LMFDB - Group of Dirichlet characters of modulus 374790

Show commands: PariGP / SageMath

sage: H = DirichletGroup(374790)

pari: g = idealstar(,374790,2)

Character group

sage: G.order() pari: g.no
Order	=	89280
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{12}\times C_{1860}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{374790}(124931,\cdot)$, $\chi_{374790}(149917,\cdot)$, $\chi_{374790}(86491,\cdot)$, $\chi_{374790}(26911,\cdot)$

First 32 of 89280 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	$-1$	$1$	$7$	$11$	$17$	$19$	$23$	$29$	$37$	$41$	$43$	$47$
$\chi_{374790}(1,\cdot)$	374790.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{374790}(7,\cdot)$	374790.bbm	1860	no	$1$	$1$	$e\left(\frac{412}{465}\right)$	$e\left(\frac{1763}{1860}\right)$	$e\left(\frac{847}{1860}\right)$	$e\left(\frac{919}{1860}\right)$	$e\left(\frac{877}{1860}\right)$	$e\left(\frac{857}{930}\right)$	$e\left(\frac{14}{31}\right)$	$e\left(\frac{509}{1860}\right)$	$e\left(\frac{1069}{1860}\right)$	$e\left(\frac{148}{155}\right)$
$\chi_{374790}(11,\cdot)$	374790.bdc	1860	no	$-1$	$1$	$e\left(\frac{1763}{1860}\right)$	$e\left(\frac{1423}{1860}\right)$	$e\left(\frac{151}{930}\right)$	$e\left(\frac{449}{1860}\right)$	$e\left(\frac{511}{930}\right)$	$e\left(\frac{116}{465}\right)$	$e\left(\frac{11}{124}\right)$	$e\left(\frac{1459}{1860}\right)$	$e\left(\frac{431}{465}\right)$	$e\left(\frac{227}{620}\right)$
$\chi_{374790}(17,\cdot)$	374790.bdr	1860	no	$-1$	$1$	$e\left(\frac{847}{1860}\right)$	$e\left(\frac{151}{930}\right)$	$e\left(\frac{733}{1860}\right)$	$e\left(\frac{289}{465}\right)$	$e\left(\frac{1723}{1860}\right)$	$e\left(\frac{443}{930}\right)$	$e\left(\frac{19}{124}\right)$	$e\left(\frac{239}{465}\right)$	$e\left(\frac{61}{1860}\right)$	$e\left(\frac{223}{620}\right)$
$\chi_{374790}(19,\cdot)$	374790.bcn	1860	no	$-1$	$1$	$e\left(\frac{919}{1860}\right)$	$e\left(\frac{449}{1860}\right)$	$e\left(\frac{289}{465}\right)$	$e\left(\frac{607}{1860}\right)$	$e\left(\frac{319}{465}\right)$	$e\left(\frac{133}{465}\right)$	$e\left(\frac{69}{124}\right)$	$e\left(\frac{827}{1860}\right)$	$e\left(\frac{418}{465}\right)$	$e\left(\frac{601}{620}\right)$
$\chi_{374790}(23,\cdot)$	374790.bdq	1860	no	$-1$	$1$	$e\left(\frac{877}{1860}\right)$	$e\left(\frac{511}{930}\right)$	$e\left(\frac{1723}{1860}\right)$	$e\left(\frac{319}{465}\right)$	$e\left(\frac{413}{1860}\right)$	$e\left(\frac{253}{930}\right)$	$e\left(\frac{259}{372}\right)$	$e\left(\frac{119}{465}\right)$	$e\left(\frac{151}{1860}\right)$	$e\left(\frac{613}{620}\right)$
$\chi_{374790}(29,\cdot)$	374790.bab	930	no	$1$	$1$	$e\left(\frac{857}{930}\right)$	$e\left(\frac{116}{465}\right)$	$e\left(\frac{443}{930}\right)$	$e\left(\frac{133}{465}\right)$	$e\left(\frac{253}{930}\right)$	$e\left(\frac{173}{465}\right)$	$e\left(\frac{88}{93}\right)$	$e\left(\frac{331}{930}\right)$	$e\left(\frac{433}{465}\right)$	$e\left(\frac{99}{155}\right)$
$\chi_{374790}(37,\cdot)$	374790.uc	372	no	$-1$	$1$	$e\left(\frac{14}{31}\right)$	$e\left(\frac{11}{124}\right)$	$e\left(\frac{19}{124}\right)$	$e\left(\frac{69}{124}\right)$	$e\left(\frac{259}{372}\right)$	$e\left(\frac{88}{93}\right)$	$e\left(\frac{7}{186}\right)$	$e\left(\frac{3}{124}\right)$	$e\left(\frac{13}{124}\right)$	$e\left(\frac{19}{31}\right)$
$\chi_{374790}(41,\cdot)$	374790.bct	1860	no	$1$	$1$	$e\left(\frac{509}{1860}\right)$	$e\left(\frac{1459}{1860}\right)$	$e\left(\frac{239}{465}\right)$	$e\left(\frac{827}{1860}\right)$	$e\left(\frac{119}{465}\right)$	$e\left(\frac{331}{930}\right)$	$e\left(\frac{3}{124}\right)$	$e\left(\frac{877}{1860}\right)$	$e\left(\frac{841}{930}\right)$	$e\left(\frac{541}{620}\right)$
$\chi_{374790}(43,\cdot)$	374790.bby	1860	no	$1$	$1$	$e\left(\frac{1069}{1860}\right)$	$e\left(\frac{431}{465}\right)$	$e\left(\frac{61}{1860}\right)$	$e\left(\frac{418}{465}\right)$	$e\left(\frac{151}{1860}\right)$	$e\left(\frac{433}{465}\right)$	$e\left(\frac{13}{124}\right)$	$e\left(\frac{841}{930}\right)$	$e\left(\frac{727}{1860}\right)$	$e\left(\frac{71}{620}\right)$
$\chi_{374790}(47,\cdot)$	374790.ys	620	no	$-1$	$1$	$e\left(\frac{148}{155}\right)$	$e\left(\frac{227}{620}\right)$	$e\left(\frac{223}{620}\right)$	$e\left(\frac{601}{620}\right)$	$e\left(\frac{613}{620}\right)$	$e\left(\frac{99}{155}\right)$	$e\left(\frac{19}{31}\right)$	$e\left(\frac{541}{620}\right)$	$e\left(\frac{71}{620}\right)$	$e\left(\frac{167}{310}\right)$
$\chi_{374790}(49,\cdot)$	374790.zt	930	no	$1$	$1$	$e\left(\frac{359}{465}\right)$	$e\left(\frac{833}{930}\right)$	$e\left(\frac{847}{930}\right)$	$e\left(\frac{919}{930}\right)$	$e\left(\frac{877}{930}\right)$	$e\left(\frac{392}{465}\right)$	$e\left(\frac{28}{31}\right)$	$e\left(\frac{509}{930}\right)$	$e\left(\frac{139}{930}\right)$	$e\left(\frac{141}{155}\right)$
$\chi_{374790}(53,\cdot)$	374790.bcd	1860	no	$-1$	$1$	$e\left(\frac{727}{1860}\right)$	$e\left(\frac{53}{465}\right)$	$e\left(\frac{1423}{1860}\right)$	$e\left(\frac{803}{930}\right)$	$e\left(\frac{151}{620}\right)$	$e\left(\frac{91}{310}\right)$	$e\left(\frac{365}{372}\right)$	$e\left(\frac{43}{930}\right)$	$e\left(\frac{631}{1860}\right)$	$e\left(\frac{523}{620}\right)$
$\chi_{374790}(59,\cdot)$	374790.bdg	1860	no	$1$	$1$	$e\left(\frac{1801}{1860}\right)$	$e\left(\frac{41}{1860}\right)$	$e\left(\frac{437}{930}\right)$	$e\left(\frac{973}{1860}\right)$	$e\left(\frac{167}{930}\right)$	$e\left(\frac{539}{930}\right)$	$e\left(\frac{15}{124}\right)$	$e\left(\frac{1223}{1860}\right)$	$e\left(\frac{382}{465}\right)$	$e\left(\frac{349}{620}\right)$
$\chi_{374790}(61,\cdot)$	374790.sp	186	no	$-1$	$1$	$e\left(\frac{34}{93}\right)$	$e\left(\frac{175}{186}\right)$	$e\left(\frac{167}{186}\right)$	$e\left(\frac{43}{93}\right)$	$e\left(\frac{79}{186}\right)$	$e\left(\frac{79}{186}\right)$	$e\left(\frac{109}{186}\right)$	$e\left(\frac{14}{93}\right)$	$e\left(\frac{173}{186}\right)$	$e\left(\frac{8}{31}\right)$
$\chi_{374790}(67,\cdot)$	374790.uj	372	no	$1$	$1$	$e\left(\frac{125}{186}\right)$	$e\left(\frac{17}{372}\right)$	$e\left(\frac{283}{372}\right)$	$e\left(\frac{349}{372}\right)$	$e\left(\frac{109}{372}\right)$	$e\left(\frac{101}{186}\right)$	$e\left(\frac{25}{62}\right)$	$e\left(\frac{371}{372}\right)$	$e\left(\frac{37}{372}\right)$	$e\left(\frac{13}{62}\right)$
$\chi_{374790}(71,\cdot)$	374790.bdm	1860	no	$1$	$1$	$e\left(\frac{479}{620}\right)$	$e\left(\frac{429}{620}\right)$	$e\left(\frac{69}{155}\right)$	$e\left(\frac{397}{620}\right)$	$e\left(\frac{22}{465}\right)$	$e\left(\frac{323}{930}\right)$	$e\left(\frac{289}{372}\right)$	$e\left(\frac{427}{620}\right)$	$e\left(\frac{21}{310}\right)$	$e\left(\frac{453}{620}\right)$
$\chi_{374790}(73,\cdot)$	374790.bep	1860	no	$-1$	$1$	$e\left(\frac{449}{930}\right)$	$e\left(\frac{1433}{1860}\right)$	$e\left(\frac{1207}{1860}\right)$	$e\left(\frac{1639}{1860}\right)$	$e\left(\frac{359}{620}\right)$	$e\left(\frac{82}{155}\right)$	$e\left(\frac{35}{93}\right)$	$e\left(\frac{1349}{1860}\right)$	$e\left(\frac{1609}{1860}\right)$	$e\left(\frac{71}{310}\right)$
$\chi_{374790}(77,\cdot)$	374790.yd	620	no	$-1$	$1$	$e\left(\frac{517}{620}\right)$	$e\left(\frac{221}{310}\right)$	$e\left(\frac{383}{620}\right)$	$e\left(\frac{114}{155}\right)$	$e\left(\frac{13}{620}\right)$	$e\left(\frac{53}{310}\right)$	$e\left(\frac{67}{124}\right)$	$e\left(\frac{9}{155}\right)$	$e\left(\frac{311}{620}\right)$	$e\left(\frac{199}{620}\right)$
$\chi_{374790}(79,\cdot)$	374790.bao	930	no	$-1$	$1$	$e\left(\frac{481}{930}\right)$	$e\left(\frac{911}{930}\right)$	$e\left(\frac{47}{465}\right)$	$e\left(\frac{404}{465}\right)$	$e\left(\frac{104}{155}\right)$	$e\left(\frac{301}{310}\right)$	$e\left(\frac{58}{93}\right)$	$e\left(\frac{244}{465}\right)$	$e\left(\frac{179}{465}\right)$	$e\left(\frac{239}{310}\right)$
$\chi_{374790}(83,\cdot)$	374790.bbg	1860	no	$1$	$1$	$e\left(\frac{76}{465}\right)$	$e\left(\frac{569}{1860}\right)$	$e\left(\frac{1321}{1860}\right)$	$e\left(\frac{937}{1860}\right)$	$e\left(\frac{77}{620}\right)$	$e\left(\frac{147}{310}\right)$	$e\left(\frac{79}{186}\right)$	$e\left(\frac{437}{1860}\right)$	$e\left(\frac{757}{1860}\right)$	$e\left(\frac{23}{310}\right)$
$\chi_{374790}(89,\cdot)$	374790.bco	1860	no	$-1$	$1$	$e\left(\frac{553}{1860}\right)$	$e\left(\frac{1523}{1860}\right)$	$e\left(\frac{13}{465}\right)$	$e\left(\frac{1189}{1860}\right)$	$e\left(\frac{83}{465}\right)$	$e\left(\frac{176}{465}\right)$	$e\left(\frac{235}{372}\right)$	$e\left(\frac{359}{1860}\right)$	$e\left(\frac{287}{930}\right)$	$e\left(\frac{617}{620}\right)$
$\chi_{374790}(97,\cdot)$	374790.bel	1860	no	$1$	$1$	$e\left(\frac{409}{930}\right)$	$e\left(\frac{133}{1860}\right)$	$e\left(\frac{1667}{1860}\right)$	$e\left(\frac{389}{1860}\right)$	$e\left(\frac{1057}{1860}\right)$	$e\left(\frac{17}{930}\right)$	$e\left(\frac{121}{186}\right)$	$e\left(\frac{1699}{1860}\right)$	$e\left(\frac{749}{1860}\right)$	$e\left(\frac{171}{310}\right)$
$\chi_{374790}(101,\cdot)$	374790.bag	930	no	$-1$	$1$	$e\left(\frac{431}{930}\right)$	$e\left(\frac{398}{465}\right)$	$e\left(\frac{149}{930}\right)$	$e\left(\frac{143}{930}\right)$	$e\left(\frac{379}{930}\right)$	$e\left(\frac{193}{930}\right)$	$e\left(\frac{17}{186}\right)$	$e\left(\frac{179}{465}\right)$	$e\left(\frac{259}{465}\right)$	$e\left(\frac{27}{155}\right)$
$\chi_{374790}(103,\cdot)$	374790.bdp	1860	no	$-1$	$1$	$e\left(\frac{1309}{1860}\right)$	$e\left(\frac{487}{930}\right)$	$e\left(\frac{1471}{1860}\right)$	$e\left(\frac{193}{465}\right)$	$e\left(\frac{587}{620}\right)$	$e\left(\frac{247}{310}\right)$	$e\left(\frac{353}{372}\right)$	$e\left(\frac{781}{930}\right)$	$e\left(\frac{517}{1860}\right)$	$e\left(\frac{91}{620}\right)$
$\chi_{374790}(107,\cdot)$	374790.bbs	1860	no	$1$	$1$	$e\left(\frac{619}{620}\right)$	$e\left(\frac{267}{310}\right)$	$e\left(\frac{401}{620}\right)$	$e\left(\frac{91}{310}\right)$	$e\left(\frac{1433}{1860}\right)$	$e\left(\frac{149}{465}\right)$	$e\left(\frac{17}{372}\right)$	$e\left(\frac{101}{310}\right)$	$e\left(\frac{617}{620}\right)$	$e\left(\frac{333}{620}\right)$
$\chi_{374790}(109,\cdot)$	374790.yl	620	no	$-1$	$1$	$e\left(\frac{397}{620}\right)$	$e\left(\frac{507}{620}\right)$	$e\left(\frac{152}{155}\right)$	$e\left(\frac{441}{620}\right)$	$e\left(\frac{112}{155}\right)$	$e\left(\frac{19}{155}\right)$	$e\left(\frac{65}{124}\right)$	$e\left(\frac{561}{620}\right)$	$e\left(\frac{104}{155}\right)$	$e\left(\frac{169}{620}\right)$
$\chi_{374790}(113,\cdot)$	374790.bbs	1860	no	$1$	$1$	$e\left(\frac{441}{620}\right)$	$e\left(\frac{53}{310}\right)$	$e\left(\frac{479}{620}\right)$	$e\left(\frac{169}{310}\right)$	$e\left(\frac{1687}{1860}\right)$	$e\left(\frac{166}{465}\right)$	$e\left(\frac{67}{372}\right)$	$e\left(\frac{99}{310}\right)$	$e\left(\frac{83}{620}\right)$	$e\left(\frac{87}{620}\right)$
$\chi_{374790}(119,\cdot)$	374790.we	372	no	$-1$	$1$	$e\left(\frac{127}{372}\right)$	$e\left(\frac{41}{372}\right)$	$e\left(\frac{79}{93}\right)$	$e\left(\frac{43}{372}\right)$	$e\left(\frac{37}{93}\right)$	$e\left(\frac{37}{93}\right)$	$e\left(\frac{75}{124}\right)$	$e\left(\frac{293}{372}\right)$	$e\left(\frac{113}{186}\right)$	$e\left(\frac{39}{124}\right)$
$\chi_{374790}(121,\cdot)$	374790.bas	930	no	$1$	$1$	$e\left(\frac{833}{930}\right)$	$e\left(\frac{493}{930}\right)$	$e\left(\frac{151}{465}\right)$	$e\left(\frac{449}{930}\right)$	$e\left(\frac{46}{465}\right)$	$e\left(\frac{232}{465}\right)$	$e\left(\frac{11}{62}\right)$	$e\left(\frac{529}{930}\right)$	$e\left(\frac{397}{465}\right)$	$e\left(\frac{227}{310}\right)$
$\chi_{374790}(127,\cdot)$	374790.bec	1860	no	$1$	$1$	$e\left(\frac{477}{620}\right)$	$e\left(\frac{103}{155}\right)$	$e\left(\frac{613}{620}\right)$	$e\left(\frac{74}{155}\right)$	$e\left(\frac{629}{1860}\right)$	$e\left(\frac{227}{465}\right)$	$e\left(\frac{137}{372}\right)$	$e\left(\frac{183}{310}\right)$	$e\left(\frac{191}{620}\right)$	$e\left(\frac{189}{620}\right)$
$\chi_{374790}(131,\cdot)$	374790.zm	930	no	$-1$	$1$	$e\left(\frac{452}{465}\right)$	$e\left(\frac{89}{930}\right)$	$e\left(\frac{661}{930}\right)$	$e\left(\frac{41}{465}\right)$	$e\left(\frac{127}{310}\right)$	$e\left(\frac{189}{310}\right)$	$e\left(\frac{22}{93}\right)$	$e\left(\frac{137}{930}\right)$	$e\left(\frac{116}{465}\right)$	$e\left(\frac{251}{310}\right)$

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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	$374790$
Structure	\(C_{2}\times C_{2}\times C_{12}\times C_{1860}\)
Order	$89280$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(7\)	\(11\)	\(17\)	\(19\)	\(23\)	\(29\)	\(37\)	\(41\)	\(43\)	\(47\)
\(\chi_{374790}(1,\cdot)\)	374790.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{374790}(7,\cdot)\)	374790.bbm	1860	no	\(1\)	\(1\)	\(e\left(\frac{412}{465}\right)\)	\(e\left(\frac{1763}{1860}\right)\)	\(e\left(\frac{847}{1860}\right)\)	\(e\left(\frac{919}{1860}\right)\)	\(e\left(\frac{877}{1860}\right)\)	\(e\left(\frac{857}{930}\right)\)	\(e\left(\frac{14}{31}\right)\)	\(e\left(\frac{509}{1860}\right)\)	\(e\left(\frac{1069}{1860}\right)\)	\(e\left(\frac{148}{155}\right)\)
\(\chi_{374790}(11,\cdot)\)	374790.bdc	1860	no	\(-1\)	\(1\)	\(e\left(\frac{1763}{1860}\right)\)	\(e\left(\frac{1423}{1860}\right)\)	\(e\left(\frac{151}{930}\right)\)	\(e\left(\frac{449}{1860}\right)\)	\(e\left(\frac{511}{930}\right)\)	\(e\left(\frac{116}{465}\right)\)	\(e\left(\frac{11}{124}\right)\)	\(e\left(\frac{1459}{1860}\right)\)	\(e\left(\frac{431}{465}\right)\)	\(e\left(\frac{227}{620}\right)\)
\(\chi_{374790}(17,\cdot)\)	374790.bdr	1860	no	\(-1\)	\(1\)	\(e\left(\frac{847}{1860}\right)\)	\(e\left(\frac{151}{930}\right)\)	\(e\left(\frac{733}{1860}\right)\)	\(e\left(\frac{289}{465}\right)\)	\(e\left(\frac{1723}{1860}\right)\)	\(e\left(\frac{443}{930}\right)\)	\(e\left(\frac{19}{124}\right)\)	\(e\left(\frac{239}{465}\right)\)	\(e\left(\frac{61}{1860}\right)\)	\(e\left(\frac{223}{620}\right)\)
\(\chi_{374790}(19,\cdot)\)	374790.bcn	1860	no	\(-1\)	\(1\)	\(e\left(\frac{919}{1860}\right)\)	\(e\left(\frac{449}{1860}\right)\)	\(e\left(\frac{289}{465}\right)\)	\(e\left(\frac{607}{1860}\right)\)	\(e\left(\frac{319}{465}\right)\)	\(e\left(\frac{133}{465}\right)\)	\(e\left(\frac{69}{124}\right)\)	\(e\left(\frac{827}{1860}\right)\)	\(e\left(\frac{418}{465}\right)\)	\(e\left(\frac{601}{620}\right)\)
\(\chi_{374790}(23,\cdot)\)	374790.bdq	1860	no	\(-1\)	\(1\)	\(e\left(\frac{877}{1860}\right)\)	\(e\left(\frac{511}{930}\right)\)	\(e\left(\frac{1723}{1860}\right)\)	\(e\left(\frac{319}{465}\right)\)	\(e\left(\frac{413}{1860}\right)\)	\(e\left(\frac{253}{930}\right)\)	\(e\left(\frac{259}{372}\right)\)	\(e\left(\frac{119}{465}\right)\)	\(e\left(\frac{151}{1860}\right)\)	\(e\left(\frac{613}{620}\right)\)
\(\chi_{374790}(29,\cdot)\)	374790.bab	930	no	\(1\)	\(1\)	\(e\left(\frac{857}{930}\right)\)	\(e\left(\frac{116}{465}\right)\)	\(e\left(\frac{443}{930}\right)\)	\(e\left(\frac{133}{465}\right)\)	\(e\left(\frac{253}{930}\right)\)	\(e\left(\frac{173}{465}\right)\)	\(e\left(\frac{88}{93}\right)\)	\(e\left(\frac{331}{930}\right)\)	\(e\left(\frac{433}{465}\right)\)	\(e\left(\frac{99}{155}\right)\)
\(\chi_{374790}(37,\cdot)\)	374790.uc	372	no	\(-1\)	\(1\)	\(e\left(\frac{14}{31}\right)\)	\(e\left(\frac{11}{124}\right)\)	\(e\left(\frac{19}{124}\right)\)	\(e\left(\frac{69}{124}\right)\)	\(e\left(\frac{259}{372}\right)\)	\(e\left(\frac{88}{93}\right)\)	\(e\left(\frac{7}{186}\right)\)	\(e\left(\frac{3}{124}\right)\)	\(e\left(\frac{13}{124}\right)\)	\(e\left(\frac{19}{31}\right)\)
\(\chi_{374790}(41,\cdot)\)	374790.bct	1860	no	\(1\)	\(1\)	\(e\left(\frac{509}{1860}\right)\)	\(e\left(\frac{1459}{1860}\right)\)	\(e\left(\frac{239}{465}\right)\)	\(e\left(\frac{827}{1860}\right)\)	\(e\left(\frac{119}{465}\right)\)	\(e\left(\frac{331}{930}\right)\)	\(e\left(\frac{3}{124}\right)\)	\(e\left(\frac{877}{1860}\right)\)	\(e\left(\frac{841}{930}\right)\)	\(e\left(\frac{541}{620}\right)\)
\(\chi_{374790}(43,\cdot)\)	374790.bby	1860	no	\(1\)	\(1\)	\(e\left(\frac{1069}{1860}\right)\)	\(e\left(\frac{431}{465}\right)\)	\(e\left(\frac{61}{1860}\right)\)	\(e\left(\frac{418}{465}\right)\)	\(e\left(\frac{151}{1860}\right)\)	\(e\left(\frac{433}{465}\right)\)	\(e\left(\frac{13}{124}\right)\)	\(e\left(\frac{841}{930}\right)\)	\(e\left(\frac{727}{1860}\right)\)	\(e\left(\frac{71}{620}\right)\)
\(\chi_{374790}(47,\cdot)\)	374790.ys	620	no	\(-1\)	\(1\)	\(e\left(\frac{148}{155}\right)\)	\(e\left(\frac{227}{620}\right)\)	\(e\left(\frac{223}{620}\right)\)	\(e\left(\frac{601}{620}\right)\)	\(e\left(\frac{613}{620}\right)\)	\(e\left(\frac{99}{155}\right)\)	\(e\left(\frac{19}{31}\right)\)	\(e\left(\frac{541}{620}\right)\)	\(e\left(\frac{71}{620}\right)\)	\(e\left(\frac{167}{310}\right)\)
\(\chi_{374790}(49,\cdot)\)	374790.zt	930	no	\(1\)	\(1\)	\(e\left(\frac{359}{465}\right)\)	\(e\left(\frac{833}{930}\right)\)	\(e\left(\frac{847}{930}\right)\)	\(e\left(\frac{919}{930}\right)\)	\(e\left(\frac{877}{930}\right)\)	\(e\left(\frac{392}{465}\right)\)	\(e\left(\frac{28}{31}\right)\)	\(e\left(\frac{509}{930}\right)\)	\(e\left(\frac{139}{930}\right)\)	\(e\left(\frac{141}{155}\right)\)
\(\chi_{374790}(53,\cdot)\)	374790.bcd	1860	no	\(-1\)	\(1\)	\(e\left(\frac{727}{1860}\right)\)	\(e\left(\frac{53}{465}\right)\)	\(e\left(\frac{1423}{1860}\right)\)	\(e\left(\frac{803}{930}\right)\)	\(e\left(\frac{151}{620}\right)\)	\(e\left(\frac{91}{310}\right)\)	\(e\left(\frac{365}{372}\right)\)	\(e\left(\frac{43}{930}\right)\)	\(e\left(\frac{631}{1860}\right)\)	\(e\left(\frac{523}{620}\right)\)
\(\chi_{374790}(59,\cdot)\)	374790.bdg	1860	no	\(1\)	\(1\)	\(e\left(\frac{1801}{1860}\right)\)	\(e\left(\frac{41}{1860}\right)\)	\(e\left(\frac{437}{930}\right)\)	\(e\left(\frac{973}{1860}\right)\)	\(e\left(\frac{167}{930}\right)\)	\(e\left(\frac{539}{930}\right)\)	\(e\left(\frac{15}{124}\right)\)	\(e\left(\frac{1223}{1860}\right)\)	\(e\left(\frac{382}{465}\right)\)	\(e\left(\frac{349}{620}\right)\)
\(\chi_{374790}(61,\cdot)\)	374790.sp	186	no	\(-1\)	\(1\)	\(e\left(\frac{34}{93}\right)\)	\(e\left(\frac{175}{186}\right)\)	\(e\left(\frac{167}{186}\right)\)	\(e\left(\frac{43}{93}\right)\)	\(e\left(\frac{79}{186}\right)\)	\(e\left(\frac{79}{186}\right)\)	\(e\left(\frac{109}{186}\right)\)	\(e\left(\frac{14}{93}\right)\)	\(e\left(\frac{173}{186}\right)\)	\(e\left(\frac{8}{31}\right)\)
\(\chi_{374790}(67,\cdot)\)	374790.uj	372	no	\(1\)	\(1\)	\(e\left(\frac{125}{186}\right)\)	\(e\left(\frac{17}{372}\right)\)	\(e\left(\frac{283}{372}\right)\)	\(e\left(\frac{349}{372}\right)\)	\(e\left(\frac{109}{372}\right)\)	\(e\left(\frac{101}{186}\right)\)	\(e\left(\frac{25}{62}\right)\)	\(e\left(\frac{371}{372}\right)\)	\(e\left(\frac{37}{372}\right)\)	\(e\left(\frac{13}{62}\right)\)
\(\chi_{374790}(71,\cdot)\)	374790.bdm	1860	no	\(1\)	\(1\)	\(e\left(\frac{479}{620}\right)\)	\(e\left(\frac{429}{620}\right)\)	\(e\left(\frac{69}{155}\right)\)	\(e\left(\frac{397}{620}\right)\)	\(e\left(\frac{22}{465}\right)\)	\(e\left(\frac{323}{930}\right)\)	\(e\left(\frac{289}{372}\right)\)	\(e\left(\frac{427}{620}\right)\)	\(e\left(\frac{21}{310}\right)\)	\(e\left(\frac{453}{620}\right)\)
\(\chi_{374790}(73,\cdot)\)	374790.bep	1860	no	\(-1\)	\(1\)	\(e\left(\frac{449}{930}\right)\)	\(e\left(\frac{1433}{1860}\right)\)	\(e\left(\frac{1207}{1860}\right)\)	\(e\left(\frac{1639}{1860}\right)\)	\(e\left(\frac{359}{620}\right)\)	\(e\left(\frac{82}{155}\right)\)	\(e\left(\frac{35}{93}\right)\)	\(e\left(\frac{1349}{1860}\right)\)	\(e\left(\frac{1609}{1860}\right)\)	\(e\left(\frac{71}{310}\right)\)
\(\chi_{374790}(77,\cdot)\)	374790.yd	620	no	\(-1\)	\(1\)	\(e\left(\frac{517}{620}\right)\)	\(e\left(\frac{221}{310}\right)\)	\(e\left(\frac{383}{620}\right)\)	\(e\left(\frac{114}{155}\right)\)	\(e\left(\frac{13}{620}\right)\)	\(e\left(\frac{53}{310}\right)\)	\(e\left(\frac{67}{124}\right)\)	\(e\left(\frac{9}{155}\right)\)	\(e\left(\frac{311}{620}\right)\)	\(e\left(\frac{199}{620}\right)\)
\(\chi_{374790}(79,\cdot)\)	374790.bao	930	no	\(-1\)	\(1\)	\(e\left(\frac{481}{930}\right)\)	\(e\left(\frac{911}{930}\right)\)	\(e\left(\frac{47}{465}\right)\)	\(e\left(\frac{404}{465}\right)\)	\(e\left(\frac{104}{155}\right)\)	\(e\left(\frac{301}{310}\right)\)	\(e\left(\frac{58}{93}\right)\)	\(e\left(\frac{244}{465}\right)\)	\(e\left(\frac{179}{465}\right)\)	\(e\left(\frac{239}{310}\right)\)
\(\chi_{374790}(83,\cdot)\)	374790.bbg	1860	no	\(1\)	\(1\)	\(e\left(\frac{76}{465}\right)\)	\(e\left(\frac{569}{1860}\right)\)	\(e\left(\frac{1321}{1860}\right)\)	\(e\left(\frac{937}{1860}\right)\)	\(e\left(\frac{77}{620}\right)\)	\(e\left(\frac{147}{310}\right)\)	\(e\left(\frac{79}{186}\right)\)	\(e\left(\frac{437}{1860}\right)\)	\(e\left(\frac{757}{1860}\right)\)	\(e\left(\frac{23}{310}\right)\)
\(\chi_{374790}(89,\cdot)\)	374790.bco	1860	no	\(-1\)	\(1\)	\(e\left(\frac{553}{1860}\right)\)	\(e\left(\frac{1523}{1860}\right)\)	\(e\left(\frac{13}{465}\right)\)	\(e\left(\frac{1189}{1860}\right)\)	\(e\left(\frac{83}{465}\right)\)	\(e\left(\frac{176}{465}\right)\)	\(e\left(\frac{235}{372}\right)\)	\(e\left(\frac{359}{1860}\right)\)	\(e\left(\frac{287}{930}\right)\)	\(e\left(\frac{617}{620}\right)\)
\(\chi_{374790}(97,\cdot)\)	374790.bel	1860	no	\(1\)	\(1\)	\(e\left(\frac{409}{930}\right)\)	\(e\left(\frac{133}{1860}\right)\)	\(e\left(\frac{1667}{1860}\right)\)	\(e\left(\frac{389}{1860}\right)\)	\(e\left(\frac{1057}{1860}\right)\)	\(e\left(\frac{17}{930}\right)\)	\(e\left(\frac{121}{186}\right)\)	\(e\left(\frac{1699}{1860}\right)\)	\(e\left(\frac{749}{1860}\right)\)	\(e\left(\frac{171}{310}\right)\)
\(\chi_{374790}(101,\cdot)\)	374790.bag	930	no	\(-1\)	\(1\)	\(e\left(\frac{431}{930}\right)\)	\(e\left(\frac{398}{465}\right)\)	\(e\left(\frac{149}{930}\right)\)	\(e\left(\frac{143}{930}\right)\)	\(e\left(\frac{379}{930}\right)\)	\(e\left(\frac{193}{930}\right)\)	\(e\left(\frac{17}{186}\right)\)	\(e\left(\frac{179}{465}\right)\)	\(e\left(\frac{259}{465}\right)\)	\(e\left(\frac{27}{155}\right)\)
\(\chi_{374790}(103,\cdot)\)	374790.bdp	1860	no	\(-1\)	\(1\)	\(e\left(\frac{1309}{1860}\right)\)	\(e\left(\frac{487}{930}\right)\)	\(e\left(\frac{1471}{1860}\right)\)	\(e\left(\frac{193}{465}\right)\)	\(e\left(\frac{587}{620}\right)\)	\(e\left(\frac{247}{310}\right)\)	\(e\left(\frac{353}{372}\right)\)	\(e\left(\frac{781}{930}\right)\)	\(e\left(\frac{517}{1860}\right)\)	\(e\left(\frac{91}{620}\right)\)
\(\chi_{374790}(107,\cdot)\)	374790.bbs	1860	no	\(1\)	\(1\)	\(e\left(\frac{619}{620}\right)\)	\(e\left(\frac{267}{310}\right)\)	\(e\left(\frac{401}{620}\right)\)	\(e\left(\frac{91}{310}\right)\)	\(e\left(\frac{1433}{1860}\right)\)	\(e\left(\frac{149}{465}\right)\)	\(e\left(\frac{17}{372}\right)\)	\(e\left(\frac{101}{310}\right)\)	\(e\left(\frac{617}{620}\right)\)	\(e\left(\frac{333}{620}\right)\)
\(\chi_{374790}(109,\cdot)\)	374790.yl	620	no	\(-1\)	\(1\)	\(e\left(\frac{397}{620}\right)\)	\(e\left(\frac{507}{620}\right)\)	\(e\left(\frac{152}{155}\right)\)	\(e\left(\frac{441}{620}\right)\)	\(e\left(\frac{112}{155}\right)\)	\(e\left(\frac{19}{155}\right)\)	\(e\left(\frac{65}{124}\right)\)	\(e\left(\frac{561}{620}\right)\)	\(e\left(\frac{104}{155}\right)\)	\(e\left(\frac{169}{620}\right)\)
\(\chi_{374790}(113,\cdot)\)	374790.bbs	1860	no	\(1\)	\(1\)	\(e\left(\frac{441}{620}\right)\)	\(e\left(\frac{53}{310}\right)\)	\(e\left(\frac{479}{620}\right)\)	\(e\left(\frac{169}{310}\right)\)	\(e\left(\frac{1687}{1860}\right)\)	\(e\left(\frac{166}{465}\right)\)	\(e\left(\frac{67}{372}\right)\)	\(e\left(\frac{99}{310}\right)\)	\(e\left(\frac{83}{620}\right)\)	\(e\left(\frac{87}{620}\right)\)
\(\chi_{374790}(119,\cdot)\)	374790.we	372	no	\(-1\)	\(1\)	\(e\left(\frac{127}{372}\right)\)	\(e\left(\frac{41}{372}\right)\)	\(e\left(\frac{79}{93}\right)\)	\(e\left(\frac{43}{372}\right)\)	\(e\left(\frac{37}{93}\right)\)	\(e\left(\frac{37}{93}\right)\)	\(e\left(\frac{75}{124}\right)\)	\(e\left(\frac{293}{372}\right)\)	\(e\left(\frac{113}{186}\right)\)	\(e\left(\frac{39}{124}\right)\)
\(\chi_{374790}(121,\cdot)\)	374790.bas	930	no	\(1\)	\(1\)	\(e\left(\frac{833}{930}\right)\)	\(e\left(\frac{493}{930}\right)\)	\(e\left(\frac{151}{465}\right)\)	\(e\left(\frac{449}{930}\right)\)	\(e\left(\frac{46}{465}\right)\)	\(e\left(\frac{232}{465}\right)\)	\(e\left(\frac{11}{62}\right)\)	\(e\left(\frac{529}{930}\right)\)	\(e\left(\frac{397}{465}\right)\)	\(e\left(\frac{227}{310}\right)\)
\(\chi_{374790}(127,\cdot)\)	374790.bec	1860	no	\(1\)	\(1\)	\(e\left(\frac{477}{620}\right)\)	\(e\left(\frac{103}{155}\right)\)	\(e\left(\frac{613}{620}\right)\)	\(e\left(\frac{74}{155}\right)\)	\(e\left(\frac{629}{1860}\right)\)	\(e\left(\frac{227}{465}\right)\)	\(e\left(\frac{137}{372}\right)\)	\(e\left(\frac{183}{310}\right)\)	\(e\left(\frac{191}{620}\right)\)	\(e\left(\frac{189}{620}\right)\)
\(\chi_{374790}(131,\cdot)\)	374790.zm	930	no	\(-1\)	\(1\)	\(e\left(\frac{452}{465}\right)\)	\(e\left(\frac{89}{930}\right)\)	\(e\left(\frac{661}{930}\right)\)	\(e\left(\frac{41}{465}\right)\)	\(e\left(\frac{127}{310}\right)\)	\(e\left(\frac{189}{310}\right)\)	\(e\left(\frac{22}{93}\right)\)	\(e\left(\frac{137}{930}\right)\)	\(e\left(\frac{116}{465}\right)\)	\(e\left(\frac{251}{310}\right)\)

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.