LMFDB - Group of Dirichlet characters of modulus 6002

Show commands: PariGP / SageMath

sage: H = DirichletGroup(6002)

pari: g = idealstar(,6002,2)

Character group

sage: G.order() pari: g.no
Order	=	3000
sage: H.invariants() pari: g.cyc
Structure	=	$C_{3000}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{6002}(3015,\cdot)$

First 32 of 3000 characters

Each row describes a character. When available, the columns show the orbit label, order of the character, whether the character is primitive, and several values of the character.

Character	Orbit	Order	Primitive	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{6002}(1,\cdot)$	6002.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{6002}(3,\cdot)$	6002.ba	500	no	$1$	$1$	$e\left(\frac{167}{250}\right)$	$e\left(\frac{11}{125}\right)$	$e\left(\frac{489}{500}\right)$	$e\left(\frac{42}{125}\right)$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{43}{100}\right)$	$e\left(\frac{189}{250}\right)$	$e\left(\frac{79}{125}\right)$	$e\left(\frac{23}{100}\right)$	$e\left(\frac{323}{500}\right)$
$\chi_{6002}(5,\cdot)$	6002.x	250	no	$1$	$1$	$e\left(\frac{11}{125}\right)$	$e\left(\frac{101}{125}\right)$	$e\left(\frac{137}{250}\right)$	$e\left(\frac{22}{125}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{19}{50}\right)$	$e\left(\frac{112}{125}\right)$	$e\left(\frac{89}{125}\right)$	$e\left(\frac{9}{50}\right)$	$e\left(\frac{159}{250}\right)$
$\chi_{6002}(7,\cdot)$	6002.bd	1000	no	$-1$	$1$	$e\left(\frac{489}{500}\right)$	$e\left(\frac{137}{250}\right)$	$e\left(\frac{363}{1000}\right)$	$e\left(\frac{239}{250}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{81}{200}\right)$	$e\left(\frac{263}{500}\right)$	$e\left(\frac{9}{125}\right)$	$e\left(\frac{141}{200}\right)$	$e\left(\frac{341}{1000}\right)$
$\chi_{6002}(9,\cdot)$	6002.x	250	no	$1$	$1$	$e\left(\frac{42}{125}\right)$	$e\left(\frac{22}{125}\right)$	$e\left(\frac{239}{250}\right)$	$e\left(\frac{84}{125}\right)$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{43}{50}\right)$	$e\left(\frac{64}{125}\right)$	$e\left(\frac{33}{125}\right)$	$e\left(\frac{23}{50}\right)$	$e\left(\frac{73}{250}\right)$
$\chi_{6002}(11,\cdot)$	6002.m	25	no	$1$	$1$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{25}\right)$
$\chi_{6002}(13,\cdot)$	6002.bb	600	no	$-1$	$1$	$e\left(\frac{43}{100}\right)$	$e\left(\frac{19}{50}\right)$	$e\left(\frac{81}{200}\right)$	$e\left(\frac{43}{50}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{120}\right)$	$e\left(\frac{81}{100}\right)$	$e\left(\frac{74}{75}\right)$	$e\left(\frac{101}{120}\right)$	$e\left(\frac{167}{200}\right)$
$\chi_{6002}(15,\cdot)$	6002.ba	500	no	$1$	$1$	$e\left(\frac{189}{250}\right)$	$e\left(\frac{112}{125}\right)$	$e\left(\frac{263}{500}\right)$	$e\left(\frac{64}{125}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{81}{100}\right)$	$e\left(\frac{163}{250}\right)$	$e\left(\frac{43}{125}\right)$	$e\left(\frac{41}{100}\right)$	$e\left(\frac{141}{500}\right)$
$\chi_{6002}(17,\cdot)$	6002.z	375	no	$1$	$1$	$e\left(\frac{79}{125}\right)$	$e\left(\frac{89}{125}\right)$	$e\left(\frac{9}{125}\right)$	$e\left(\frac{33}{125}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{74}{75}\right)$	$e\left(\frac{43}{125}\right)$	$e\left(\frac{338}{375}\right)$	$e\left(\frac{64}{75}\right)$	$e\left(\frac{88}{125}\right)$
$\chi_{6002}(19,\cdot)$	6002.bb	600	no	$-1$	$1$	$e\left(\frac{23}{100}\right)$	$e\left(\frac{9}{50}\right)$	$e\left(\frac{141}{200}\right)$	$e\left(\frac{23}{50}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{101}{120}\right)$	$e\left(\frac{41}{100}\right)$	$e\left(\frac{64}{75}\right)$	$e\left(\frac{1}{120}\right)$	$e\left(\frac{187}{200}\right)$
$\chi_{6002}(21,\cdot)$	6002.bd	1000	no	$-1$	$1$	$e\left(\frac{323}{500}\right)$	$e\left(\frac{159}{250}\right)$	$e\left(\frac{341}{1000}\right)$	$e\left(\frac{73}{250}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{167}{200}\right)$	$e\left(\frac{141}{500}\right)$	$e\left(\frac{88}{125}\right)$	$e\left(\frac{187}{200}\right)$	$e\left(\frac{987}{1000}\right)$
$\chi_{6002}(23,\cdot)$	6002.bf	3000	no	$-1$	$1$	$e\left(\frac{203}{500}\right)$	$e\left(\frac{199}{250}\right)$	$e\left(\frac{801}{1000}\right)$	$e\left(\frac{203}{250}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{161}{600}\right)$	$e\left(\frac{101}{500}\right)$	$e\left(\frac{229}{375}\right)$	$e\left(\frac{421}{600}\right)$	$e\left(\frac{207}{1000}\right)$
$\chi_{6002}(25,\cdot)$	6002.u	125	no	$1$	$1$	$e\left(\frac{22}{125}\right)$	$e\left(\frac{77}{125}\right)$	$e\left(\frac{12}{125}\right)$	$e\left(\frac{44}{125}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{99}{125}\right)$	$e\left(\frac{53}{125}\right)$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{34}{125}\right)$
$\chi_{6002}(27,\cdot)$	6002.ba	500	no	$1$	$1$	$e\left(\frac{1}{250}\right)$	$e\left(\frac{33}{125}\right)$	$e\left(\frac{467}{500}\right)$	$e\left(\frac{1}{125}\right)$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{29}{100}\right)$	$e\left(\frac{67}{250}\right)$	$e\left(\frac{112}{125}\right)$	$e\left(\frac{69}{100}\right)$	$e\left(\frac{469}{500}\right)$
$\chi_{6002}(29,\cdot)$	6002.bf	3000	no	$-1$	$1$	$e\left(\frac{129}{500}\right)$	$e\left(\frac{7}{250}\right)$	$e\left(\frac{243}{1000}\right)$	$e\left(\frac{129}{250}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{523}{600}\right)$	$e\left(\frac{143}{500}\right)$	$e\left(\frac{47}{375}\right)$	$e\left(\frac{503}{600}\right)$	$e\left(\frac{501}{1000}\right)$
$\chi_{6002}(31,\cdot)$	6002.z	375	no	$1$	$1$	$e\left(\frac{91}{125}\right)$	$e\left(\frac{6}{125}\right)$	$e\left(\frac{61}{125}\right)$	$e\left(\frac{57}{125}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{46}{75}\right)$	$e\left(\frac{97}{125}\right)$	$e\left(\frac{277}{375}\right)$	$e\left(\frac{56}{75}\right)$	$e\left(\frac{27}{125}\right)$
$\chi_{6002}(33,\cdot)$	6002.ba	500	no	$1$	$1$	$e\left(\frac{237}{250}\right)$	$e\left(\frac{71}{125}\right)$	$e\left(\frac{429}{500}\right)$	$e\left(\frac{112}{125}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{23}{100}\right)$	$e\left(\frac{129}{250}\right)$	$e\left(\frac{44}{125}\right)$	$e\left(\frac{3}{100}\right)$	$e\left(\frac{403}{500}\right)$
$\chi_{6002}(35,\cdot)$	6002.bd	1000	no	$-1$	$1$	$e\left(\frac{33}{500}\right)$	$e\left(\frac{89}{250}\right)$	$e\left(\frac{911}{1000}\right)$	$e\left(\frac{33}{250}\right)$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{157}{200}\right)$	$e\left(\frac{211}{500}\right)$	$e\left(\frac{98}{125}\right)$	$e\left(\frac{177}{200}\right)$	$e\left(\frac{977}{1000}\right)$
$\chi_{6002}(37,\cdot)$	6002.r	75	no	$1$	$1$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{22}{75}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{22}{25}\right)$
$\chi_{6002}(39,\cdot)$	6002.bf	3000	no	$-1$	$1$	$e\left(\frac{49}{500}\right)$	$e\left(\frac{117}{250}\right)$	$e\left(\frac{383}{1000}\right)$	$e\left(\frac{49}{250}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{263}{600}\right)$	$e\left(\frac{283}{500}\right)$	$e\left(\frac{232}{375}\right)$	$e\left(\frac{43}{600}\right)$	$e\left(\frac{481}{1000}\right)$
$\chi_{6002}(41,\cdot)$	6002.u	125	no	$1$	$1$	$e\left(\frac{69}{125}\right)$	$e\left(\frac{54}{125}\right)$	$e\left(\frac{49}{125}\right)$	$e\left(\frac{13}{125}\right)$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{123}{125}\right)$	$e\left(\frac{81}{125}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{118}{125}\right)$
$\chi_{6002}(43,\cdot)$	6002.bf	3000	no	$-1$	$1$	$e\left(\frac{457}{500}\right)$	$e\left(\frac{81}{250}\right)$	$e\left(\frac{419}{1000}\right)$	$e\left(\frac{207}{250}\right)$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{259}{600}\right)$	$e\left(\frac{119}{500}\right)$	$e\left(\frac{26}{375}\right)$	$e\left(\frac{599}{600}\right)$	$e\left(\frac{333}{1000}\right)$
$\chi_{6002}(45,\cdot)$	6002.u	125	no	$1$	$1$	$e\left(\frac{53}{125}\right)$	$e\left(\frac{123}{125}\right)$	$e\left(\frac{63}{125}\right)$	$e\left(\frac{106}{125}\right)$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{51}{125}\right)$	$e\left(\frac{122}{125}\right)$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{116}{125}\right)$
$\chi_{6002}(47,\cdot)$	6002.bd	1000	no	$-1$	$1$	$e\left(\frac{421}{500}\right)$	$e\left(\frac{143}{250}\right)$	$e\left(\frac{607}{1000}\right)$	$e\left(\frac{171}{250}\right)$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{109}{200}\right)$	$e\left(\frac{207}{500}\right)$	$e\left(\frac{76}{125}\right)$	$e\left(\frac{49}{200}\right)$	$e\left(\frac{449}{1000}\right)$
$\chi_{6002}(49,\cdot)$	6002.ba	500	no	$1$	$1$	$e\left(\frac{239}{250}\right)$	$e\left(\frac{12}{125}\right)$	$e\left(\frac{363}{500}\right)$	$e\left(\frac{114}{125}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{81}{100}\right)$	$e\left(\frac{13}{250}\right)$	$e\left(\frac{18}{125}\right)$	$e\left(\frac{41}{100}\right)$	$e\left(\frac{341}{500}\right)$
$\chi_{6002}(51,\cdot)$	6002.q	60	no	$1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{5}\right)$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{20}\right)$
$\chi_{6002}(53,\cdot)$	6002.bd	1000	no	$-1$	$1$	$e\left(\frac{451}{500}\right)$	$e\left(\frac{133}{250}\right)$	$e\left(\frac{117}{1000}\right)$	$e\left(\frac{201}{250}\right)$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{79}{200}\right)$	$e\left(\frac{217}{500}\right)$	$e\left(\frac{6}{125}\right)$	$e\left(\frac{19}{200}\right)$	$e\left(\frac{19}{1000}\right)$
$\chi_{6002}(55,\cdot)$	6002.x	250	no	$1$	$1$	$e\left(\frac{46}{125}\right)$	$e\left(\frac{36}{125}\right)$	$e\left(\frac{107}{250}\right)$	$e\left(\frac{92}{125}\right)$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{9}{50}\right)$	$e\left(\frac{82}{125}\right)$	$e\left(\frac{54}{125}\right)$	$e\left(\frac{49}{50}\right)$	$e\left(\frac{199}{250}\right)$
$\chi_{6002}(57,\cdot)$	6002.bf	3000	no	$-1$	$1$	$e\left(\frac{449}{500}\right)$	$e\left(\frac{67}{250}\right)$	$e\left(\frac{683}{1000}\right)$	$e\left(\frac{199}{250}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{163}{600}\right)$	$e\left(\frac{83}{500}\right)$	$e\left(\frac{182}{375}\right)$	$e\left(\frac{143}{600}\right)$	$e\left(\frac{581}{1000}\right)$
$\chi_{6002}(59,\cdot)$	6002.bc	750	no	$1$	$1$	$e\left(\frac{96}{125}\right)$	$e\left(\frac{86}{125}\right)$	$e\left(\frac{207}{250}\right)$	$e\left(\frac{67}{125}\right)$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{77}{150}\right)$	$e\left(\frac{57}{125}\right)$	$e\left(\frac{262}{375}\right)$	$e\left(\frac{97}{150}\right)$	$e\left(\frac{149}{250}\right)$
$\chi_{6002}(61,\cdot)$	6002.bc	750	no	$1$	$1$	$e\left(\frac{53}{125}\right)$	$e\left(\frac{123}{125}\right)$	$e\left(\frac{1}{250}\right)$	$e\left(\frac{106}{125}\right)$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{61}{150}\right)$	$e\left(\frac{51}{125}\right)$	$e\left(\frac{116}{375}\right)$	$e\left(\frac{71}{150}\right)$	$e\left(\frac{107}{250}\right)$
$\chi_{6002}(63,\cdot)$	6002.bd	1000	no	$-1$	$1$	$e\left(\frac{157}{500}\right)$	$e\left(\frac{181}{250}\right)$	$e\left(\frac{319}{1000}\right)$	$e\left(\frac{157}{250}\right)$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{53}{200}\right)$	$e\left(\frac{19}{500}\right)$	$e\left(\frac{42}{125}\right)$	$e\left(\frac{33}{200}\right)$	$e\left(\frac{633}{1000}\right)$

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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	$6002$
Structure	\(C_{3000}\)
Order	$3000$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{6002}(1,\cdot)\)	6002.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{6002}(3,\cdot)\)	6002.ba	500	no	\(1\)	\(1\)	\(e\left(\frac{167}{250}\right)\)	\(e\left(\frac{11}{125}\right)\)	\(e\left(\frac{489}{500}\right)\)	\(e\left(\frac{42}{125}\right)\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{43}{100}\right)\)	\(e\left(\frac{189}{250}\right)\)	\(e\left(\frac{79}{125}\right)\)	\(e\left(\frac{23}{100}\right)\)	\(e\left(\frac{323}{500}\right)\)
\(\chi_{6002}(5,\cdot)\)	6002.x	250	no	\(1\)	\(1\)	\(e\left(\frac{11}{125}\right)\)	\(e\left(\frac{101}{125}\right)\)	\(e\left(\frac{137}{250}\right)\)	\(e\left(\frac{22}{125}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{19}{50}\right)\)	\(e\left(\frac{112}{125}\right)\)	\(e\left(\frac{89}{125}\right)\)	\(e\left(\frac{9}{50}\right)\)	\(e\left(\frac{159}{250}\right)\)
\(\chi_{6002}(7,\cdot)\)	6002.bd	1000	no	\(-1\)	\(1\)	\(e\left(\frac{489}{500}\right)\)	\(e\left(\frac{137}{250}\right)\)	\(e\left(\frac{363}{1000}\right)\)	\(e\left(\frac{239}{250}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{81}{200}\right)\)	\(e\left(\frac{263}{500}\right)\)	\(e\left(\frac{9}{125}\right)\)	\(e\left(\frac{141}{200}\right)\)	\(e\left(\frac{341}{1000}\right)\)
\(\chi_{6002}(9,\cdot)\)	6002.x	250	no	\(1\)	\(1\)	\(e\left(\frac{42}{125}\right)\)	\(e\left(\frac{22}{125}\right)\)	\(e\left(\frac{239}{250}\right)\)	\(e\left(\frac{84}{125}\right)\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{43}{50}\right)\)	\(e\left(\frac{64}{125}\right)\)	\(e\left(\frac{33}{125}\right)\)	\(e\left(\frac{23}{50}\right)\)	\(e\left(\frac{73}{250}\right)\)
\(\chi_{6002}(11,\cdot)\)	6002.m	25	no	\(1\)	\(1\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{4}{25}\right)\)
\(\chi_{6002}(13,\cdot)\)	6002.bb	600	no	\(-1\)	\(1\)	\(e\left(\frac{43}{100}\right)\)	\(e\left(\frac{19}{50}\right)\)	\(e\left(\frac{81}{200}\right)\)	\(e\left(\frac{43}{50}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{120}\right)\)	\(e\left(\frac{81}{100}\right)\)	\(e\left(\frac{74}{75}\right)\)	\(e\left(\frac{101}{120}\right)\)	\(e\left(\frac{167}{200}\right)\)
\(\chi_{6002}(15,\cdot)\)	6002.ba	500	no	\(1\)	\(1\)	\(e\left(\frac{189}{250}\right)\)	\(e\left(\frac{112}{125}\right)\)	\(e\left(\frac{263}{500}\right)\)	\(e\left(\frac{64}{125}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{81}{100}\right)\)	\(e\left(\frac{163}{250}\right)\)	\(e\left(\frac{43}{125}\right)\)	\(e\left(\frac{41}{100}\right)\)	\(e\left(\frac{141}{500}\right)\)
\(\chi_{6002}(17,\cdot)\)	6002.z	375	no	\(1\)	\(1\)	\(e\left(\frac{79}{125}\right)\)	\(e\left(\frac{89}{125}\right)\)	\(e\left(\frac{9}{125}\right)\)	\(e\left(\frac{33}{125}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{74}{75}\right)\)	\(e\left(\frac{43}{125}\right)\)	\(e\left(\frac{338}{375}\right)\)	\(e\left(\frac{64}{75}\right)\)	\(e\left(\frac{88}{125}\right)\)
\(\chi_{6002}(19,\cdot)\)	6002.bb	600	no	\(-1\)	\(1\)	\(e\left(\frac{23}{100}\right)\)	\(e\left(\frac{9}{50}\right)\)	\(e\left(\frac{141}{200}\right)\)	\(e\left(\frac{23}{50}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{101}{120}\right)\)	\(e\left(\frac{41}{100}\right)\)	\(e\left(\frac{64}{75}\right)\)	\(e\left(\frac{1}{120}\right)\)	\(e\left(\frac{187}{200}\right)\)
\(\chi_{6002}(21,\cdot)\)	6002.bd	1000	no	\(-1\)	\(1\)	\(e\left(\frac{323}{500}\right)\)	\(e\left(\frac{159}{250}\right)\)	\(e\left(\frac{341}{1000}\right)\)	\(e\left(\frac{73}{250}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{167}{200}\right)\)	\(e\left(\frac{141}{500}\right)\)	\(e\left(\frac{88}{125}\right)\)	\(e\left(\frac{187}{200}\right)\)	\(e\left(\frac{987}{1000}\right)\)
\(\chi_{6002}(23,\cdot)\)	6002.bf	3000	no	\(-1\)	\(1\)	\(e\left(\frac{203}{500}\right)\)	\(e\left(\frac{199}{250}\right)\)	\(e\left(\frac{801}{1000}\right)\)	\(e\left(\frac{203}{250}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{161}{600}\right)\)	\(e\left(\frac{101}{500}\right)\)	\(e\left(\frac{229}{375}\right)\)	\(e\left(\frac{421}{600}\right)\)	\(e\left(\frac{207}{1000}\right)\)
\(\chi_{6002}(25,\cdot)\)	6002.u	125	no	\(1\)	\(1\)	\(e\left(\frac{22}{125}\right)\)	\(e\left(\frac{77}{125}\right)\)	\(e\left(\frac{12}{125}\right)\)	\(e\left(\frac{44}{125}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{99}{125}\right)\)	\(e\left(\frac{53}{125}\right)\)	\(e\left(\frac{9}{25}\right)\)	\(e\left(\frac{34}{125}\right)\)
\(\chi_{6002}(27,\cdot)\)	6002.ba	500	no	\(1\)	\(1\)	\(e\left(\frac{1}{250}\right)\)	\(e\left(\frac{33}{125}\right)\)	\(e\left(\frac{467}{500}\right)\)	\(e\left(\frac{1}{125}\right)\)	\(e\left(\frac{21}{25}\right)\)	\(e\left(\frac{29}{100}\right)\)	\(e\left(\frac{67}{250}\right)\)	\(e\left(\frac{112}{125}\right)\)	\(e\left(\frac{69}{100}\right)\)	\(e\left(\frac{469}{500}\right)\)
\(\chi_{6002}(29,\cdot)\)	6002.bf	3000	no	\(-1\)	\(1\)	\(e\left(\frac{129}{500}\right)\)	\(e\left(\frac{7}{250}\right)\)	\(e\left(\frac{243}{1000}\right)\)	\(e\left(\frac{129}{250}\right)\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{523}{600}\right)\)	\(e\left(\frac{143}{500}\right)\)	\(e\left(\frac{47}{375}\right)\)	\(e\left(\frac{503}{600}\right)\)	\(e\left(\frac{501}{1000}\right)\)
\(\chi_{6002}(31,\cdot)\)	6002.z	375	no	\(1\)	\(1\)	\(e\left(\frac{91}{125}\right)\)	\(e\left(\frac{6}{125}\right)\)	\(e\left(\frac{61}{125}\right)\)	\(e\left(\frac{57}{125}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{46}{75}\right)\)	\(e\left(\frac{97}{125}\right)\)	\(e\left(\frac{277}{375}\right)\)	\(e\left(\frac{56}{75}\right)\)	\(e\left(\frac{27}{125}\right)\)
\(\chi_{6002}(33,\cdot)\)	6002.ba	500	no	\(1\)	\(1\)	\(e\left(\frac{237}{250}\right)\)	\(e\left(\frac{71}{125}\right)\)	\(e\left(\frac{429}{500}\right)\)	\(e\left(\frac{112}{125}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{23}{100}\right)\)	\(e\left(\frac{129}{250}\right)\)	\(e\left(\frac{44}{125}\right)\)	\(e\left(\frac{3}{100}\right)\)	\(e\left(\frac{403}{500}\right)\)
\(\chi_{6002}(35,\cdot)\)	6002.bd	1000	no	\(-1\)	\(1\)	\(e\left(\frac{33}{500}\right)\)	\(e\left(\frac{89}{250}\right)\)	\(e\left(\frac{911}{1000}\right)\)	\(e\left(\frac{33}{250}\right)\)	\(e\left(\frac{9}{25}\right)\)	\(e\left(\frac{157}{200}\right)\)	\(e\left(\frac{211}{500}\right)\)	\(e\left(\frac{98}{125}\right)\)	\(e\left(\frac{177}{200}\right)\)	\(e\left(\frac{977}{1000}\right)\)
\(\chi_{6002}(37,\cdot)\)	6002.r	75	no	\(1\)	\(1\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{16}{25}\right)\)	\(e\left(\frac{21}{25}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{22}{75}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{22}{25}\right)\)
\(\chi_{6002}(39,\cdot)\)	6002.bf	3000	no	\(-1\)	\(1\)	\(e\left(\frac{49}{500}\right)\)	\(e\left(\frac{117}{250}\right)\)	\(e\left(\frac{383}{1000}\right)\)	\(e\left(\frac{49}{250}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{263}{600}\right)\)	\(e\left(\frac{283}{500}\right)\)	\(e\left(\frac{232}{375}\right)\)	\(e\left(\frac{43}{600}\right)\)	\(e\left(\frac{481}{1000}\right)\)
\(\chi_{6002}(41,\cdot)\)	6002.u	125	no	\(1\)	\(1\)	\(e\left(\frac{69}{125}\right)\)	\(e\left(\frac{54}{125}\right)\)	\(e\left(\frac{49}{125}\right)\)	\(e\left(\frac{13}{125}\right)\)	\(e\left(\frac{23}{25}\right)\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{123}{125}\right)\)	\(e\left(\frac{81}{125}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{118}{125}\right)\)
\(\chi_{6002}(43,\cdot)\)	6002.bf	3000	no	\(-1\)	\(1\)	\(e\left(\frac{457}{500}\right)\)	\(e\left(\frac{81}{250}\right)\)	\(e\left(\frac{419}{1000}\right)\)	\(e\left(\frac{207}{250}\right)\)	\(e\left(\frac{11}{25}\right)\)	\(e\left(\frac{259}{600}\right)\)	\(e\left(\frac{119}{500}\right)\)	\(e\left(\frac{26}{375}\right)\)	\(e\left(\frac{599}{600}\right)\)	\(e\left(\frac{333}{1000}\right)\)
\(\chi_{6002}(45,\cdot)\)	6002.u	125	no	\(1\)	\(1\)	\(e\left(\frac{53}{125}\right)\)	\(e\left(\frac{123}{125}\right)\)	\(e\left(\frac{63}{125}\right)\)	\(e\left(\frac{106}{125}\right)\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{6}{25}\right)\)	\(e\left(\frac{51}{125}\right)\)	\(e\left(\frac{122}{125}\right)\)	\(e\left(\frac{16}{25}\right)\)	\(e\left(\frac{116}{125}\right)\)
\(\chi_{6002}(47,\cdot)\)	6002.bd	1000	no	\(-1\)	\(1\)	\(e\left(\frac{421}{500}\right)\)	\(e\left(\frac{143}{250}\right)\)	\(e\left(\frac{607}{1000}\right)\)	\(e\left(\frac{171}{250}\right)\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{109}{200}\right)\)	\(e\left(\frac{207}{500}\right)\)	\(e\left(\frac{76}{125}\right)\)	\(e\left(\frac{49}{200}\right)\)	\(e\left(\frac{449}{1000}\right)\)
\(\chi_{6002}(49,\cdot)\)	6002.ba	500	no	\(1\)	\(1\)	\(e\left(\frac{239}{250}\right)\)	\(e\left(\frac{12}{125}\right)\)	\(e\left(\frac{363}{500}\right)\)	\(e\left(\frac{114}{125}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{81}{100}\right)\)	\(e\left(\frac{13}{250}\right)\)	\(e\left(\frac{18}{125}\right)\)	\(e\left(\frac{41}{100}\right)\)	\(e\left(\frac{341}{500}\right)\)
\(\chi_{6002}(51,\cdot)\)	6002.q	60	no	\(1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{20}\right)\)
\(\chi_{6002}(53,\cdot)\)	6002.bd	1000	no	\(-1\)	\(1\)	\(e\left(\frac{451}{500}\right)\)	\(e\left(\frac{133}{250}\right)\)	\(e\left(\frac{117}{1000}\right)\)	\(e\left(\frac{201}{250}\right)\)	\(e\left(\frac{23}{25}\right)\)	\(e\left(\frac{79}{200}\right)\)	\(e\left(\frac{217}{500}\right)\)	\(e\left(\frac{6}{125}\right)\)	\(e\left(\frac{19}{200}\right)\)	\(e\left(\frac{19}{1000}\right)\)
\(\chi_{6002}(55,\cdot)\)	6002.x	250	no	\(1\)	\(1\)	\(e\left(\frac{46}{125}\right)\)	\(e\left(\frac{36}{125}\right)\)	\(e\left(\frac{107}{250}\right)\)	\(e\left(\frac{92}{125}\right)\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{9}{50}\right)\)	\(e\left(\frac{82}{125}\right)\)	\(e\left(\frac{54}{125}\right)\)	\(e\left(\frac{49}{50}\right)\)	\(e\left(\frac{199}{250}\right)\)
\(\chi_{6002}(57,\cdot)\)	6002.bf	3000	no	\(-1\)	\(1\)	\(e\left(\frac{449}{500}\right)\)	\(e\left(\frac{67}{250}\right)\)	\(e\left(\frac{683}{1000}\right)\)	\(e\left(\frac{199}{250}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{163}{600}\right)\)	\(e\left(\frac{83}{500}\right)\)	\(e\left(\frac{182}{375}\right)\)	\(e\left(\frac{143}{600}\right)\)	\(e\left(\frac{581}{1000}\right)\)
\(\chi_{6002}(59,\cdot)\)	6002.bc	750	no	\(1\)	\(1\)	\(e\left(\frac{96}{125}\right)\)	\(e\left(\frac{86}{125}\right)\)	\(e\left(\frac{207}{250}\right)\)	\(e\left(\frac{67}{125}\right)\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{77}{150}\right)\)	\(e\left(\frac{57}{125}\right)\)	\(e\left(\frac{262}{375}\right)\)	\(e\left(\frac{97}{150}\right)\)	\(e\left(\frac{149}{250}\right)\)
\(\chi_{6002}(61,\cdot)\)	6002.bc	750	no	\(1\)	\(1\)	\(e\left(\frac{53}{125}\right)\)	\(e\left(\frac{123}{125}\right)\)	\(e\left(\frac{1}{250}\right)\)	\(e\left(\frac{106}{125}\right)\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{61}{150}\right)\)	\(e\left(\frac{51}{125}\right)\)	\(e\left(\frac{116}{375}\right)\)	\(e\left(\frac{71}{150}\right)\)	\(e\left(\frac{107}{250}\right)\)
\(\chi_{6002}(63,\cdot)\)	6002.bd	1000	no	\(-1\)	\(1\)	\(e\left(\frac{157}{500}\right)\)	\(e\left(\frac{181}{250}\right)\)	\(e\left(\frac{319}{1000}\right)\)	\(e\left(\frac{157}{250}\right)\)	\(e\left(\frac{11}{25}\right)\)	\(e\left(\frac{53}{200}\right)\)	\(e\left(\frac{19}{500}\right)\)	\(e\left(\frac{42}{125}\right)\)	\(e\left(\frac{33}{200}\right)\)	\(e\left(\frac{633}{1000}\right)\)

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.