LMFDB - Group of Dirichlet characters of modulus 6036

Show commands: PariGP / SageMath

sage: H = DirichletGroup(6036)

pari: g = idealstar(,6036,2)

Character group

sage: G.order() pari: g.no
Order	=	2008
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{502}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{6036}(3019,\cdot)$, $\chi_{6036}(4025,\cdot)$, $\chi_{6036}(2017,\cdot)$

First 32 of 2008 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	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$
$\chi_{6036}(1,\cdot)$	6036.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{6036}(5,\cdot)$	6036.j	502	no	$1$	$1$	$e\left(\frac{126}{251}\right)$	$e\left(\frac{43}{251}\right)$	$e\left(\frac{293}{502}\right)$	$e\left(\frac{62}{251}\right)$	$e\left(\frac{240}{251}\right)$	$e\left(\frac{237}{502}\right)$	$e\left(\frac{163}{502}\right)$	$e\left(\frac{1}{251}\right)$	$e\left(\frac{238}{251}\right)$	$e\left(\frac{31}{502}\right)$
$\chi_{6036}(7,\cdot)$	6036.l	502	no	$-1$	$1$	$e\left(\frac{43}{251}\right)$	$e\left(\frac{117}{502}\right)$	$e\left(\frac{349}{502}\right)$	$e\left(\frac{61}{251}\right)$	$e\left(\frac{58}{251}\right)$	$e\left(\frac{51}{502}\right)$	$e\left(\frac{213}{502}\right)$	$e\left(\frac{86}{251}\right)$	$e\left(\frac{137}{251}\right)$	$e\left(\frac{407}{502}\right)$
$\chi_{6036}(11,\cdot)$	6036.o	502	yes	$1$	$1$	$e\left(\frac{293}{502}\right)$	$e\left(\frac{349}{502}\right)$	$e\left(\frac{129}{251}\right)$	$e\left(\frac{94}{251}\right)$	$e\left(\frac{331}{502}\right)$	$e\left(\frac{165}{502}\right)$	$e\left(\frac{160}{251}\right)$	$e\left(\frac{42}{251}\right)$	$e\left(\frac{163}{502}\right)$	$e\left(\frac{47}{502}\right)$
$\chi_{6036}(13,\cdot)$	6036.i	251	no	$1$	$1$	$e\left(\frac{62}{251}\right)$	$e\left(\frac{61}{251}\right)$	$e\left(\frac{94}{251}\right)$	$e\left(\frac{158}{251}\right)$	$e\left(\frac{142}{251}\right)$	$e\left(\frac{136}{251}\right)$	$e\left(\frac{66}{251}\right)$	$e\left(\frac{124}{251}\right)$	$e\left(\frac{145}{251}\right)$	$e\left(\frac{165}{251}\right)$
$\chi_{6036}(17,\cdot)$	6036.j	502	no	$1$	$1$	$e\left(\frac{240}{251}\right)$	$e\left(\frac{58}{251}\right)$	$e\left(\frac{331}{502}\right)$	$e\left(\frac{142}{251}\right)$	$e\left(\frac{242}{251}\right)$	$e\left(\frac{57}{502}\right)$	$e\left(\frac{179}{502}\right)$	$e\left(\frac{229}{251}\right)$	$e\left(\frac{35}{251}\right)$	$e\left(\frac{71}{502}\right)$
$\chi_{6036}(19,\cdot)$	6036.p	502	no	$1$	$1$	$e\left(\frac{237}{502}\right)$	$e\left(\frac{51}{502}\right)$	$e\left(\frac{165}{502}\right)$	$e\left(\frac{136}{251}\right)$	$e\left(\frac{57}{502}\right)$	$e\left(\frac{98}{251}\right)$	$e\left(\frac{479}{502}\right)$	$e\left(\frac{237}{251}\right)$	$e\left(\frac{113}{502}\right)$	$e\left(\frac{34}{251}\right)$
$\chi_{6036}(23,\cdot)$	6036.o	502	yes	$1$	$1$	$e\left(\frac{163}{502}\right)$	$e\left(\frac{213}{502}\right)$	$e\left(\frac{160}{251}\right)$	$e\left(\frac{66}{251}\right)$	$e\left(\frac{179}{502}\right)$	$e\left(\frac{479}{502}\right)$	$e\left(\frac{107}{251}\right)$	$e\left(\frac{163}{251}\right)$	$e\left(\frac{29}{502}\right)$	$e\left(\frac{33}{502}\right)$
$\chi_{6036}(25,\cdot)$	6036.i	251	no	$1$	$1$	$e\left(\frac{1}{251}\right)$	$e\left(\frac{86}{251}\right)$	$e\left(\frac{42}{251}\right)$	$e\left(\frac{124}{251}\right)$	$e\left(\frac{229}{251}\right)$	$e\left(\frac{237}{251}\right)$	$e\left(\frac{163}{251}\right)$	$e\left(\frac{2}{251}\right)$	$e\left(\frac{225}{251}\right)$	$e\left(\frac{31}{251}\right)$
$\chi_{6036}(29,\cdot)$	6036.j	502	no	$1$	$1$	$e\left(\frac{238}{251}\right)$	$e\left(\frac{137}{251}\right)$	$e\left(\frac{163}{502}\right)$	$e\left(\frac{145}{251}\right)$	$e\left(\frac{35}{251}\right)$	$e\left(\frac{113}{502}\right)$	$e\left(\frac{29}{502}\right)$	$e\left(\frac{225}{251}\right)$	$e\left(\frac{87}{251}\right)$	$e\left(\frac{449}{502}\right)$
$\chi_{6036}(31,\cdot)$	6036.p	502	no	$1$	$1$	$e\left(\frac{31}{502}\right)$	$e\left(\frac{407}{502}\right)$	$e\left(\frac{47}{502}\right)$	$e\left(\frac{165}{251}\right)$	$e\left(\frac{71}{502}\right)$	$e\left(\frac{34}{251}\right)$	$e\left(\frac{33}{502}\right)$	$e\left(\frac{31}{251}\right)$	$e\left(\frac{449}{502}\right)$	$e\left(\frac{104}{251}\right)$
$\chi_{6036}(35,\cdot)$	6036.k	502	yes	$-1$	$1$	$e\left(\frac{169}{251}\right)$	$e\left(\frac{203}{502}\right)$	$e\left(\frac{70}{251}\right)$	$e\left(\frac{123}{251}\right)$	$e\left(\frac{47}{251}\right)$	$e\left(\frac{144}{251}\right)$	$e\left(\frac{188}{251}\right)$	$e\left(\frac{87}{251}\right)$	$e\left(\frac{124}{251}\right)$	$e\left(\frac{219}{251}\right)$
$\chi_{6036}(37,\cdot)$	6036.m	502	no	$-1$	$1$	$e\left(\frac{371}{502}\right)$	$e\left(\frac{140}{251}\right)$	$e\left(\frac{10}{251}\right)$	$e\left(\frac{161}{251}\right)$	$e\left(\frac{121}{502}\right)$	$e\left(\frac{77}{502}\right)$	$e\left(\frac{242}{251}\right)$	$e\left(\frac{120}{251}\right)$	$e\left(\frac{143}{502}\right)$	$e\left(\frac{457}{502}\right)$
$\chi_{6036}(41,\cdot)$	6036.j	502	no	$1$	$1$	$e\left(\frac{243}{251}\right)$	$e\left(\frac{65}{251}\right)$	$e\left(\frac{81}{502}\right)$	$e\left(\frac{12}{251}\right)$	$e\left(\frac{176}{251}\right)$	$e\left(\frac{475}{502}\right)$	$e\left(\frac{153}{502}\right)$	$e\left(\frac{235}{251}\right)$	$e\left(\frac{208}{251}\right)$	$e\left(\frac{257}{502}\right)$
$\chi_{6036}(43,\cdot)$	6036.l	502	no	$-1$	$1$	$e\left(\frac{33}{251}\right)$	$e\left(\frac{405}{502}\right)$	$e\left(\frac{11}{502}\right)$	$e\left(\frac{76}{251}\right)$	$e\left(\frac{27}{251}\right)$	$e\left(\frac{331}{502}\right)$	$e\left(\frac{467}{502}\right)$	$e\left(\frac{66}{251}\right)$	$e\left(\frac{146}{251}\right)$	$e\left(\frac{289}{502}\right)$
$\chi_{6036}(47,\cdot)$	6036.o	502	yes	$1$	$1$	$e\left(\frac{497}{502}\right)$	$e\left(\frac{323}{502}\right)$	$e\left(\frac{146}{251}\right)$	$e\left(\frac{192}{251}\right)$	$e\left(\frac{361}{502}\right)$	$e\left(\frac{321}{502}\right)$	$e\left(\frac{220}{251}\right)$	$e\left(\frac{246}{251}\right)$	$e\left(\frac{381}{502}\right)$	$e\left(\frac{347}{502}\right)$
$\chi_{6036}(49,\cdot)$	6036.i	251	no	$1$	$1$	$e\left(\frac{86}{251}\right)$	$e\left(\frac{117}{251}\right)$	$e\left(\frac{98}{251}\right)$	$e\left(\frac{122}{251}\right)$	$e\left(\frac{116}{251}\right)$	$e\left(\frac{51}{251}\right)$	$e\left(\frac{213}{251}\right)$	$e\left(\frac{172}{251}\right)$	$e\left(\frac{23}{251}\right)$	$e\left(\frac{156}{251}\right)$
$\chi_{6036}(53,\cdot)$	6036.j	502	no	$1$	$1$	$e\left(\frac{7}{251}\right)$	$e\left(\frac{100}{251}\right)$	$e\left(\frac{337}{502}\right)$	$e\left(\frac{115}{251}\right)$	$e\left(\frac{97}{251}\right)$	$e\left(\frac{55}{502}\right)$	$e\left(\frac{23}{502}\right)$	$e\left(\frac{14}{251}\right)$	$e\left(\frac{69}{251}\right)$	$e\left(\frac{183}{502}\right)$
$\chi_{6036}(55,\cdot)$	6036.p	502	no	$1$	$1$	$e\left(\frac{43}{502}\right)$	$e\left(\frac{435}{502}\right)$	$e\left(\frac{49}{502}\right)$	$e\left(\frac{156}{251}\right)$	$e\left(\frac{309}{502}\right)$	$e\left(\frac{201}{251}\right)$	$e\left(\frac{483}{502}\right)$	$e\left(\frac{43}{251}\right)$	$e\left(\frac{137}{502}\right)$	$e\left(\frac{39}{251}\right)$
$\chi_{6036}(59,\cdot)$	6036.o	502	yes	$1$	$1$	$e\left(\frac{429}{502}\right)$	$e\left(\frac{499}{502}\right)$	$e\left(\frac{224}{251}\right)$	$e\left(\frac{243}{251}\right)$	$e\left(\frac{351}{502}\right)$	$e\left(\frac{269}{502}\right)$	$e\left(\frac{200}{251}\right)$	$e\left(\frac{178}{251}\right)$	$e\left(\frac{141}{502}\right)$	$e\left(\frac{247}{502}\right)$
$\chi_{6036}(61,\cdot)$	6036.i	251	no	$1$	$1$	$e\left(\frac{152}{251}\right)$	$e\left(\frac{20}{251}\right)$	$e\left(\frac{109}{251}\right)$	$e\left(\frac{23}{251}\right)$	$e\left(\frac{170}{251}\right)$	$e\left(\frac{131}{251}\right)$	$e\left(\frac{178}{251}\right)$	$e\left(\frac{53}{251}\right)$	$e\left(\frac{64}{251}\right)$	$e\left(\frac{194}{251}\right)$
$\chi_{6036}(65,\cdot)$	6036.j	502	no	$1$	$1$	$e\left(\frac{188}{251}\right)$	$e\left(\frac{104}{251}\right)$	$e\left(\frac{481}{502}\right)$	$e\left(\frac{220}{251}\right)$	$e\left(\frac{131}{251}\right)$	$e\left(\frac{7}{502}\right)$	$e\left(\frac{295}{502}\right)$	$e\left(\frac{125}{251}\right)$	$e\left(\frac{132}{251}\right)$	$e\left(\frac{361}{502}\right)$
$\chi_{6036}(67,\cdot)$	6036.l	502	no	$-1$	$1$	$e\left(\frac{47}{251}\right)$	$e\left(\frac{303}{502}\right)$	$e\left(\frac{183}{502}\right)$	$e\left(\frac{55}{251}\right)$	$e\left(\frac{221}{251}\right)$	$e\left(\frac{441}{502}\right)$	$e\left(\frac{11}{502}\right)$	$e\left(\frac{94}{251}\right)$	$e\left(\frac{33}{251}\right)$	$e\left(\frac{153}{502}\right)$
$\chi_{6036}(71,\cdot)$	6036.k	502	yes	$-1$	$1$	$e\left(\frac{136}{251}\right)$	$e\left(\frac{49}{502}\right)$	$e\left(\frac{190}{251}\right)$	$e\left(\frac{47}{251}\right)$	$e\left(\frac{20}{251}\right)$	$e\left(\frac{104}{251}\right)$	$e\left(\frac{80}{251}\right)$	$e\left(\frac{21}{251}\right)$	$e\left(\frac{229}{251}\right)$	$e\left(\frac{200}{251}\right)$
$\chi_{6036}(73,\cdot)$	6036.i	251	no	$1$	$1$	$e\left(\frac{9}{251}\right)$	$e\left(\frac{21}{251}\right)$	$e\left(\frac{127}{251}\right)$	$e\left(\frac{112}{251}\right)$	$e\left(\frac{53}{251}\right)$	$e\left(\frac{125}{251}\right)$	$e\left(\frac{212}{251}\right)$	$e\left(\frac{18}{251}\right)$	$e\left(\frac{17}{251}\right)$	$e\left(\frac{28}{251}\right)$
$\chi_{6036}(77,\cdot)$	6036.n	502	no	$-1$	$1$	$e\left(\frac{379}{502}\right)$	$e\left(\frac{233}{251}\right)$	$e\left(\frac{105}{502}\right)$	$e\left(\frac{155}{251}\right)$	$e\left(\frac{447}{502}\right)$	$e\left(\frac{108}{251}\right)$	$e\left(\frac{31}{502}\right)$	$e\left(\frac{128}{251}\right)$	$e\left(\frac{437}{502}\right)$	$e\left(\frac{227}{251}\right)$
$\chi_{6036}(79,\cdot)$	6036.l	502	no	$-1$	$1$	$e\left(\frac{59}{251}\right)$	$e\left(\frac{359}{502}\right)$	$e\left(\frac{187}{502}\right)$	$e\left(\frac{37}{251}\right)$	$e\left(\frac{208}{251}\right)$	$e\left(\frac{105}{502}\right)$	$e\left(\frac{409}{502}\right)$	$e\left(\frac{118}{251}\right)$	$e\left(\frac{223}{251}\right)$	$e\left(\frac{395}{502}\right)$
$\chi_{6036}(83,\cdot)$	6036.o	502	yes	$1$	$1$	$e\left(\frac{145}{502}\right)$	$e\left(\frac{171}{502}\right)$	$e\left(\frac{33}{251}\right)$	$e\left(\frac{205}{251}\right)$	$e\left(\frac{73}{502}\right)$	$e\left(\frac{229}{502}\right)$	$e\left(\frac{146}{251}\right)$	$e\left(\frac{145}{251}\right)$	$e\left(\frac{497}{502}\right)$	$e\left(\frac{479}{502}\right)$
$\chi_{6036}(85,\cdot)$	6036.i	251	no	$1$	$1$	$e\left(\frac{115}{251}\right)$	$e\left(\frac{101}{251}\right)$	$e\left(\frac{61}{251}\right)$	$e\left(\frac{204}{251}\right)$	$e\left(\frac{231}{251}\right)$	$e\left(\frac{147}{251}\right)$	$e\left(\frac{171}{251}\right)$	$e\left(\frac{230}{251}\right)$	$e\left(\frac{22}{251}\right)$	$e\left(\frac{51}{251}\right)$
$\chi_{6036}(89,\cdot)$	6036.j	502	no	$1$	$1$	$e\left(\frac{213}{251}\right)$	$e\left(\frac{246}{251}\right)$	$e\left(\frac{71}{502}\right)$	$e\left(\frac{57}{251}\right)$	$e\left(\frac{83}{251}\right)$	$e\left(\frac{311}{502}\right)$	$e\left(\frac{413}{502}\right)$	$e\left(\frac{175}{251}\right)$	$e\left(\frac{235}{251}\right)$	$e\left(\frac{405}{502}\right)$
$\chi_{6036}(91,\cdot)$	6036.l	502	no	$-1$	$1$	$e\left(\frac{105}{251}\right)$	$e\left(\frac{239}{502}\right)$	$e\left(\frac{35}{502}\right)$	$e\left(\frac{219}{251}\right)$	$e\left(\frac{200}{251}\right)$	$e\left(\frac{323}{502}\right)$	$e\left(\frac{345}{502}\right)$	$e\left(\frac{210}{251}\right)$	$e\left(\frac{31}{251}\right)$	$e\left(\frac{235}{502}\right)$
$\chi_{6036}(95,\cdot)$	6036.o	502	yes	$1$	$1$	$e\left(\frac{489}{502}\right)$	$e\left(\frac{137}{502}\right)$	$e\left(\frac{229}{251}\right)$	$e\left(\frac{198}{251}\right)$	$e\left(\frac{35}{502}\right)$	$e\left(\frac{433}{502}\right)$	$e\left(\frac{70}{251}\right)$	$e\left(\frac{238}{251}\right)$	$e\left(\frac{87}{502}\right)$	$e\left(\frac{99}{502}\right)$

Click here to search among the remaining 1976 characters.

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	$6036$
Structure	\(C_{2}\times C_{2}\times C_{502}\)
Order	$2008$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)
\(\chi_{6036}(1,\cdot)\)	6036.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{6036}(5,\cdot)\)	6036.j	502	no	\(1\)	\(1\)	\(e\left(\frac{126}{251}\right)\)	\(e\left(\frac{43}{251}\right)\)	\(e\left(\frac{293}{502}\right)\)	\(e\left(\frac{62}{251}\right)\)	\(e\left(\frac{240}{251}\right)\)	\(e\left(\frac{237}{502}\right)\)	\(e\left(\frac{163}{502}\right)\)	\(e\left(\frac{1}{251}\right)\)	\(e\left(\frac{238}{251}\right)\)	\(e\left(\frac{31}{502}\right)\)
\(\chi_{6036}(7,\cdot)\)	6036.l	502	no	\(-1\)	\(1\)	\(e\left(\frac{43}{251}\right)\)	\(e\left(\frac{117}{502}\right)\)	\(e\left(\frac{349}{502}\right)\)	\(e\left(\frac{61}{251}\right)\)	\(e\left(\frac{58}{251}\right)\)	\(e\left(\frac{51}{502}\right)\)	\(e\left(\frac{213}{502}\right)\)	\(e\left(\frac{86}{251}\right)\)	\(e\left(\frac{137}{251}\right)\)	\(e\left(\frac{407}{502}\right)\)
\(\chi_{6036}(11,\cdot)\)	6036.o	502	yes	\(1\)	\(1\)	\(e\left(\frac{293}{502}\right)\)	\(e\left(\frac{349}{502}\right)\)	\(e\left(\frac{129}{251}\right)\)	\(e\left(\frac{94}{251}\right)\)	\(e\left(\frac{331}{502}\right)\)	\(e\left(\frac{165}{502}\right)\)	\(e\left(\frac{160}{251}\right)\)	\(e\left(\frac{42}{251}\right)\)	\(e\left(\frac{163}{502}\right)\)	\(e\left(\frac{47}{502}\right)\)
\(\chi_{6036}(13,\cdot)\)	6036.i	251	no	\(1\)	\(1\)	\(e\left(\frac{62}{251}\right)\)	\(e\left(\frac{61}{251}\right)\)	\(e\left(\frac{94}{251}\right)\)	\(e\left(\frac{158}{251}\right)\)	\(e\left(\frac{142}{251}\right)\)	\(e\left(\frac{136}{251}\right)\)	\(e\left(\frac{66}{251}\right)\)	\(e\left(\frac{124}{251}\right)\)	\(e\left(\frac{145}{251}\right)\)	\(e\left(\frac{165}{251}\right)\)
\(\chi_{6036}(17,\cdot)\)	6036.j	502	no	\(1\)	\(1\)	\(e\left(\frac{240}{251}\right)\)	\(e\left(\frac{58}{251}\right)\)	\(e\left(\frac{331}{502}\right)\)	\(e\left(\frac{142}{251}\right)\)	\(e\left(\frac{242}{251}\right)\)	\(e\left(\frac{57}{502}\right)\)	\(e\left(\frac{179}{502}\right)\)	\(e\left(\frac{229}{251}\right)\)	\(e\left(\frac{35}{251}\right)\)	\(e\left(\frac{71}{502}\right)\)
\(\chi_{6036}(19,\cdot)\)	6036.p	502	no	\(1\)	\(1\)	\(e\left(\frac{237}{502}\right)\)	\(e\left(\frac{51}{502}\right)\)	\(e\left(\frac{165}{502}\right)\)	\(e\left(\frac{136}{251}\right)\)	\(e\left(\frac{57}{502}\right)\)	\(e\left(\frac{98}{251}\right)\)	\(e\left(\frac{479}{502}\right)\)	\(e\left(\frac{237}{251}\right)\)	\(e\left(\frac{113}{502}\right)\)	\(e\left(\frac{34}{251}\right)\)
\(\chi_{6036}(23,\cdot)\)	6036.o	502	yes	\(1\)	\(1\)	\(e\left(\frac{163}{502}\right)\)	\(e\left(\frac{213}{502}\right)\)	\(e\left(\frac{160}{251}\right)\)	\(e\left(\frac{66}{251}\right)\)	\(e\left(\frac{179}{502}\right)\)	\(e\left(\frac{479}{502}\right)\)	\(e\left(\frac{107}{251}\right)\)	\(e\left(\frac{163}{251}\right)\)	\(e\left(\frac{29}{502}\right)\)	\(e\left(\frac{33}{502}\right)\)
\(\chi_{6036}(25,\cdot)\)	6036.i	251	no	\(1\)	\(1\)	\(e\left(\frac{1}{251}\right)\)	\(e\left(\frac{86}{251}\right)\)	\(e\left(\frac{42}{251}\right)\)	\(e\left(\frac{124}{251}\right)\)	\(e\left(\frac{229}{251}\right)\)	\(e\left(\frac{237}{251}\right)\)	\(e\left(\frac{163}{251}\right)\)	\(e\left(\frac{2}{251}\right)\)	\(e\left(\frac{225}{251}\right)\)	\(e\left(\frac{31}{251}\right)\)
\(\chi_{6036}(29,\cdot)\)	6036.j	502	no	\(1\)	\(1\)	\(e\left(\frac{238}{251}\right)\)	\(e\left(\frac{137}{251}\right)\)	\(e\left(\frac{163}{502}\right)\)	\(e\left(\frac{145}{251}\right)\)	\(e\left(\frac{35}{251}\right)\)	\(e\left(\frac{113}{502}\right)\)	\(e\left(\frac{29}{502}\right)\)	\(e\left(\frac{225}{251}\right)\)	\(e\left(\frac{87}{251}\right)\)	\(e\left(\frac{449}{502}\right)\)
\(\chi_{6036}(31,\cdot)\)	6036.p	502	no	\(1\)	\(1\)	\(e\left(\frac{31}{502}\right)\)	\(e\left(\frac{407}{502}\right)\)	\(e\left(\frac{47}{502}\right)\)	\(e\left(\frac{165}{251}\right)\)	\(e\left(\frac{71}{502}\right)\)	\(e\left(\frac{34}{251}\right)\)	\(e\left(\frac{33}{502}\right)\)	\(e\left(\frac{31}{251}\right)\)	\(e\left(\frac{449}{502}\right)\)	\(e\left(\frac{104}{251}\right)\)
\(\chi_{6036}(35,\cdot)\)	6036.k	502	yes	\(-1\)	\(1\)	\(e\left(\frac{169}{251}\right)\)	\(e\left(\frac{203}{502}\right)\)	\(e\left(\frac{70}{251}\right)\)	\(e\left(\frac{123}{251}\right)\)	\(e\left(\frac{47}{251}\right)\)	\(e\left(\frac{144}{251}\right)\)	\(e\left(\frac{188}{251}\right)\)	\(e\left(\frac{87}{251}\right)\)	\(e\left(\frac{124}{251}\right)\)	\(e\left(\frac{219}{251}\right)\)
\(\chi_{6036}(37,\cdot)\)	6036.m	502	no	\(-1\)	\(1\)	\(e\left(\frac{371}{502}\right)\)	\(e\left(\frac{140}{251}\right)\)	\(e\left(\frac{10}{251}\right)\)	\(e\left(\frac{161}{251}\right)\)	\(e\left(\frac{121}{502}\right)\)	\(e\left(\frac{77}{502}\right)\)	\(e\left(\frac{242}{251}\right)\)	\(e\left(\frac{120}{251}\right)\)	\(e\left(\frac{143}{502}\right)\)	\(e\left(\frac{457}{502}\right)\)
\(\chi_{6036}(41,\cdot)\)	6036.j	502	no	\(1\)	\(1\)	\(e\left(\frac{243}{251}\right)\)	\(e\left(\frac{65}{251}\right)\)	\(e\left(\frac{81}{502}\right)\)	\(e\left(\frac{12}{251}\right)\)	\(e\left(\frac{176}{251}\right)\)	\(e\left(\frac{475}{502}\right)\)	\(e\left(\frac{153}{502}\right)\)	\(e\left(\frac{235}{251}\right)\)	\(e\left(\frac{208}{251}\right)\)	\(e\left(\frac{257}{502}\right)\)
\(\chi_{6036}(43,\cdot)\)	6036.l	502	no	\(-1\)	\(1\)	\(e\left(\frac{33}{251}\right)\)	\(e\left(\frac{405}{502}\right)\)	\(e\left(\frac{11}{502}\right)\)	\(e\left(\frac{76}{251}\right)\)	\(e\left(\frac{27}{251}\right)\)	\(e\left(\frac{331}{502}\right)\)	\(e\left(\frac{467}{502}\right)\)	\(e\left(\frac{66}{251}\right)\)	\(e\left(\frac{146}{251}\right)\)	\(e\left(\frac{289}{502}\right)\)
\(\chi_{6036}(47,\cdot)\)	6036.o	502	yes	\(1\)	\(1\)	\(e\left(\frac{497}{502}\right)\)	\(e\left(\frac{323}{502}\right)\)	\(e\left(\frac{146}{251}\right)\)	\(e\left(\frac{192}{251}\right)\)	\(e\left(\frac{361}{502}\right)\)	\(e\left(\frac{321}{502}\right)\)	\(e\left(\frac{220}{251}\right)\)	\(e\left(\frac{246}{251}\right)\)	\(e\left(\frac{381}{502}\right)\)	\(e\left(\frac{347}{502}\right)\)
\(\chi_{6036}(49,\cdot)\)	6036.i	251	no	\(1\)	\(1\)	\(e\left(\frac{86}{251}\right)\)	\(e\left(\frac{117}{251}\right)\)	\(e\left(\frac{98}{251}\right)\)	\(e\left(\frac{122}{251}\right)\)	\(e\left(\frac{116}{251}\right)\)	\(e\left(\frac{51}{251}\right)\)	\(e\left(\frac{213}{251}\right)\)	\(e\left(\frac{172}{251}\right)\)	\(e\left(\frac{23}{251}\right)\)	\(e\left(\frac{156}{251}\right)\)
\(\chi_{6036}(53,\cdot)\)	6036.j	502	no	\(1\)	\(1\)	\(e\left(\frac{7}{251}\right)\)	\(e\left(\frac{100}{251}\right)\)	\(e\left(\frac{337}{502}\right)\)	\(e\left(\frac{115}{251}\right)\)	\(e\left(\frac{97}{251}\right)\)	\(e\left(\frac{55}{502}\right)\)	\(e\left(\frac{23}{502}\right)\)	\(e\left(\frac{14}{251}\right)\)	\(e\left(\frac{69}{251}\right)\)	\(e\left(\frac{183}{502}\right)\)
\(\chi_{6036}(55,\cdot)\)	6036.p	502	no	\(1\)	\(1\)	\(e\left(\frac{43}{502}\right)\)	\(e\left(\frac{435}{502}\right)\)	\(e\left(\frac{49}{502}\right)\)	\(e\left(\frac{156}{251}\right)\)	\(e\left(\frac{309}{502}\right)\)	\(e\left(\frac{201}{251}\right)\)	\(e\left(\frac{483}{502}\right)\)	\(e\left(\frac{43}{251}\right)\)	\(e\left(\frac{137}{502}\right)\)	\(e\left(\frac{39}{251}\right)\)
\(\chi_{6036}(59,\cdot)\)	6036.o	502	yes	\(1\)	\(1\)	\(e\left(\frac{429}{502}\right)\)	\(e\left(\frac{499}{502}\right)\)	\(e\left(\frac{224}{251}\right)\)	\(e\left(\frac{243}{251}\right)\)	\(e\left(\frac{351}{502}\right)\)	\(e\left(\frac{269}{502}\right)\)	\(e\left(\frac{200}{251}\right)\)	\(e\left(\frac{178}{251}\right)\)	\(e\left(\frac{141}{502}\right)\)	\(e\left(\frac{247}{502}\right)\)
\(\chi_{6036}(61,\cdot)\)	6036.i	251	no	\(1\)	\(1\)	\(e\left(\frac{152}{251}\right)\)	\(e\left(\frac{20}{251}\right)\)	\(e\left(\frac{109}{251}\right)\)	\(e\left(\frac{23}{251}\right)\)	\(e\left(\frac{170}{251}\right)\)	\(e\left(\frac{131}{251}\right)\)	\(e\left(\frac{178}{251}\right)\)	\(e\left(\frac{53}{251}\right)\)	\(e\left(\frac{64}{251}\right)\)	\(e\left(\frac{194}{251}\right)\)
\(\chi_{6036}(65,\cdot)\)	6036.j	502	no	\(1\)	\(1\)	\(e\left(\frac{188}{251}\right)\)	\(e\left(\frac{104}{251}\right)\)	\(e\left(\frac{481}{502}\right)\)	\(e\left(\frac{220}{251}\right)\)	\(e\left(\frac{131}{251}\right)\)	\(e\left(\frac{7}{502}\right)\)	\(e\left(\frac{295}{502}\right)\)	\(e\left(\frac{125}{251}\right)\)	\(e\left(\frac{132}{251}\right)\)	\(e\left(\frac{361}{502}\right)\)
\(\chi_{6036}(67,\cdot)\)	6036.l	502	no	\(-1\)	\(1\)	\(e\left(\frac{47}{251}\right)\)	\(e\left(\frac{303}{502}\right)\)	\(e\left(\frac{183}{502}\right)\)	\(e\left(\frac{55}{251}\right)\)	\(e\left(\frac{221}{251}\right)\)	\(e\left(\frac{441}{502}\right)\)	\(e\left(\frac{11}{502}\right)\)	\(e\left(\frac{94}{251}\right)\)	\(e\left(\frac{33}{251}\right)\)	\(e\left(\frac{153}{502}\right)\)
\(\chi_{6036}(71,\cdot)\)	6036.k	502	yes	\(-1\)	\(1\)	\(e\left(\frac{136}{251}\right)\)	\(e\left(\frac{49}{502}\right)\)	\(e\left(\frac{190}{251}\right)\)	\(e\left(\frac{47}{251}\right)\)	\(e\left(\frac{20}{251}\right)\)	\(e\left(\frac{104}{251}\right)\)	\(e\left(\frac{80}{251}\right)\)	\(e\left(\frac{21}{251}\right)\)	\(e\left(\frac{229}{251}\right)\)	\(e\left(\frac{200}{251}\right)\)
\(\chi_{6036}(73,\cdot)\)	6036.i	251	no	\(1\)	\(1\)	\(e\left(\frac{9}{251}\right)\)	\(e\left(\frac{21}{251}\right)\)	\(e\left(\frac{127}{251}\right)\)	\(e\left(\frac{112}{251}\right)\)	\(e\left(\frac{53}{251}\right)\)	\(e\left(\frac{125}{251}\right)\)	\(e\left(\frac{212}{251}\right)\)	\(e\left(\frac{18}{251}\right)\)	\(e\left(\frac{17}{251}\right)\)	\(e\left(\frac{28}{251}\right)\)
\(\chi_{6036}(77,\cdot)\)	6036.n	502	no	\(-1\)	\(1\)	\(e\left(\frac{379}{502}\right)\)	\(e\left(\frac{233}{251}\right)\)	\(e\left(\frac{105}{502}\right)\)	\(e\left(\frac{155}{251}\right)\)	\(e\left(\frac{447}{502}\right)\)	\(e\left(\frac{108}{251}\right)\)	\(e\left(\frac{31}{502}\right)\)	\(e\left(\frac{128}{251}\right)\)	\(e\left(\frac{437}{502}\right)\)	\(e\left(\frac{227}{251}\right)\)
\(\chi_{6036}(79,\cdot)\)	6036.l	502	no	\(-1\)	\(1\)	\(e\left(\frac{59}{251}\right)\)	\(e\left(\frac{359}{502}\right)\)	\(e\left(\frac{187}{502}\right)\)	\(e\left(\frac{37}{251}\right)\)	\(e\left(\frac{208}{251}\right)\)	\(e\left(\frac{105}{502}\right)\)	\(e\left(\frac{409}{502}\right)\)	\(e\left(\frac{118}{251}\right)\)	\(e\left(\frac{223}{251}\right)\)	\(e\left(\frac{395}{502}\right)\)
\(\chi_{6036}(83,\cdot)\)	6036.o	502	yes	\(1\)	\(1\)	\(e\left(\frac{145}{502}\right)\)	\(e\left(\frac{171}{502}\right)\)	\(e\left(\frac{33}{251}\right)\)	\(e\left(\frac{205}{251}\right)\)	\(e\left(\frac{73}{502}\right)\)	\(e\left(\frac{229}{502}\right)\)	\(e\left(\frac{146}{251}\right)\)	\(e\left(\frac{145}{251}\right)\)	\(e\left(\frac{497}{502}\right)\)	\(e\left(\frac{479}{502}\right)\)
\(\chi_{6036}(85,\cdot)\)	6036.i	251	no	\(1\)	\(1\)	\(e\left(\frac{115}{251}\right)\)	\(e\left(\frac{101}{251}\right)\)	\(e\left(\frac{61}{251}\right)\)	\(e\left(\frac{204}{251}\right)\)	\(e\left(\frac{231}{251}\right)\)	\(e\left(\frac{147}{251}\right)\)	\(e\left(\frac{171}{251}\right)\)	\(e\left(\frac{230}{251}\right)\)	\(e\left(\frac{22}{251}\right)\)	\(e\left(\frac{51}{251}\right)\)
\(\chi_{6036}(89,\cdot)\)	6036.j	502	no	\(1\)	\(1\)	\(e\left(\frac{213}{251}\right)\)	\(e\left(\frac{246}{251}\right)\)	\(e\left(\frac{71}{502}\right)\)	\(e\left(\frac{57}{251}\right)\)	\(e\left(\frac{83}{251}\right)\)	\(e\left(\frac{311}{502}\right)\)	\(e\left(\frac{413}{502}\right)\)	\(e\left(\frac{175}{251}\right)\)	\(e\left(\frac{235}{251}\right)\)	\(e\left(\frac{405}{502}\right)\)
\(\chi_{6036}(91,\cdot)\)	6036.l	502	no	\(-1\)	\(1\)	\(e\left(\frac{105}{251}\right)\)	\(e\left(\frac{239}{502}\right)\)	\(e\left(\frac{35}{502}\right)\)	\(e\left(\frac{219}{251}\right)\)	\(e\left(\frac{200}{251}\right)\)	\(e\left(\frac{323}{502}\right)\)	\(e\left(\frac{345}{502}\right)\)	\(e\left(\frac{210}{251}\right)\)	\(e\left(\frac{31}{251}\right)\)	\(e\left(\frac{235}{502}\right)\)
\(\chi_{6036}(95,\cdot)\)	6036.o	502	yes	\(1\)	\(1\)	\(e\left(\frac{489}{502}\right)\)	\(e\left(\frac{137}{502}\right)\)	\(e\left(\frac{229}{251}\right)\)	\(e\left(\frac{198}{251}\right)\)	\(e\left(\frac{35}{502}\right)\)	\(e\left(\frac{433}{502}\right)\)	\(e\left(\frac{70}{251}\right)\)	\(e\left(\frac{238}{251}\right)\)	\(e\left(\frac{87}{502}\right)\)	\(e\left(\frac{99}{502}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Character group

First 32 of 2008 characters

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.