LMFDB - Group of Dirichlet characters of modulus 15030

Show commands: PariGP / SageMath

sage: H = DirichletGroup(15030)

pari: g = idealstar(,15030,2)

Character group

sage: G.order() pari: g.no
Order	=	3984
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{996}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{15030}(3341,\cdot)$, $\chi_{15030}(3007,\cdot)$, $\chi_{15030}(4681,\cdot)$

First 32 of 3984 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	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{15030}(1,\cdot)$	15030.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{15030}(7,\cdot)$	15030.bv	996	no	$-1$	$1$	$e\left(\frac{793}{996}\right)$	$e\left(\frac{142}{249}\right)$	$e\left(\frac{299}{996}\right)$	$e\left(\frac{307}{332}\right)$	$e\left(\frac{121}{166}\right)$	$e\left(\frac{455}{996}\right)$	$e\left(\frac{395}{498}\right)$	$e\left(\frac{77}{249}\right)$	$e\left(\frac{203}{332}\right)$	$e\left(\frac{71}{249}\right)$
$\chi_{15030}(11,\cdot)$	15030.bq	498	no	$-1$	$1$	$e\left(\frac{142}{249}\right)$	$e\left(\frac{443}{498}\right)$	$e\left(\frac{176}{249}\right)$	$e\left(\frac{73}{166}\right)$	$e\left(\frac{65}{83}\right)$	$e\left(\frac{265}{498}\right)$	$e\left(\frac{233}{498}\right)$	$e\left(\frac{128}{249}\right)$	$e\left(\frac{24}{83}\right)$	$e\left(\frac{97}{498}\right)$
$\chi_{15030}(13,\cdot)$	15030.bu	996	no	$1$	$1$	$e\left(\frac{299}{996}\right)$	$e\left(\frac{176}{249}\right)$	$e\left(\frac{823}{996}\right)$	$e\left(\frac{211}{332}\right)$	$e\left(\frac{81}{166}\right)$	$e\left(\frac{343}{996}\right)$	$e\left(\frac{451}{498}\right)$	$e\left(\frac{127}{249}\right)$	$e\left(\frac{199}{332}\right)$	$e\left(\frac{425}{498}\right)$
$\chi_{15030}(17,\cdot)$	15030.bj	332	no	$-1$	$1$	$e\left(\frac{307}{332}\right)$	$e\left(\frac{73}{166}\right)$	$e\left(\frac{211}{332}\right)$	$e\left(\frac{223}{332}\right)$	$e\left(\frac{3}{166}\right)$	$e\left(\frac{285}{332}\right)$	$e\left(\frac{74}{83}\right)$	$e\left(\frac{61}{83}\right)$	$e\left(\frac{241}{332}\right)$	$e\left(\frac{39}{83}\right)$
$\chi_{15030}(19,\cdot)$	15030.bd	166	no	$1$	$1$	$e\left(\frac{121}{166}\right)$	$e\left(\frac{65}{83}\right)$	$e\left(\frac{81}{166}\right)$	$e\left(\frac{3}{166}\right)$	$e\left(\frac{22}{83}\right)$	$e\left(\frac{15}{166}\right)$	$e\left(\frac{34}{83}\right)$	$e\left(\frac{37}{83}\right)$	$e\left(\frac{135}{166}\right)$	$e\left(\frac{74}{83}\right)$
$\chi_{15030}(23,\cdot)$	15030.bt	996	no	$-1$	$1$	$e\left(\frac{455}{996}\right)$	$e\left(\frac{265}{498}\right)$	$e\left(\frac{343}{996}\right)$	$e\left(\frac{285}{332}\right)$	$e\left(\frac{15}{166}\right)$	$e\left(\frac{457}{996}\right)$	$e\left(\frac{197}{249}\right)$	$e\left(\frac{85}{249}\right)$	$e\left(\frac{43}{332}\right)$	$e\left(\frac{4}{249}\right)$
$\chi_{15030}(29,\cdot)$	15030.bl	498	no	$-1$	$1$	$e\left(\frac{395}{498}\right)$	$e\left(\frac{233}{498}\right)$	$e\left(\frac{451}{498}\right)$	$e\left(\frac{74}{83}\right)$	$e\left(\frac{34}{83}\right)$	$e\left(\frac{197}{249}\right)$	$e\left(\frac{353}{498}\right)$	$e\left(\frac{164}{249}\right)$	$e\left(\frac{103}{166}\right)$	$e\left(\frac{241}{498}\right)$
$\chi_{15030}(31,\cdot)$	15030.bg	249	no	$1$	$1$	$e\left(\frac{77}{249}\right)$	$e\left(\frac{128}{249}\right)$	$e\left(\frac{127}{249}\right)$	$e\left(\frac{61}{83}\right)$	$e\left(\frac{37}{83}\right)$	$e\left(\frac{85}{249}\right)$	$e\left(\frac{164}{249}\right)$	$e\left(\frac{115}{249}\right)$	$e\left(\frac{6}{83}\right)$	$e\left(\frac{64}{249}\right)$
$\chi_{15030}(37,\cdot)$	15030.bi	332	no	$1$	$1$	$e\left(\frac{203}{332}\right)$	$e\left(\frac{24}{83}\right)$	$e\left(\frac{199}{332}\right)$	$e\left(\frac{241}{332}\right)$	$e\left(\frac{135}{166}\right)$	$e\left(\frac{43}{332}\right)$	$e\left(\frac{103}{166}\right)$	$e\left(\frac{6}{83}\right)$	$e\left(\frac{221}{332}\right)$	$e\left(\frac{107}{166}\right)$
$\chi_{15030}(41,\cdot)$	15030.bp	498	no	$1$	$1$	$e\left(\frac{71}{249}\right)$	$e\left(\frac{97}{498}\right)$	$e\left(\frac{425}{498}\right)$	$e\left(\frac{39}{83}\right)$	$e\left(\frac{74}{83}\right)$	$e\left(\frac{4}{249}\right)$	$e\left(\frac{241}{498}\right)$	$e\left(\frac{64}{249}\right)$	$e\left(\frac{107}{166}\right)$	$e\left(\frac{211}{249}\right)$
$\chi_{15030}(43,\cdot)$	15030.bu	996	no	$1$	$1$	$e\left(\frac{259}{996}\right)$	$e\left(\frac{85}{249}\right)$	$e\left(\frac{563}{996}\right)$	$e\left(\frac{175}{332}\right)$	$e\left(\frac{149}{166}\right)$	$e\left(\frac{467}{996}\right)$	$e\left(\frac{389}{498}\right)$	$e\left(\frac{125}{249}\right)$	$e\left(\frac{239}{332}\right)$	$e\left(\frac{85}{498}\right)$
$\chi_{15030}(47,\cdot)$	15030.bs	996	no	$1$	$1$	$e\left(\frac{745}{996}\right)$	$e\left(\frac{215}{498}\right)$	$e\left(\frac{983}{996}\right)$	$e\left(\frac{297}{332}\right)$	$e\left(\frac{103}{166}\right)$	$e\left(\frac{305}{996}\right)$	$e\left(\frac{235}{249}\right)$	$e\left(\frac{224}{249}\right)$	$e\left(\frac{251}{332}\right)$	$e\left(\frac{481}{498}\right)$
$\chi_{15030}(49,\cdot)$	15030.bn	498	no	$1$	$1$	$e\left(\frac{295}{498}\right)$	$e\left(\frac{35}{249}\right)$	$e\left(\frac{299}{498}\right)$	$e\left(\frac{141}{166}\right)$	$e\left(\frac{38}{83}\right)$	$e\left(\frac{455}{498}\right)$	$e\left(\frac{146}{249}\right)$	$e\left(\frac{154}{249}\right)$	$e\left(\frac{37}{166}\right)$	$e\left(\frac{142}{249}\right)$
$\chi_{15030}(53,\cdot)$	15030.bj	332	no	$-1$	$1$	$e\left(\frac{77}{332}\right)$	$e\left(\frac{147}{166}\right)$	$e\left(\frac{293}{332}\right)$	$e\left(\frac{17}{332}\right)$	$e\left(\frac{97}{166}\right)$	$e\left(\frac{251}{332}\right)$	$e\left(\frac{41}{83}\right)$	$e\left(\frac{8}{83}\right)$	$e\left(\frac{267}{332}\right)$	$e\left(\frac{16}{83}\right)$
$\chi_{15030}(59,\cdot)$	15030.bm	498	no	$1$	$1$	$e\left(\frac{79}{498}\right)$	$e\left(\frac{445}{498}\right)$	$e\left(\frac{70}{249}\right)$	$e\left(\frac{13}{166}\right)$	$e\left(\frac{40}{83}\right)$	$e\left(\frac{29}{498}\right)$	$e\left(\frac{469}{498}\right)$	$e\left(\frac{232}{249}\right)$	$e\left(\frac{2}{83}\right)$	$e\left(\frac{49}{249}\right)$
$\chi_{15030}(61,\cdot)$	15030.bg	249	no	$1$	$1$	$e\left(\frac{145}{249}\right)$	$e\left(\frac{199}{249}\right)$	$e\left(\frac{71}{249}\right)$	$e\left(\frac{6}{83}\right)$	$e\left(\frac{5}{83}\right)$	$e\left(\frac{173}{249}\right)$	$e\left(\frac{76}{249}\right)$	$e\left(\frac{29}{249}\right)$	$e\left(\frac{21}{83}\right)$	$e\left(\frac{224}{249}\right)$
$\chi_{15030}(67,\cdot)$	15030.bu	996	no	$1$	$1$	$e\left(\frac{869}{996}\right)$	$e\left(\frac{41}{249}\right)$	$e\left(\frac{793}{996}\right)$	$e\left(\frac{309}{332}\right)$	$e\left(\frac{25}{166}\right)$	$e\left(\frac{817}{996}\right)$	$e\left(\frac{463}{498}\right)$	$e\left(\frac{31}{249}\right)$	$e\left(\frac{293}{332}\right)$	$e\left(\frac{41}{498}\right)$
$\chi_{15030}(71,\cdot)$	15030.bb	166	no	$1$	$1$	$e\left(\frac{82}{83}\right)$	$e\left(\frac{15}{166}\right)$	$e\left(\frac{153}{166}\right)$	$e\left(\frac{72}{83}\right)$	$e\left(\frac{60}{83}\right)$	$e\left(\frac{28}{83}\right)$	$e\left(\frac{27}{166}\right)$	$e\left(\frac{33}{83}\right)$	$e\left(\frac{89}{166}\right)$	$e\left(\frac{66}{83}\right)$
$\chi_{15030}(73,\cdot)$	15030.bi	332	no	$1$	$1$	$e\left(\frac{5}{332}\right)$	$e\left(\frac{1}{83}\right)$	$e\left(\frac{157}{332}\right)$	$e\left(\frac{55}{332}\right)$	$e\left(\frac{99}{166}\right)$	$e\left(\frac{109}{332}\right)$	$e\left(\frac{153}{166}\right)$	$e\left(\frac{21}{83}\right)$	$e\left(\frac{151}{332}\right)$	$e\left(\frac{1}{166}\right)$
$\chi_{15030}(77,\cdot)$	15030.bs	996	no	$1$	$1$	$e\left(\frac{365}{996}\right)$	$e\left(\frac{229}{498}\right)$	$e\left(\frac{7}{996}\right)$	$e\left(\frac{121}{332}\right)$	$e\left(\frac{85}{166}\right)$	$e\left(\frac{985}{996}\right)$	$e\left(\frac{65}{249}\right)$	$e\left(\frac{205}{249}\right)$	$e\left(\frac{299}{332}\right)$	$e\left(\frac{239}{498}\right)$
$\chi_{15030}(79,\cdot)$	15030.bo	498	no	$-1$	$1$	$e\left(\frac{185}{498}\right)$	$e\left(\frac{157}{249}\right)$	$e\left(\frac{41}{249}\right)$	$e\left(\frac{21}{83}\right)$	$e\left(\frac{59}{83}\right)$	$e\left(\frac{149}{249}\right)$	$e\left(\frac{100}{249}\right)$	$e\left(\frac{143}{249}\right)$	$e\left(\frac{32}{83}\right)$	$e\left(\frac{157}{498}\right)$
$\chi_{15030}(83,\cdot)$	15030.bt	996	no	$-1$	$1$	$e\left(\frac{979}{996}\right)$	$e\left(\frac{209}{498}\right)$	$e\left(\frac{263}{996}\right)$	$e\left(\frac{325}{332}\right)$	$e\left(\frac{87}{166}\right)$	$e\left(\frac{725}{996}\right)$	$e\left(\frac{130}{249}\right)$	$e\left(\frac{161}{249}\right)$	$e\left(\frac{183}{332}\right)$	$e\left(\frac{239}{249}\right)$
$\chi_{15030}(89,\cdot)$	15030.bf	166	no	$-1$	$1$	$e\left(\frac{161}{166}\right)$	$e\left(\frac{79}{166}\right)$	$e\left(\frac{9}{166}\right)$	$e\left(\frac{14}{83}\right)$	$e\left(\frac{67}{83}\right)$	$e\left(\frac{70}{83}\right)$	$e\left(\frac{109}{166}\right)$	$e\left(\frac{41}{83}\right)$	$e\left(\frac{15}{166}\right)$	$e\left(\frac{81}{166}\right)$
$\chi_{15030}(91,\cdot)$	15030.z	166	no	$-1$	$1$	$e\left(\frac{8}{83}\right)$	$e\left(\frac{23}{83}\right)$	$e\left(\frac{21}{166}\right)$	$e\left(\frac{93}{166}\right)$	$e\left(\frac{18}{83}\right)$	$e\left(\frac{133}{166}\right)$	$e\left(\frac{58}{83}\right)$	$e\left(\frac{68}{83}\right)$	$e\left(\frac{35}{166}\right)$	$e\left(\frac{23}{166}\right)$
$\chi_{15030}(97,\cdot)$	15030.bv	996	no	$-1$	$1$	$e\left(\frac{937}{996}\right)$	$e\left(\frac{121}{249}\right)$	$e\left(\frac{239}{996}\right)$	$e\left(\frac{171}{332}\right)$	$e\left(\frac{9}{166}\right)$	$e\left(\frac{407}{996}\right)$	$e\left(\frac{419}{498}\right)$	$e\left(\frac{134}{249}\right)$	$e\left(\frac{59}{332}\right)$	$e\left(\frac{185}{249}\right)$
$\chi_{15030}(101,\cdot)$	15030.bp	498	no	$1$	$1$	$e\left(\frac{205}{249}\right)$	$e\left(\frac{245}{498}\right)$	$e\left(\frac{175}{498}\right)$	$e\left(\frac{60}{83}\right)$	$e\left(\frac{50}{83}\right)$	$e\left(\frac{236}{249}\right)$	$e\left(\frac{275}{498}\right)$	$e\left(\frac{41}{249}\right)$	$e\left(\frac{5}{166}\right)$	$e\left(\frac{248}{249}\right)$
$\chi_{15030}(103,\cdot)$	15030.bu	996	no	$1$	$1$	$e\left(\frac{683}{996}\right)$	$e\left(\frac{203}{249}\right)$	$e\left(\frac{331}{996}\right)$	$e\left(\frac{291}{332}\right)$	$e\left(\frac{59}{166}\right)$	$e\left(\frac{547}{996}\right)$	$e\left(\frac{349}{498}\right)$	$e\left(\frac{196}{249}\right)$	$e\left(\frac{147}{332}\right)$	$e\left(\frac{203}{498}\right)$
$\chi_{15030}(107,\cdot)$	15030.bk	332	no	$1$	$1$	$e\left(\frac{215}{332}\right)$	$e\left(\frac{3}{166}\right)$	$e\left(\frac{277}{332}\right)$	$e\left(\frac{41}{332}\right)$	$e\left(\frac{107}{166}\right)$	$e\left(\frac{39}{332}\right)$	$e\left(\frac{11}{83}\right)$	$e\left(\frac{73}{83}\right)$	$e\left(\frac{19}{332}\right)$	$e\left(\frac{43}{166}\right)$
$\chi_{15030}(109,\cdot)$	15030.bc	166	no	$-1$	$1$	$e\left(\frac{93}{166}\right)$	$e\left(\frac{4}{83}\right)$	$e\left(\frac{74}{83}\right)$	$e\left(\frac{55}{83}\right)$	$e\left(\frac{32}{83}\right)$	$e\left(\frac{26}{83}\right)$	$e\left(\frac{57}{83}\right)$	$e\left(\frac{1}{83}\right)$	$e\left(\frac{68}{83}\right)$	$e\left(\frac{87}{166}\right)$
$\chi_{15030}(113,\cdot)$	15030.bt	996	no	$-1$	$1$	$e\left(\frac{971}{996}\right)$	$e\left(\frac{73}{498}\right)$	$e\left(\frac{211}{996}\right)$	$e\left(\frac{185}{332}\right)$	$e\left(\frac{1}{166}\right)$	$e\left(\frac{949}{996}\right)$	$e\left(\frac{74}{249}\right)$	$e\left(\frac{61}{249}\right)$	$e\left(\frac{191}{332}\right)$	$e\left(\frac{205}{249}\right)$
$\chi_{15030}(119,\cdot)$	15030.bm	498	no	$1$	$1$	$e\left(\frac{359}{498}\right)$	$e\left(\frac{5}{498}\right)$	$e\left(\frac{233}{249}\right)$	$e\left(\frac{99}{166}\right)$	$e\left(\frac{62}{83}\right)$	$e\left(\frac{157}{498}\right)$	$e\left(\frac{341}{498}\right)$	$e\left(\frac{11}{249}\right)$	$e\left(\frac{28}{83}\right)$	$e\left(\frac{188}{249}\right)$

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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	$15030$
Structure	\(C_{2}\times C_{2}\times C_{996}\)
Order	$3984$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{15030}(1,\cdot)\)	15030.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{15030}(7,\cdot)\)	15030.bv	996	no	\(-1\)	\(1\)	\(e\left(\frac{793}{996}\right)\)	\(e\left(\frac{142}{249}\right)\)	\(e\left(\frac{299}{996}\right)\)	\(e\left(\frac{307}{332}\right)\)	\(e\left(\frac{121}{166}\right)\)	\(e\left(\frac{455}{996}\right)\)	\(e\left(\frac{395}{498}\right)\)	\(e\left(\frac{77}{249}\right)\)	\(e\left(\frac{203}{332}\right)\)	\(e\left(\frac{71}{249}\right)\)
\(\chi_{15030}(11,\cdot)\)	15030.bq	498	no	\(-1\)	\(1\)	\(e\left(\frac{142}{249}\right)\)	\(e\left(\frac{443}{498}\right)\)	\(e\left(\frac{176}{249}\right)\)	\(e\left(\frac{73}{166}\right)\)	\(e\left(\frac{65}{83}\right)\)	\(e\left(\frac{265}{498}\right)\)	\(e\left(\frac{233}{498}\right)\)	\(e\left(\frac{128}{249}\right)\)	\(e\left(\frac{24}{83}\right)\)	\(e\left(\frac{97}{498}\right)\)
\(\chi_{15030}(13,\cdot)\)	15030.bu	996	no	\(1\)	\(1\)	\(e\left(\frac{299}{996}\right)\)	\(e\left(\frac{176}{249}\right)\)	\(e\left(\frac{823}{996}\right)\)	\(e\left(\frac{211}{332}\right)\)	\(e\left(\frac{81}{166}\right)\)	\(e\left(\frac{343}{996}\right)\)	\(e\left(\frac{451}{498}\right)\)	\(e\left(\frac{127}{249}\right)\)	\(e\left(\frac{199}{332}\right)\)	\(e\left(\frac{425}{498}\right)\)
\(\chi_{15030}(17,\cdot)\)	15030.bj	332	no	\(-1\)	\(1\)	\(e\left(\frac{307}{332}\right)\)	\(e\left(\frac{73}{166}\right)\)	\(e\left(\frac{211}{332}\right)\)	\(e\left(\frac{223}{332}\right)\)	\(e\left(\frac{3}{166}\right)\)	\(e\left(\frac{285}{332}\right)\)	\(e\left(\frac{74}{83}\right)\)	\(e\left(\frac{61}{83}\right)\)	\(e\left(\frac{241}{332}\right)\)	\(e\left(\frac{39}{83}\right)\)
\(\chi_{15030}(19,\cdot)\)	15030.bd	166	no	\(1\)	\(1\)	\(e\left(\frac{121}{166}\right)\)	\(e\left(\frac{65}{83}\right)\)	\(e\left(\frac{81}{166}\right)\)	\(e\left(\frac{3}{166}\right)\)	\(e\left(\frac{22}{83}\right)\)	\(e\left(\frac{15}{166}\right)\)	\(e\left(\frac{34}{83}\right)\)	\(e\left(\frac{37}{83}\right)\)	\(e\left(\frac{135}{166}\right)\)	\(e\left(\frac{74}{83}\right)\)
\(\chi_{15030}(23,\cdot)\)	15030.bt	996	no	\(-1\)	\(1\)	\(e\left(\frac{455}{996}\right)\)	\(e\left(\frac{265}{498}\right)\)	\(e\left(\frac{343}{996}\right)\)	\(e\left(\frac{285}{332}\right)\)	\(e\left(\frac{15}{166}\right)\)	\(e\left(\frac{457}{996}\right)\)	\(e\left(\frac{197}{249}\right)\)	\(e\left(\frac{85}{249}\right)\)	\(e\left(\frac{43}{332}\right)\)	\(e\left(\frac{4}{249}\right)\)
\(\chi_{15030}(29,\cdot)\)	15030.bl	498	no	\(-1\)	\(1\)	\(e\left(\frac{395}{498}\right)\)	\(e\left(\frac{233}{498}\right)\)	\(e\left(\frac{451}{498}\right)\)	\(e\left(\frac{74}{83}\right)\)	\(e\left(\frac{34}{83}\right)\)	\(e\left(\frac{197}{249}\right)\)	\(e\left(\frac{353}{498}\right)\)	\(e\left(\frac{164}{249}\right)\)	\(e\left(\frac{103}{166}\right)\)	\(e\left(\frac{241}{498}\right)\)
\(\chi_{15030}(31,\cdot)\)	15030.bg	249	no	\(1\)	\(1\)	\(e\left(\frac{77}{249}\right)\)	\(e\left(\frac{128}{249}\right)\)	\(e\left(\frac{127}{249}\right)\)	\(e\left(\frac{61}{83}\right)\)	\(e\left(\frac{37}{83}\right)\)	\(e\left(\frac{85}{249}\right)\)	\(e\left(\frac{164}{249}\right)\)	\(e\left(\frac{115}{249}\right)\)	\(e\left(\frac{6}{83}\right)\)	\(e\left(\frac{64}{249}\right)\)
\(\chi_{15030}(37,\cdot)\)	15030.bi	332	no	\(1\)	\(1\)	\(e\left(\frac{203}{332}\right)\)	\(e\left(\frac{24}{83}\right)\)	\(e\left(\frac{199}{332}\right)\)	\(e\left(\frac{241}{332}\right)\)	\(e\left(\frac{135}{166}\right)\)	\(e\left(\frac{43}{332}\right)\)	\(e\left(\frac{103}{166}\right)\)	\(e\left(\frac{6}{83}\right)\)	\(e\left(\frac{221}{332}\right)\)	\(e\left(\frac{107}{166}\right)\)
\(\chi_{15030}(41,\cdot)\)	15030.bp	498	no	\(1\)	\(1\)	\(e\left(\frac{71}{249}\right)\)	\(e\left(\frac{97}{498}\right)\)	\(e\left(\frac{425}{498}\right)\)	\(e\left(\frac{39}{83}\right)\)	\(e\left(\frac{74}{83}\right)\)	\(e\left(\frac{4}{249}\right)\)	\(e\left(\frac{241}{498}\right)\)	\(e\left(\frac{64}{249}\right)\)	\(e\left(\frac{107}{166}\right)\)	\(e\left(\frac{211}{249}\right)\)
\(\chi_{15030}(43,\cdot)\)	15030.bu	996	no	\(1\)	\(1\)	\(e\left(\frac{259}{996}\right)\)	\(e\left(\frac{85}{249}\right)\)	\(e\left(\frac{563}{996}\right)\)	\(e\left(\frac{175}{332}\right)\)	\(e\left(\frac{149}{166}\right)\)	\(e\left(\frac{467}{996}\right)\)	\(e\left(\frac{389}{498}\right)\)	\(e\left(\frac{125}{249}\right)\)	\(e\left(\frac{239}{332}\right)\)	\(e\left(\frac{85}{498}\right)\)
\(\chi_{15030}(47,\cdot)\)	15030.bs	996	no	\(1\)	\(1\)	\(e\left(\frac{745}{996}\right)\)	\(e\left(\frac{215}{498}\right)\)	\(e\left(\frac{983}{996}\right)\)	\(e\left(\frac{297}{332}\right)\)	\(e\left(\frac{103}{166}\right)\)	\(e\left(\frac{305}{996}\right)\)	\(e\left(\frac{235}{249}\right)\)	\(e\left(\frac{224}{249}\right)\)	\(e\left(\frac{251}{332}\right)\)	\(e\left(\frac{481}{498}\right)\)
\(\chi_{15030}(49,\cdot)\)	15030.bn	498	no	\(1\)	\(1\)	\(e\left(\frac{295}{498}\right)\)	\(e\left(\frac{35}{249}\right)\)	\(e\left(\frac{299}{498}\right)\)	\(e\left(\frac{141}{166}\right)\)	\(e\left(\frac{38}{83}\right)\)	\(e\left(\frac{455}{498}\right)\)	\(e\left(\frac{146}{249}\right)\)	\(e\left(\frac{154}{249}\right)\)	\(e\left(\frac{37}{166}\right)\)	\(e\left(\frac{142}{249}\right)\)
\(\chi_{15030}(53,\cdot)\)	15030.bj	332	no	\(-1\)	\(1\)	\(e\left(\frac{77}{332}\right)\)	\(e\left(\frac{147}{166}\right)\)	\(e\left(\frac{293}{332}\right)\)	\(e\left(\frac{17}{332}\right)\)	\(e\left(\frac{97}{166}\right)\)	\(e\left(\frac{251}{332}\right)\)	\(e\left(\frac{41}{83}\right)\)	\(e\left(\frac{8}{83}\right)\)	\(e\left(\frac{267}{332}\right)\)	\(e\left(\frac{16}{83}\right)\)
\(\chi_{15030}(59,\cdot)\)	15030.bm	498	no	\(1\)	\(1\)	\(e\left(\frac{79}{498}\right)\)	\(e\left(\frac{445}{498}\right)\)	\(e\left(\frac{70}{249}\right)\)	\(e\left(\frac{13}{166}\right)\)	\(e\left(\frac{40}{83}\right)\)	\(e\left(\frac{29}{498}\right)\)	\(e\left(\frac{469}{498}\right)\)	\(e\left(\frac{232}{249}\right)\)	\(e\left(\frac{2}{83}\right)\)	\(e\left(\frac{49}{249}\right)\)
\(\chi_{15030}(61,\cdot)\)	15030.bg	249	no	\(1\)	\(1\)	\(e\left(\frac{145}{249}\right)\)	\(e\left(\frac{199}{249}\right)\)	\(e\left(\frac{71}{249}\right)\)	\(e\left(\frac{6}{83}\right)\)	\(e\left(\frac{5}{83}\right)\)	\(e\left(\frac{173}{249}\right)\)	\(e\left(\frac{76}{249}\right)\)	\(e\left(\frac{29}{249}\right)\)	\(e\left(\frac{21}{83}\right)\)	\(e\left(\frac{224}{249}\right)\)
\(\chi_{15030}(67,\cdot)\)	15030.bu	996	no	\(1\)	\(1\)	\(e\left(\frac{869}{996}\right)\)	\(e\left(\frac{41}{249}\right)\)	\(e\left(\frac{793}{996}\right)\)	\(e\left(\frac{309}{332}\right)\)	\(e\left(\frac{25}{166}\right)\)	\(e\left(\frac{817}{996}\right)\)	\(e\left(\frac{463}{498}\right)\)	\(e\left(\frac{31}{249}\right)\)	\(e\left(\frac{293}{332}\right)\)	\(e\left(\frac{41}{498}\right)\)
\(\chi_{15030}(71,\cdot)\)	15030.bb	166	no	\(1\)	\(1\)	\(e\left(\frac{82}{83}\right)\)	\(e\left(\frac{15}{166}\right)\)	\(e\left(\frac{153}{166}\right)\)	\(e\left(\frac{72}{83}\right)\)	\(e\left(\frac{60}{83}\right)\)	\(e\left(\frac{28}{83}\right)\)	\(e\left(\frac{27}{166}\right)\)	\(e\left(\frac{33}{83}\right)\)	\(e\left(\frac{89}{166}\right)\)	\(e\left(\frac{66}{83}\right)\)
\(\chi_{15030}(73,\cdot)\)	15030.bi	332	no	\(1\)	\(1\)	\(e\left(\frac{5}{332}\right)\)	\(e\left(\frac{1}{83}\right)\)	\(e\left(\frac{157}{332}\right)\)	\(e\left(\frac{55}{332}\right)\)	\(e\left(\frac{99}{166}\right)\)	\(e\left(\frac{109}{332}\right)\)	\(e\left(\frac{153}{166}\right)\)	\(e\left(\frac{21}{83}\right)\)	\(e\left(\frac{151}{332}\right)\)	\(e\left(\frac{1}{166}\right)\)
\(\chi_{15030}(77,\cdot)\)	15030.bs	996	no	\(1\)	\(1\)	\(e\left(\frac{365}{996}\right)\)	\(e\left(\frac{229}{498}\right)\)	\(e\left(\frac{7}{996}\right)\)	\(e\left(\frac{121}{332}\right)\)	\(e\left(\frac{85}{166}\right)\)	\(e\left(\frac{985}{996}\right)\)	\(e\left(\frac{65}{249}\right)\)	\(e\left(\frac{205}{249}\right)\)	\(e\left(\frac{299}{332}\right)\)	\(e\left(\frac{239}{498}\right)\)
\(\chi_{15030}(79,\cdot)\)	15030.bo	498	no	\(-1\)	\(1\)	\(e\left(\frac{185}{498}\right)\)	\(e\left(\frac{157}{249}\right)\)	\(e\left(\frac{41}{249}\right)\)	\(e\left(\frac{21}{83}\right)\)	\(e\left(\frac{59}{83}\right)\)	\(e\left(\frac{149}{249}\right)\)	\(e\left(\frac{100}{249}\right)\)	\(e\left(\frac{143}{249}\right)\)	\(e\left(\frac{32}{83}\right)\)	\(e\left(\frac{157}{498}\right)\)
\(\chi_{15030}(83,\cdot)\)	15030.bt	996	no	\(-1\)	\(1\)	\(e\left(\frac{979}{996}\right)\)	\(e\left(\frac{209}{498}\right)\)	\(e\left(\frac{263}{996}\right)\)	\(e\left(\frac{325}{332}\right)\)	\(e\left(\frac{87}{166}\right)\)	\(e\left(\frac{725}{996}\right)\)	\(e\left(\frac{130}{249}\right)\)	\(e\left(\frac{161}{249}\right)\)	\(e\left(\frac{183}{332}\right)\)	\(e\left(\frac{239}{249}\right)\)
\(\chi_{15030}(89,\cdot)\)	15030.bf	166	no	\(-1\)	\(1\)	\(e\left(\frac{161}{166}\right)\)	\(e\left(\frac{79}{166}\right)\)	\(e\left(\frac{9}{166}\right)\)	\(e\left(\frac{14}{83}\right)\)	\(e\left(\frac{67}{83}\right)\)	\(e\left(\frac{70}{83}\right)\)	\(e\left(\frac{109}{166}\right)\)	\(e\left(\frac{41}{83}\right)\)	\(e\left(\frac{15}{166}\right)\)	\(e\left(\frac{81}{166}\right)\)
\(\chi_{15030}(91,\cdot)\)	15030.z	166	no	\(-1\)	\(1\)	\(e\left(\frac{8}{83}\right)\)	\(e\left(\frac{23}{83}\right)\)	\(e\left(\frac{21}{166}\right)\)	\(e\left(\frac{93}{166}\right)\)	\(e\left(\frac{18}{83}\right)\)	\(e\left(\frac{133}{166}\right)\)	\(e\left(\frac{58}{83}\right)\)	\(e\left(\frac{68}{83}\right)\)	\(e\left(\frac{35}{166}\right)\)	\(e\left(\frac{23}{166}\right)\)
\(\chi_{15030}(97,\cdot)\)	15030.bv	996	no	\(-1\)	\(1\)	\(e\left(\frac{937}{996}\right)\)	\(e\left(\frac{121}{249}\right)\)	\(e\left(\frac{239}{996}\right)\)	\(e\left(\frac{171}{332}\right)\)	\(e\left(\frac{9}{166}\right)\)	\(e\left(\frac{407}{996}\right)\)	\(e\left(\frac{419}{498}\right)\)	\(e\left(\frac{134}{249}\right)\)	\(e\left(\frac{59}{332}\right)\)	\(e\left(\frac{185}{249}\right)\)
\(\chi_{15030}(101,\cdot)\)	15030.bp	498	no	\(1\)	\(1\)	\(e\left(\frac{205}{249}\right)\)	\(e\left(\frac{245}{498}\right)\)	\(e\left(\frac{175}{498}\right)\)	\(e\left(\frac{60}{83}\right)\)	\(e\left(\frac{50}{83}\right)\)	\(e\left(\frac{236}{249}\right)\)	\(e\left(\frac{275}{498}\right)\)	\(e\left(\frac{41}{249}\right)\)	\(e\left(\frac{5}{166}\right)\)	\(e\left(\frac{248}{249}\right)\)
\(\chi_{15030}(103,\cdot)\)	15030.bu	996	no	\(1\)	\(1\)	\(e\left(\frac{683}{996}\right)\)	\(e\left(\frac{203}{249}\right)\)	\(e\left(\frac{331}{996}\right)\)	\(e\left(\frac{291}{332}\right)\)	\(e\left(\frac{59}{166}\right)\)	\(e\left(\frac{547}{996}\right)\)	\(e\left(\frac{349}{498}\right)\)	\(e\left(\frac{196}{249}\right)\)	\(e\left(\frac{147}{332}\right)\)	\(e\left(\frac{203}{498}\right)\)
\(\chi_{15030}(107,\cdot)\)	15030.bk	332	no	\(1\)	\(1\)	\(e\left(\frac{215}{332}\right)\)	\(e\left(\frac{3}{166}\right)\)	\(e\left(\frac{277}{332}\right)\)	\(e\left(\frac{41}{332}\right)\)	\(e\left(\frac{107}{166}\right)\)	\(e\left(\frac{39}{332}\right)\)	\(e\left(\frac{11}{83}\right)\)	\(e\left(\frac{73}{83}\right)\)	\(e\left(\frac{19}{332}\right)\)	\(e\left(\frac{43}{166}\right)\)
\(\chi_{15030}(109,\cdot)\)	15030.bc	166	no	\(-1\)	\(1\)	\(e\left(\frac{93}{166}\right)\)	\(e\left(\frac{4}{83}\right)\)	\(e\left(\frac{74}{83}\right)\)	\(e\left(\frac{55}{83}\right)\)	\(e\left(\frac{32}{83}\right)\)	\(e\left(\frac{26}{83}\right)\)	\(e\left(\frac{57}{83}\right)\)	\(e\left(\frac{1}{83}\right)\)	\(e\left(\frac{68}{83}\right)\)	\(e\left(\frac{87}{166}\right)\)
\(\chi_{15030}(113,\cdot)\)	15030.bt	996	no	\(-1\)	\(1\)	\(e\left(\frac{971}{996}\right)\)	\(e\left(\frac{73}{498}\right)\)	\(e\left(\frac{211}{996}\right)\)	\(e\left(\frac{185}{332}\right)\)	\(e\left(\frac{1}{166}\right)\)	\(e\left(\frac{949}{996}\right)\)	\(e\left(\frac{74}{249}\right)\)	\(e\left(\frac{61}{249}\right)\)	\(e\left(\frac{191}{332}\right)\)	\(e\left(\frac{205}{249}\right)\)
\(\chi_{15030}(119,\cdot)\)	15030.bm	498	no	\(1\)	\(1\)	\(e\left(\frac{359}{498}\right)\)	\(e\left(\frac{5}{498}\right)\)	\(e\left(\frac{233}{249}\right)\)	\(e\left(\frac{99}{166}\right)\)	\(e\left(\frac{62}{83}\right)\)	\(e\left(\frac{157}{498}\right)\)	\(e\left(\frac{341}{498}\right)\)	\(e\left(\frac{11}{249}\right)\)	\(e\left(\frac{28}{83}\right)\)	\(e\left(\frac{188}{249}\right)\)

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.