{421}(3,\cdot)\)	421.u	105	yes	\(1\)	\(1\)	\(e\left(\frac{101}{105}\right)\)	\(e\left(\frac{64}{105}\right)\)	\(e\left(\frac{97}{105}\right)\)	\(e\left(\frac{43}{105}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{23}{105}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{71}{105}\right)\)
\(\chi_{421}(4,\cdot)\)	421.w	210	yes	\(1\)	\(1\)	\(e\left(\frac{1}{210}\right)\)	\(e\left(\frac{97}{105}\right)\)	\(e\left(\frac{1}{105}\right)\)	\(e\left(\frac{34}{105}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{89}{105}\right)\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{83}{105}\right)\)
\(\chi_{421}(5,\cdot)\)	421.w	210	yes	\(1\)	\(1\)	\(e\left(\frac{139}{210}\right)\)	\(e\left(\frac{43}{105}\right)\)	\(e\left(\frac{34}{105}\right)\)	\(e\left(\frac{1}{105}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{86}{105}\right)\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{92}{105}\right)\)
\(\chi_{421}(6,\cdot)\)	421.n	28	yes	\(-1\)	\(1\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{4}{7}\right)\)
\(\chi_{421}(7,\cdot)\)	421.s	70	yes	\(1\)	\(1\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{23}{35}\right)\)
\(\chi_{421}(8,\cdot)\)	421.v	140	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{140}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{3}{140}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{139}{140}\right)\)	\(e\left(\frac{24}{35}\right)\)
\(\chi_{421}(9,\cdot)\)	421.u	105	yes	\(1\)	\(1\)	\(e\left(\frac{97}{105}\right)\)	\(e\left(\frac{23}{105}\right)\)	\(e\left(\frac{89}{105}\right)\)	\(e\left(\frac{86}{105}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{46}{105}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{37}{105}\right)\)
\(\chi_{421}(10,\cdot)\)	421.v	140	yes	\(-1\)	\(1\)	\(e\left(\frac{93}{140}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{139}{140}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{47}{140}\right)\)	\(e\left(\frac{27}{35}\right)\)
\(\chi_{421}(11,\cdot)\)	421.u	105	yes	\(1\)	\(1\)	\(e\left(\frac{94}{105}\right)\)	\(e\left(\frac{71}{105}\right)\)	\(e\left(\frac{83}{105}\right)\)	\(e\left(\frac{92}{105}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{37}{105}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{64}{105}\right)\)
\(\chi_{421}(12,\cdot)\)	421.o	30	yes	\(1\)	\(1\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(-1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{15}\right)\)
\(\chi_{421}(13,\cdot)\)	421.l	20	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(-i\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{421}(14,\cdot)\)	421.x	420	yes	\(-1\)	\(1\)	\(e\left(\frac{367}{420}\right)\)	\(e\left(\frac{2}{105}\right)\)	\(e\left(\frac{157}{210}\right)\)	\(e\left(\frac{193}{210}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{87}{140}\right)\)	\(e\left(\frac{4}{105}\right)\)	\(e\left(\frac{111}{140}\right)\)	\(e\left(\frac{58}{105}\right)\)
\(\chi_{421}(15,\cdot)\)	421.w	210	yes	\(1\)	\(1\)	\(e\left(\frac{131}{210}\right)\)	\(e\left(\frac{2}{105}\right)\)	\(e\left(\frac{26}{105}\right)\)	\(e\left(\frac{44}{105}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{4}{105}\right)\)	\(e\left(\frac{3}{70}\right)\)	\(e\left(\frac{58}{105}\right)\)
\(\chi_{421}(16,\cdot)\)	421.u	105	yes	\(1\)	\(1\)	\(e\left(\frac{1}{105}\right)\)	\(e\left(\frac{89}{105}\right)\)	\(e\left(\frac{2}{105}\right)\)	\(e\left(\frac{68}{105}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{73}{105}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{61}{105}\right)\)
\(\chi_{421}(17,\cdot)\)	421.w	210	yes	\(1\)	\(1\)	\(e\left(\frac{143}{210}\right)\)	\(e\left(\frac{11}{105}\right)\)	\(e\left(\frac{38}{105}\right)\)	\(e\left(\frac{32}{105}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{3}{70}\right)\)	\(e\left(\frac{22}{105}\right)\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{4}{105}\right)\)
\(\chi_{421}(18,\cdot)\)	421.x	420	yes	\(-1\)	\(1\)	\(e\left(\frac{389}{420}\right)\)	\(e\left(\frac{19}{105}\right)\)	\(e\left(\frac{179}{210}\right)\)	\(e\left(\frac{101}{210}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{109}{140}\right)\)	\(e\left(\frac{38}{105}\right)\)	\(e\left(\frac{57}{140}\right)\)	\(e\left(\frac{26}{105}\right)\)
\(\chi_{421}(19,\cdot)\)	421.v	140	yes	\(-1\)	\(1\)	\(e\left(\frac{79}{140}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{97}{140}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{61}{140}\right)\)	\(e\left(\frac{6}{35}\right)\)
\(\chi_{421}(20,\cdot)\)	421.c	3	yes	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{421}(21,\cdot)\)	421.f	6	yes	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{421}(22,\cdot)\)	421.x	420	yes	\(-1\)	\(1\)	\(e\left(\frac{377}{420}\right)\)	\(e\left(\frac{67}{105}\right)\)	\(e\left(\frac{167}{210}\right)\)	\(e\left(\frac{113}{210}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{97}{140}\right)\)	\(e\left(\frac{29}{105}\right)\)	\(e\left(\frac{61}{140}\right)\)	\(e\left(\frac{53}{105}\right)\)
\(\chi_{421}(23,\cdot)\)	421.x	420	yes	\(-1\)	\(1\)	\(e\left(\frac{187}{420}\right)\)	\(e\left(\frac{92}{105}\right)\)	\(e\left(\frac{187}{210}\right)\)	\(e\left(\frac{163}{210}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{47}{140}\right)\)	\(e\left(\frac{79}{105}\right)\)	\(e\left(\frac{31}{140}\right)\)	\(e\left(\frac{43}{105}\right)\)
\(\chi_{421}(24,\cdot)\)	421.x	420	yes	\(-1\)	\(1\)	\(e\left(\frac{407}{420}\right)\)	\(e\left(\frac{52}{105}\right)\)	\(e\left(\frac{197}{210}\right)\)	\(e\left(\frac{83}{210}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{127}{140}\right)\)	\(e\left(\frac{104}{105}\right)\)	\(e\left(\frac{51}{140}\right)\)	\(e\left(\frac{38}{105}\right)\)
\(\chi_{421}(25,\cdot)\)	421.u	105	yes	\(1\)	\(1\)	\(e\left(\frac{34}{105}\right)\)	\(e\left(\frac{86}{105}\right)\)	\(e\left(\frac{68}{105}\right)\)	\(e\left(\frac{2}{105}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{67}{105}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{79}{105}\right)\)
\(\chi_{421}(26,\cdot)\)	421.u	105	yes	\(1\)	\(1\)	\(e\left(\frac{16}{105}\right)\)	\(e\left(\frac{59}{105}\right)\)	\(e\left(\frac{32}{105}\right)\)	\(e\left(\frac{38}{105}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{13}{105}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{31}{105}\right)\)
\(\chi_{421}(27,\cdot)\)	421.p	35	yes	\(1\)	\(1\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{1}{35}\right)\)
\(\chi_{421}(28,\cdot)\)	421.u	105	yes	\(1\)	\(1\)	\(e\left(\frac{92}{105}\right)\)	\(e\left(\frac{103}{105}\right)\)	\(e\left(\frac{79}{105}\right)\)	\(e\left(\frac{61}{105}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{101}{105}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{47}{105}\right)\)
\(\chi_{421}(29,\cdot)\)	421.d	4	yes	\(-1\)	\(1\)	\(i\)	\(1\)	\(-1\)	\(-1\)	\(i\)	\(-1\)	\(-i\)	\(1\)	\(-i\)	\(1\)
\(\chi_{421}(30,\cdot)\)	421.x	420	yes	\(-1\)	\(1\)	\(e\left(\frac{263}{420}\right)\)	\(e\left(\frac{103}{105}\right)\)	\(e\left(\frac{53}{210}\right)\)	\(e\left(\frac{17}{210}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{123}{140}\right)\)	\(e\left(\frac{101}{105}\right)\)	\(e\left(\frac{99}{140}\right)\)	\(e\left(\frac{47}{105}\right)\)
\(\chi_{421}(31,\cdot)\)	421.u	105	yes	\(1\)	\(1\)	\(e\left(\frac{29}{105}\right)\)	\(e\left(\frac{61}{105}\right)\)	\(e\left(\frac{58}{105}\right)\)	\(e\left(\frac{82}{105}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{17}{105}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{89}{105}\right)\)
\(\chi_{421}(32,\cdot)\)	421.t	84	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{10}{21}\right)\)

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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.