LMFDB - Group of Dirichlet characters of modulus 619

Show commands: PariGP / SageMath

sage: H = DirichletGroup(619)

pari: g = idealstar(,619,2)

Character group

sage: G.order() pari: g.no
Order	=	618
sage: H.invariants() pari: g.cyc
Structure	=	$C_{618}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{619}(2,\cdot)$

First 32 of 618 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{619}(1,\cdot)$	619.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{619}(2,\cdot)$	619.h	618	yes	$-1$	$1$	$e\left(\frac{1}{618}\right)$	$e\left(\frac{25}{206}\right)$	$e\left(\frac{1}{309}\right)$	$e\left(\frac{164}{309}\right)$	$e\left(\frac{38}{309}\right)$	$e\left(\frac{130}{309}\right)$	$e\left(\frac{1}{206}\right)$	$e\left(\frac{25}{103}\right)$	$e\left(\frac{329}{618}\right)$	$e\left(\frac{121}{618}\right)$
$\chi_{619}(3,\cdot)$	619.f	206	yes	$-1$	$1$	$e\left(\frac{25}{206}\right)$	$e\left(\frac{21}{206}\right)$	$e\left(\frac{25}{103}\right)$	$e\left(\frac{83}{103}\right)$	$e\left(\frac{23}{103}\right)$	$e\left(\frac{57}{103}\right)$	$e\left(\frac{75}{206}\right)$	$e\left(\frac{21}{103}\right)$	$e\left(\frac{191}{206}\right)$	$e\left(\frac{141}{206}\right)$
$\chi_{619}(4,\cdot)$	619.g	309	yes	$1$	$1$	$e\left(\frac{1}{309}\right)$	$e\left(\frac{25}{103}\right)$	$e\left(\frac{2}{309}\right)$	$e\left(\frac{19}{309}\right)$	$e\left(\frac{76}{309}\right)$	$e\left(\frac{260}{309}\right)$	$e\left(\frac{1}{103}\right)$	$e\left(\frac{50}{103}\right)$	$e\left(\frac{20}{309}\right)$	$e\left(\frac{121}{309}\right)$
$\chi_{619}(5,\cdot)$	619.g	309	yes	$1$	$1$	$e\left(\frac{164}{309}\right)$	$e\left(\frac{83}{103}\right)$	$e\left(\frac{19}{309}\right)$	$e\left(\frac{26}{309}\right)$	$e\left(\frac{104}{309}\right)$	$e\left(\frac{307}{309}\right)$	$e\left(\frac{61}{103}\right)$	$e\left(\frac{63}{103}\right)$	$e\left(\frac{190}{309}\right)$	$e\left(\frac{68}{309}\right)$
$\chi_{619}(6,\cdot)$	619.g	309	yes	$1$	$1$	$e\left(\frac{38}{309}\right)$	$e\left(\frac{23}{103}\right)$	$e\left(\frac{76}{309}\right)$	$e\left(\frac{104}{309}\right)$	$e\left(\frac{107}{309}\right)$	$e\left(\frac{301}{309}\right)$	$e\left(\frac{38}{103}\right)$	$e\left(\frac{46}{103}\right)$	$e\left(\frac{142}{309}\right)$	$e\left(\frac{272}{309}\right)$
$\chi_{619}(7,\cdot)$	619.g	309	yes	$1$	$1$	$e\left(\frac{130}{309}\right)$	$e\left(\frac{57}{103}\right)$	$e\left(\frac{260}{309}\right)$	$e\left(\frac{307}{309}\right)$	$e\left(\frac{301}{309}\right)$	$e\left(\frac{119}{309}\right)$	$e\left(\frac{27}{103}\right)$	$e\left(\frac{11}{103}\right)$	$e\left(\frac{128}{309}\right)$	$e\left(\frac{280}{309}\right)$
$\chi_{619}(8,\cdot)$	619.f	206	yes	$-1$	$1$	$e\left(\frac{1}{206}\right)$	$e\left(\frac{75}{206}\right)$	$e\left(\frac{1}{103}\right)$	$e\left(\frac{61}{103}\right)$	$e\left(\frac{38}{103}\right)$	$e\left(\frac{27}{103}\right)$	$e\left(\frac{3}{206}\right)$	$e\left(\frac{75}{103}\right)$	$e\left(\frac{123}{206}\right)$	$e\left(\frac{121}{206}\right)$
$\chi_{619}(9,\cdot)$	619.e	103	yes	$1$	$1$	$e\left(\frac{25}{103}\right)$	$e\left(\frac{21}{103}\right)$	$e\left(\frac{50}{103}\right)$	$e\left(\frac{63}{103}\right)$	$e\left(\frac{46}{103}\right)$	$e\left(\frac{11}{103}\right)$	$e\left(\frac{75}{103}\right)$	$e\left(\frac{42}{103}\right)$	$e\left(\frac{88}{103}\right)$	$e\left(\frac{38}{103}\right)$
$\chi_{619}(10,\cdot)$	619.h	618	yes	$-1$	$1$	$e\left(\frac{329}{618}\right)$	$e\left(\frac{191}{206}\right)$	$e\left(\frac{20}{309}\right)$	$e\left(\frac{190}{309}\right)$	$e\left(\frac{142}{309}\right)$	$e\left(\frac{128}{309}\right)$	$e\left(\frac{123}{206}\right)$	$e\left(\frac{88}{103}\right)$	$e\left(\frac{91}{618}\right)$	$e\left(\frac{257}{618}\right)$
$\chi_{619}(11,\cdot)$	619.h	618	yes	$-1$	$1$	$e\left(\frac{121}{618}\right)$	$e\left(\frac{141}{206}\right)$	$e\left(\frac{121}{309}\right)$	$e\left(\frac{68}{309}\right)$	$e\left(\frac{272}{309}\right)$	$e\left(\frac{280}{309}\right)$	$e\left(\frac{121}{206}\right)$	$e\left(\frac{38}{103}\right)$	$e\left(\frac{257}{618}\right)$	$e\left(\frac{427}{618}\right)$
$\chi_{619}(12,\cdot)$	619.h	618	yes	$-1$	$1$	$e\left(\frac{77}{618}\right)$	$e\left(\frac{71}{206}\right)$	$e\left(\frac{77}{309}\right)$	$e\left(\frac{268}{309}\right)$	$e\left(\frac{145}{309}\right)$	$e\left(\frac{122}{309}\right)$	$e\left(\frac{77}{206}\right)$	$e\left(\frac{71}{103}\right)$	$e\left(\frac{613}{618}\right)$	$e\left(\frac{47}{618}\right)$
$\chi_{619}(13,\cdot)$	619.f	206	yes	$-1$	$1$	$e\left(\frac{83}{206}\right)$	$e\left(\frac{45}{206}\right)$	$e\left(\frac{83}{103}\right)$	$e\left(\frac{16}{103}\right)$	$e\left(\frac{64}{103}\right)$	$e\left(\frac{78}{103}\right)$	$e\left(\frac{43}{206}\right)$	$e\left(\frac{45}{103}\right)$	$e\left(\frac{115}{206}\right)$	$e\left(\frac{155}{206}\right)$
$\chi_{619}(14,\cdot)$	619.f	206	yes	$-1$	$1$	$e\left(\frac{87}{206}\right)$	$e\left(\frac{139}{206}\right)$	$e\left(\frac{87}{103}\right)$	$e\left(\frac{54}{103}\right)$	$e\left(\frac{10}{103}\right)$	$e\left(\frac{83}{103}\right)$	$e\left(\frac{55}{206}\right)$	$e\left(\frac{36}{103}\right)$	$e\left(\frac{195}{206}\right)$	$e\left(\frac{21}{206}\right)$
$\chi_{619}(15,\cdot)$	619.h	618	yes	$-1$	$1$	$e\left(\frac{403}{618}\right)$	$e\left(\frac{187}{206}\right)$	$e\left(\frac{94}{309}\right)$	$e\left(\frac{275}{309}\right)$	$e\left(\frac{173}{309}\right)$	$e\left(\frac{169}{309}\right)$	$e\left(\frac{197}{206}\right)$	$e\left(\frac{84}{103}\right)$	$e\left(\frac{335}{618}\right)$	$e\left(\frac{559}{618}\right)$
$\chi_{619}(16,\cdot)$	619.g	309	yes	$1$	$1$	$e\left(\frac{2}{309}\right)$	$e\left(\frac{50}{103}\right)$	$e\left(\frac{4}{309}\right)$	$e\left(\frac{38}{309}\right)$	$e\left(\frac{152}{309}\right)$	$e\left(\frac{211}{309}\right)$	$e\left(\frac{2}{103}\right)$	$e\left(\frac{100}{103}\right)$	$e\left(\frac{40}{309}\right)$	$e\left(\frac{242}{309}\right)$
$\chi_{619}(17,\cdot)$	619.f	206	yes	$-1$	$1$	$e\left(\frac{139}{206}\right)$	$e\left(\frac{125}{206}\right)$	$e\left(\frac{36}{103}\right)$	$e\left(\frac{33}{103}\right)$	$e\left(\frac{29}{103}\right)$	$e\left(\frac{45}{103}\right)$	$e\left(\frac{5}{206}\right)$	$e\left(\frac{22}{103}\right)$	$e\left(\frac{205}{206}\right)$	$e\left(\frac{133}{206}\right)$
$\chi_{619}(18,\cdot)$	619.h	618	yes	$-1$	$1$	$e\left(\frac{151}{618}\right)$	$e\left(\frac{67}{206}\right)$	$e\left(\frac{151}{309}\right)$	$e\left(\frac{44}{309}\right)$	$e\left(\frac{176}{309}\right)$	$e\left(\frac{163}{309}\right)$	$e\left(\frac{151}{206}\right)$	$e\left(\frac{67}{103}\right)$	$e\left(\frac{239}{618}\right)$	$e\left(\frac{349}{618}\right)$
$\chi_{619}(19,\cdot)$	619.h	618	yes	$-1$	$1$	$e\left(\frac{425}{618}\right)$	$e\left(\frac{119}{206}\right)$	$e\left(\frac{116}{309}\right)$	$e\left(\frac{175}{309}\right)$	$e\left(\frac{82}{309}\right)$	$e\left(\frac{248}{309}\right)$	$e\left(\frac{13}{206}\right)$	$e\left(\frac{16}{103}\right)$	$e\left(\frac{157}{618}\right)$	$e\left(\frac{131}{618}\right)$
$\chi_{619}(20,\cdot)$	619.e	103	yes	$1$	$1$	$e\left(\frac{55}{103}\right)$	$e\left(\frac{5}{103}\right)$	$e\left(\frac{7}{103}\right)$	$e\left(\frac{15}{103}\right)$	$e\left(\frac{60}{103}\right)$	$e\left(\frac{86}{103}\right)$	$e\left(\frac{62}{103}\right)$	$e\left(\frac{10}{103}\right)$	$e\left(\frac{70}{103}\right)$	$e\left(\frac{63}{103}\right)$
$\chi_{619}(21,\cdot)$	619.h	618	yes	$-1$	$1$	$e\left(\frac{335}{618}\right)$	$e\left(\frac{135}{206}\right)$	$e\left(\frac{26}{309}\right)$	$e\left(\frac{247}{309}\right)$	$e\left(\frac{61}{309}\right)$	$e\left(\frac{290}{309}\right)$	$e\left(\frac{129}{206}\right)$	$e\left(\frac{32}{103}\right)$	$e\left(\frac{211}{618}\right)$	$e\left(\frac{365}{618}\right)$
$\chi_{619}(22,\cdot)$	619.g	309	yes	$1$	$1$	$e\left(\frac{61}{309}\right)$	$e\left(\frac{83}{103}\right)$	$e\left(\frac{122}{309}\right)$	$e\left(\frac{232}{309}\right)$	$e\left(\frac{1}{309}\right)$	$e\left(\frac{101}{309}\right)$	$e\left(\frac{61}{103}\right)$	$e\left(\frac{63}{103}\right)$	$e\left(\frac{293}{309}\right)$	$e\left(\frac{274}{309}\right)$
$\chi_{619}(23,\cdot)$	619.g	309	yes	$1$	$1$	$e\left(\frac{197}{309}\right)$	$e\left(\frac{84}{103}\right)$	$e\left(\frac{85}{309}\right)$	$e\left(\frac{35}{309}\right)$	$e\left(\frac{140}{309}\right)$	$e\left(\frac{235}{309}\right)$	$e\left(\frac{94}{103}\right)$	$e\left(\frac{65}{103}\right)$	$e\left(\frac{232}{309}\right)$	$e\left(\frac{44}{309}\right)$
$\chi_{619}(24,\cdot)$	619.e	103	yes	$1$	$1$	$e\left(\frac{13}{103}\right)$	$e\left(\frac{48}{103}\right)$	$e\left(\frac{26}{103}\right)$	$e\left(\frac{41}{103}\right)$	$e\left(\frac{61}{103}\right)$	$e\left(\frac{84}{103}\right)$	$e\left(\frac{39}{103}\right)$	$e\left(\frac{96}{103}\right)$	$e\left(\frac{54}{103}\right)$	$e\left(\frac{28}{103}\right)$
$\chi_{619}(25,\cdot)$	619.g	309	yes	$1$	$1$	$e\left(\frac{19}{309}\right)$	$e\left(\frac{63}{103}\right)$	$e\left(\frac{38}{309}\right)$	$e\left(\frac{52}{309}\right)$	$e\left(\frac{208}{309}\right)$	$e\left(\frac{305}{309}\right)$	$e\left(\frac{19}{103}\right)$	$e\left(\frac{23}{103}\right)$	$e\left(\frac{71}{309}\right)$	$e\left(\frac{136}{309}\right)$
$\chi_{619}(26,\cdot)$	619.g	309	yes	$1$	$1$	$e\left(\frac{125}{309}\right)$	$e\left(\frac{35}{103}\right)$	$e\left(\frac{250}{309}\right)$	$e\left(\frac{212}{309}\right)$	$e\left(\frac{230}{309}\right)$	$e\left(\frac{55}{309}\right)$	$e\left(\frac{22}{103}\right)$	$e\left(\frac{70}{103}\right)$	$e\left(\frac{28}{309}\right)$	$e\left(\frac{293}{309}\right)$
$\chi_{619}(27,\cdot)$	619.f	206	yes	$-1$	$1$	$e\left(\frac{75}{206}\right)$	$e\left(\frac{63}{206}\right)$	$e\left(\frac{75}{103}\right)$	$e\left(\frac{43}{103}\right)$	$e\left(\frac{69}{103}\right)$	$e\left(\frac{68}{103}\right)$	$e\left(\frac{19}{206}\right)$	$e\left(\frac{63}{103}\right)$	$e\left(\frac{161}{206}\right)$	$e\left(\frac{11}{206}\right)$
$\chi_{619}(28,\cdot)$	619.g	309	yes	$1$	$1$	$e\left(\frac{131}{309}\right)$	$e\left(\frac{82}{103}\right)$	$e\left(\frac{262}{309}\right)$	$e\left(\frac{17}{309}\right)$	$e\left(\frac{68}{309}\right)$	$e\left(\frac{70}{309}\right)$	$e\left(\frac{28}{103}\right)$	$e\left(\frac{61}{103}\right)$	$e\left(\frac{148}{309}\right)$	$e\left(\frac{92}{309}\right)$
$\chi_{619}(29,\cdot)$	619.f	206	yes	$-1$	$1$	$e\left(\frac{101}{206}\right)$	$e\left(\frac{159}{206}\right)$	$e\left(\frac{101}{103}\right)$	$e\left(\frac{84}{103}\right)$	$e\left(\frac{27}{103}\right)$	$e\left(\frac{49}{103}\right)$	$e\left(\frac{97}{206}\right)$	$e\left(\frac{56}{103}\right)$	$e\left(\frac{63}{206}\right)$	$e\left(\frac{67}{206}\right)$
$\chi_{619}(30,\cdot)$	619.g	309	yes	$1$	$1$	$e\left(\frac{202}{309}\right)$	$e\left(\frac{3}{103}\right)$	$e\left(\frac{95}{309}\right)$	$e\left(\frac{130}{309}\right)$	$e\left(\frac{211}{309}\right)$	$e\left(\frac{299}{309}\right)$	$e\left(\frac{99}{103}\right)$	$e\left(\frac{6}{103}\right)$	$e\left(\frac{23}{309}\right)$	$e\left(\frac{31}{309}\right)$
$\chi_{619}(31,\cdot)$	619.e	103	yes	$1$	$1$	$e\left(\frac{48}{103}\right)$	$e\left(\frac{98}{103}\right)$	$e\left(\frac{96}{103}\right)$	$e\left(\frac{88}{103}\right)$	$e\left(\frac{43}{103}\right)$	$e\left(\frac{17}{103}\right)$	$e\left(\frac{41}{103}\right)$	$e\left(\frac{93}{103}\right)$	$e\left(\frac{33}{103}\right)$	$e\left(\frac{40}{103}\right)$
$\chi_{619}(32,\cdot)$	619.h	618	yes	$-1$	$1$	$e\left(\frac{5}{618}\right)$	$e\left(\frac{125}{206}\right)$	$e\left(\frac{5}{309}\right)$	$e\left(\frac{202}{309}\right)$	$e\left(\frac{190}{309}\right)$	$e\left(\frac{32}{309}\right)$	$e\left(\frac{5}{206}\right)$	$e\left(\frac{22}{103}\right)$	$e\left(\frac{409}{618}\right)$	$e\left(\frac{605}{618}\right)$

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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	$619$
Structure	\(C_{618}\)
Order	$618$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{619}(1,\cdot)\)	619.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{619}(2,\cdot)\)	619.h	618	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{618}\right)\)	\(e\left(\frac{25}{206}\right)\)	\(e\left(\frac{1}{309}\right)\)	\(e\left(\frac{164}{309}\right)\)	\(e\left(\frac{38}{309}\right)\)	\(e\left(\frac{130}{309}\right)\)	\(e\left(\frac{1}{206}\right)\)	\(e\left(\frac{25}{103}\right)\)	\(e\left(\frac{329}{618}\right)\)	\(e\left(\frac{121}{618}\right)\)
\(\chi_{619}(3,\cdot)\)	619.f	206	yes	\(-1\)	\(1\)	\(e\left(\frac{25}{206}\right)\)	\(e\left(\frac{21}{206}\right)\)	\(e\left(\frac{25}{103}\right)\)	\(e\left(\frac{83}{103}\right)\)	\(e\left(\frac{23}{103}\right)\)	\(e\left(\frac{57}{103}\right)\)	\(e\left(\frac{75}{206}\right)\)	\(e\left(\frac{21}{103}\right)\)	\(e\left(\frac{191}{206}\right)\)	\(e\left(\frac{141}{206}\right)\)
\(\chi_{619}(4,\cdot)\)	619.g	309	yes	\(1\)	\(1\)	\(e\left(\frac{1}{309}\right)\)	\(e\left(\frac{25}{103}\right)\)	\(e\left(\frac{2}{309}\right)\)	\(e\left(\frac{19}{309}\right)\)	\(e\left(\frac{76}{309}\right)\)	\(e\left(\frac{260}{309}\right)\)	\(e\left(\frac{1}{103}\right)\)	\(e\left(\frac{50}{103}\right)\)	\(e\left(\frac{20}{309}\right)\)	\(e\left(\frac{121}{309}\right)\)
\(\chi_{619}(5,\cdot)\)	619.g	309	yes	\(1\)	\(1\)	\(e\left(\frac{164}{309}\right)\)	\(e\left(\frac{83}{103}\right)\)	\(e\left(\frac{19}{309}\right)\)	\(e\left(\frac{26}{309}\right)\)	\(e\left(\frac{104}{309}\right)\)	\(e\left(\frac{307}{309}\right)\)	\(e\left(\frac{61}{103}\right)\)	\(e\left(\frac{63}{103}\right)\)	\(e\left(\frac{190}{309}\right)\)	\(e\left(\frac{68}{309}\right)\)
\(\chi_{619}(6,\cdot)\)	619.g	309	yes	\(1\)	\(1\)	\(e\left(\frac{38}{309}\right)\)	\(e\left(\frac{23}{103}\right)\)	\(e\left(\frac{76}{309}\right)\)	\(e\left(\frac{104}{309}\right)\)	\(e\left(\frac{107}{309}\right)\)	\(e\left(\frac{301}{309}\right)\)	\(e\left(\frac{38}{103}\right)\)	\(e\left(\frac{46}{103}\right)\)	\(e\left(\frac{142}{309}\right)\)	\(e\left(\frac{272}{309}\right)\)
\(\chi_{619}(7,\cdot)\)	619.g	309	yes	\(1\)	\(1\)	\(e\left(\frac{130}{309}\right)\)	\(e\left(\frac{57}{103}\right)\)	\(e\left(\frac{260}{309}\right)\)	\(e\left(\frac{307}{309}\right)\)	\(e\left(\frac{301}{309}\right)\)	\(e\left(\frac{119}{309}\right)\)	\(e\left(\frac{27}{103}\right)\)	\(e\left(\frac{11}{103}\right)\)	\(e\left(\frac{128}{309}\right)\)	\(e\left(\frac{280}{309}\right)\)
\(\chi_{619}(8,\cdot)\)	619.f	206	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{206}\right)\)	\(e\left(\frac{75}{206}\right)\)	\(e\left(\frac{1}{103}\right)\)	\(e\left(\frac{61}{103}\right)\)	\(e\left(\frac{38}{103}\right)\)	\(e\left(\frac{27}{103}\right)\)	\(e\left(\frac{3}{206}\right)\)	\(e\left(\frac{75}{103}\right)\)	\(e\left(\frac{123}{206}\right)\)	\(e\left(\frac{121}{206}\right)\)
\(\chi_{619}(9,\cdot)\)	619.e	103	yes	\(1\)	\(1\)	\(e\left(\frac{25}{103}\right)\)	\(e\left(\frac{21}{103}\right)\)	\(e\left(\frac{50}{103}\right)\)	\(e\left(\frac{63}{103}\right)\)	\(e\left(\frac{46}{103}\right)\)	\(e\left(\frac{11}{103}\right)\)	\(e\left(\frac{75}{103}\right)\)	\(e\left(\frac{42}{103}\right)\)	\(e\left(\frac{88}{103}\right)\)	\(e\left(\frac{38}{103}\right)\)
\(\chi_{619}(10,\cdot)\)	619.h	618	yes	\(-1\)	\(1\)	\(e\left(\frac{329}{618}\right)\)	\(e\left(\frac{191}{206}\right)\)	\(e\left(\frac{20}{309}\right)\)	\(e\left(\frac{190}{309}\right)\)	\(e\left(\frac{142}{309}\right)\)	\(e\left(\frac{128}{309}\right)\)	\(e\left(\frac{123}{206}\right)\)	\(e\left(\frac{88}{103}\right)\)	\(e\left(\frac{91}{618}\right)\)	\(e\left(\frac{257}{618}\right)\)
\(\chi_{619}(11,\cdot)\)	619.h	618	yes	\(-1\)	\(1\)	\(e\left(\frac{121}{618}\right)\)	\(e\left(\frac{141}{206}\right)\)	\(e\left(\frac{121}{309}\right)\)	\(e\left(\frac{68}{309}\right)\)	\(e\left(\frac{272}{309}\right)\)	\(e\left(\frac{280}{309}\right)\)	\(e\left(\frac{121}{206}\right)\)	\(e\left(\frac{38}{103}\right)\)	\(e\left(\frac{257}{618}\right)\)	\(e\left(\frac{427}{618}\right)\)
\(\chi_{619}(12,\cdot)\)	619.h	618	yes	\(-1\)	\(1\)	\(e\left(\frac{77}{618}\right)\)	\(e\left(\frac{71}{206}\right)\)	\(e\left(\frac{77}{309}\right)\)	\(e\left(\frac{268}{309}\right)\)	\(e\left(\frac{145}{309}\right)\)	\(e\left(\frac{122}{309}\right)\)	\(e\left(\frac{77}{206}\right)\)	\(e\left(\frac{71}{103}\right)\)	\(e\left(\frac{613}{618}\right)\)	\(e\left(\frac{47}{618}\right)\)
\(\chi_{619}(13,\cdot)\)	619.f	206	yes	\(-1\)	\(1\)	\(e\left(\frac{83}{206}\right)\)	\(e\left(\frac{45}{206}\right)\)	\(e\left(\frac{83}{103}\right)\)	\(e\left(\frac{16}{103}\right)\)	\(e\left(\frac{64}{103}\right)\)	\(e\left(\frac{78}{103}\right)\)	\(e\left(\frac{43}{206}\right)\)	\(e\left(\frac{45}{103}\right)\)	\(e\left(\frac{115}{206}\right)\)	\(e\left(\frac{155}{206}\right)\)
\(\chi_{619}(14,\cdot)\)	619.f	206	yes	\(-1\)	\(1\)	\(e\left(\frac{87}{206}\right)\)	\(e\left(\frac{139}{206}\right)\)	\(e\left(\frac{87}{103}\right)\)	\(e\left(\frac{54}{103}\right)\)	\(e\left(\frac{10}{103}\right)\)	\(e\left(\frac{83}{103}\right)\)	\(e\left(\frac{55}{206}\right)\)	\(e\left(\frac{36}{103}\right)\)	\(e\left(\frac{195}{206}\right)\)	\(e\left(\frac{21}{206}\right)\)
\(\chi_{619}(15,\cdot)\)	619.h	618	yes	\(-1\)	\(1\)	\(e\left(\frac{403}{618}\right)\)	\(e\left(\frac{187}{206}\right)\)	\(e\left(\frac{94}{309}\right)\)	\(e\left(\frac{275}{309}\right)\)	\(e\left(\frac{173}{309}\right)\)	\(e\left(\frac{169}{309}\right)\)	\(e\left(\frac{197}{206}\right)\)	\(e\left(\frac{84}{103}\right)\)	\(e\left(\frac{335}{618}\right)\)	\(e\left(\frac{559}{618}\right)\)
\(\chi_{619}(16,\cdot)\)	619.g	309	yes	\(1\)	\(1\)	\(e\left(\frac{2}{309}\right)\)	\(e\left(\frac{50}{103}\right)\)	\(e\left(\frac{4}{309}\right)\)	\(e\left(\frac{38}{309}\right)\)	\(e\left(\frac{152}{309}\right)\)	\(e\left(\frac{211}{309}\right)\)	\(e\left(\frac{2}{103}\right)\)	\(e\left(\frac{100}{103}\right)\)	\(e\left(\frac{40}{309}\right)\)	\(e\left(\frac{242}{309}\right)\)
\(\chi_{619}(17,\cdot)\)	619.f	206	yes	\(-1\)	\(1\)	\(e\left(\frac{139}{206}\right)\)	\(e\left(\frac{125}{206}\right)\)	\(e\left(\frac{36}{103}\right)\)	\(e\left(\frac{33}{103}\right)\)	\(e\left(\frac{29}{103}\right)\)	\(e\left(\frac{45}{103}\right)\)	\(e\left(\frac{5}{206}\right)\)	\(e\left(\frac{22}{103}\right)\)	\(e\left(\frac{205}{206}\right)\)	\(e\left(\frac{133}{206}\right)\)
\(\chi_{619}(18,\cdot)\)	619.h	618	yes	\(-1\)	\(1\)	\(e\left(\frac{151}{618}\right)\)	\(e\left(\frac{67}{206}\right)\)	\(e\left(\frac{151}{309}\right)\)	\(e\left(\frac{44}{309}\right)\)	\(e\left(\frac{176}{309}\right)\)	\(e\left(\frac{163}{309}\right)\)	\(e\left(\frac{151}{206}\right)\)	\(e\left(\frac{67}{103}\right)\)	\(e\left(\frac{239}{618}\right)\)	\(e\left(\frac{349}{618}\right)\)
\(\chi_{619}(19,\cdot)\)	619.h	618	yes	\(-1\)	\(1\)	\(e\left(\frac{425}{618}\right)\)	\(e\left(\frac{119}{206}\right)\)	\(e\left(\frac{116}{309}\right)\)	\(e\left(\frac{175}{309}\right)\)	\(e\left(\frac{82}{309}\right)\)	\(e\left(\frac{248}{309}\right)\)	\(e\left(\frac{13}{206}\right)\)	\(e\left(\frac{16}{103}\right)\)	\(e\left(\frac{157}{618}\right)\)	\(e\left(\frac{131}{618}\right)\)
\(\chi_{619}(20,\cdot)\)	619.e	103	yes	\(1\)	\(1\)	\(e\left(\frac{55}{103}\right)\)	\(e\left(\frac{5}{103}\right)\)	\(e\left(\frac{7}{103}\right)\)	\(e\left(\frac{15}{103}\right)\)	\(e\left(\frac{60}{103}\right)\)	\(e\left(\frac{86}{103}\right)\)	\(e\left(\frac{62}{103}\right)\)	\(e\left(\frac{10}{103}\right)\)	\(e\left(\frac{70}{103}\right)\)	\(e\left(\frac{63}{103}\right)\)
\(\chi_{619}(21,\cdot)\)	619.h	618	yes	\(-1\)	\(1\)	\(e\left(\frac{335}{618}\right)\)	\(e\left(\frac{135}{206}\right)\)	\(e\left(\frac{26}{309}\right)\)	\(e\left(\frac{247}{309}\right)\)	\(e\left(\frac{61}{309}\right)\)	\(e\left(\frac{290}{309}\right)\)	\(e\left(\frac{129}{206}\right)\)	\(e\left(\frac{32}{103}\right)\)	\(e\left(\frac{211}{618}\right)\)	\(e\left(\frac{365}{618}\right)\)
\(\chi_{619}(22,\cdot)\)	619.g	309	yes	\(1\)	\(1\)	\(e\left(\frac{61}{309}\right)\)	\(e\left(\frac{83}{103}\right)\)	\(e\left(\frac{122}{309}\right)\)	\(e\left(\frac{232}{309}\right)\)	\(e\left(\frac{1}{309}\right)\)	\(e\left(\frac{101}{309}\right)\)	\(e\left(\frac{61}{103}\right)\)	\(e\left(\frac{63}{103}\right)\)	\(e\left(\frac{293}{309}\right)\)	\(e\left(\frac{274}{309}\right)\)
\(\chi_{619}(23,\cdot)\)	619.g	309	yes	\(1\)	\(1\)	\(e\left(\frac{197}{309}\right)\)	\(e\left(\frac{84}{103}\right)\)	\(e\left(\frac{85}{309}\right)\)	\(e\left(\frac{35}{309}\right)\)	\(e\left(\frac{140}{309}\right)\)	\(e\left(\frac{235}{309}\right)\)	\(e\left(\frac{94}{103}\right)\)	\(e\left(\frac{65}{103}\right)\)	\(e\left(\frac{232}{309}\right)\)	\(e\left(\frac{44}{309}\right)\)
\(\chi_{619}(24,\cdot)\)	619.e	103	yes	\(1\)	\(1\)	\(e\left(\frac{13}{103}\right)\)	\(e\left(\frac{48}{103}\right)\)	\(e\left(\frac{26}{103}\right)\)	\(e\left(\frac{41}{103}\right)\)	\(e\left(\frac{61}{103}\right)\)	\(e\left(\frac{84}{103}\right)\)	\(e\left(\frac{39}{103}\right)\)	\(e\left(\frac{96}{103}\right)\)	\(e\left(\frac{54}{103}\right)\)	\(e\left(\frac{28}{103}\right)\)
\(\chi_{619}(25,\cdot)\)	619.g	309	yes	\(1\)	\(1\)	\(e\left(\frac{19}{309}\right)\)	\(e\left(\frac{63}{103}\right)\)	\(e\left(\frac{38}{309}\right)\)	\(e\left(\frac{52}{309}\right)\)	\(e\left(\frac{208}{309}\right)\)	\(e\left(\frac{305}{309}\right)\)	\(e\left(\frac{19}{103}\right)\)	\(e\left(\frac{23}{103}\right)\)	\(e\left(\frac{71}{309}\right)\)	\(e\left(\frac{136}{309}\right)\)
\(\chi_{619}(26,\cdot)\)	619.g	309	yes	\(1\)	\(1\)	\(e\left(\frac{125}{309}\right)\)	\(e\left(\frac{35}{103}\right)\)	\(e\left(\frac{250}{309}\right)\)	\(e\left(\frac{212}{309}\right)\)	\(e\left(\frac{230}{309}\right)\)	\(e\left(\frac{55}{309}\right)\)	\(e\left(\frac{22}{103}\right)\)	\(e\left(\frac{70}{103}\right)\)	\(e\left(\frac{28}{309}\right)\)	\(e\left(\frac{293}{309}\right)\)
\(\chi_{619}(27,\cdot)\)	619.f	206	yes	\(-1\)	\(1\)	\(e\left(\frac{75}{206}\right)\)	\(e\left(\frac{63}{206}\right)\)	\(e\left(\frac{75}{103}\right)\)	\(e\left(\frac{43}{103}\right)\)	\(e\left(\frac{69}{103}\right)\)	\(e\left(\frac{68}{103}\right)\)	\(e\left(\frac{19}{206}\right)\)	\(e\left(\frac{63}{103}\right)\)	\(e\left(\frac{161}{206}\right)\)	\(e\left(\frac{11}{206}\right)\)
\(\chi_{619}(28,\cdot)\)	619.g	309	yes	\(1\)	\(1\)	\(e\left(\frac{131}{309}\right)\)	\(e\left(\frac{82}{103}\right)\)	\(e\left(\frac{262}{309}\right)\)	\(e\left(\frac{17}{309}\right)\)	\(e\left(\frac{68}{309}\right)\)	\(e\left(\frac{70}{309}\right)\)	\(e\left(\frac{28}{103}\right)\)	\(e\left(\frac{61}{103}\right)\)	\(e\left(\frac{148}{309}\right)\)	\(e\left(\frac{92}{309}\right)\)
\(\chi_{619}(29,\cdot)\)	619.f	206	yes	\(-1\)	\(1\)	\(e\left(\frac{101}{206}\right)\)	\(e\left(\frac{159}{206}\right)\)	\(e\left(\frac{101}{103}\right)\)	\(e\left(\frac{84}{103}\right)\)	\(e\left(\frac{27}{103}\right)\)	\(e\left(\frac{49}{103}\right)\)	\(e\left(\frac{97}{206}\right)\)	\(e\left(\frac{56}{103}\right)\)	\(e\left(\frac{63}{206}\right)\)	\(e\left(\frac{67}{206}\right)\)
\(\chi_{619}(30,\cdot)\)	619.g	309	yes	\(1\)	\(1\)	\(e\left(\frac{202}{309}\right)\)	\(e\left(\frac{3}{103}\right)\)	\(e\left(\frac{95}{309}\right)\)	\(e\left(\frac{130}{309}\right)\)	\(e\left(\frac{211}{309}\right)\)	\(e\left(\frac{299}{309}\right)\)	\(e\left(\frac{99}{103}\right)\)	\(e\left(\frac{6}{103}\right)\)	\(e\left(\frac{23}{309}\right)\)	\(e\left(\frac{31}{309}\right)\)
\(\chi_{619}(31,\cdot)\)	619.e	103	yes	\(1\)	\(1\)	\(e\left(\frac{48}{103}\right)\)	\(e\left(\frac{98}{103}\right)\)	\(e\left(\frac{96}{103}\right)\)	\(e\left(\frac{88}{103}\right)\)	\(e\left(\frac{43}{103}\right)\)	\(e\left(\frac{17}{103}\right)\)	\(e\left(\frac{41}{103}\right)\)	\(e\left(\frac{93}{103}\right)\)	\(e\left(\frac{33}{103}\right)\)	\(e\left(\frac{40}{103}\right)\)
\(\chi_{619}(32,\cdot)\)	619.h	618	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{618}\right)\)	\(e\left(\frac{125}{206}\right)\)	\(e\left(\frac{5}{309}\right)\)	\(e\left(\frac{202}{309}\right)\)	\(e\left(\frac{190}{309}\right)\)	\(e\left(\frac{32}{309}\right)\)	\(e\left(\frac{5}{206}\right)\)	\(e\left(\frac{22}{103}\right)\)	\(e\left(\frac{409}{618}\right)\)	\(e\left(\frac{605}{618}\right)\)

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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.