LMFDB - Group of Dirichlet characters of modulus 1029

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1029)

pari: g = idealstar(,1029,2)

Character group

sage: G.order() pari: g.no
Order	=	588
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{294}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{1029}(344,\cdot)$, $\chi_{1029}(346,\cdot)$

First 32 of 588 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	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$11$	$13$	$16$	$17$	$19$
$\chi_{1029}(1,\cdot)$	1029.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1029}(2,\cdot)$	1029.v	294	yes	$-1$	$1$	$e\left(\frac{151}{294}\right)$	$e\left(\frac{4}{147}\right)$	$e\left(\frac{187}{294}\right)$	$e\left(\frac{53}{98}\right)$	$e\left(\frac{22}{147}\right)$	$e\left(\frac{221}{294}\right)$	$e\left(\frac{3}{49}\right)$	$e\left(\frac{8}{147}\right)$	$e\left(\frac{293}{294}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{1029}(4,\cdot)$	1029.u	147	no	$1$	$1$	$e\left(\frac{4}{147}\right)$	$e\left(\frac{8}{147}\right)$	$e\left(\frac{40}{147}\right)$	$e\left(\frac{4}{49}\right)$	$e\left(\frac{44}{147}\right)$	$e\left(\frac{74}{147}\right)$	$e\left(\frac{6}{49}\right)$	$e\left(\frac{16}{147}\right)$	$e\left(\frac{146}{147}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{1029}(5,\cdot)$	1029.x	294	yes	$1$	$1$	$e\left(\frac{187}{294}\right)$	$e\left(\frac{40}{147}\right)$	$e\left(\frac{53}{147}\right)$	$e\left(\frac{89}{98}\right)$	$e\left(\frac{293}{294}\right)$	$e\left(\frac{5}{294}\right)$	$e\left(\frac{11}{98}\right)$	$e\left(\frac{80}{147}\right)$	$e\left(\frac{142}{147}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{1029}(8,\cdot)$	1029.t	98	yes	$-1$	$1$	$e\left(\frac{53}{98}\right)$	$e\left(\frac{4}{49}\right)$	$e\left(\frac{89}{98}\right)$	$e\left(\frac{61}{98}\right)$	$e\left(\frac{22}{49}\right)$	$e\left(\frac{25}{98}\right)$	$e\left(\frac{9}{49}\right)$	$e\left(\frac{8}{49}\right)$	$e\left(\frac{97}{98}\right)$	$1$
$\chi_{1029}(10,\cdot)$	1029.w	294	no	$-1$	$1$	$e\left(\frac{22}{147}\right)$	$e\left(\frac{44}{147}\right)$	$e\left(\frac{293}{294}\right)$	$e\left(\frac{22}{49}\right)$	$e\left(\frac{43}{294}\right)$	$e\left(\frac{113}{147}\right)$	$e\left(\frac{17}{98}\right)$	$e\left(\frac{88}{147}\right)$	$e\left(\frac{283}{294}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{1029}(11,\cdot)$	1029.v	294	yes	$-1$	$1$	$e\left(\frac{221}{294}\right)$	$e\left(\frac{74}{147}\right)$	$e\left(\frac{5}{294}\right)$	$e\left(\frac{25}{98}\right)$	$e\left(\frac{113}{147}\right)$	$e\left(\frac{193}{294}\right)$	$e\left(\frac{31}{49}\right)$	$e\left(\frac{1}{147}\right)$	$e\left(\frac{55}{294}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{1029}(13,\cdot)$	1029.r	98	no	$-1$	$1$	$e\left(\frac{3}{49}\right)$	$e\left(\frac{6}{49}\right)$	$e\left(\frac{11}{98}\right)$	$e\left(\frac{9}{49}\right)$	$e\left(\frac{17}{98}\right)$	$e\left(\frac{31}{49}\right)$	$e\left(\frac{27}{98}\right)$	$e\left(\frac{12}{49}\right)$	$e\left(\frac{23}{98}\right)$	$-1$
$\chi_{1029}(16,\cdot)$	1029.u	147	no	$1$	$1$	$e\left(\frac{8}{147}\right)$	$e\left(\frac{16}{147}\right)$	$e\left(\frac{80}{147}\right)$	$e\left(\frac{8}{49}\right)$	$e\left(\frac{88}{147}\right)$	$e\left(\frac{1}{147}\right)$	$e\left(\frac{12}{49}\right)$	$e\left(\frac{32}{147}\right)$	$e\left(\frac{145}{147}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{1029}(17,\cdot)$	1029.x	294	yes	$1$	$1$	$e\left(\frac{293}{294}\right)$	$e\left(\frac{146}{147}\right)$	$e\left(\frac{142}{147}\right)$	$e\left(\frac{97}{98}\right)$	$e\left(\frac{283}{294}\right)$	$e\left(\frac{55}{294}\right)$	$e\left(\frac{23}{98}\right)$	$e\left(\frac{145}{147}\right)$	$e\left(\frac{92}{147}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{1029}(19,\cdot)$	1029.f	6	no	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{1029}(20,\cdot)$	1029.s	98	yes	$1$	$1$	$e\left(\frac{65}{98}\right)$	$e\left(\frac{16}{49}\right)$	$e\left(\frac{31}{49}\right)$	$e\left(\frac{97}{98}\right)$	$e\left(\frac{29}{98}\right)$	$e\left(\frac{51}{98}\right)$	$e\left(\frac{23}{98}\right)$	$e\left(\frac{32}{49}\right)$	$e\left(\frac{47}{49}\right)$	$-1$
$\chi_{1029}(22,\cdot)$	1029.q	49	no	$1$	$1$	$e\left(\frac{13}{49}\right)$	$e\left(\frac{26}{49}\right)$	$e\left(\frac{32}{49}\right)$	$e\left(\frac{39}{49}\right)$	$e\left(\frac{45}{49}\right)$	$e\left(\frac{20}{49}\right)$	$e\left(\frac{34}{49}\right)$	$e\left(\frac{3}{49}\right)$	$e\left(\frac{9}{49}\right)$	$1$
$\chi_{1029}(23,\cdot)$	1029.v	294	yes	$-1$	$1$	$e\left(\frac{211}{294}\right)$	$e\left(\frac{64}{147}\right)$	$e\left(\frac{199}{294}\right)$	$e\left(\frac{15}{98}\right)$	$e\left(\frac{58}{147}\right)$	$e\left(\frac{155}{294}\right)$	$e\left(\frac{48}{49}\right)$	$e\left(\frac{128}{147}\right)$	$e\left(\frac{131}{294}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{1029}(25,\cdot)$	1029.u	147	no	$1$	$1$	$e\left(\frac{40}{147}\right)$	$e\left(\frac{80}{147}\right)$	$e\left(\frac{106}{147}\right)$	$e\left(\frac{40}{49}\right)$	$e\left(\frac{146}{147}\right)$	$e\left(\frac{5}{147}\right)$	$e\left(\frac{11}{49}\right)$	$e\left(\frac{13}{147}\right)$	$e\left(\frac{137}{147}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{1029}(26,\cdot)$	1029.x	294	yes	$1$	$1$	$e\left(\frac{169}{294}\right)$	$e\left(\frac{22}{147}\right)$	$e\left(\frac{110}{147}\right)$	$e\left(\frac{71}{98}\right)$	$e\left(\frac{95}{294}\right)$	$e\left(\frac{113}{294}\right)$	$e\left(\frac{33}{98}\right)$	$e\left(\frac{44}{147}\right)$	$e\left(\frac{34}{147}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{1029}(29,\cdot)$	1029.t	98	yes	$-1$	$1$	$e\left(\frac{93}{98}\right)$	$e\left(\frac{44}{49}\right)$	$e\left(\frac{97}{98}\right)$	$e\left(\frac{83}{98}\right)$	$e\left(\frac{46}{49}\right)$	$e\left(\frac{79}{98}\right)$	$e\left(\frac{1}{49}\right)$	$e\left(\frac{39}{49}\right)$	$e\left(\frac{87}{98}\right)$	$1$
$\chi_{1029}(31,\cdot)$	1029.p	42	no	$-1$	$1$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{1029}(32,\cdot)$	1029.v	294	yes	$-1$	$1$	$e\left(\frac{167}{294}\right)$	$e\left(\frac{20}{147}\right)$	$e\left(\frac{53}{294}\right)$	$e\left(\frac{69}{98}\right)$	$e\left(\frac{110}{147}\right)$	$e\left(\frac{223}{294}\right)$	$e\left(\frac{15}{49}\right)$	$e\left(\frac{40}{147}\right)$	$e\left(\frac{289}{294}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{1029}(34,\cdot)$	1029.r	98	no	$-1$	$1$	$e\left(\frac{25}{49}\right)$	$e\left(\frac{1}{49}\right)$	$e\left(\frac{59}{98}\right)$	$e\left(\frac{26}{49}\right)$	$e\left(\frac{11}{98}\right)$	$e\left(\frac{46}{49}\right)$	$e\left(\frac{29}{98}\right)$	$e\left(\frac{2}{49}\right)$	$e\left(\frac{61}{98}\right)$	$-1$
$\chi_{1029}(37,\cdot)$	1029.u	147	no	$1$	$1$	$e\left(\frac{122}{147}\right)$	$e\left(\frac{97}{147}\right)$	$e\left(\frac{44}{147}\right)$	$e\left(\frac{24}{49}\right)$	$e\left(\frac{19}{147}\right)$	$e\left(\frac{52}{147}\right)$	$e\left(\frac{36}{49}\right)$	$e\left(\frac{47}{147}\right)$	$e\left(\frac{43}{147}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{1029}(38,\cdot)$	1029.x	294	yes	$1$	$1$	$e\left(\frac{53}{294}\right)$	$e\left(\frac{53}{147}\right)$	$e\left(\frac{118}{147}\right)$	$e\left(\frac{53}{98}\right)$	$e\left(\frac{289}{294}\right)$	$e\left(\frac{25}{294}\right)$	$e\left(\frac{55}{98}\right)$	$e\left(\frac{106}{147}\right)$	$e\left(\frac{122}{147}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{1029}(40,\cdot)$	1029.w	294	no	$-1$	$1$	$e\left(\frac{26}{147}\right)$	$e\left(\frac{52}{147}\right)$	$e\left(\frac{79}{294}\right)$	$e\left(\frac{26}{49}\right)$	$e\left(\frac{131}{294}\right)$	$e\left(\frac{40}{147}\right)$	$e\left(\frac{29}{98}\right)$	$e\left(\frac{104}{147}\right)$	$e\left(\frac{281}{294}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{1029}(41,\cdot)$	1029.s	98	yes	$1$	$1$	$e\left(\frac{25}{98}\right)$	$e\left(\frac{25}{49}\right)$	$e\left(\frac{27}{49}\right)$	$e\left(\frac{75}{98}\right)$	$e\left(\frac{79}{98}\right)$	$e\left(\frac{95}{98}\right)$	$e\left(\frac{39}{98}\right)$	$e\left(\frac{1}{49}\right)$	$e\left(\frac{3}{49}\right)$	$-1$
$\chi_{1029}(43,\cdot)$	1029.q	49	no	$1$	$1$	$e\left(\frac{47}{49}\right)$	$e\left(\frac{45}{49}\right)$	$e\left(\frac{29}{49}\right)$	$e\left(\frac{43}{49}\right)$	$e\left(\frac{27}{49}\right)$	$e\left(\frac{12}{49}\right)$	$e\left(\frac{40}{49}\right)$	$e\left(\frac{41}{49}\right)$	$e\left(\frac{25}{49}\right)$	$1$
$\chi_{1029}(44,\cdot)$	1029.v	294	yes	$-1$	$1$	$e\left(\frac{229}{294}\right)$	$e\left(\frac{82}{147}\right)$	$e\left(\frac{85}{294}\right)$	$e\left(\frac{33}{98}\right)$	$e\left(\frac{10}{147}\right)$	$e\left(\frac{47}{294}\right)$	$e\left(\frac{37}{49}\right)$	$e\left(\frac{17}{147}\right)$	$e\left(\frac{53}{294}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{1029}(46,\cdot)$	1029.u	147	no	$1$	$1$	$e\left(\frac{34}{147}\right)$	$e\left(\frac{68}{147}\right)$	$e\left(\frac{46}{147}\right)$	$e\left(\frac{34}{49}\right)$	$e\left(\frac{80}{147}\right)$	$e\left(\frac{41}{147}\right)$	$e\left(\frac{2}{49}\right)$	$e\left(\frac{136}{147}\right)$	$e\left(\frac{65}{147}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{1029}(47,\cdot)$	1029.x	294	yes	$1$	$1$	$e\left(\frac{109}{294}\right)$	$e\left(\frac{109}{147}\right)$	$e\left(\frac{104}{147}\right)$	$e\left(\frac{11}{98}\right)$	$e\left(\frac{23}{294}\right)$	$e\left(\frac{179}{294}\right)$	$e\left(\frac{41}{98}\right)$	$e\left(\frac{71}{147}\right)$	$e\left(\frac{115}{147}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{1029}(50,\cdot)$	1029.l	14	no	$-1$	$1$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{13}{14}\right)$	$1$
$\chi_{1029}(52,\cdot)$	1029.w	294	no	$-1$	$1$	$e\left(\frac{13}{147}\right)$	$e\left(\frac{26}{147}\right)$	$e\left(\frac{113}{294}\right)$	$e\left(\frac{13}{49}\right)$	$e\left(\frac{139}{294}\right)$	$e\left(\frac{20}{147}\right)$	$e\left(\frac{39}{98}\right)$	$e\left(\frac{52}{147}\right)$	$e\left(\frac{67}{294}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{1029}(53,\cdot)$	1029.v	294	yes	$-1$	$1$	$e\left(\frac{29}{294}\right)$	$e\left(\frac{29}{147}\right)$	$e\left(\frac{143}{294}\right)$	$e\left(\frac{29}{98}\right)$	$e\left(\frac{86}{147}\right)$	$e\left(\frac{169}{294}\right)$	$e\left(\frac{34}{49}\right)$	$e\left(\frac{58}{147}\right)$	$e\left(\frac{103}{294}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{1029}(55,\cdot)$	1029.r	98	no	$-1$	$1$	$e\left(\frac{19}{49}\right)$	$e\left(\frac{38}{49}\right)$	$e\left(\frac{37}{98}\right)$	$e\left(\frac{8}{49}\right)$	$e\left(\frac{75}{98}\right)$	$e\left(\frac{33}{49}\right)$	$e\left(\frac{73}{98}\right)$	$e\left(\frac{27}{49}\right)$	$e\left(\frac{15}{98}\right)$	$-1$

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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	$1029$
Structure	\(C_{2}\times C_{294}\)
Order	$588$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(8\)	\(10\)	\(11\)	\(13\)	\(16\)	\(17\)	\(19\)
\(\chi_{1029}(1,\cdot)\)	1029.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1029}(2,\cdot)\)	1029.v	294	yes	\(-1\)	\(1\)	\(e\left(\frac{151}{294}\right)\)	\(e\left(\frac{4}{147}\right)\)	\(e\left(\frac{187}{294}\right)\)	\(e\left(\frac{53}{98}\right)\)	\(e\left(\frac{22}{147}\right)\)	\(e\left(\frac{221}{294}\right)\)	\(e\left(\frac{3}{49}\right)\)	\(e\left(\frac{8}{147}\right)\)	\(e\left(\frac{293}{294}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{1029}(4,\cdot)\)	1029.u	147	no	\(1\)	\(1\)	\(e\left(\frac{4}{147}\right)\)	\(e\left(\frac{8}{147}\right)\)	\(e\left(\frac{40}{147}\right)\)	\(e\left(\frac{4}{49}\right)\)	\(e\left(\frac{44}{147}\right)\)	\(e\left(\frac{74}{147}\right)\)	\(e\left(\frac{6}{49}\right)\)	\(e\left(\frac{16}{147}\right)\)	\(e\left(\frac{146}{147}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{1029}(5,\cdot)\)	1029.x	294	yes	\(1\)	\(1\)	\(e\left(\frac{187}{294}\right)\)	\(e\left(\frac{40}{147}\right)\)	\(e\left(\frac{53}{147}\right)\)	\(e\left(\frac{89}{98}\right)\)	\(e\left(\frac{293}{294}\right)\)	\(e\left(\frac{5}{294}\right)\)	\(e\left(\frac{11}{98}\right)\)	\(e\left(\frac{80}{147}\right)\)	\(e\left(\frac{142}{147}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{1029}(8,\cdot)\)	1029.t	98	yes	\(-1\)	\(1\)	\(e\left(\frac{53}{98}\right)\)	\(e\left(\frac{4}{49}\right)\)	\(e\left(\frac{89}{98}\right)\)	\(e\left(\frac{61}{98}\right)\)	\(e\left(\frac{22}{49}\right)\)	\(e\left(\frac{25}{98}\right)\)	\(e\left(\frac{9}{49}\right)\)	\(e\left(\frac{8}{49}\right)\)	\(e\left(\frac{97}{98}\right)\)	\(1\)
\(\chi_{1029}(10,\cdot)\)	1029.w	294	no	\(-1\)	\(1\)	\(e\left(\frac{22}{147}\right)\)	\(e\left(\frac{44}{147}\right)\)	\(e\left(\frac{293}{294}\right)\)	\(e\left(\frac{22}{49}\right)\)	\(e\left(\frac{43}{294}\right)\)	\(e\left(\frac{113}{147}\right)\)	\(e\left(\frac{17}{98}\right)\)	\(e\left(\frac{88}{147}\right)\)	\(e\left(\frac{283}{294}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{1029}(11,\cdot)\)	1029.v	294	yes	\(-1\)	\(1\)	\(e\left(\frac{221}{294}\right)\)	\(e\left(\frac{74}{147}\right)\)	\(e\left(\frac{5}{294}\right)\)	\(e\left(\frac{25}{98}\right)\)	\(e\left(\frac{113}{147}\right)\)	\(e\left(\frac{193}{294}\right)\)	\(e\left(\frac{31}{49}\right)\)	\(e\left(\frac{1}{147}\right)\)	\(e\left(\frac{55}{294}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{1029}(13,\cdot)\)	1029.r	98	no	\(-1\)	\(1\)	\(e\left(\frac{3}{49}\right)\)	\(e\left(\frac{6}{49}\right)\)	\(e\left(\frac{11}{98}\right)\)	\(e\left(\frac{9}{49}\right)\)	\(e\left(\frac{17}{98}\right)\)	\(e\left(\frac{31}{49}\right)\)	\(e\left(\frac{27}{98}\right)\)	\(e\left(\frac{12}{49}\right)\)	\(e\left(\frac{23}{98}\right)\)	\(-1\)
\(\chi_{1029}(16,\cdot)\)	1029.u	147	no	\(1\)	\(1\)	\(e\left(\frac{8}{147}\right)\)	\(e\left(\frac{16}{147}\right)\)	\(e\left(\frac{80}{147}\right)\)	\(e\left(\frac{8}{49}\right)\)	\(e\left(\frac{88}{147}\right)\)	\(e\left(\frac{1}{147}\right)\)	\(e\left(\frac{12}{49}\right)\)	\(e\left(\frac{32}{147}\right)\)	\(e\left(\frac{145}{147}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{1029}(17,\cdot)\)	1029.x	294	yes	\(1\)	\(1\)	\(e\left(\frac{293}{294}\right)\)	\(e\left(\frac{146}{147}\right)\)	\(e\left(\frac{142}{147}\right)\)	\(e\left(\frac{97}{98}\right)\)	\(e\left(\frac{283}{294}\right)\)	\(e\left(\frac{55}{294}\right)\)	\(e\left(\frac{23}{98}\right)\)	\(e\left(\frac{145}{147}\right)\)	\(e\left(\frac{92}{147}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{1029}(19,\cdot)\)	1029.f	6	no	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{1029}(20,\cdot)\)	1029.s	98	yes	\(1\)	\(1\)	\(e\left(\frac{65}{98}\right)\)	\(e\left(\frac{16}{49}\right)\)	\(e\left(\frac{31}{49}\right)\)	\(e\left(\frac{97}{98}\right)\)	\(e\left(\frac{29}{98}\right)\)	\(e\left(\frac{51}{98}\right)\)	\(e\left(\frac{23}{98}\right)\)	\(e\left(\frac{32}{49}\right)\)	\(e\left(\frac{47}{49}\right)\)	\(-1\)
\(\chi_{1029}(22,\cdot)\)	1029.q	49	no	\(1\)	\(1\)	\(e\left(\frac{13}{49}\right)\)	\(e\left(\frac{26}{49}\right)\)	\(e\left(\frac{32}{49}\right)\)	\(e\left(\frac{39}{49}\right)\)	\(e\left(\frac{45}{49}\right)\)	\(e\left(\frac{20}{49}\right)\)	\(e\left(\frac{34}{49}\right)\)	\(e\left(\frac{3}{49}\right)\)	\(e\left(\frac{9}{49}\right)\)	\(1\)
\(\chi_{1029}(23,\cdot)\)	1029.v	294	yes	\(-1\)	\(1\)	\(e\left(\frac{211}{294}\right)\)	\(e\left(\frac{64}{147}\right)\)	\(e\left(\frac{199}{294}\right)\)	\(e\left(\frac{15}{98}\right)\)	\(e\left(\frac{58}{147}\right)\)	\(e\left(\frac{155}{294}\right)\)	\(e\left(\frac{48}{49}\right)\)	\(e\left(\frac{128}{147}\right)\)	\(e\left(\frac{131}{294}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{1029}(25,\cdot)\)	1029.u	147	no	\(1\)	\(1\)	\(e\left(\frac{40}{147}\right)\)	\(e\left(\frac{80}{147}\right)\)	\(e\left(\frac{106}{147}\right)\)	\(e\left(\frac{40}{49}\right)\)	\(e\left(\frac{146}{147}\right)\)	\(e\left(\frac{5}{147}\right)\)	\(e\left(\frac{11}{49}\right)\)	\(e\left(\frac{13}{147}\right)\)	\(e\left(\frac{137}{147}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{1029}(26,\cdot)\)	1029.x	294	yes	\(1\)	\(1\)	\(e\left(\frac{169}{294}\right)\)	\(e\left(\frac{22}{147}\right)\)	\(e\left(\frac{110}{147}\right)\)	\(e\left(\frac{71}{98}\right)\)	\(e\left(\frac{95}{294}\right)\)	\(e\left(\frac{113}{294}\right)\)	\(e\left(\frac{33}{98}\right)\)	\(e\left(\frac{44}{147}\right)\)	\(e\left(\frac{34}{147}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{1029}(29,\cdot)\)	1029.t	98	yes	\(-1\)	\(1\)	\(e\left(\frac{93}{98}\right)\)	\(e\left(\frac{44}{49}\right)\)	\(e\left(\frac{97}{98}\right)\)	\(e\left(\frac{83}{98}\right)\)	\(e\left(\frac{46}{49}\right)\)	\(e\left(\frac{79}{98}\right)\)	\(e\left(\frac{1}{49}\right)\)	\(e\left(\frac{39}{49}\right)\)	\(e\left(\frac{87}{98}\right)\)	\(1\)
\(\chi_{1029}(31,\cdot)\)	1029.p	42	no	\(-1\)	\(1\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{1029}(32,\cdot)\)	1029.v	294	yes	\(-1\)	\(1\)	\(e\left(\frac{167}{294}\right)\)	\(e\left(\frac{20}{147}\right)\)	\(e\left(\frac{53}{294}\right)\)	\(e\left(\frac{69}{98}\right)\)	\(e\left(\frac{110}{147}\right)\)	\(e\left(\frac{223}{294}\right)\)	\(e\left(\frac{15}{49}\right)\)	\(e\left(\frac{40}{147}\right)\)	\(e\left(\frac{289}{294}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{1029}(34,\cdot)\)	1029.r	98	no	\(-1\)	\(1\)	\(e\left(\frac{25}{49}\right)\)	\(e\left(\frac{1}{49}\right)\)	\(e\left(\frac{59}{98}\right)\)	\(e\left(\frac{26}{49}\right)\)	\(e\left(\frac{11}{98}\right)\)	\(e\left(\frac{46}{49}\right)\)	\(e\left(\frac{29}{98}\right)\)	\(e\left(\frac{2}{49}\right)\)	\(e\left(\frac{61}{98}\right)\)	\(-1\)
\(\chi_{1029}(37,\cdot)\)	1029.u	147	no	\(1\)	\(1\)	\(e\left(\frac{122}{147}\right)\)	\(e\left(\frac{97}{147}\right)\)	\(e\left(\frac{44}{147}\right)\)	\(e\left(\frac{24}{49}\right)\)	\(e\left(\frac{19}{147}\right)\)	\(e\left(\frac{52}{147}\right)\)	\(e\left(\frac{36}{49}\right)\)	\(e\left(\frac{47}{147}\right)\)	\(e\left(\frac{43}{147}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{1029}(38,\cdot)\)	1029.x	294	yes	\(1\)	\(1\)	\(e\left(\frac{53}{294}\right)\)	\(e\left(\frac{53}{147}\right)\)	\(e\left(\frac{118}{147}\right)\)	\(e\left(\frac{53}{98}\right)\)	\(e\left(\frac{289}{294}\right)\)	\(e\left(\frac{25}{294}\right)\)	\(e\left(\frac{55}{98}\right)\)	\(e\left(\frac{106}{147}\right)\)	\(e\left(\frac{122}{147}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{1029}(40,\cdot)\)	1029.w	294	no	\(-1\)	\(1\)	\(e\left(\frac{26}{147}\right)\)	\(e\left(\frac{52}{147}\right)\)	\(e\left(\frac{79}{294}\right)\)	\(e\left(\frac{26}{49}\right)\)	\(e\left(\frac{131}{294}\right)\)	\(e\left(\frac{40}{147}\right)\)	\(e\left(\frac{29}{98}\right)\)	\(e\left(\frac{104}{147}\right)\)	\(e\left(\frac{281}{294}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{1029}(41,\cdot)\)	1029.s	98	yes	\(1\)	\(1\)	\(e\left(\frac{25}{98}\right)\)	\(e\left(\frac{25}{49}\right)\)	\(e\left(\frac{27}{49}\right)\)	\(e\left(\frac{75}{98}\right)\)	\(e\left(\frac{79}{98}\right)\)	\(e\left(\frac{95}{98}\right)\)	\(e\left(\frac{39}{98}\right)\)	\(e\left(\frac{1}{49}\right)\)	\(e\left(\frac{3}{49}\right)\)	\(-1\)
\(\chi_{1029}(43,\cdot)\)	1029.q	49	no	\(1\)	\(1\)	\(e\left(\frac{47}{49}\right)\)	\(e\left(\frac{45}{49}\right)\)	\(e\left(\frac{29}{49}\right)\)	\(e\left(\frac{43}{49}\right)\)	\(e\left(\frac{27}{49}\right)\)	\(e\left(\frac{12}{49}\right)\)	\(e\left(\frac{40}{49}\right)\)	\(e\left(\frac{41}{49}\right)\)	\(e\left(\frac{25}{49}\right)\)	\(1\)
\(\chi_{1029}(44,\cdot)\)	1029.v	294	yes	\(-1\)	\(1\)	\(e\left(\frac{229}{294}\right)\)	\(e\left(\frac{82}{147}\right)\)	\(e\left(\frac{85}{294}\right)\)	\(e\left(\frac{33}{98}\right)\)	\(e\left(\frac{10}{147}\right)\)	\(e\left(\frac{47}{294}\right)\)	\(e\left(\frac{37}{49}\right)\)	\(e\left(\frac{17}{147}\right)\)	\(e\left(\frac{53}{294}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{1029}(46,\cdot)\)	1029.u	147	no	\(1\)	\(1\)	\(e\left(\frac{34}{147}\right)\)	\(e\left(\frac{68}{147}\right)\)	\(e\left(\frac{46}{147}\right)\)	\(e\left(\frac{34}{49}\right)\)	\(e\left(\frac{80}{147}\right)\)	\(e\left(\frac{41}{147}\right)\)	\(e\left(\frac{2}{49}\right)\)	\(e\left(\frac{136}{147}\right)\)	\(e\left(\frac{65}{147}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{1029}(47,\cdot)\)	1029.x	294	yes	\(1\)	\(1\)	\(e\left(\frac{109}{294}\right)\)	\(e\left(\frac{109}{147}\right)\)	\(e\left(\frac{104}{147}\right)\)	\(e\left(\frac{11}{98}\right)\)	\(e\left(\frac{23}{294}\right)\)	\(e\left(\frac{179}{294}\right)\)	\(e\left(\frac{41}{98}\right)\)	\(e\left(\frac{71}{147}\right)\)	\(e\left(\frac{115}{147}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{1029}(50,\cdot)\)	1029.l	14	no	\(-1\)	\(1\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(1\)
\(\chi_{1029}(52,\cdot)\)	1029.w	294	no	\(-1\)	\(1\)	\(e\left(\frac{13}{147}\right)\)	\(e\left(\frac{26}{147}\right)\)	\(e\left(\frac{113}{294}\right)\)	\(e\left(\frac{13}{49}\right)\)	\(e\left(\frac{139}{294}\right)\)	\(e\left(\frac{20}{147}\right)\)	\(e\left(\frac{39}{98}\right)\)	\(e\left(\frac{52}{147}\right)\)	\(e\left(\frac{67}{294}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{1029}(53,\cdot)\)	1029.v	294	yes	\(-1\)	\(1\)	\(e\left(\frac{29}{294}\right)\)	\(e\left(\frac{29}{147}\right)\)	\(e\left(\frac{143}{294}\right)\)	\(e\left(\frac{29}{98}\right)\)	\(e\left(\frac{86}{147}\right)\)	\(e\left(\frac{169}{294}\right)\)	\(e\left(\frac{34}{49}\right)\)	\(e\left(\frac{58}{147}\right)\)	\(e\left(\frac{103}{294}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{1029}(55,\cdot)\)	1029.r	98	no	\(-1\)	\(1\)	\(e\left(\frac{19}{49}\right)\)	\(e\left(\frac{38}{49}\right)\)	\(e\left(\frac{37}{98}\right)\)	\(e\left(\frac{8}{49}\right)\)	\(e\left(\frac{75}{98}\right)\)	\(e\left(\frac{33}{49}\right)\)	\(e\left(\frac{73}{98}\right)\)	\(e\left(\frac{27}{49}\right)\)	\(e\left(\frac{15}{98}\right)\)	\(-1\)

Introduction

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.