LMFDB - Group of Dirichlet characters of modulus 607

Show commands: PariGP / SageMath

sage: H = DirichletGroup(607)

pari: g = idealstar(,607,2)

Character group

sage: G.order() pari: g.no
Order	=	606
sage: H.invariants() pari: g.cyc
Structure	=	$C_{606}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{607}(3,\cdot)$

First 32 of 606 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{607}(1,\cdot)$	607.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{607}(2,\cdot)$	607.g	303	yes	$1$	$1$	$e\left(\frac{242}{303}\right)$	$e\left(\frac{292}{303}\right)$	$e\left(\frac{181}{303}\right)$	$e\left(\frac{55}{303}\right)$	$e\left(\frac{77}{101}\right)$	$e\left(\frac{73}{101}\right)$	$e\left(\frac{40}{101}\right)$	$e\left(\frac{281}{303}\right)$	$e\left(\frac{99}{101}\right)$	$e\left(\frac{245}{303}\right)$
$\chi_{607}(3,\cdot)$	607.h	606	yes	$-1$	$1$	$e\left(\frac{292}{303}\right)$	$e\left(\frac{1}{606}\right)$	$e\left(\frac{281}{303}\right)$	$e\left(\frac{601}{606}\right)$	$e\left(\frac{195}{202}\right)$	$e\left(\frac{38}{101}\right)$	$e\left(\frac{90}{101}\right)$	$e\left(\frac{1}{303}\right)$	$e\left(\frac{193}{202}\right)$	$e\left(\frac{223}{303}\right)$
$\chi_{607}(4,\cdot)$	607.g	303	yes	$1$	$1$	$e\left(\frac{181}{303}\right)$	$e\left(\frac{281}{303}\right)$	$e\left(\frac{59}{303}\right)$	$e\left(\frac{110}{303}\right)$	$e\left(\frac{53}{101}\right)$	$e\left(\frac{45}{101}\right)$	$e\left(\frac{80}{101}\right)$	$e\left(\frac{259}{303}\right)$	$e\left(\frac{97}{101}\right)$	$e\left(\frac{187}{303}\right)$
$\chi_{607}(5,\cdot)$	607.h	606	yes	$-1$	$1$	$e\left(\frac{55}{303}\right)$	$e\left(\frac{601}{606}\right)$	$e\left(\frac{110}{303}\right)$	$e\left(\frac{25}{606}\right)$	$e\left(\frac{35}{202}\right)$	$e\left(\frac{12}{101}\right)$	$e\left(\frac{55}{101}\right)$	$e\left(\frac{298}{303}\right)$	$e\left(\frac{45}{202}\right)$	$e\left(\frac{97}{303}\right)$
$\chi_{607}(6,\cdot)$	607.f	202	yes	$-1$	$1$	$e\left(\frac{77}{101}\right)$	$e\left(\frac{195}{202}\right)$	$e\left(\frac{53}{101}\right)$	$e\left(\frac{35}{202}\right)$	$e\left(\frac{147}{202}\right)$	$e\left(\frac{10}{101}\right)$	$e\left(\frac{29}{101}\right)$	$e\left(\frac{94}{101}\right)$	$e\left(\frac{189}{202}\right)$	$e\left(\frac{55}{101}\right)$
$\chi_{607}(7,\cdot)$	607.e	101	yes	$1$	$1$	$e\left(\frac{73}{101}\right)$	$e\left(\frac{38}{101}\right)$	$e\left(\frac{45}{101}\right)$	$e\left(\frac{12}{101}\right)$	$e\left(\frac{10}{101}\right)$	$e\left(\frac{79}{101}\right)$	$e\left(\frac{17}{101}\right)$	$e\left(\frac{76}{101}\right)$	$e\left(\frac{85}{101}\right)$	$e\left(\frac{81}{101}\right)$
$\chi_{607}(8,\cdot)$	607.e	101	yes	$1$	$1$	$e\left(\frac{40}{101}\right)$	$e\left(\frac{90}{101}\right)$	$e\left(\frac{80}{101}\right)$	$e\left(\frac{55}{101}\right)$	$e\left(\frac{29}{101}\right)$	$e\left(\frac{17}{101}\right)$	$e\left(\frac{19}{101}\right)$	$e\left(\frac{79}{101}\right)$	$e\left(\frac{95}{101}\right)$	$e\left(\frac{43}{101}\right)$
$\chi_{607}(9,\cdot)$	607.g	303	yes	$1$	$1$	$e\left(\frac{281}{303}\right)$	$e\left(\frac{1}{303}\right)$	$e\left(\frac{259}{303}\right)$	$e\left(\frac{298}{303}\right)$	$e\left(\frac{94}{101}\right)$	$e\left(\frac{76}{101}\right)$	$e\left(\frac{79}{101}\right)$	$e\left(\frac{2}{303}\right)$	$e\left(\frac{92}{101}\right)$	$e\left(\frac{143}{303}\right)$
$\chi_{607}(10,\cdot)$	607.f	202	yes	$-1$	$1$	$e\left(\frac{99}{101}\right)$	$e\left(\frac{193}{202}\right)$	$e\left(\frac{97}{101}\right)$	$e\left(\frac{45}{202}\right)$	$e\left(\frac{189}{202}\right)$	$e\left(\frac{85}{101}\right)$	$e\left(\frac{95}{101}\right)$	$e\left(\frac{92}{101}\right)$	$e\left(\frac{41}{202}\right)$	$e\left(\frac{13}{101}\right)$
$\chi_{607}(11,\cdot)$	607.g	303	yes	$1$	$1$	$e\left(\frac{245}{303}\right)$	$e\left(\frac{223}{303}\right)$	$e\left(\frac{187}{303}\right)$	$e\left(\frac{97}{303}\right)$	$e\left(\frac{55}{101}\right)$	$e\left(\frac{81}{101}\right)$	$e\left(\frac{43}{101}\right)$	$e\left(\frac{143}{303}\right)$	$e\left(\frac{13}{101}\right)$	$e\left(\frac{74}{303}\right)$
$\chi_{607}(12,\cdot)$	607.h	606	yes	$-1$	$1$	$e\left(\frac{170}{303}\right)$	$e\left(\frac{563}{606}\right)$	$e\left(\frac{37}{303}\right)$	$e\left(\frac{215}{606}\right)$	$e\left(\frac{99}{202}\right)$	$e\left(\frac{83}{101}\right)$	$e\left(\frac{69}{101}\right)$	$e\left(\frac{260}{303}\right)$	$e\left(\frac{185}{202}\right)$	$e\left(\frac{107}{303}\right)$
$\chi_{607}(13,\cdot)$	607.g	303	yes	$1$	$1$	$e\left(\frac{151}{303}\right)$	$e\left(\frac{62}{303}\right)$	$e\left(\frac{302}{303}\right)$	$e\left(\frac{296}{303}\right)$	$e\left(\frac{71}{101}\right)$	$e\left(\frac{66}{101}\right)$	$e\left(\frac{50}{101}\right)$	$e\left(\frac{124}{303}\right)$	$e\left(\frac{48}{101}\right)$	$e\left(\frac{79}{303}\right)$
$\chi_{607}(14,\cdot)$	607.g	303	yes	$1$	$1$	$e\left(\frac{158}{303}\right)$	$e\left(\frac{103}{303}\right)$	$e\left(\frac{13}{303}\right)$	$e\left(\frac{91}{303}\right)$	$e\left(\frac{87}{101}\right)$	$e\left(\frac{51}{101}\right)$	$e\left(\frac{57}{101}\right)$	$e\left(\frac{206}{303}\right)$	$e\left(\frac{83}{101}\right)$	$e\left(\frac{185}{303}\right)$
$\chi_{607}(15,\cdot)$	607.g	303	yes	$1$	$1$	$e\left(\frac{44}{303}\right)$	$e\left(\frac{301}{303}\right)$	$e\left(\frac{88}{303}\right)$	$e\left(\frac{10}{303}\right)$	$e\left(\frac{14}{101}\right)$	$e\left(\frac{50}{101}\right)$	$e\left(\frac{44}{101}\right)$	$e\left(\frac{299}{303}\right)$	$e\left(\frac{18}{101}\right)$	$e\left(\frac{17}{303}\right)$
$\chi_{607}(16,\cdot)$	607.g	303	yes	$1$	$1$	$e\left(\frac{59}{303}\right)$	$e\left(\frac{259}{303}\right)$	$e\left(\frac{118}{303}\right)$	$e\left(\frac{220}{303}\right)$	$e\left(\frac{5}{101}\right)$	$e\left(\frac{90}{101}\right)$	$e\left(\frac{59}{101}\right)$	$e\left(\frac{215}{303}\right)$	$e\left(\frac{93}{101}\right)$	$e\left(\frac{71}{303}\right)$
$\chi_{607}(17,\cdot)$	607.h	606	yes	$-1$	$1$	$e\left(\frac{199}{303}\right)$	$e\left(\frac{37}{606}\right)$	$e\left(\frac{95}{303}\right)$	$e\left(\frac{421}{606}\right)$	$e\left(\frac{145}{202}\right)$	$e\left(\frac{93}{101}\right)$	$e\left(\frac{98}{101}\right)$	$e\left(\frac{37}{303}\right)$	$e\left(\frac{71}{202}\right)$	$e\left(\frac{70}{303}\right)$
$\chi_{607}(18,\cdot)$	607.g	303	yes	$1$	$1$	$e\left(\frac{220}{303}\right)$	$e\left(\frac{293}{303}\right)$	$e\left(\frac{137}{303}\right)$	$e\left(\frac{50}{303}\right)$	$e\left(\frac{70}{101}\right)$	$e\left(\frac{48}{101}\right)$	$e\left(\frac{18}{101}\right)$	$e\left(\frac{283}{303}\right)$	$e\left(\frac{90}{101}\right)$	$e\left(\frac{85}{303}\right)$
$\chi_{607}(19,\cdot)$	607.g	303	yes	$1$	$1$	$e\left(\frac{2}{303}\right)$	$e\left(\frac{55}{303}\right)$	$e\left(\frac{4}{303}\right)$	$e\left(\frac{28}{303}\right)$	$e\left(\frac{19}{101}\right)$	$e\left(\frac{39}{101}\right)$	$e\left(\frac{2}{101}\right)$	$e\left(\frac{110}{303}\right)$	$e\left(\frac{10}{101}\right)$	$e\left(\frac{290}{303}\right)$
$\chi_{607}(20,\cdot)$	607.h	606	yes	$-1$	$1$	$e\left(\frac{236}{303}\right)$	$e\left(\frac{557}{606}\right)$	$e\left(\frac{169}{303}\right)$	$e\left(\frac{245}{606}\right)$	$e\left(\frac{141}{202}\right)$	$e\left(\frac{57}{101}\right)$	$e\left(\frac{34}{101}\right)$	$e\left(\frac{254}{303}\right)$	$e\left(\frac{37}{202}\right)$	$e\left(\frac{284}{303}\right)$
$\chi_{607}(21,\cdot)$	607.h	606	yes	$-1$	$1$	$e\left(\frac{208}{303}\right)$	$e\left(\frac{229}{606}\right)$	$e\left(\frac{113}{303}\right)$	$e\left(\frac{67}{606}\right)$	$e\left(\frac{13}{202}\right)$	$e\left(\frac{16}{101}\right)$	$e\left(\frac{6}{101}\right)$	$e\left(\frac{229}{303}\right)$	$e\left(\frac{161}{202}\right)$	$e\left(\frac{163}{303}\right)$
$\chi_{607}(22,\cdot)$	607.g	303	yes	$1$	$1$	$e\left(\frac{184}{303}\right)$	$e\left(\frac{212}{303}\right)$	$e\left(\frac{65}{303}\right)$	$e\left(\frac{152}{303}\right)$	$e\left(\frac{31}{101}\right)$	$e\left(\frac{53}{101}\right)$	$e\left(\frac{83}{101}\right)$	$e\left(\frac{121}{303}\right)$	$e\left(\frac{11}{101}\right)$	$e\left(\frac{16}{303}\right)$
$\chi_{607}(23,\cdot)$	607.h	606	yes	$-1$	$1$	$e\left(\frac{191}{303}\right)$	$e\left(\frac{203}{606}\right)$	$e\left(\frac{79}{303}\right)$	$e\left(\frac{197}{606}\right)$	$e\left(\frac{195}{202}\right)$	$e\left(\frac{38}{101}\right)$	$e\left(\frac{90}{101}\right)$	$e\left(\frac{203}{303}\right)$	$e\left(\frac{193}{202}\right)$	$e\left(\frac{122}{303}\right)$
$\chi_{607}(24,\cdot)$	607.h	606	yes	$-1$	$1$	$e\left(\frac{109}{303}\right)$	$e\left(\frac{541}{606}\right)$	$e\left(\frac{218}{303}\right)$	$e\left(\frac{325}{606}\right)$	$e\left(\frac{51}{202}\right)$	$e\left(\frac{55}{101}\right)$	$e\left(\frac{8}{101}\right)$	$e\left(\frac{238}{303}\right)$	$e\left(\frac{181}{202}\right)$	$e\left(\frac{49}{303}\right)$
$\chi_{607}(25,\cdot)$	607.g	303	yes	$1$	$1$	$e\left(\frac{110}{303}\right)$	$e\left(\frac{298}{303}\right)$	$e\left(\frac{220}{303}\right)$	$e\left(\frac{25}{303}\right)$	$e\left(\frac{35}{101}\right)$	$e\left(\frac{24}{101}\right)$	$e\left(\frac{9}{101}\right)$	$e\left(\frac{293}{303}\right)$	$e\left(\frac{45}{101}\right)$	$e\left(\frac{194}{303}\right)$
$\chi_{607}(26,\cdot)$	607.e	101	yes	$1$	$1$	$e\left(\frac{30}{101}\right)$	$e\left(\frac{17}{101}\right)$	$e\left(\frac{60}{101}\right)$	$e\left(\frac{16}{101}\right)$	$e\left(\frac{47}{101}\right)$	$e\left(\frac{38}{101}\right)$	$e\left(\frac{90}{101}\right)$	$e\left(\frac{34}{101}\right)$	$e\left(\frac{46}{101}\right)$	$e\left(\frac{7}{101}\right)$
$\chi_{607}(27,\cdot)$	607.f	202	yes	$-1$	$1$	$e\left(\frac{90}{101}\right)$	$e\left(\frac{1}{202}\right)$	$e\left(\frac{79}{101}\right)$	$e\left(\frac{197}{202}\right)$	$e\left(\frac{181}{202}\right)$	$e\left(\frac{13}{101}\right)$	$e\left(\frac{68}{101}\right)$	$e\left(\frac{1}{101}\right)$	$e\left(\frac{175}{202}\right)$	$e\left(\frac{21}{101}\right)$
$\chi_{607}(28,\cdot)$	607.g	303	yes	$1$	$1$	$e\left(\frac{97}{303}\right)$	$e\left(\frac{92}{303}\right)$	$e\left(\frac{194}{303}\right)$	$e\left(\frac{146}{303}\right)$	$e\left(\frac{63}{101}\right)$	$e\left(\frac{23}{101}\right)$	$e\left(\frac{97}{101}\right)$	$e\left(\frac{184}{303}\right)$	$e\left(\frac{81}{101}\right)$	$e\left(\frac{127}{303}\right)$
$\chi_{607}(29,\cdot)$	607.h	606	yes	$-1$	$1$	$e\left(\frac{34}{303}\right)$	$e\left(\frac{355}{606}\right)$	$e\left(\frac{68}{303}\right)$	$e\left(\frac{43}{606}\right)$	$e\left(\frac{141}{202}\right)$	$e\left(\frac{57}{101}\right)$	$e\left(\frac{34}{101}\right)$	$e\left(\frac{52}{303}\right)$	$e\left(\frac{37}{202}\right)$	$e\left(\frac{82}{303}\right)$
$\chi_{607}(30,\cdot)$	607.g	303	yes	$1$	$1$	$e\left(\frac{286}{303}\right)$	$e\left(\frac{290}{303}\right)$	$e\left(\frac{269}{303}\right)$	$e\left(\frac{65}{303}\right)$	$e\left(\frac{91}{101}\right)$	$e\left(\frac{22}{101}\right)$	$e\left(\frac{84}{101}\right)$	$e\left(\frac{277}{303}\right)$	$e\left(\frac{16}{101}\right)$	$e\left(\frac{262}{303}\right)$
$\chi_{607}(31,\cdot)$	607.h	606	yes	$-1$	$1$	$e\left(\frac{218}{303}\right)$	$e\left(\frac{173}{606}\right)$	$e\left(\frac{133}{303}\right)$	$e\left(\frac{347}{606}\right)$	$e\left(\frac{1}{202}\right)$	$e\left(\frac{9}{101}\right)$	$e\left(\frac{16}{101}\right)$	$e\left(\frac{173}{303}\right)$	$e\left(\frac{59}{202}\right)$	$e\left(\frac{98}{303}\right)$
$\chi_{607}(32,\cdot)$	607.g	303	yes	$1$	$1$	$e\left(\frac{301}{303}\right)$	$e\left(\frac{248}{303}\right)$	$e\left(\frac{299}{303}\right)$	$e\left(\frac{275}{303}\right)$	$e\left(\frac{82}{101}\right)$	$e\left(\frac{62}{101}\right)$	$e\left(\frac{99}{101}\right)$	$e\left(\frac{193}{303}\right)$	$e\left(\frac{91}{101}\right)$	$e\left(\frac{13}{303}\right)$

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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	$607$
Structure	\(C_{606}\)
Order	$606$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{607}(1,\cdot)\)	607.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{607}(2,\cdot)\)	607.g	303	yes	\(1\)	\(1\)	\(e\left(\frac{242}{303}\right)\)	\(e\left(\frac{292}{303}\right)\)	\(e\left(\frac{181}{303}\right)\)	\(e\left(\frac{55}{303}\right)\)	\(e\left(\frac{77}{101}\right)\)	\(e\left(\frac{73}{101}\right)\)	\(e\left(\frac{40}{101}\right)\)	\(e\left(\frac{281}{303}\right)\)	\(e\left(\frac{99}{101}\right)\)	\(e\left(\frac{245}{303}\right)\)
\(\chi_{607}(3,\cdot)\)	607.h	606	yes	\(-1\)	\(1\)	\(e\left(\frac{292}{303}\right)\)	\(e\left(\frac{1}{606}\right)\)	\(e\left(\frac{281}{303}\right)\)	\(e\left(\frac{601}{606}\right)\)	\(e\left(\frac{195}{202}\right)\)	\(e\left(\frac{38}{101}\right)\)	\(e\left(\frac{90}{101}\right)\)	\(e\left(\frac{1}{303}\right)\)	\(e\left(\frac{193}{202}\right)\)	\(e\left(\frac{223}{303}\right)\)
\(\chi_{607}(4,\cdot)\)	607.g	303	yes	\(1\)	\(1\)	\(e\left(\frac{181}{303}\right)\)	\(e\left(\frac{281}{303}\right)\)	\(e\left(\frac{59}{303}\right)\)	\(e\left(\frac{110}{303}\right)\)	\(e\left(\frac{53}{101}\right)\)	\(e\left(\frac{45}{101}\right)\)	\(e\left(\frac{80}{101}\right)\)	\(e\left(\frac{259}{303}\right)\)	\(e\left(\frac{97}{101}\right)\)	\(e\left(\frac{187}{303}\right)\)
\(\chi_{607}(5,\cdot)\)	607.h	606	yes	\(-1\)	\(1\)	\(e\left(\frac{55}{303}\right)\)	\(e\left(\frac{601}{606}\right)\)	\(e\left(\frac{110}{303}\right)\)	\(e\left(\frac{25}{606}\right)\)	\(e\left(\frac{35}{202}\right)\)	\(e\left(\frac{12}{101}\right)\)	\(e\left(\frac{55}{101}\right)\)	\(e\left(\frac{298}{303}\right)\)	\(e\left(\frac{45}{202}\right)\)	\(e\left(\frac{97}{303}\right)\)
\(\chi_{607}(6,\cdot)\)	607.f	202	yes	\(-1\)	\(1\)	\(e\left(\frac{77}{101}\right)\)	\(e\left(\frac{195}{202}\right)\)	\(e\left(\frac{53}{101}\right)\)	\(e\left(\frac{35}{202}\right)\)	\(e\left(\frac{147}{202}\right)\)	\(e\left(\frac{10}{101}\right)\)	\(e\left(\frac{29}{101}\right)\)	\(e\left(\frac{94}{101}\right)\)	\(e\left(\frac{189}{202}\right)\)	\(e\left(\frac{55}{101}\right)\)
\(\chi_{607}(7,\cdot)\)	607.e	101	yes	\(1\)	\(1\)	\(e\left(\frac{73}{101}\right)\)	\(e\left(\frac{38}{101}\right)\)	\(e\left(\frac{45}{101}\right)\)	\(e\left(\frac{12}{101}\right)\)	\(e\left(\frac{10}{101}\right)\)	\(e\left(\frac{79}{101}\right)\)	\(e\left(\frac{17}{101}\right)\)	\(e\left(\frac{76}{101}\right)\)	\(e\left(\frac{85}{101}\right)\)	\(e\left(\frac{81}{101}\right)\)
\(\chi_{607}(8,\cdot)\)	607.e	101	yes	\(1\)	\(1\)	\(e\left(\frac{40}{101}\right)\)	\(e\left(\frac{90}{101}\right)\)	\(e\left(\frac{80}{101}\right)\)	\(e\left(\frac{55}{101}\right)\)	\(e\left(\frac{29}{101}\right)\)	\(e\left(\frac{17}{101}\right)\)	\(e\left(\frac{19}{101}\right)\)	\(e\left(\frac{79}{101}\right)\)	\(e\left(\frac{95}{101}\right)\)	\(e\left(\frac{43}{101}\right)\)
\(\chi_{607}(9,\cdot)\)	607.g	303	yes	\(1\)	\(1\)	\(e\left(\frac{281}{303}\right)\)	\(e\left(\frac{1}{303}\right)\)	\(e\left(\frac{259}{303}\right)\)	\(e\left(\frac{298}{303}\right)\)	\(e\left(\frac{94}{101}\right)\)	\(e\left(\frac{76}{101}\right)\)	\(e\left(\frac{79}{101}\right)\)	\(e\left(\frac{2}{303}\right)\)	\(e\left(\frac{92}{101}\right)\)	\(e\left(\frac{143}{303}\right)\)
\(\chi_{607}(10,\cdot)\)	607.f	202	yes	\(-1\)	\(1\)	\(e\left(\frac{99}{101}\right)\)	\(e\left(\frac{193}{202}\right)\)	\(e\left(\frac{97}{101}\right)\)	\(e\left(\frac{45}{202}\right)\)	\(e\left(\frac{189}{202}\right)\)	\(e\left(\frac{85}{101}\right)\)	\(e\left(\frac{95}{101}\right)\)	\(e\left(\frac{92}{101}\right)\)	\(e\left(\frac{41}{202}\right)\)	\(e\left(\frac{13}{101}\right)\)
\(\chi_{607}(11,\cdot)\)	607.g	303	yes	\(1\)	\(1\)	\(e\left(\frac{245}{303}\right)\)	\(e\left(\frac{223}{303}\right)\)	\(e\left(\frac{187}{303}\right)\)	\(e\left(\frac{97}{303}\right)\)	\(e\left(\frac{55}{101}\right)\)	\(e\left(\frac{81}{101}\right)\)	\(e\left(\frac{43}{101}\right)\)	\(e\left(\frac{143}{303}\right)\)	\(e\left(\frac{13}{101}\right)\)	\(e\left(\frac{74}{303}\right)\)
\(\chi_{607}(12,\cdot)\)	607.h	606	yes	\(-1\)	\(1\)	\(e\left(\frac{170}{303}\right)\)	\(e\left(\frac{563}{606}\right)\)	\(e\left(\frac{37}{303}\right)\)	\(e\left(\frac{215}{606}\right)\)	\(e\left(\frac{99}{202}\right)\)	\(e\left(\frac{83}{101}\right)\)	\(e\left(\frac{69}{101}\right)\)	\(e\left(\frac{260}{303}\right)\)	\(e\left(\frac{185}{202}\right)\)	\(e\left(\frac{107}{303}\right)\)
\(\chi_{607}(13,\cdot)\)	607.g	303	yes	\(1\)	\(1\)	\(e\left(\frac{151}{303}\right)\)	\(e\left(\frac{62}{303}\right)\)	\(e\left(\frac{302}{303}\right)\)	\(e\left(\frac{296}{303}\right)\)	\(e\left(\frac{71}{101}\right)\)	\(e\left(\frac{66}{101}\right)\)	\(e\left(\frac{50}{101}\right)\)	\(e\left(\frac{124}{303}\right)\)	\(e\left(\frac{48}{101}\right)\)	\(e\left(\frac{79}{303}\right)\)
\(\chi_{607}(14,\cdot)\)	607.g	303	yes	\(1\)	\(1\)	\(e\left(\frac{158}{303}\right)\)	\(e\left(\frac{103}{303}\right)\)	\(e\left(\frac{13}{303}\right)\)	\(e\left(\frac{91}{303}\right)\)	\(e\left(\frac{87}{101}\right)\)	\(e\left(\frac{51}{101}\right)\)	\(e\left(\frac{57}{101}\right)\)	\(e\left(\frac{206}{303}\right)\)	\(e\left(\frac{83}{101}\right)\)	\(e\left(\frac{185}{303}\right)\)
\(\chi_{607}(15,\cdot)\)	607.g	303	yes	\(1\)	\(1\)	\(e\left(\frac{44}{303}\right)\)	\(e\left(\frac{301}{303}\right)\)	\(e\left(\frac{88}{303}\right)\)	\(e\left(\frac{10}{303}\right)\)	\(e\left(\frac{14}{101}\right)\)	\(e\left(\frac{50}{101}\right)\)	\(e\left(\frac{44}{101}\right)\)	\(e\left(\frac{299}{303}\right)\)	\(e\left(\frac{18}{101}\right)\)	\(e\left(\frac{17}{303}\right)\)
\(\chi_{607}(16,\cdot)\)	607.g	303	yes	\(1\)	\(1\)	\(e\left(\frac{59}{303}\right)\)	\(e\left(\frac{259}{303}\right)\)	\(e\left(\frac{118}{303}\right)\)	\(e\left(\frac{220}{303}\right)\)	\(e\left(\frac{5}{101}\right)\)	\(e\left(\frac{90}{101}\right)\)	\(e\left(\frac{59}{101}\right)\)	\(e\left(\frac{215}{303}\right)\)	\(e\left(\frac{93}{101}\right)\)	\(e\left(\frac{71}{303}\right)\)
\(\chi_{607}(17,\cdot)\)	607.h	606	yes	\(-1\)	\(1\)	\(e\left(\frac{199}{303}\right)\)	\(e\left(\frac{37}{606}\right)\)	\(e\left(\frac{95}{303}\right)\)	\(e\left(\frac{421}{606}\right)\)	\(e\left(\frac{145}{202}\right)\)	\(e\left(\frac{93}{101}\right)\)	\(e\left(\frac{98}{101}\right)\)	\(e\left(\frac{37}{303}\right)\)	\(e\left(\frac{71}{202}\right)\)	\(e\left(\frac{70}{303}\right)\)
\(\chi_{607}(18,\cdot)\)	607.g	303	yes	\(1\)	\(1\)	\(e\left(\frac{220}{303}\right)\)	\(e\left(\frac{293}{303}\right)\)	\(e\left(\frac{137}{303}\right)\)	\(e\left(\frac{50}{303}\right)\)	\(e\left(\frac{70}{101}\right)\)	\(e\left(\frac{48}{101}\right)\)	\(e\left(\frac{18}{101}\right)\)	\(e\left(\frac{283}{303}\right)\)	\(e\left(\frac{90}{101}\right)\)	\(e\left(\frac{85}{303}\right)\)
\(\chi_{607}(19,\cdot)\)	607.g	303	yes	\(1\)	\(1\)	\(e\left(\frac{2}{303}\right)\)	\(e\left(\frac{55}{303}\right)\)	\(e\left(\frac{4}{303}\right)\)	\(e\left(\frac{28}{303}\right)\)	\(e\left(\frac{19}{101}\right)\)	\(e\left(\frac{39}{101}\right)\)	\(e\left(\frac{2}{101}\right)\)	\(e\left(\frac{110}{303}\right)\)	\(e\left(\frac{10}{101}\right)\)	\(e\left(\frac{290}{303}\right)\)
\(\chi_{607}(20,\cdot)\)	607.h	606	yes	\(-1\)	\(1\)	\(e\left(\frac{236}{303}\right)\)	\(e\left(\frac{557}{606}\right)\)	\(e\left(\frac{169}{303}\right)\)	\(e\left(\frac{245}{606}\right)\)	\(e\left(\frac{141}{202}\right)\)	\(e\left(\frac{57}{101}\right)\)	\(e\left(\frac{34}{101}\right)\)	\(e\left(\frac{254}{303}\right)\)	\(e\left(\frac{37}{202}\right)\)	\(e\left(\frac{284}{303}\right)\)
\(\chi_{607}(21,\cdot)\)	607.h	606	yes	\(-1\)	\(1\)	\(e\left(\frac{208}{303}\right)\)	\(e\left(\frac{229}{606}\right)\)	\(e\left(\frac{113}{303}\right)\)	\(e\left(\frac{67}{606}\right)\)	\(e\left(\frac{13}{202}\right)\)	\(e\left(\frac{16}{101}\right)\)	\(e\left(\frac{6}{101}\right)\)	\(e\left(\frac{229}{303}\right)\)	\(e\left(\frac{161}{202}\right)\)	\(e\left(\frac{163}{303}\right)\)
\(\chi_{607}(22,\cdot)\)	607.g	303	yes	\(1\)	\(1\)	\(e\left(\frac{184}{303}\right)\)	\(e\left(\frac{212}{303}\right)\)	\(e\left(\frac{65}{303}\right)\)	\(e\left(\frac{152}{303}\right)\)	\(e\left(\frac{31}{101}\right)\)	\(e\left(\frac{53}{101}\right)\)	\(e\left(\frac{83}{101}\right)\)	\(e\left(\frac{121}{303}\right)\)	\(e\left(\frac{11}{101}\right)\)	\(e\left(\frac{16}{303}\right)\)
\(\chi_{607}(23,\cdot)\)	607.h	606	yes	\(-1\)	\(1\)	\(e\left(\frac{191}{303}\right)\)	\(e\left(\frac{203}{606}\right)\)	\(e\left(\frac{79}{303}\right)\)	\(e\left(\frac{197}{606}\right)\)	\(e\left(\frac{195}{202}\right)\)	\(e\left(\frac{38}{101}\right)\)	\(e\left(\frac{90}{101}\right)\)	\(e\left(\frac{203}{303}\right)\)	\(e\left(\frac{193}{202}\right)\)	\(e\left(\frac{122}{303}\right)\)
\(\chi_{607}(24,\cdot)\)	607.h	606	yes	\(-1\)	\(1\)	\(e\left(\frac{109}{303}\right)\)	\(e\left(\frac{541}{606}\right)\)	\(e\left(\frac{218}{303}\right)\)	\(e\left(\frac{325}{606}\right)\)	\(e\left(\frac{51}{202}\right)\)	\(e\left(\frac{55}{101}\right)\)	\(e\left(\frac{8}{101}\right)\)	\(e\left(\frac{238}{303}\right)\)	\(e\left(\frac{181}{202}\right)\)	\(e\left(\frac{49}{303}\right)\)
\(\chi_{607}(25,\cdot)\)	607.g	303	yes	\(1\)	\(1\)	\(e\left(\frac{110}{303}\right)\)	\(e\left(\frac{298}{303}\right)\)	\(e\left(\frac{220}{303}\right)\)	\(e\left(\frac{25}{303}\right)\)	\(e\left(\frac{35}{101}\right)\)	\(e\left(\frac{24}{101}\right)\)	\(e\left(\frac{9}{101}\right)\)	\(e\left(\frac{293}{303}\right)\)	\(e\left(\frac{45}{101}\right)\)	\(e\left(\frac{194}{303}\right)\)
\(\chi_{607}(26,\cdot)\)	607.e	101	yes	\(1\)	\(1\)	\(e\left(\frac{30}{101}\right)\)	\(e\left(\frac{17}{101}\right)\)	\(e\left(\frac{60}{101}\right)\)	\(e\left(\frac{16}{101}\right)\)	\(e\left(\frac{47}{101}\right)\)	\(e\left(\frac{38}{101}\right)\)	\(e\left(\frac{90}{101}\right)\)	\(e\left(\frac{34}{101}\right)\)	\(e\left(\frac{46}{101}\right)\)	\(e\left(\frac{7}{101}\right)\)
\(\chi_{607}(27,\cdot)\)	607.f	202	yes	\(-1\)	\(1\)	\(e\left(\frac{90}{101}\right)\)	\(e\left(\frac{1}{202}\right)\)	\(e\left(\frac{79}{101}\right)\)	\(e\left(\frac{197}{202}\right)\)	\(e\left(\frac{181}{202}\right)\)	\(e\left(\frac{13}{101}\right)\)	\(e\left(\frac{68}{101}\right)\)	\(e\left(\frac{1}{101}\right)\)	\(e\left(\frac{175}{202}\right)\)	\(e\left(\frac{21}{101}\right)\)
\(\chi_{607}(28,\cdot)\)	607.g	303	yes	\(1\)	\(1\)	\(e\left(\frac{97}{303}\right)\)	\(e\left(\frac{92}{303}\right)\)	\(e\left(\frac{194}{303}\right)\)	\(e\left(\frac{146}{303}\right)\)	\(e\left(\frac{63}{101}\right)\)	\(e\left(\frac{23}{101}\right)\)	\(e\left(\frac{97}{101}\right)\)	\(e\left(\frac{184}{303}\right)\)	\(e\left(\frac{81}{101}\right)\)	\(e\left(\frac{127}{303}\right)\)
\(\chi_{607}(29,\cdot)\)	607.h	606	yes	\(-1\)	\(1\)	\(e\left(\frac{34}{303}\right)\)	\(e\left(\frac{355}{606}\right)\)	\(e\left(\frac{68}{303}\right)\)	\(e\left(\frac{43}{606}\right)\)	\(e\left(\frac{141}{202}\right)\)	\(e\left(\frac{57}{101}\right)\)	\(e\left(\frac{34}{101}\right)\)	\(e\left(\frac{52}{303}\right)\)	\(e\left(\frac{37}{202}\right)\)	\(e\left(\frac{82}{303}\right)\)
\(\chi_{607}(30,\cdot)\)	607.g	303	yes	\(1\)	\(1\)	\(e\left(\frac{286}{303}\right)\)	\(e\left(\frac{290}{303}\right)\)	\(e\left(\frac{269}{303}\right)\)	\(e\left(\frac{65}{303}\right)\)	\(e\left(\frac{91}{101}\right)\)	\(e\left(\frac{22}{101}\right)\)	\(e\left(\frac{84}{101}\right)\)	\(e\left(\frac{277}{303}\right)\)	\(e\left(\frac{16}{101}\right)\)	\(e\left(\frac{262}{303}\right)\)
\(\chi_{607}(31,\cdot)\)	607.h	606	yes	\(-1\)	\(1\)	\(e\left(\frac{218}{303}\right)\)	\(e\left(\frac{173}{606}\right)\)	\(e\left(\frac{133}{303}\right)\)	\(e\left(\frac{347}{606}\right)\)	\(e\left(\frac{1}{202}\right)\)	\(e\left(\frac{9}{101}\right)\)	\(e\left(\frac{16}{101}\right)\)	\(e\left(\frac{173}{303}\right)\)	\(e\left(\frac{59}{202}\right)\)	\(e\left(\frac{98}{303}\right)\)
\(\chi_{607}(32,\cdot)\)	607.g	303	yes	\(1\)	\(1\)	\(e\left(\frac{301}{303}\right)\)	\(e\left(\frac{248}{303}\right)\)	\(e\left(\frac{299}{303}\right)\)	\(e\left(\frac{275}{303}\right)\)	\(e\left(\frac{82}{101}\right)\)	\(e\left(\frac{62}{101}\right)\)	\(e\left(\frac{99}{101}\right)\)	\(e\left(\frac{193}{303}\right)\)	\(e\left(\frac{91}{101}\right)\)	\(e\left(\frac{13}{303}\right)\)

Introduction

L-functions

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Character group

First 32 of 606 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.