LMFDB - Group of Dirichlet characters of modulus 40310

Show commands: PariGP / SageMath

sage: H = DirichletGroup(40310)

pari: g = idealstar(,40310,2)

Character group

sage: G.order() pari: g.no
Order	=	15456
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{4}\times C_{1932}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{40310}(24187,\cdot)$, $\chi_{40310}(19461,\cdot)$, $\chi_{40310}(16821,\cdot)$

First 32 of 15456 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	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{40310}(1,\cdot)$	40310.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{40310}(3,\cdot)$	40310.gc	1932	no	$-1$	$1$	$e\left(\frac{313}{966}\right)$	$e\left(\frac{1445}{1932}\right)$	$e\left(\frac{313}{483}\right)$	$e\left(\frac{85}{1932}\right)$	$e\left(\frac{925}{1932}\right)$	$e\left(\frac{20}{69}\right)$	$e\left(\frac{445}{1932}\right)$	$e\left(\frac{139}{1932}\right)$	$e\left(\frac{543}{644}\right)$	$e\left(\frac{313}{322}\right)$
$\chi_{40310}(7,\cdot)$	40310.fx	1932	no	$-1$	$1$	$e\left(\frac{1445}{1932}\right)$	$e\left(\frac{983}{1932}\right)$	$e\left(\frac{479}{966}\right)$	$e\left(\frac{121}{483}\right)$	$e\left(\frac{1261}{1932}\right)$	$e\left(\frac{5}{276}\right)$	$e\left(\frac{443}{966}\right)$	$e\left(\frac{124}{483}\right)$	$e\left(\frac{67}{644}\right)$	$e\left(\frac{157}{644}\right)$
$\chi_{40310}(9,\cdot)$	40310.fn	966	no	$1$	$1$	$e\left(\frac{313}{483}\right)$	$e\left(\frac{479}{966}\right)$	$e\left(\frac{143}{483}\right)$	$e\left(\frac{85}{966}\right)$	$e\left(\frac{925}{966}\right)$	$e\left(\frac{40}{69}\right)$	$e\left(\frac{445}{966}\right)$	$e\left(\frac{139}{966}\right)$	$e\left(\frac{221}{322}\right)$	$e\left(\frac{152}{161}\right)$
$\chi_{40310}(11,\cdot)$	40310.fv	1932	no	$-1$	$1$	$e\left(\frac{85}{1932}\right)$	$e\left(\frac{121}{483}\right)$	$e\left(\frac{85}{966}\right)$	$e\left(\frac{341}{1932}\right)$	$e\left(\frac{307}{966}\right)$	$e\left(\frac{187}{276}\right)$	$e\left(\frac{1217}{1932}\right)$	$e\left(\frac{569}{1932}\right)$	$e\left(\frac{117}{161}\right)$	$e\left(\frac{85}{644}\right)$
$\chi_{40310}(13,\cdot)$	40310.fy	1932	no	$-1$	$1$	$e\left(\frac{925}{1932}\right)$	$e\left(\frac{1261}{1932}\right)$	$e\left(\frac{925}{966}\right)$	$e\left(\frac{307}{966}\right)$	$e\left(\frac{971}{1932}\right)$	$e\left(\frac{241}{276}\right)$	$e\left(\frac{278}{483}\right)$	$e\left(\frac{127}{966}\right)$	$e\left(\frac{405}{644}\right)$	$e\left(\frac{281}{644}\right)$
$\chi_{40310}(17,\cdot)$	40310.ep	276	no	$-1$	$1$	$e\left(\frac{20}{69}\right)$	$e\left(\frac{5}{276}\right)$	$e\left(\frac{40}{69}\right)$	$e\left(\frac{187}{276}\right)$	$e\left(\frac{241}{276}\right)$	$e\left(\frac{133}{138}\right)$	$e\left(\frac{151}{276}\right)$	$e\left(\frac{85}{276}\right)$	$e\left(\frac{63}{92}\right)$	$e\left(\frac{20}{23}\right)$
$\chi_{40310}(19,\cdot)$	40310.gb	1932	no	$1$	$1$	$e\left(\frac{445}{1932}\right)$	$e\left(\frac{443}{966}\right)$	$e\left(\frac{445}{966}\right)$	$e\left(\frac{1217}{1932}\right)$	$e\left(\frac{278}{483}\right)$	$e\left(\frac{151}{276}\right)$	$e\left(\frac{1655}{1932}\right)$	$e\left(\frac{1331}{1932}\right)$	$e\left(\frac{139}{161}\right)$	$e\left(\frac{445}{644}\right)$
$\chi_{40310}(21,\cdot)$	40310.fu	1932	no	$1$	$1$	$e\left(\frac{139}{1932}\right)$	$e\left(\frac{124}{483}\right)$	$e\left(\frac{139}{966}\right)$	$e\left(\frac{569}{1932}\right)$	$e\left(\frac{127}{966}\right)$	$e\left(\frac{85}{276}\right)$	$e\left(\frac{1331}{1932}\right)$	$e\left(\frac{635}{1932}\right)$	$e\left(\frac{305}{322}\right)$	$e\left(\frac{139}{644}\right)$
$\chi_{40310}(23,\cdot)$	40310.fg	644	no	$1$	$1$	$e\left(\frac{543}{644}\right)$	$e\left(\frac{67}{644}\right)$	$e\left(\frac{221}{322}\right)$	$e\left(\frac{117}{161}\right)$	$e\left(\frac{405}{644}\right)$	$e\left(\frac{63}{92}\right)$	$e\left(\frac{139}{161}\right)$	$e\left(\frac{305}{322}\right)$	$e\left(\frac{527}{644}\right)$	$e\left(\frac{341}{644}\right)$
$\chi_{40310}(27,\cdot)$	40310.fa	644	no	$-1$	$1$	$e\left(\frac{313}{322}\right)$	$e\left(\frac{157}{644}\right)$	$e\left(\frac{152}{161}\right)$	$e\left(\frac{85}{644}\right)$	$e\left(\frac{281}{644}\right)$	$e\left(\frac{20}{23}\right)$	$e\left(\frac{445}{644}\right)$	$e\left(\frac{139}{644}\right)$	$e\left(\frac{341}{644}\right)$	$e\left(\frac{295}{322}\right)$
$\chi_{40310}(31,\cdot)$	40310.fv	1932	no	$-1$	$1$	$e\left(\frac{1577}{1932}\right)$	$e\left(\frac{347}{483}\right)$	$e\left(\frac{611}{966}\right)$	$e\left(\frac{1417}{1932}\right)$	$e\left(\frac{593}{966}\right)$	$e\left(\frac{47}{276}\right)$	$e\left(\frac{145}{1932}\right)$	$e\left(\frac{1033}{1932}\right)$	$e\left(\frac{108}{161}\right)$	$e\left(\frac{289}{644}\right)$
$\chi_{40310}(33,\cdot)$	40310.fd	644	no	$1$	$1$	$e\left(\frac{237}{644}\right)$	$e\left(\frac{643}{644}\right)$	$e\left(\frac{237}{322}\right)$	$e\left(\frac{71}{322}\right)$	$e\left(\frac{513}{644}\right)$	$e\left(\frac{89}{92}\right)$	$e\left(\frac{277}{322}\right)$	$e\left(\frac{59}{161}\right)$	$e\left(\frac{367}{644}\right)$	$e\left(\frac{67}{644}\right)$
$\chi_{40310}(37,\cdot)$	40310.fs	1932	no	$1$	$1$	$e\left(\frac{26}{483}\right)$	$e\left(\frac{1007}{1932}\right)$	$e\left(\frac{52}{483}\right)$	$e\left(\frac{1423}{1932}\right)$	$e\left(\frac{1507}{1932}\right)$	$e\left(\frac{73}{138}\right)$	$e\left(\frac{1597}{1932}\right)$	$e\left(\frac{1111}{1932}\right)$	$e\left(\frac{351}{644}\right)$	$e\left(\frac{26}{161}\right)$
$\chi_{40310}(39,\cdot)$	40310.fc	644	no	$1$	$1$	$e\left(\frac{517}{644}\right)$	$e\left(\frac{129}{322}\right)$	$e\left(\frac{195}{322}\right)$	$e\left(\frac{233}{644}\right)$	$e\left(\frac{158}{161}\right)$	$e\left(\frac{15}{92}\right)$	$e\left(\frac{519}{644}\right)$	$e\left(\frac{131}{644}\right)$	$e\left(\frac{76}{161}\right)$	$e\left(\frac{263}{644}\right)$
$\chi_{40310}(41,\cdot)$	40310.en	276	no	$-1$	$1$	$e\left(\frac{209}{276}\right)$	$e\left(\frac{41}{69}\right)$	$e\left(\frac{71}{138}\right)$	$e\left(\frac{241}{276}\right)$	$e\left(\frac{47}{138}\right)$	$e\left(\frac{17}{276}\right)$	$e\left(\frac{109}{276}\right)$	$e\left(\frac{97}{276}\right)$	$e\left(\frac{6}{23}\right)$	$e\left(\frac{25}{92}\right)$
$\chi_{40310}(43,\cdot)$	40310.da	84	no	$-1$	$1$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{3}{14}\right)$
$\chi_{40310}(47,\cdot)$	40310.fs	1932	no	$1$	$1$	$e\left(\frac{401}{483}\right)$	$e\left(\frac{911}{1932}\right)$	$e\left(\frac{319}{483}\right)$	$e\left(\frac{1531}{1932}\right)$	$e\left(\frac{523}{1932}\right)$	$e\left(\frac{67}{138}\right)$	$e\left(\frac{685}{1932}\right)$	$e\left(\frac{583}{1932}\right)$	$e\left(\frac{503}{644}\right)$	$e\left(\frac{79}{161}\right)$
$\chi_{40310}(49,\cdot)$	40310.fq	966	no	$1$	$1$	$e\left(\frac{479}{966}\right)$	$e\left(\frac{17}{966}\right)$	$e\left(\frac{479}{483}\right)$	$e\left(\frac{242}{483}\right)$	$e\left(\frac{295}{966}\right)$	$e\left(\frac{5}{138}\right)$	$e\left(\frac{443}{483}\right)$	$e\left(\frac{248}{483}\right)$	$e\left(\frac{67}{322}\right)$	$e\left(\frac{157}{322}\right)$
$\chi_{40310}(51,\cdot)$	40310.fp	966	no	$1$	$1$	$e\left(\frac{593}{966}\right)$	$e\left(\frac{370}{483}\right)$	$e\left(\frac{110}{483}\right)$	$e\left(\frac{697}{966}\right)$	$e\left(\frac{170}{483}\right)$	$e\left(\frac{35}{138}\right)$	$e\left(\frac{751}{966}\right)$	$e\left(\frac{367}{966}\right)$	$e\left(\frac{85}{161}\right)$	$e\left(\frac{271}{322}\right)$
$\chi_{40310}(53,\cdot)$	40310.fw	1932	no	$1$	$1$	$e\left(\frac{1241}{1932}\right)$	$e\left(\frac{401}{1932}\right)$	$e\left(\frac{275}{966}\right)$	$e\left(\frac{13}{483}\right)$	$e\left(\frac{367}{1932}\right)$	$e\left(\frac{53}{276}\right)$	$e\left(\frac{409}{483}\right)$	$e\left(\frac{821}{966}\right)$	$e\left(\frac{103}{644}\right)$	$e\left(\frac{597}{644}\right)$
$\chi_{40310}(57,\cdot)$	40310.dr	92	no	$-1$	$1$	$e\left(\frac{51}{92}\right)$	$e\left(\frac{19}{92}\right)$	$e\left(\frac{5}{46}\right)$	$e\left(\frac{31}{46}\right)$	$e\left(\frac{5}{92}\right)$	$e\left(\frac{77}{92}\right)$	$e\left(\frac{2}{23}\right)$	$e\left(\frac{35}{46}\right)$	$e\left(\frac{65}{92}\right)$	$e\left(\frac{61}{92}\right)$
$\chi_{40310}(59,\cdot)$	40310.cs	46	no	$-1$	$1$	$e\left(\frac{17}{23}\right)$	$e\left(\frac{5}{46}\right)$	$e\left(\frac{11}{23}\right)$	$e\left(\frac{13}{23}\right)$	$e\left(\frac{11}{46}\right)$	$e\left(\frac{18}{23}\right)$	$e\left(\frac{13}{46}\right)$	$e\left(\frac{39}{46}\right)$	$e\left(\frac{14}{23}\right)$	$e\left(\frac{5}{23}\right)$
$\chi_{40310}(61,\cdot)$	40310.fu	1932	no	$1$	$1$	$e\left(\frac{1711}{1932}\right)$	$e\left(\frac{265}{483}\right)$	$e\left(\frac{745}{966}\right)$	$e\left(\frac{1625}{1932}\right)$	$e\left(\frac{361}{966}\right)$	$e\left(\frac{121}{276}\right)$	$e\left(\frac{1859}{1932}\right)$	$e\left(\frac{839}{1932}\right)$	$e\left(\frac{261}{322}\right)$	$e\left(\frac{423}{644}\right)$
$\chi_{40310}(63,\cdot)$	40310.fe	644	no	$-1$	$1$	$e\left(\frac{255}{644}\right)$	$e\left(\frac{3}{644}\right)$	$e\left(\frac{255}{322}\right)$	$e\left(\frac{109}{322}\right)$	$e\left(\frac{393}{644}\right)$	$e\left(\frac{55}{92}\right)$	$e\left(\frac{148}{161}\right)$	$e\left(\frac{129}{322}\right)$	$e\left(\frac{509}{644}\right)$	$e\left(\frac{121}{644}\right)$
$\chi_{40310}(67,\cdot)$	40310.fy	1932	no	$-1$	$1$	$e\left(\frac{559}{1932}\right)$	$e\left(\frac{643}{1932}\right)$	$e\left(\frac{559}{966}\right)$	$e\left(\frac{715}{966}\right)$	$e\left(\frac{1157}{1932}\right)$	$e\left(\frac{43}{276}\right)$	$e\left(\frac{380}{483}\right)$	$e\left(\frac{601}{966}\right)$	$e\left(\frac{15}{644}\right)$	$e\left(\frac{559}{644}\right)$
$\chi_{40310}(69,\cdot)$	40310.ga	1932	no	$-1$	$1$	$e\left(\frac{323}{1932}\right)$	$e\left(\frac{823}{966}\right)$	$e\left(\frac{323}{966}\right)$	$e\left(\frac{1489}{1932}\right)$	$e\left(\frac{52}{483}\right)$	$e\left(\frac{269}{276}\right)$	$e\left(\frac{181}{1932}\right)$	$e\left(\frac{37}{1932}\right)$	$e\left(\frac{213}{322}\right)$	$e\left(\frac{323}{644}\right)$
$\chi_{40310}(71,\cdot)$	40310.fp	966	no	$1$	$1$	$e\left(\frac{95}{966}\right)$	$e\left(\frac{100}{483}\right)$	$e\left(\frac{95}{483}\right)$	$e\left(\frac{97}{966}\right)$	$e\left(\frac{59}{483}\right)$	$e\left(\frac{71}{138}\right)$	$e\left(\frac{451}{966}\right)$	$e\left(\frac{295}{966}\right)$	$e\left(\frac{110}{161}\right)$	$e\left(\frac{95}{322}\right)$
$\chi_{40310}(73,\cdot)$	40310.ft	1932	no	$-1$	$1$	$e\left(\frac{304}{483}\right)$	$e\left(\frac{145}{1932}\right)$	$e\left(\frac{125}{483}\right)$	$e\left(\frac{179}{1932}\right)$	$e\left(\frac{641}{1932}\right)$	$e\left(\frac{137}{138}\right)$	$e\left(\frac{1619}{1932}\right)$	$e\left(\frac{1361}{1932}\right)$	$e\left(\frac{79}{644}\right)$	$e\left(\frac{143}{161}\right)$
$\chi_{40310}(77,\cdot)$	40310.ez	644	no	$1$	$1$	$e\left(\frac{255}{322}\right)$	$e\left(\frac{489}{644}\right)$	$e\left(\frac{94}{161}\right)$	$e\left(\frac{275}{644}\right)$	$e\left(\frac{625}{644}\right)$	$e\left(\frac{16}{23}\right)$	$e\left(\frac{57}{644}\right)$	$e\left(\frac{355}{644}\right)$	$e\left(\frac{535}{644}\right)$	$e\left(\frac{121}{322}\right)$
$\chi_{40310}(79,\cdot)$	40310.fb	644	no	$-1$	$1$	$e\left(\frac{233}{644}\right)$	$e\left(\frac{169}{322}\right)$	$e\left(\frac{233}{322}\right)$	$e\left(\frac{143}{644}\right)$	$e\left(\frac{41}{161}\right)$	$e\left(\frac{71}{92}\right)$	$e\left(\frac{635}{644}\right)$	$e\left(\frac{571}{644}\right)$	$e\left(\frac{123}{322}\right)$	$e\left(\frac{55}{644}\right)$
$\chi_{40310}(81,\cdot)$	40310.ey	483	no	$1$	$1$	$e\left(\frac{143}{483}\right)$	$e\left(\frac{479}{483}\right)$	$e\left(\frac{286}{483}\right)$	$e\left(\frac{85}{483}\right)$	$e\left(\frac{442}{483}\right)$	$e\left(\frac{11}{69}\right)$	$e\left(\frac{445}{483}\right)$	$e\left(\frac{139}{483}\right)$	$e\left(\frac{60}{161}\right)$	$e\left(\frac{143}{161}\right)$

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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	$40310$
Structure	\(C_{2}\times C_{4}\times C_{1932}\)
Order	$15456$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)
\(\chi_{40310}(1,\cdot)\)	40310.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{40310}(3,\cdot)\)	40310.gc	1932	no	\(-1\)	\(1\)	\(e\left(\frac{313}{966}\right)\)	\(e\left(\frac{1445}{1932}\right)\)	\(e\left(\frac{313}{483}\right)\)	\(e\left(\frac{85}{1932}\right)\)	\(e\left(\frac{925}{1932}\right)\)	\(e\left(\frac{20}{69}\right)\)	\(e\left(\frac{445}{1932}\right)\)	\(e\left(\frac{139}{1932}\right)\)	\(e\left(\frac{543}{644}\right)\)	\(e\left(\frac{313}{322}\right)\)
\(\chi_{40310}(7,\cdot)\)	40310.fx	1932	no	\(-1\)	\(1\)	\(e\left(\frac{1445}{1932}\right)\)	\(e\left(\frac{983}{1932}\right)\)	\(e\left(\frac{479}{966}\right)\)	\(e\left(\frac{121}{483}\right)\)	\(e\left(\frac{1261}{1932}\right)\)	\(e\left(\frac{5}{276}\right)\)	\(e\left(\frac{443}{966}\right)\)	\(e\left(\frac{124}{483}\right)\)	\(e\left(\frac{67}{644}\right)\)	\(e\left(\frac{157}{644}\right)\)
\(\chi_{40310}(9,\cdot)\)	40310.fn	966	no	\(1\)	\(1\)	\(e\left(\frac{313}{483}\right)\)	\(e\left(\frac{479}{966}\right)\)	\(e\left(\frac{143}{483}\right)\)	\(e\left(\frac{85}{966}\right)\)	\(e\left(\frac{925}{966}\right)\)	\(e\left(\frac{40}{69}\right)\)	\(e\left(\frac{445}{966}\right)\)	\(e\left(\frac{139}{966}\right)\)	\(e\left(\frac{221}{322}\right)\)	\(e\left(\frac{152}{161}\right)\)
\(\chi_{40310}(11,\cdot)\)	40310.fv	1932	no	\(-1\)	\(1\)	\(e\left(\frac{85}{1932}\right)\)	\(e\left(\frac{121}{483}\right)\)	\(e\left(\frac{85}{966}\right)\)	\(e\left(\frac{341}{1932}\right)\)	\(e\left(\frac{307}{966}\right)\)	\(e\left(\frac{187}{276}\right)\)	\(e\left(\frac{1217}{1932}\right)\)	\(e\left(\frac{569}{1932}\right)\)	\(e\left(\frac{117}{161}\right)\)	\(e\left(\frac{85}{644}\right)\)
\(\chi_{40310}(13,\cdot)\)	40310.fy	1932	no	\(-1\)	\(1\)	\(e\left(\frac{925}{1932}\right)\)	\(e\left(\frac{1261}{1932}\right)\)	\(e\left(\frac{925}{966}\right)\)	\(e\left(\frac{307}{966}\right)\)	\(e\left(\frac{971}{1932}\right)\)	\(e\left(\frac{241}{276}\right)\)	\(e\left(\frac{278}{483}\right)\)	\(e\left(\frac{127}{966}\right)\)	\(e\left(\frac{405}{644}\right)\)	\(e\left(\frac{281}{644}\right)\)
\(\chi_{40310}(17,\cdot)\)	40310.ep	276	no	\(-1\)	\(1\)	\(e\left(\frac{20}{69}\right)\)	\(e\left(\frac{5}{276}\right)\)	\(e\left(\frac{40}{69}\right)\)	\(e\left(\frac{187}{276}\right)\)	\(e\left(\frac{241}{276}\right)\)	\(e\left(\frac{133}{138}\right)\)	\(e\left(\frac{151}{276}\right)\)	\(e\left(\frac{85}{276}\right)\)	\(e\left(\frac{63}{92}\right)\)	\(e\left(\frac{20}{23}\right)\)
\(\chi_{40310}(19,\cdot)\)	40310.gb	1932	no	\(1\)	\(1\)	\(e\left(\frac{445}{1932}\right)\)	\(e\left(\frac{443}{966}\right)\)	\(e\left(\frac{445}{966}\right)\)	\(e\left(\frac{1217}{1932}\right)\)	\(e\left(\frac{278}{483}\right)\)	\(e\left(\frac{151}{276}\right)\)	\(e\left(\frac{1655}{1932}\right)\)	\(e\left(\frac{1331}{1932}\right)\)	\(e\left(\frac{139}{161}\right)\)	\(e\left(\frac{445}{644}\right)\)
\(\chi_{40310}(21,\cdot)\)	40310.fu	1932	no	\(1\)	\(1\)	\(e\left(\frac{139}{1932}\right)\)	\(e\left(\frac{124}{483}\right)\)	\(e\left(\frac{139}{966}\right)\)	\(e\left(\frac{569}{1932}\right)\)	\(e\left(\frac{127}{966}\right)\)	\(e\left(\frac{85}{276}\right)\)	\(e\left(\frac{1331}{1932}\right)\)	\(e\left(\frac{635}{1932}\right)\)	\(e\left(\frac{305}{322}\right)\)	\(e\left(\frac{139}{644}\right)\)
\(\chi_{40310}(23,\cdot)\)	40310.fg	644	no	\(1\)	\(1\)	\(e\left(\frac{543}{644}\right)\)	\(e\left(\frac{67}{644}\right)\)	\(e\left(\frac{221}{322}\right)\)	\(e\left(\frac{117}{161}\right)\)	\(e\left(\frac{405}{644}\right)\)	\(e\left(\frac{63}{92}\right)\)	\(e\left(\frac{139}{161}\right)\)	\(e\left(\frac{305}{322}\right)\)	\(e\left(\frac{527}{644}\right)\)	\(e\left(\frac{341}{644}\right)\)
\(\chi_{40310}(27,\cdot)\)	40310.fa	644	no	\(-1\)	\(1\)	\(e\left(\frac{313}{322}\right)\)	\(e\left(\frac{157}{644}\right)\)	\(e\left(\frac{152}{161}\right)\)	\(e\left(\frac{85}{644}\right)\)	\(e\left(\frac{281}{644}\right)\)	\(e\left(\frac{20}{23}\right)\)	\(e\left(\frac{445}{644}\right)\)	\(e\left(\frac{139}{644}\right)\)	\(e\left(\frac{341}{644}\right)\)	\(e\left(\frac{295}{322}\right)\)
\(\chi_{40310}(31,\cdot)\)	40310.fv	1932	no	\(-1\)	\(1\)	\(e\left(\frac{1577}{1932}\right)\)	\(e\left(\frac{347}{483}\right)\)	\(e\left(\frac{611}{966}\right)\)	\(e\left(\frac{1417}{1932}\right)\)	\(e\left(\frac{593}{966}\right)\)	\(e\left(\frac{47}{276}\right)\)	\(e\left(\frac{145}{1932}\right)\)	\(e\left(\frac{1033}{1932}\right)\)	\(e\left(\frac{108}{161}\right)\)	\(e\left(\frac{289}{644}\right)\)
\(\chi_{40310}(33,\cdot)\)	40310.fd	644	no	\(1\)	\(1\)	\(e\left(\frac{237}{644}\right)\)	\(e\left(\frac{643}{644}\right)\)	\(e\left(\frac{237}{322}\right)\)	\(e\left(\frac{71}{322}\right)\)	\(e\left(\frac{513}{644}\right)\)	\(e\left(\frac{89}{92}\right)\)	\(e\left(\frac{277}{322}\right)\)	\(e\left(\frac{59}{161}\right)\)	\(e\left(\frac{367}{644}\right)\)	\(e\left(\frac{67}{644}\right)\)
\(\chi_{40310}(37,\cdot)\)	40310.fs	1932	no	\(1\)	\(1\)	\(e\left(\frac{26}{483}\right)\)	\(e\left(\frac{1007}{1932}\right)\)	\(e\left(\frac{52}{483}\right)\)	\(e\left(\frac{1423}{1932}\right)\)	\(e\left(\frac{1507}{1932}\right)\)	\(e\left(\frac{73}{138}\right)\)	\(e\left(\frac{1597}{1932}\right)\)	\(e\left(\frac{1111}{1932}\right)\)	\(e\left(\frac{351}{644}\right)\)	\(e\left(\frac{26}{161}\right)\)
\(\chi_{40310}(39,\cdot)\)	40310.fc	644	no	\(1\)	\(1\)	\(e\left(\frac{517}{644}\right)\)	\(e\left(\frac{129}{322}\right)\)	\(e\left(\frac{195}{322}\right)\)	\(e\left(\frac{233}{644}\right)\)	\(e\left(\frac{158}{161}\right)\)	\(e\left(\frac{15}{92}\right)\)	\(e\left(\frac{519}{644}\right)\)	\(e\left(\frac{131}{644}\right)\)	\(e\left(\frac{76}{161}\right)\)	\(e\left(\frac{263}{644}\right)\)
\(\chi_{40310}(41,\cdot)\)	40310.en	276	no	\(-1\)	\(1\)	\(e\left(\frac{209}{276}\right)\)	\(e\left(\frac{41}{69}\right)\)	\(e\left(\frac{71}{138}\right)\)	\(e\left(\frac{241}{276}\right)\)	\(e\left(\frac{47}{138}\right)\)	\(e\left(\frac{17}{276}\right)\)	\(e\left(\frac{109}{276}\right)\)	\(e\left(\frac{97}{276}\right)\)	\(e\left(\frac{6}{23}\right)\)	\(e\left(\frac{25}{92}\right)\)
\(\chi_{40310}(43,\cdot)\)	40310.da	84	no	\(-1\)	\(1\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{3}{14}\right)\)
\(\chi_{40310}(47,\cdot)\)	40310.fs	1932	no	\(1\)	\(1\)	\(e\left(\frac{401}{483}\right)\)	\(e\left(\frac{911}{1932}\right)\)	\(e\left(\frac{319}{483}\right)\)	\(e\left(\frac{1531}{1932}\right)\)	\(e\left(\frac{523}{1932}\right)\)	\(e\left(\frac{67}{138}\right)\)	\(e\left(\frac{685}{1932}\right)\)	\(e\left(\frac{583}{1932}\right)\)	\(e\left(\frac{503}{644}\right)\)	\(e\left(\frac{79}{161}\right)\)
\(\chi_{40310}(49,\cdot)\)	40310.fq	966	no	\(1\)	\(1\)	\(e\left(\frac{479}{966}\right)\)	\(e\left(\frac{17}{966}\right)\)	\(e\left(\frac{479}{483}\right)\)	\(e\left(\frac{242}{483}\right)\)	\(e\left(\frac{295}{966}\right)\)	\(e\left(\frac{5}{138}\right)\)	\(e\left(\frac{443}{483}\right)\)	\(e\left(\frac{248}{483}\right)\)	\(e\left(\frac{67}{322}\right)\)	\(e\left(\frac{157}{322}\right)\)
\(\chi_{40310}(51,\cdot)\)	40310.fp	966	no	\(1\)	\(1\)	\(e\left(\frac{593}{966}\right)\)	\(e\left(\frac{370}{483}\right)\)	\(e\left(\frac{110}{483}\right)\)	\(e\left(\frac{697}{966}\right)\)	\(e\left(\frac{170}{483}\right)\)	\(e\left(\frac{35}{138}\right)\)	\(e\left(\frac{751}{966}\right)\)	\(e\left(\frac{367}{966}\right)\)	\(e\left(\frac{85}{161}\right)\)	\(e\left(\frac{271}{322}\right)\)
\(\chi_{40310}(53,\cdot)\)	40310.fw	1932	no	\(1\)	\(1\)	\(e\left(\frac{1241}{1932}\right)\)	\(e\left(\frac{401}{1932}\right)\)	\(e\left(\frac{275}{966}\right)\)	\(e\left(\frac{13}{483}\right)\)	\(e\left(\frac{367}{1932}\right)\)	\(e\left(\frac{53}{276}\right)\)	\(e\left(\frac{409}{483}\right)\)	\(e\left(\frac{821}{966}\right)\)	\(e\left(\frac{103}{644}\right)\)	\(e\left(\frac{597}{644}\right)\)
\(\chi_{40310}(57,\cdot)\)	40310.dr	92	no	\(-1\)	\(1\)	\(e\left(\frac{51}{92}\right)\)	\(e\left(\frac{19}{92}\right)\)	\(e\left(\frac{5}{46}\right)\)	\(e\left(\frac{31}{46}\right)\)	\(e\left(\frac{5}{92}\right)\)	\(e\left(\frac{77}{92}\right)\)	\(e\left(\frac{2}{23}\right)\)	\(e\left(\frac{35}{46}\right)\)	\(e\left(\frac{65}{92}\right)\)	\(e\left(\frac{61}{92}\right)\)
\(\chi_{40310}(59,\cdot)\)	40310.cs	46	no	\(-1\)	\(1\)	\(e\left(\frac{17}{23}\right)\)	\(e\left(\frac{5}{46}\right)\)	\(e\left(\frac{11}{23}\right)\)	\(e\left(\frac{13}{23}\right)\)	\(e\left(\frac{11}{46}\right)\)	\(e\left(\frac{18}{23}\right)\)	\(e\left(\frac{13}{46}\right)\)	\(e\left(\frac{39}{46}\right)\)	\(e\left(\frac{14}{23}\right)\)	\(e\left(\frac{5}{23}\right)\)
\(\chi_{40310}(61,\cdot)\)	40310.fu	1932	no	\(1\)	\(1\)	\(e\left(\frac{1711}{1932}\right)\)	\(e\left(\frac{265}{483}\right)\)	\(e\left(\frac{745}{966}\right)\)	\(e\left(\frac{1625}{1932}\right)\)	\(e\left(\frac{361}{966}\right)\)	\(e\left(\frac{121}{276}\right)\)	\(e\left(\frac{1859}{1932}\right)\)	\(e\left(\frac{839}{1932}\right)\)	\(e\left(\frac{261}{322}\right)\)	\(e\left(\frac{423}{644}\right)\)
\(\chi_{40310}(63,\cdot)\)	40310.fe	644	no	\(-1\)	\(1\)	\(e\left(\frac{255}{644}\right)\)	\(e\left(\frac{3}{644}\right)\)	\(e\left(\frac{255}{322}\right)\)	\(e\left(\frac{109}{322}\right)\)	\(e\left(\frac{393}{644}\right)\)	\(e\left(\frac{55}{92}\right)\)	\(e\left(\frac{148}{161}\right)\)	\(e\left(\frac{129}{322}\right)\)	\(e\left(\frac{509}{644}\right)\)	\(e\left(\frac{121}{644}\right)\)
\(\chi_{40310}(67,\cdot)\)	40310.fy	1932	no	\(-1\)	\(1\)	\(e\left(\frac{559}{1932}\right)\)	\(e\left(\frac{643}{1932}\right)\)	\(e\left(\frac{559}{966}\right)\)	\(e\left(\frac{715}{966}\right)\)	\(e\left(\frac{1157}{1932}\right)\)	\(e\left(\frac{43}{276}\right)\)	\(e\left(\frac{380}{483}\right)\)	\(e\left(\frac{601}{966}\right)\)	\(e\left(\frac{15}{644}\right)\)	\(e\left(\frac{559}{644}\right)\)
\(\chi_{40310}(69,\cdot)\)	40310.ga	1932	no	\(-1\)	\(1\)	\(e\left(\frac{323}{1932}\right)\)	\(e\left(\frac{823}{966}\right)\)	\(e\left(\frac{323}{966}\right)\)	\(e\left(\frac{1489}{1932}\right)\)	\(e\left(\frac{52}{483}\right)\)	\(e\left(\frac{269}{276}\right)\)	\(e\left(\frac{181}{1932}\right)\)	\(e\left(\frac{37}{1932}\right)\)	\(e\left(\frac{213}{322}\right)\)	\(e\left(\frac{323}{644}\right)\)
\(\chi_{40310}(71,\cdot)\)	40310.fp	966	no	\(1\)	\(1\)	\(e\left(\frac{95}{966}\right)\)	\(e\left(\frac{100}{483}\right)\)	\(e\left(\frac{95}{483}\right)\)	\(e\left(\frac{97}{966}\right)\)	\(e\left(\frac{59}{483}\right)\)	\(e\left(\frac{71}{138}\right)\)	\(e\left(\frac{451}{966}\right)\)	\(e\left(\frac{295}{966}\right)\)	\(e\left(\frac{110}{161}\right)\)	\(e\left(\frac{95}{322}\right)\)
\(\chi_{40310}(73,\cdot)\)	40310.ft	1932	no	\(-1\)	\(1\)	\(e\left(\frac{304}{483}\right)\)	\(e\left(\frac{145}{1932}\right)\)	\(e\left(\frac{125}{483}\right)\)	\(e\left(\frac{179}{1932}\right)\)	\(e\left(\frac{641}{1932}\right)\)	\(e\left(\frac{137}{138}\right)\)	\(e\left(\frac{1619}{1932}\right)\)	\(e\left(\frac{1361}{1932}\right)\)	\(e\left(\frac{79}{644}\right)\)	\(e\left(\frac{143}{161}\right)\)
\(\chi_{40310}(77,\cdot)\)	40310.ez	644	no	\(1\)	\(1\)	\(e\left(\frac{255}{322}\right)\)	\(e\left(\frac{489}{644}\right)\)	\(e\left(\frac{94}{161}\right)\)	\(e\left(\frac{275}{644}\right)\)	\(e\left(\frac{625}{644}\right)\)	\(e\left(\frac{16}{23}\right)\)	\(e\left(\frac{57}{644}\right)\)	\(e\left(\frac{355}{644}\right)\)	\(e\left(\frac{535}{644}\right)\)	\(e\left(\frac{121}{322}\right)\)
\(\chi_{40310}(79,\cdot)\)	40310.fb	644	no	\(-1\)	\(1\)	\(e\left(\frac{233}{644}\right)\)	\(e\left(\frac{169}{322}\right)\)	\(e\left(\frac{233}{322}\right)\)	\(e\left(\frac{143}{644}\right)\)	\(e\left(\frac{41}{161}\right)\)	\(e\left(\frac{71}{92}\right)\)	\(e\left(\frac{635}{644}\right)\)	\(e\left(\frac{571}{644}\right)\)	\(e\left(\frac{123}{322}\right)\)	\(e\left(\frac{55}{644}\right)\)
\(\chi_{40310}(81,\cdot)\)	40310.ey	483	no	\(1\)	\(1\)	\(e\left(\frac{143}{483}\right)\)	\(e\left(\frac{479}{483}\right)\)	\(e\left(\frac{286}{483}\right)\)	\(e\left(\frac{85}{483}\right)\)	\(e\left(\frac{442}{483}\right)\)	\(e\left(\frac{11}{69}\right)\)	\(e\left(\frac{445}{483}\right)\)	\(e\left(\frac{139}{483}\right)\)	\(e\left(\frac{60}{161}\right)\)	\(e\left(\frac{143}{161}\right)\)

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.