LMFDB - Group of Dirichlet characters of modulus 7742

Show commands: PariGP / SageMath

sage: H = DirichletGroup(7742)

pari: g = idealstar(,7742,2)

Character group

sage: G.order() pari: g.no
Order	=	3276
sage: H.invariants() pari: g.cyc
Structure	=	$C_{6}\times C_{546}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{7742}(2845,\cdot)$, $\chi_{7742}(4901,\cdot)$

First 32 of 3276 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	$-1$	$1$	$3$	$5$	$9$	$11$	$13$	$15$	$17$	$19$	$23$	$25$
$\chi_{7742}(1,\cdot)$	7742.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{7742}(3,\cdot)$	7742.cu	546	no	$1$	$1$	$e\left(\frac{10}{273}\right)$	$e\left(\frac{265}{546}\right)$	$e\left(\frac{20}{273}\right)$	$e\left(\frac{75}{91}\right)$	$e\left(\frac{121}{546}\right)$	$e\left(\frac{95}{182}\right)$	$e\left(\frac{236}{273}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{265}{273}\right)$
$\chi_{7742}(5,\cdot)$	7742.da	546	no	$-1$	$1$	$e\left(\frac{265}{546}\right)$	$e\left(\frac{167}{546}\right)$	$e\left(\frac{265}{273}\right)$	$e\left(\frac{61}{91}\right)$	$e\left(\frac{443}{546}\right)$	$e\left(\frac{72}{91}\right)$	$e\left(\frac{521}{546}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{167}{273}\right)$
$\chi_{7742}(9,\cdot)$	7742.co	273	no	$1$	$1$	$e\left(\frac{20}{273}\right)$	$e\left(\frac{265}{273}\right)$	$e\left(\frac{40}{273}\right)$	$e\left(\frac{59}{91}\right)$	$e\left(\frac{121}{273}\right)$	$e\left(\frac{4}{91}\right)$	$e\left(\frac{199}{273}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{257}{273}\right)$
$\chi_{7742}(11,\cdot)$	7742.cp	273	no	$1$	$1$	$e\left(\frac{75}{91}\right)$	$e\left(\frac{61}{91}\right)$	$e\left(\frac{59}{91}\right)$	$e\left(\frac{103}{273}\right)$	$e\left(\frac{19}{273}\right)$	$e\left(\frac{45}{91}\right)$	$e\left(\frac{32}{273}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{31}{91}\right)$
$\chi_{7742}(13,\cdot)$	7742.cz	546	no	$-1$	$1$	$e\left(\frac{121}{546}\right)$	$e\left(\frac{443}{546}\right)$	$e\left(\frac{121}{273}\right)$	$e\left(\frac{19}{273}\right)$	$e\left(\frac{409}{546}\right)$	$e\left(\frac{3}{91}\right)$	$e\left(\frac{145}{182}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{170}{273}\right)$
$\chi_{7742}(15,\cdot)$	7742.ck	182	no	$-1$	$1$	$e\left(\frac{95}{182}\right)$	$e\left(\frac{72}{91}\right)$	$e\left(\frac{4}{91}\right)$	$e\left(\frac{45}{91}\right)$	$e\left(\frac{3}{91}\right)$	$e\left(\frac{57}{182}\right)$	$e\left(\frac{149}{182}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{53}{91}\right)$
$\chi_{7742}(17,\cdot)$	7742.cs	546	no	$1$	$1$	$e\left(\frac{236}{273}\right)$	$e\left(\frac{521}{546}\right)$	$e\left(\frac{199}{273}\right)$	$e\left(\frac{32}{273}\right)$	$e\left(\frac{145}{182}\right)$	$e\left(\frac{149}{182}\right)$	$e\left(\frac{146}{273}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{248}{273}\right)$
$\chi_{7742}(19,\cdot)$	7742.bx	78	no	$-1$	$1$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{8}{39}\right)$
$\chi_{7742}(23,\cdot)$	7742.ba	21	no	$1$	$1$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{17}{21}\right)$
$\chi_{7742}(25,\cdot)$	7742.co	273	no	$1$	$1$	$e\left(\frac{265}{273}\right)$	$e\left(\frac{167}{273}\right)$	$e\left(\frac{257}{273}\right)$	$e\left(\frac{31}{91}\right)$	$e\left(\frac{170}{273}\right)$	$e\left(\frac{53}{91}\right)$	$e\left(\frac{248}{273}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{61}{273}\right)$
$\chi_{7742}(27,\cdot)$	7742.cl	182	no	$1$	$1$	$e\left(\frac{10}{91}\right)$	$e\left(\frac{83}{182}\right)$	$e\left(\frac{20}{91}\right)$	$e\left(\frac{43}{91}\right)$	$e\left(\frac{121}{182}\right)$	$e\left(\frac{103}{182}\right)$	$e\left(\frac{54}{91}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{83}{91}\right)$
$\chi_{7742}(29,\cdot)$	7742.cv	546	no	$-1$	$1$	$e\left(\frac{311}{546}\right)$	$e\left(\frac{47}{273}\right)$	$e\left(\frac{38}{273}\right)$	$e\left(\frac{200}{273}\right)$	$e\left(\frac{256}{273}\right)$	$e\left(\frac{135}{182}\right)$	$e\left(\frac{123}{182}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{94}{273}\right)$
$\chi_{7742}(31,\cdot)$	7742.ch	78	no	$-1$	$1$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{21}{26}\right)$	$1$	$e\left(\frac{9}{13}\right)$
$\chi_{7742}(33,\cdot)$	7742.cs	546	no	$1$	$1$	$e\left(\frac{235}{273}\right)$	$e\left(\frac{85}{546}\right)$	$e\left(\frac{197}{273}\right)$	$e\left(\frac{55}{273}\right)$	$e\left(\frac{53}{182}\right)$	$e\left(\frac{3}{182}\right)$	$e\left(\frac{268}{273}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{85}{273}\right)$
$\chi_{7742}(37,\cdot)$	7742.cr	546	no	$-1$	$1$	$e\left(\frac{1}{182}\right)$	$e\left(\frac{18}{91}\right)$	$e\left(\frac{1}{91}\right)$	$e\left(\frac{11}{273}\right)$	$e\left(\frac{116}{273}\right)$	$e\left(\frac{37}{182}\right)$	$e\left(\frac{89}{546}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{36}{91}\right)$
$\chi_{7742}(39,\cdot)$	7742.cr	546	no	$-1$	$1$	$e\left(\frac{47}{182}\right)$	$e\left(\frac{27}{91}\right)$	$e\left(\frac{47}{91}\right)$	$e\left(\frac{244}{273}\right)$	$e\left(\frac{265}{273}\right)$	$e\left(\frac{101}{182}\right)$	$e\left(\frac{361}{546}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{54}{91}\right)$
$\chi_{7742}(41,\cdot)$	7742.cl	182	no	$1$	$1$	$e\left(\frac{29}{91}\right)$	$e\left(\frac{177}{182}\right)$	$e\left(\frac{58}{91}\right)$	$e\left(\frac{61}{91}\right)$	$e\left(\frac{87}{182}\right)$	$e\left(\frac{53}{182}\right)$	$e\left(\frac{11}{91}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{86}{91}\right)$
$\chi_{7742}(43,\cdot)$	7742.cv	546	no	$-1$	$1$	$e\left(\frac{421}{546}\right)$	$e\left(\frac{25}{273}\right)$	$e\left(\frac{148}{273}\right)$	$e\left(\frac{118}{273}\right)$	$e\left(\frac{20}{273}\right)$	$e\left(\frac{157}{182}\right)$	$e\left(\frac{139}{182}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{50}{273}\right)$
$\chi_{7742}(45,\cdot)$	7742.da	546	no	$-1$	$1$	$e\left(\frac{305}{546}\right)$	$e\left(\frac{151}{546}\right)$	$e\left(\frac{32}{273}\right)$	$e\left(\frac{29}{91}\right)$	$e\left(\frac{139}{546}\right)$	$e\left(\frac{76}{91}\right)$	$e\left(\frac{373}{546}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{151}{273}\right)$
$\chi_{7742}(47,\cdot)$	7742.cu	546	no	$1$	$1$	$e\left(\frac{239}{273}\right)$	$e\left(\frac{191}{546}\right)$	$e\left(\frac{205}{273}\right)$	$e\left(\frac{18}{91}\right)$	$e\left(\frac{353}{546}\right)$	$e\left(\frac{41}{182}\right)$	$e\left(\frac{235}{273}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{191}{273}\right)$
$\chi_{7742}(51,\cdot)$	7742.cp	273	no	$1$	$1$	$e\left(\frac{82}{91}\right)$	$e\left(\frac{40}{91}\right)$	$e\left(\frac{73}{91}\right)$	$e\left(\frac{257}{273}\right)$	$e\left(\frac{5}{273}\right)$	$e\left(\frac{31}{91}\right)$	$e\left(\frac{109}{273}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{80}{91}\right)$
$\chi_{7742}(53,\cdot)$	7742.cr	546	no	$-1$	$1$	$e\left(\frac{41}{182}\right)$	$e\left(\frac{10}{91}\right)$	$e\left(\frac{41}{91}\right)$	$e\left(\frac{178}{273}\right)$	$e\left(\frac{115}{273}\right)$	$e\left(\frac{61}{182}\right)$	$e\left(\frac{373}{546}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{20}{91}\right)$
$\chi_{7742}(55,\cdot)$	7742.bm	42	no	$-1$	$1$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{20}{21}\right)$
$\chi_{7742}(57,\cdot)$	7742.ck	182	no	$-1$	$1$	$e\left(\frac{51}{182}\right)$	$e\left(\frac{8}{91}\right)$	$e\left(\frac{51}{91}\right)$	$e\left(\frac{5}{91}\right)$	$e\left(\frac{61}{91}\right)$	$e\left(\frac{67}{182}\right)$	$e\left(\frac{57}{182}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{16}{91}\right)$
$\chi_{7742}(59,\cdot)$	7742.cu	546	no	$1$	$1$	$e\left(\frac{193}{273}\right)$	$e\left(\frac{337}{546}\right)$	$e\left(\frac{113}{273}\right)$	$e\left(\frac{37}{91}\right)$	$e\left(\frac{397}{546}\right)$	$e\left(\frac{59}{182}\right)$	$e\left(\frac{23}{273}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{64}{273}\right)$
$\chi_{7742}(61,\cdot)$	7742.cs	546	no	$1$	$1$	$e\left(\frac{229}{273}\right)$	$e\left(\frac{199}{546}\right)$	$e\left(\frac{185}{273}\right)$	$e\left(\frac{193}{273}\right)$	$e\left(\frac{47}{182}\right)$	$e\left(\frac{37}{182}\right)$	$e\left(\frac{181}{273}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{199}{273}\right)$
$\chi_{7742}(65,\cdot)$	7742.cn	273	no	$1$	$1$	$e\left(\frac{193}{273}\right)$	$e\left(\frac{32}{273}\right)$	$e\left(\frac{113}{273}\right)$	$e\left(\frac{202}{273}\right)$	$e\left(\frac{51}{91}\right)$	$e\left(\frac{75}{91}\right)$	$e\left(\frac{205}{273}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{64}{273}\right)$
$\chi_{7742}(67,\cdot)$	7742.bi	39	no	$1$	$1$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{38}{39}\right)$
$\chi_{7742}(69,\cdot)$	7742.cl	182	no	$1$	$1$	$e\left(\frac{25}{91}\right)$	$e\left(\frac{71}{182}\right)$	$e\left(\frac{50}{91}\right)$	$e\left(\frac{62}{91}\right)$	$e\left(\frac{75}{182}\right)$	$e\left(\frac{121}{182}\right)$	$e\left(\frac{44}{91}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{71}{91}\right)$
$\chi_{7742}(71,\cdot)$	7742.ck	182	no	$-1$	$1$	$e\left(\frac{41}{182}\right)$	$e\left(\frac{10}{91}\right)$	$e\left(\frac{41}{91}\right)$	$e\left(\frac{29}{91}\right)$	$e\left(\frac{8}{91}\right)$	$e\left(\frac{61}{182}\right)$	$e\left(\frac{3}{182}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{20}{91}\right)$
$\chi_{7742}(73,\cdot)$	7742.cq	546	no	$-1$	$1$	$e\left(\frac{81}{182}\right)$	$e\left(\frac{95}{182}\right)$	$e\left(\frac{81}{91}\right)$	$e\left(\frac{163}{273}\right)$	$e\left(\frac{137}{546}\right)$	$e\left(\frac{88}{91}\right)$	$e\left(\frac{475}{546}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{4}{91}\right)$

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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	$7742$
Structure	\(C_{6}\times C_{546}\)
Order	$3276$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(23\)	\(25\)
\(\chi_{7742}(1,\cdot)\)	7742.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{7742}(3,\cdot)\)	7742.cu	546	no	\(1\)	\(1\)	\(e\left(\frac{10}{273}\right)\)	\(e\left(\frac{265}{546}\right)\)	\(e\left(\frac{20}{273}\right)\)	\(e\left(\frac{75}{91}\right)\)	\(e\left(\frac{121}{546}\right)\)	\(e\left(\frac{95}{182}\right)\)	\(e\left(\frac{236}{273}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{265}{273}\right)\)
\(\chi_{7742}(5,\cdot)\)	7742.da	546	no	\(-1\)	\(1\)	\(e\left(\frac{265}{546}\right)\)	\(e\left(\frac{167}{546}\right)\)	\(e\left(\frac{265}{273}\right)\)	\(e\left(\frac{61}{91}\right)\)	\(e\left(\frac{443}{546}\right)\)	\(e\left(\frac{72}{91}\right)\)	\(e\left(\frac{521}{546}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{167}{273}\right)\)
\(\chi_{7742}(9,\cdot)\)	7742.co	273	no	\(1\)	\(1\)	\(e\left(\frac{20}{273}\right)\)	\(e\left(\frac{265}{273}\right)\)	\(e\left(\frac{40}{273}\right)\)	\(e\left(\frac{59}{91}\right)\)	\(e\left(\frac{121}{273}\right)\)	\(e\left(\frac{4}{91}\right)\)	\(e\left(\frac{199}{273}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{257}{273}\right)\)
\(\chi_{7742}(11,\cdot)\)	7742.cp	273	no	\(1\)	\(1\)	\(e\left(\frac{75}{91}\right)\)	\(e\left(\frac{61}{91}\right)\)	\(e\left(\frac{59}{91}\right)\)	\(e\left(\frac{103}{273}\right)\)	\(e\left(\frac{19}{273}\right)\)	\(e\left(\frac{45}{91}\right)\)	\(e\left(\frac{32}{273}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{31}{91}\right)\)
\(\chi_{7742}(13,\cdot)\)	7742.cz	546	no	\(-1\)	\(1\)	\(e\left(\frac{121}{546}\right)\)	\(e\left(\frac{443}{546}\right)\)	\(e\left(\frac{121}{273}\right)\)	\(e\left(\frac{19}{273}\right)\)	\(e\left(\frac{409}{546}\right)\)	\(e\left(\frac{3}{91}\right)\)	\(e\left(\frac{145}{182}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{170}{273}\right)\)
\(\chi_{7742}(15,\cdot)\)	7742.ck	182	no	\(-1\)	\(1\)	\(e\left(\frac{95}{182}\right)\)	\(e\left(\frac{72}{91}\right)\)	\(e\left(\frac{4}{91}\right)\)	\(e\left(\frac{45}{91}\right)\)	\(e\left(\frac{3}{91}\right)\)	\(e\left(\frac{57}{182}\right)\)	\(e\left(\frac{149}{182}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{53}{91}\right)\)
\(\chi_{7742}(17,\cdot)\)	7742.cs	546	no	\(1\)	\(1\)	\(e\left(\frac{236}{273}\right)\)	\(e\left(\frac{521}{546}\right)\)	\(e\left(\frac{199}{273}\right)\)	\(e\left(\frac{32}{273}\right)\)	\(e\left(\frac{145}{182}\right)\)	\(e\left(\frac{149}{182}\right)\)	\(e\left(\frac{146}{273}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{248}{273}\right)\)
\(\chi_{7742}(19,\cdot)\)	7742.bx	78	no	\(-1\)	\(1\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{8}{39}\right)\)
\(\chi_{7742}(23,\cdot)\)	7742.ba	21	no	\(1\)	\(1\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)
\(\chi_{7742}(25,\cdot)\)	7742.co	273	no	\(1\)	\(1\)	\(e\left(\frac{265}{273}\right)\)	\(e\left(\frac{167}{273}\right)\)	\(e\left(\frac{257}{273}\right)\)	\(e\left(\frac{31}{91}\right)\)	\(e\left(\frac{170}{273}\right)\)	\(e\left(\frac{53}{91}\right)\)	\(e\left(\frac{248}{273}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{61}{273}\right)\)
\(\chi_{7742}(27,\cdot)\)	7742.cl	182	no	\(1\)	\(1\)	\(e\left(\frac{10}{91}\right)\)	\(e\left(\frac{83}{182}\right)\)	\(e\left(\frac{20}{91}\right)\)	\(e\left(\frac{43}{91}\right)\)	\(e\left(\frac{121}{182}\right)\)	\(e\left(\frac{103}{182}\right)\)	\(e\left(\frac{54}{91}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{83}{91}\right)\)
\(\chi_{7742}(29,\cdot)\)	7742.cv	546	no	\(-1\)	\(1\)	\(e\left(\frac{311}{546}\right)\)	\(e\left(\frac{47}{273}\right)\)	\(e\left(\frac{38}{273}\right)\)	\(e\left(\frac{200}{273}\right)\)	\(e\left(\frac{256}{273}\right)\)	\(e\left(\frac{135}{182}\right)\)	\(e\left(\frac{123}{182}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{94}{273}\right)\)
\(\chi_{7742}(31,\cdot)\)	7742.ch	78	no	\(-1\)	\(1\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(1\)	\(e\left(\frac{9}{13}\right)\)
\(\chi_{7742}(33,\cdot)\)	7742.cs	546	no	\(1\)	\(1\)	\(e\left(\frac{235}{273}\right)\)	\(e\left(\frac{85}{546}\right)\)	\(e\left(\frac{197}{273}\right)\)	\(e\left(\frac{55}{273}\right)\)	\(e\left(\frac{53}{182}\right)\)	\(e\left(\frac{3}{182}\right)\)	\(e\left(\frac{268}{273}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{85}{273}\right)\)
\(\chi_{7742}(37,\cdot)\)	7742.cr	546	no	\(-1\)	\(1\)	\(e\left(\frac{1}{182}\right)\)	\(e\left(\frac{18}{91}\right)\)	\(e\left(\frac{1}{91}\right)\)	\(e\left(\frac{11}{273}\right)\)	\(e\left(\frac{116}{273}\right)\)	\(e\left(\frac{37}{182}\right)\)	\(e\left(\frac{89}{546}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{36}{91}\right)\)
\(\chi_{7742}(39,\cdot)\)	7742.cr	546	no	\(-1\)	\(1\)	\(e\left(\frac{47}{182}\right)\)	\(e\left(\frac{27}{91}\right)\)	\(e\left(\frac{47}{91}\right)\)	\(e\left(\frac{244}{273}\right)\)	\(e\left(\frac{265}{273}\right)\)	\(e\left(\frac{101}{182}\right)\)	\(e\left(\frac{361}{546}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{54}{91}\right)\)
\(\chi_{7742}(41,\cdot)\)	7742.cl	182	no	\(1\)	\(1\)	\(e\left(\frac{29}{91}\right)\)	\(e\left(\frac{177}{182}\right)\)	\(e\left(\frac{58}{91}\right)\)	\(e\left(\frac{61}{91}\right)\)	\(e\left(\frac{87}{182}\right)\)	\(e\left(\frac{53}{182}\right)\)	\(e\left(\frac{11}{91}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{86}{91}\right)\)
\(\chi_{7742}(43,\cdot)\)	7742.cv	546	no	\(-1\)	\(1\)	\(e\left(\frac{421}{546}\right)\)	\(e\left(\frac{25}{273}\right)\)	\(e\left(\frac{148}{273}\right)\)	\(e\left(\frac{118}{273}\right)\)	\(e\left(\frac{20}{273}\right)\)	\(e\left(\frac{157}{182}\right)\)	\(e\left(\frac{139}{182}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{50}{273}\right)\)
\(\chi_{7742}(45,\cdot)\)	7742.da	546	no	\(-1\)	\(1\)	\(e\left(\frac{305}{546}\right)\)	\(e\left(\frac{151}{546}\right)\)	\(e\left(\frac{32}{273}\right)\)	\(e\left(\frac{29}{91}\right)\)	\(e\left(\frac{139}{546}\right)\)	\(e\left(\frac{76}{91}\right)\)	\(e\left(\frac{373}{546}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{151}{273}\right)\)
\(\chi_{7742}(47,\cdot)\)	7742.cu	546	no	\(1\)	\(1\)	\(e\left(\frac{239}{273}\right)\)	\(e\left(\frac{191}{546}\right)\)	\(e\left(\frac{205}{273}\right)\)	\(e\left(\frac{18}{91}\right)\)	\(e\left(\frac{353}{546}\right)\)	\(e\left(\frac{41}{182}\right)\)	\(e\left(\frac{235}{273}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{191}{273}\right)\)
\(\chi_{7742}(51,\cdot)\)	7742.cp	273	no	\(1\)	\(1\)	\(e\left(\frac{82}{91}\right)\)	\(e\left(\frac{40}{91}\right)\)	\(e\left(\frac{73}{91}\right)\)	\(e\left(\frac{257}{273}\right)\)	\(e\left(\frac{5}{273}\right)\)	\(e\left(\frac{31}{91}\right)\)	\(e\left(\frac{109}{273}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{80}{91}\right)\)
\(\chi_{7742}(53,\cdot)\)	7742.cr	546	no	\(-1\)	\(1\)	\(e\left(\frac{41}{182}\right)\)	\(e\left(\frac{10}{91}\right)\)	\(e\left(\frac{41}{91}\right)\)	\(e\left(\frac{178}{273}\right)\)	\(e\left(\frac{115}{273}\right)\)	\(e\left(\frac{61}{182}\right)\)	\(e\left(\frac{373}{546}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{20}{91}\right)\)
\(\chi_{7742}(55,\cdot)\)	7742.bm	42	no	\(-1\)	\(1\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{20}{21}\right)\)
\(\chi_{7742}(57,\cdot)\)	7742.ck	182	no	\(-1\)	\(1\)	\(e\left(\frac{51}{182}\right)\)	\(e\left(\frac{8}{91}\right)\)	\(e\left(\frac{51}{91}\right)\)	\(e\left(\frac{5}{91}\right)\)	\(e\left(\frac{61}{91}\right)\)	\(e\left(\frac{67}{182}\right)\)	\(e\left(\frac{57}{182}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{16}{91}\right)\)
\(\chi_{7742}(59,\cdot)\)	7742.cu	546	no	\(1\)	\(1\)	\(e\left(\frac{193}{273}\right)\)	\(e\left(\frac{337}{546}\right)\)	\(e\left(\frac{113}{273}\right)\)	\(e\left(\frac{37}{91}\right)\)	\(e\left(\frac{397}{546}\right)\)	\(e\left(\frac{59}{182}\right)\)	\(e\left(\frac{23}{273}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{64}{273}\right)\)
\(\chi_{7742}(61,\cdot)\)	7742.cs	546	no	\(1\)	\(1\)	\(e\left(\frac{229}{273}\right)\)	\(e\left(\frac{199}{546}\right)\)	\(e\left(\frac{185}{273}\right)\)	\(e\left(\frac{193}{273}\right)\)	\(e\left(\frac{47}{182}\right)\)	\(e\left(\frac{37}{182}\right)\)	\(e\left(\frac{181}{273}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{199}{273}\right)\)
\(\chi_{7742}(65,\cdot)\)	7742.cn	273	no	\(1\)	\(1\)	\(e\left(\frac{193}{273}\right)\)	\(e\left(\frac{32}{273}\right)\)	\(e\left(\frac{113}{273}\right)\)	\(e\left(\frac{202}{273}\right)\)	\(e\left(\frac{51}{91}\right)\)	\(e\left(\frac{75}{91}\right)\)	\(e\left(\frac{205}{273}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{64}{273}\right)\)
\(\chi_{7742}(67,\cdot)\)	7742.bi	39	no	\(1\)	\(1\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{38}{39}\right)\)
\(\chi_{7742}(69,\cdot)\)	7742.cl	182	no	\(1\)	\(1\)	\(e\left(\frac{25}{91}\right)\)	\(e\left(\frac{71}{182}\right)\)	\(e\left(\frac{50}{91}\right)\)	\(e\left(\frac{62}{91}\right)\)	\(e\left(\frac{75}{182}\right)\)	\(e\left(\frac{121}{182}\right)\)	\(e\left(\frac{44}{91}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{71}{91}\right)\)
\(\chi_{7742}(71,\cdot)\)	7742.ck	182	no	\(-1\)	\(1\)	\(e\left(\frac{41}{182}\right)\)	\(e\left(\frac{10}{91}\right)\)	\(e\left(\frac{41}{91}\right)\)	\(e\left(\frac{29}{91}\right)\)	\(e\left(\frac{8}{91}\right)\)	\(e\left(\frac{61}{182}\right)\)	\(e\left(\frac{3}{182}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{20}{91}\right)\)
\(\chi_{7742}(73,\cdot)\)	7742.cq	546	no	\(-1\)	\(1\)	\(e\left(\frac{81}{182}\right)\)	\(e\left(\frac{95}{182}\right)\)	\(e\left(\frac{81}{91}\right)\)	\(e\left(\frac{163}{273}\right)\)	\(e\left(\frac{137}{546}\right)\)	\(e\left(\frac{88}{91}\right)\)	\(e\left(\frac{475}{546}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{4}{91}\right)\)

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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.