LMFDB - Group of Dirichlet characters of modulus 839

Show commands: PariGP / SageMath

sage: H = DirichletGroup(839)

pari: g = idealstar(,839,2)

Character group

sage: G.order() pari: g.no
Order	=	838
sage: H.invariants() pari: g.cyc
Structure	=	$C_{838}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{839}(11,\cdot)$

First 32 of 838 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{839}(1,\cdot)$	839.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{839}(2,\cdot)$	839.c	419	yes	$1$	$1$	$e\left(\frac{359}{419}\right)$	$e\left(\frac{147}{419}\right)$	$e\left(\frac{299}{419}\right)$	$e\left(\frac{280}{419}\right)$	$e\left(\frac{87}{419}\right)$	$e\left(\frac{172}{419}\right)$	$e\left(\frac{239}{419}\right)$	$e\left(\frac{294}{419}\right)$	$e\left(\frac{220}{419}\right)$	$e\left(\frac{243}{419}\right)$
$\chi_{839}(3,\cdot)$	839.c	419	yes	$1$	$1$	$e\left(\frac{147}{419}\right)$	$e\left(\frac{415}{419}\right)$	$e\left(\frac{294}{419}\right)$	$e\left(\frac{152}{419}\right)$	$e\left(\frac{143}{419}\right)$	$e\left(\frac{249}{419}\right)$	$e\left(\frac{22}{419}\right)$	$e\left(\frac{411}{419}\right)$	$e\left(\frac{299}{419}\right)$	$e\left(\frac{96}{419}\right)$
$\chi_{839}(4,\cdot)$	839.c	419	yes	$1$	$1$	$e\left(\frac{299}{419}\right)$	$e\left(\frac{294}{419}\right)$	$e\left(\frac{179}{419}\right)$	$e\left(\frac{141}{419}\right)$	$e\left(\frac{174}{419}\right)$	$e\left(\frac{344}{419}\right)$	$e\left(\frac{59}{419}\right)$	$e\left(\frac{169}{419}\right)$	$e\left(\frac{21}{419}\right)$	$e\left(\frac{67}{419}\right)$
$\chi_{839}(5,\cdot)$	839.c	419	yes	$1$	$1$	$e\left(\frac{280}{419}\right)$	$e\left(\frac{152}{419}\right)$	$e\left(\frac{141}{419}\right)$	$e\left(\frac{90}{419}\right)$	$e\left(\frac{13}{419}\right)$	$e\left(\frac{175}{419}\right)$	$e\left(\frac{2}{419}\right)$	$e\left(\frac{304}{419}\right)$	$e\left(\frac{370}{419}\right)$	$e\left(\frac{123}{419}\right)$
$\chi_{839}(6,\cdot)$	839.c	419	yes	$1$	$1$	$e\left(\frac{87}{419}\right)$	$e\left(\frac{143}{419}\right)$	$e\left(\frac{174}{419}\right)$	$e\left(\frac{13}{419}\right)$	$e\left(\frac{230}{419}\right)$	$e\left(\frac{2}{419}\right)$	$e\left(\frac{261}{419}\right)$	$e\left(\frac{286}{419}\right)$	$e\left(\frac{100}{419}\right)$	$e\left(\frac{339}{419}\right)$
$\chi_{839}(7,\cdot)$	839.c	419	yes	$1$	$1$	$e\left(\frac{172}{419}\right)$	$e\left(\frac{249}{419}\right)$	$e\left(\frac{344}{419}\right)$	$e\left(\frac{175}{419}\right)$	$e\left(\frac{2}{419}\right)$	$e\left(\frac{317}{419}\right)$	$e\left(\frac{97}{419}\right)$	$e\left(\frac{79}{419}\right)$	$e\left(\frac{347}{419}\right)$	$e\left(\frac{309}{419}\right)$
$\chi_{839}(8,\cdot)$	839.c	419	yes	$1$	$1$	$e\left(\frac{239}{419}\right)$	$e\left(\frac{22}{419}\right)$	$e\left(\frac{59}{419}\right)$	$e\left(\frac{2}{419}\right)$	$e\left(\frac{261}{419}\right)$	$e\left(\frac{97}{419}\right)$	$e\left(\frac{298}{419}\right)$	$e\left(\frac{44}{419}\right)$	$e\left(\frac{241}{419}\right)$	$e\left(\frac{310}{419}\right)$
$\chi_{839}(9,\cdot)$	839.c	419	yes	$1$	$1$	$e\left(\frac{294}{419}\right)$	$e\left(\frac{411}{419}\right)$	$e\left(\frac{169}{419}\right)$	$e\left(\frac{304}{419}\right)$	$e\left(\frac{286}{419}\right)$	$e\left(\frac{79}{419}\right)$	$e\left(\frac{44}{419}\right)$	$e\left(\frac{403}{419}\right)$	$e\left(\frac{179}{419}\right)$	$e\left(\frac{192}{419}\right)$
$\chi_{839}(10,\cdot)$	839.c	419	yes	$1$	$1$	$e\left(\frac{220}{419}\right)$	$e\left(\frac{299}{419}\right)$	$e\left(\frac{21}{419}\right)$	$e\left(\frac{370}{419}\right)$	$e\left(\frac{100}{419}\right)$	$e\left(\frac{347}{419}\right)$	$e\left(\frac{241}{419}\right)$	$e\left(\frac{179}{419}\right)$	$e\left(\frac{171}{419}\right)$	$e\left(\frac{366}{419}\right)$
$\chi_{839}(11,\cdot)$	839.d	838	yes	$-1$	$1$	$e\left(\frac{243}{419}\right)$	$e\left(\frac{96}{419}\right)$	$e\left(\frac{67}{419}\right)$	$e\left(\frac{123}{419}\right)$	$e\left(\frac{339}{419}\right)$	$e\left(\frac{309}{419}\right)$	$e\left(\frac{310}{419}\right)$	$e\left(\frac{192}{419}\right)$	$e\left(\frac{366}{419}\right)$	$e\left(\frac{1}{838}\right)$
$\chi_{839}(12,\cdot)$	839.c	419	yes	$1$	$1$	$e\left(\frac{27}{419}\right)$	$e\left(\frac{290}{419}\right)$	$e\left(\frac{54}{419}\right)$	$e\left(\frac{293}{419}\right)$	$e\left(\frac{317}{419}\right)$	$e\left(\frac{174}{419}\right)$	$e\left(\frac{81}{419}\right)$	$e\left(\frac{161}{419}\right)$	$e\left(\frac{320}{419}\right)$	$e\left(\frac{163}{419}\right)$
$\chi_{839}(13,\cdot)$	839.d	838	yes	$-1$	$1$	$e\left(\frac{113}{419}\right)$	$e\left(\frac{205}{419}\right)$	$e\left(\frac{226}{419}\right)$	$e\left(\frac{171}{419}\right)$	$e\left(\frac{318}{419}\right)$	$e\left(\frac{123}{419}\right)$	$e\left(\frac{339}{419}\right)$	$e\left(\frac{410}{419}\right)$	$e\left(\frac{284}{419}\right)$	$e\left(\frac{635}{838}\right)$
$\chi_{839}(14,\cdot)$	839.c	419	yes	$1$	$1$	$e\left(\frac{112}{419}\right)$	$e\left(\frac{396}{419}\right)$	$e\left(\frac{224}{419}\right)$	$e\left(\frac{36}{419}\right)$	$e\left(\frac{89}{419}\right)$	$e\left(\frac{70}{419}\right)$	$e\left(\frac{336}{419}\right)$	$e\left(\frac{373}{419}\right)$	$e\left(\frac{148}{419}\right)$	$e\left(\frac{133}{419}\right)$
$\chi_{839}(15,\cdot)$	839.c	419	yes	$1$	$1$	$e\left(\frac{8}{419}\right)$	$e\left(\frac{148}{419}\right)$	$e\left(\frac{16}{419}\right)$	$e\left(\frac{242}{419}\right)$	$e\left(\frac{156}{419}\right)$	$e\left(\frac{5}{419}\right)$	$e\left(\frac{24}{419}\right)$	$e\left(\frac{296}{419}\right)$	$e\left(\frac{250}{419}\right)$	$e\left(\frac{219}{419}\right)$
$\chi_{839}(16,\cdot)$	839.c	419	yes	$1$	$1$	$e\left(\frac{179}{419}\right)$	$e\left(\frac{169}{419}\right)$	$e\left(\frac{358}{419}\right)$	$e\left(\frac{282}{419}\right)$	$e\left(\frac{348}{419}\right)$	$e\left(\frac{269}{419}\right)$	$e\left(\frac{118}{419}\right)$	$e\left(\frac{338}{419}\right)$	$e\left(\frac{42}{419}\right)$	$e\left(\frac{134}{419}\right)$
$\chi_{839}(17,\cdot)$	839.d	838	yes	$-1$	$1$	$e\left(\frac{162}{419}\right)$	$e\left(\frac{64}{419}\right)$	$e\left(\frac{324}{419}\right)$	$e\left(\frac{82}{419}\right)$	$e\left(\frac{226}{419}\right)$	$e\left(\frac{206}{419}\right)$	$e\left(\frac{67}{419}\right)$	$e\left(\frac{128}{419}\right)$	$e\left(\frac{244}{419}\right)$	$e\left(\frac{699}{838}\right)$
$\chi_{839}(18,\cdot)$	839.c	419	yes	$1$	$1$	$e\left(\frac{234}{419}\right)$	$e\left(\frac{139}{419}\right)$	$e\left(\frac{49}{419}\right)$	$e\left(\frac{165}{419}\right)$	$e\left(\frac{373}{419}\right)$	$e\left(\frac{251}{419}\right)$	$e\left(\frac{283}{419}\right)$	$e\left(\frac{278}{419}\right)$	$e\left(\frac{399}{419}\right)$	$e\left(\frac{16}{419}\right)$
$\chi_{839}(19,\cdot)$	839.c	419	yes	$1$	$1$	$e\left(\frac{24}{419}\right)$	$e\left(\frac{25}{419}\right)$	$e\left(\frac{48}{419}\right)$	$e\left(\frac{307}{419}\right)$	$e\left(\frac{49}{419}\right)$	$e\left(\frac{15}{419}\right)$	$e\left(\frac{72}{419}\right)$	$e\left(\frac{50}{419}\right)$	$e\left(\frac{331}{419}\right)$	$e\left(\frac{238}{419}\right)$
$\chi_{839}(20,\cdot)$	839.c	419	yes	$1$	$1$	$e\left(\frac{160}{419}\right)$	$e\left(\frac{27}{419}\right)$	$e\left(\frac{320}{419}\right)$	$e\left(\frac{231}{419}\right)$	$e\left(\frac{187}{419}\right)$	$e\left(\frac{100}{419}\right)$	$e\left(\frac{61}{419}\right)$	$e\left(\frac{54}{419}\right)$	$e\left(\frac{391}{419}\right)$	$e\left(\frac{190}{419}\right)$
$\chi_{839}(21,\cdot)$	839.c	419	yes	$1$	$1$	$e\left(\frac{319}{419}\right)$	$e\left(\frac{245}{419}\right)$	$e\left(\frac{219}{419}\right)$	$e\left(\frac{327}{419}\right)$	$e\left(\frac{145}{419}\right)$	$e\left(\frac{147}{419}\right)$	$e\left(\frac{119}{419}\right)$	$e\left(\frac{71}{419}\right)$	$e\left(\frac{227}{419}\right)$	$e\left(\frac{405}{419}\right)$
$\chi_{839}(22,\cdot)$	839.d	838	yes	$-1$	$1$	$e\left(\frac{183}{419}\right)$	$e\left(\frac{243}{419}\right)$	$e\left(\frac{366}{419}\right)$	$e\left(\frac{403}{419}\right)$	$e\left(\frac{7}{419}\right)$	$e\left(\frac{62}{419}\right)$	$e\left(\frac{130}{419}\right)$	$e\left(\frac{67}{419}\right)$	$e\left(\frac{167}{419}\right)$	$e\left(\frac{487}{838}\right)$
$\chi_{839}(23,\cdot)$	839.c	419	yes	$1$	$1$	$e\left(\frac{69}{419}\right)$	$e\left(\frac{229}{419}\right)$	$e\left(\frac{138}{419}\right)$	$e\left(\frac{97}{419}\right)$	$e\left(\frac{298}{419}\right)$	$e\left(\frac{305}{419}\right)$	$e\left(\frac{207}{419}\right)$	$e\left(\frac{39}{419}\right)$	$e\left(\frac{166}{419}\right)$	$e\left(\frac{370}{419}\right)$
$\chi_{839}(24,\cdot)$	839.c	419	yes	$1$	$1$	$e\left(\frac{386}{419}\right)$	$e\left(\frac{18}{419}\right)$	$e\left(\frac{353}{419}\right)$	$e\left(\frac{154}{419}\right)$	$e\left(\frac{404}{419}\right)$	$e\left(\frac{346}{419}\right)$	$e\left(\frac{320}{419}\right)$	$e\left(\frac{36}{419}\right)$	$e\left(\frac{121}{419}\right)$	$e\left(\frac{406}{419}\right)$
$\chi_{839}(25,\cdot)$	839.c	419	yes	$1$	$1$	$e\left(\frac{141}{419}\right)$	$e\left(\frac{304}{419}\right)$	$e\left(\frac{282}{419}\right)$	$e\left(\frac{180}{419}\right)$	$e\left(\frac{26}{419}\right)$	$e\left(\frac{350}{419}\right)$	$e\left(\frac{4}{419}\right)$	$e\left(\frac{189}{419}\right)$	$e\left(\frac{321}{419}\right)$	$e\left(\frac{246}{419}\right)$
$\chi_{839}(26,\cdot)$	839.d	838	yes	$-1$	$1$	$e\left(\frac{53}{419}\right)$	$e\left(\frac{352}{419}\right)$	$e\left(\frac{106}{419}\right)$	$e\left(\frac{32}{419}\right)$	$e\left(\frac{405}{419}\right)$	$e\left(\frac{295}{419}\right)$	$e\left(\frac{159}{419}\right)$	$e\left(\frac{285}{419}\right)$	$e\left(\frac{85}{419}\right)$	$e\left(\frac{283}{838}\right)$
$\chi_{839}(27,\cdot)$	839.c	419	yes	$1$	$1$	$e\left(\frac{22}{419}\right)$	$e\left(\frac{407}{419}\right)$	$e\left(\frac{44}{419}\right)$	$e\left(\frac{37}{419}\right)$	$e\left(\frac{10}{419}\right)$	$e\left(\frac{328}{419}\right)$	$e\left(\frac{66}{419}\right)$	$e\left(\frac{395}{419}\right)$	$e\left(\frac{59}{419}\right)$	$e\left(\frac{288}{419}\right)$
$\chi_{839}(28,\cdot)$	839.c	419	yes	$1$	$1$	$e\left(\frac{52}{419}\right)$	$e\left(\frac{124}{419}\right)$	$e\left(\frac{104}{419}\right)$	$e\left(\frac{316}{419}\right)$	$e\left(\frac{176}{419}\right)$	$e\left(\frac{242}{419}\right)$	$e\left(\frac{156}{419}\right)$	$e\left(\frac{248}{419}\right)$	$e\left(\frac{368}{419}\right)$	$e\left(\frac{376}{419}\right)$
$\chi_{839}(29,\cdot)$	839.d	838	yes	$-1$	$1$	$e\left(\frac{389}{419}\right)$	$e\left(\frac{283}{419}\right)$	$e\left(\frac{359}{419}\right)$	$e\left(\frac{140}{419}\right)$	$e\left(\frac{253}{419}\right)$	$e\left(\frac{86}{419}\right)$	$e\left(\frac{329}{419}\right)$	$e\left(\frac{147}{419}\right)$	$e\left(\frac{110}{419}\right)$	$e\left(\frac{243}{838}\right)$
$\chi_{839}(30,\cdot)$	839.c	419	yes	$1$	$1$	$e\left(\frac{367}{419}\right)$	$e\left(\frac{295}{419}\right)$	$e\left(\frac{315}{419}\right)$	$e\left(\frac{103}{419}\right)$	$e\left(\frac{243}{419}\right)$	$e\left(\frac{177}{419}\right)$	$e\left(\frac{263}{419}\right)$	$e\left(\frac{171}{419}\right)$	$e\left(\frac{51}{419}\right)$	$e\left(\frac{43}{419}\right)$
$\chi_{839}(31,\cdot)$	839.d	838	yes	$-1$	$1$	$e\left(\frac{337}{419}\right)$	$e\left(\frac{159}{419}\right)$	$e\left(\frac{255}{419}\right)$	$e\left(\frac{243}{419}\right)$	$e\left(\frac{77}{419}\right)$	$e\left(\frac{263}{419}\right)$	$e\left(\frac{173}{419}\right)$	$e\left(\frac{318}{419}\right)$	$e\left(\frac{161}{419}\right)$	$e\left(\frac{329}{838}\right)$
$\chi_{839}(32,\cdot)$	839.c	419	yes	$1$	$1$	$e\left(\frac{119}{419}\right)$	$e\left(\frac{316}{419}\right)$	$e\left(\frac{238}{419}\right)$	$e\left(\frac{143}{419}\right)$	$e\left(\frac{16}{419}\right)$	$e\left(\frac{22}{419}\right)$	$e\left(\frac{357}{419}\right)$	$e\left(\frac{213}{419}\right)$	$e\left(\frac{262}{419}\right)$	$e\left(\frac{377}{419}\right)$

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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	$839$
Structure	\(C_{838}\)
Order	$838$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{839}(1,\cdot)\)	839.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{839}(2,\cdot)\)	839.c	419	yes	\(1\)	\(1\)	\(e\left(\frac{359}{419}\right)\)	\(e\left(\frac{147}{419}\right)\)	\(e\left(\frac{299}{419}\right)\)	\(e\left(\frac{280}{419}\right)\)	\(e\left(\frac{87}{419}\right)\)	\(e\left(\frac{172}{419}\right)\)	\(e\left(\frac{239}{419}\right)\)	\(e\left(\frac{294}{419}\right)\)	\(e\left(\frac{220}{419}\right)\)	\(e\left(\frac{243}{419}\right)\)
\(\chi_{839}(3,\cdot)\)	839.c	419	yes	\(1\)	\(1\)	\(e\left(\frac{147}{419}\right)\)	\(e\left(\frac{415}{419}\right)\)	\(e\left(\frac{294}{419}\right)\)	\(e\left(\frac{152}{419}\right)\)	\(e\left(\frac{143}{419}\right)\)	\(e\left(\frac{249}{419}\right)\)	\(e\left(\frac{22}{419}\right)\)	\(e\left(\frac{411}{419}\right)\)	\(e\left(\frac{299}{419}\right)\)	\(e\left(\frac{96}{419}\right)\)
\(\chi_{839}(4,\cdot)\)	839.c	419	yes	\(1\)	\(1\)	\(e\left(\frac{299}{419}\right)\)	\(e\left(\frac{294}{419}\right)\)	\(e\left(\frac{179}{419}\right)\)	\(e\left(\frac{141}{419}\right)\)	\(e\left(\frac{174}{419}\right)\)	\(e\left(\frac{344}{419}\right)\)	\(e\left(\frac{59}{419}\right)\)	\(e\left(\frac{169}{419}\right)\)	\(e\left(\frac{21}{419}\right)\)	\(e\left(\frac{67}{419}\right)\)
\(\chi_{839}(5,\cdot)\)	839.c	419	yes	\(1\)	\(1\)	\(e\left(\frac{280}{419}\right)\)	\(e\left(\frac{152}{419}\right)\)	\(e\left(\frac{141}{419}\right)\)	\(e\left(\frac{90}{419}\right)\)	\(e\left(\frac{13}{419}\right)\)	\(e\left(\frac{175}{419}\right)\)	\(e\left(\frac{2}{419}\right)\)	\(e\left(\frac{304}{419}\right)\)	\(e\left(\frac{370}{419}\right)\)	\(e\left(\frac{123}{419}\right)\)
\(\chi_{839}(6,\cdot)\)	839.c	419	yes	\(1\)	\(1\)	\(e\left(\frac{87}{419}\right)\)	\(e\left(\frac{143}{419}\right)\)	\(e\left(\frac{174}{419}\right)\)	\(e\left(\frac{13}{419}\right)\)	\(e\left(\frac{230}{419}\right)\)	\(e\left(\frac{2}{419}\right)\)	\(e\left(\frac{261}{419}\right)\)	\(e\left(\frac{286}{419}\right)\)	\(e\left(\frac{100}{419}\right)\)	\(e\left(\frac{339}{419}\right)\)
\(\chi_{839}(7,\cdot)\)	839.c	419	yes	\(1\)	\(1\)	\(e\left(\frac{172}{419}\right)\)	\(e\left(\frac{249}{419}\right)\)	\(e\left(\frac{344}{419}\right)\)	\(e\left(\frac{175}{419}\right)\)	\(e\left(\frac{2}{419}\right)\)	\(e\left(\frac{317}{419}\right)\)	\(e\left(\frac{97}{419}\right)\)	\(e\left(\frac{79}{419}\right)\)	\(e\left(\frac{347}{419}\right)\)	\(e\left(\frac{309}{419}\right)\)
\(\chi_{839}(8,\cdot)\)	839.c	419	yes	\(1\)	\(1\)	\(e\left(\frac{239}{419}\right)\)	\(e\left(\frac{22}{419}\right)\)	\(e\left(\frac{59}{419}\right)\)	\(e\left(\frac{2}{419}\right)\)	\(e\left(\frac{261}{419}\right)\)	\(e\left(\frac{97}{419}\right)\)	\(e\left(\frac{298}{419}\right)\)	\(e\left(\frac{44}{419}\right)\)	\(e\left(\frac{241}{419}\right)\)	\(e\left(\frac{310}{419}\right)\)
\(\chi_{839}(9,\cdot)\)	839.c	419	yes	\(1\)	\(1\)	\(e\left(\frac{294}{419}\right)\)	\(e\left(\frac{411}{419}\right)\)	\(e\left(\frac{169}{419}\right)\)	\(e\left(\frac{304}{419}\right)\)	\(e\left(\frac{286}{419}\right)\)	\(e\left(\frac{79}{419}\right)\)	\(e\left(\frac{44}{419}\right)\)	\(e\left(\frac{403}{419}\right)\)	\(e\left(\frac{179}{419}\right)\)	\(e\left(\frac{192}{419}\right)\)
\(\chi_{839}(10,\cdot)\)	839.c	419	yes	\(1\)	\(1\)	\(e\left(\frac{220}{419}\right)\)	\(e\left(\frac{299}{419}\right)\)	\(e\left(\frac{21}{419}\right)\)	\(e\left(\frac{370}{419}\right)\)	\(e\left(\frac{100}{419}\right)\)	\(e\left(\frac{347}{419}\right)\)	\(e\left(\frac{241}{419}\right)\)	\(e\left(\frac{179}{419}\right)\)	\(e\left(\frac{171}{419}\right)\)	\(e\left(\frac{366}{419}\right)\)
\(\chi_{839}(11,\cdot)\)	839.d	838	yes	\(-1\)	\(1\)	\(e\left(\frac{243}{419}\right)\)	\(e\left(\frac{96}{419}\right)\)	\(e\left(\frac{67}{419}\right)\)	\(e\left(\frac{123}{419}\right)\)	\(e\left(\frac{339}{419}\right)\)	\(e\left(\frac{309}{419}\right)\)	\(e\left(\frac{310}{419}\right)\)	\(e\left(\frac{192}{419}\right)\)	\(e\left(\frac{366}{419}\right)\)	\(e\left(\frac{1}{838}\right)\)
\(\chi_{839}(12,\cdot)\)	839.c	419	yes	\(1\)	\(1\)	\(e\left(\frac{27}{419}\right)\)	\(e\left(\frac{290}{419}\right)\)	\(e\left(\frac{54}{419}\right)\)	\(e\left(\frac{293}{419}\right)\)	\(e\left(\frac{317}{419}\right)\)	\(e\left(\frac{174}{419}\right)\)	\(e\left(\frac{81}{419}\right)\)	\(e\left(\frac{161}{419}\right)\)	\(e\left(\frac{320}{419}\right)\)	\(e\left(\frac{163}{419}\right)\)
\(\chi_{839}(13,\cdot)\)	839.d	838	yes	\(-1\)	\(1\)	\(e\left(\frac{113}{419}\right)\)	\(e\left(\frac{205}{419}\right)\)	\(e\left(\frac{226}{419}\right)\)	\(e\left(\frac{171}{419}\right)\)	\(e\left(\frac{318}{419}\right)\)	\(e\left(\frac{123}{419}\right)\)	\(e\left(\frac{339}{419}\right)\)	\(e\left(\frac{410}{419}\right)\)	\(e\left(\frac{284}{419}\right)\)	\(e\left(\frac{635}{838}\right)\)
\(\chi_{839}(14,\cdot)\)	839.c	419	yes	\(1\)	\(1\)	\(e\left(\frac{112}{419}\right)\)	\(e\left(\frac{396}{419}\right)\)	\(e\left(\frac{224}{419}\right)\)	\(e\left(\frac{36}{419}\right)\)	\(e\left(\frac{89}{419}\right)\)	\(e\left(\frac{70}{419}\right)\)	\(e\left(\frac{336}{419}\right)\)	\(e\left(\frac{373}{419}\right)\)	\(e\left(\frac{148}{419}\right)\)	\(e\left(\frac{133}{419}\right)\)
\(\chi_{839}(15,\cdot)\)	839.c	419	yes	\(1\)	\(1\)	\(e\left(\frac{8}{419}\right)\)	\(e\left(\frac{148}{419}\right)\)	\(e\left(\frac{16}{419}\right)\)	\(e\left(\frac{242}{419}\right)\)	\(e\left(\frac{156}{419}\right)\)	\(e\left(\frac{5}{419}\right)\)	\(e\left(\frac{24}{419}\right)\)	\(e\left(\frac{296}{419}\right)\)	\(e\left(\frac{250}{419}\right)\)	\(e\left(\frac{219}{419}\right)\)
\(\chi_{839}(16,\cdot)\)	839.c	419	yes	\(1\)	\(1\)	\(e\left(\frac{179}{419}\right)\)	\(e\left(\frac{169}{419}\right)\)	\(e\left(\frac{358}{419}\right)\)	\(e\left(\frac{282}{419}\right)\)	\(e\left(\frac{348}{419}\right)\)	\(e\left(\frac{269}{419}\right)\)	\(e\left(\frac{118}{419}\right)\)	\(e\left(\frac{338}{419}\right)\)	\(e\left(\frac{42}{419}\right)\)	\(e\left(\frac{134}{419}\right)\)
\(\chi_{839}(17,\cdot)\)	839.d	838	yes	\(-1\)	\(1\)	\(e\left(\frac{162}{419}\right)\)	\(e\left(\frac{64}{419}\right)\)	\(e\left(\frac{324}{419}\right)\)	\(e\left(\frac{82}{419}\right)\)	\(e\left(\frac{226}{419}\right)\)	\(e\left(\frac{206}{419}\right)\)	\(e\left(\frac{67}{419}\right)\)	\(e\left(\frac{128}{419}\right)\)	\(e\left(\frac{244}{419}\right)\)	\(e\left(\frac{699}{838}\right)\)
\(\chi_{839}(18,\cdot)\)	839.c	419	yes	\(1\)	\(1\)	\(e\left(\frac{234}{419}\right)\)	\(e\left(\frac{139}{419}\right)\)	\(e\left(\frac{49}{419}\right)\)	\(e\left(\frac{165}{419}\right)\)	\(e\left(\frac{373}{419}\right)\)	\(e\left(\frac{251}{419}\right)\)	\(e\left(\frac{283}{419}\right)\)	\(e\left(\frac{278}{419}\right)\)	\(e\left(\frac{399}{419}\right)\)	\(e\left(\frac{16}{419}\right)\)
\(\chi_{839}(19,\cdot)\)	839.c	419	yes	\(1\)	\(1\)	\(e\left(\frac{24}{419}\right)\)	\(e\left(\frac{25}{419}\right)\)	\(e\left(\frac{48}{419}\right)\)	\(e\left(\frac{307}{419}\right)\)	\(e\left(\frac{49}{419}\right)\)	\(e\left(\frac{15}{419}\right)\)	\(e\left(\frac{72}{419}\right)\)	\(e\left(\frac{50}{419}\right)\)	\(e\left(\frac{331}{419}\right)\)	\(e\left(\frac{238}{419}\right)\)
\(\chi_{839}(20,\cdot)\)	839.c	419	yes	\(1\)	\(1\)	\(e\left(\frac{160}{419}\right)\)	\(e\left(\frac{27}{419}\right)\)	\(e\left(\frac{320}{419}\right)\)	\(e\left(\frac{231}{419}\right)\)	\(e\left(\frac{187}{419}\right)\)	\(e\left(\frac{100}{419}\right)\)	\(e\left(\frac{61}{419}\right)\)	\(e\left(\frac{54}{419}\right)\)	\(e\left(\frac{391}{419}\right)\)	\(e\left(\frac{190}{419}\right)\)
\(\chi_{839}(21,\cdot)\)	839.c	419	yes	\(1\)	\(1\)	\(e\left(\frac{319}{419}\right)\)	\(e\left(\frac{245}{419}\right)\)	\(e\left(\frac{219}{419}\right)\)	\(e\left(\frac{327}{419}\right)\)	\(e\left(\frac{145}{419}\right)\)	\(e\left(\frac{147}{419}\right)\)	\(e\left(\frac{119}{419}\right)\)	\(e\left(\frac{71}{419}\right)\)	\(e\left(\frac{227}{419}\right)\)	\(e\left(\frac{405}{419}\right)\)
\(\chi_{839}(22,\cdot)\)	839.d	838	yes	\(-1\)	\(1\)	\(e\left(\frac{183}{419}\right)\)	\(e\left(\frac{243}{419}\right)\)	\(e\left(\frac{366}{419}\right)\)	\(e\left(\frac{403}{419}\right)\)	\(e\left(\frac{7}{419}\right)\)	\(e\left(\frac{62}{419}\right)\)	\(e\left(\frac{130}{419}\right)\)	\(e\left(\frac{67}{419}\right)\)	\(e\left(\frac{167}{419}\right)\)	\(e\left(\frac{487}{838}\right)\)
\(\chi_{839}(23,\cdot)\)	839.c	419	yes	\(1\)	\(1\)	\(e\left(\frac{69}{419}\right)\)	\(e\left(\frac{229}{419}\right)\)	\(e\left(\frac{138}{419}\right)\)	\(e\left(\frac{97}{419}\right)\)	\(e\left(\frac{298}{419}\right)\)	\(e\left(\frac{305}{419}\right)\)	\(e\left(\frac{207}{419}\right)\)	\(e\left(\frac{39}{419}\right)\)	\(e\left(\frac{166}{419}\right)\)	\(e\left(\frac{370}{419}\right)\)
\(\chi_{839}(24,\cdot)\)	839.c	419	yes	\(1\)	\(1\)	\(e\left(\frac{386}{419}\right)\)	\(e\left(\frac{18}{419}\right)\)	\(e\left(\frac{353}{419}\right)\)	\(e\left(\frac{154}{419}\right)\)	\(e\left(\frac{404}{419}\right)\)	\(e\left(\frac{346}{419}\right)\)	\(e\left(\frac{320}{419}\right)\)	\(e\left(\frac{36}{419}\right)\)	\(e\left(\frac{121}{419}\right)\)	\(e\left(\frac{406}{419}\right)\)
\(\chi_{839}(25,\cdot)\)	839.c	419	yes	\(1\)	\(1\)	\(e\left(\frac{141}{419}\right)\)	\(e\left(\frac{304}{419}\right)\)	\(e\left(\frac{282}{419}\right)\)	\(e\left(\frac{180}{419}\right)\)	\(e\left(\frac{26}{419}\right)\)	\(e\left(\frac{350}{419}\right)\)	\(e\left(\frac{4}{419}\right)\)	\(e\left(\frac{189}{419}\right)\)	\(e\left(\frac{321}{419}\right)\)	\(e\left(\frac{246}{419}\right)\)
\(\chi_{839}(26,\cdot)\)	839.d	838	yes	\(-1\)	\(1\)	\(e\left(\frac{53}{419}\right)\)	\(e\left(\frac{352}{419}\right)\)	\(e\left(\frac{106}{419}\right)\)	\(e\left(\frac{32}{419}\right)\)	\(e\left(\frac{405}{419}\right)\)	\(e\left(\frac{295}{419}\right)\)	\(e\left(\frac{159}{419}\right)\)	\(e\left(\frac{285}{419}\right)\)	\(e\left(\frac{85}{419}\right)\)	\(e\left(\frac{283}{838}\right)\)
\(\chi_{839}(27,\cdot)\)	839.c	419	yes	\(1\)	\(1\)	\(e\left(\frac{22}{419}\right)\)	\(e\left(\frac{407}{419}\right)\)	\(e\left(\frac{44}{419}\right)\)	\(e\left(\frac{37}{419}\right)\)	\(e\left(\frac{10}{419}\right)\)	\(e\left(\frac{328}{419}\right)\)	\(e\left(\frac{66}{419}\right)\)	\(e\left(\frac{395}{419}\right)\)	\(e\left(\frac{59}{419}\right)\)	\(e\left(\frac{288}{419}\right)\)
\(\chi_{839}(28,\cdot)\)	839.c	419	yes	\(1\)	\(1\)	\(e\left(\frac{52}{419}\right)\)	\(e\left(\frac{124}{419}\right)\)	\(e\left(\frac{104}{419}\right)\)	\(e\left(\frac{316}{419}\right)\)	\(e\left(\frac{176}{419}\right)\)	\(e\left(\frac{242}{419}\right)\)	\(e\left(\frac{156}{419}\right)\)	\(e\left(\frac{248}{419}\right)\)	\(e\left(\frac{368}{419}\right)\)	\(e\left(\frac{376}{419}\right)\)
\(\chi_{839}(29,\cdot)\)	839.d	838	yes	\(-1\)	\(1\)	\(e\left(\frac{389}{419}\right)\)	\(e\left(\frac{283}{419}\right)\)	\(e\left(\frac{359}{419}\right)\)	\(e\left(\frac{140}{419}\right)\)	\(e\left(\frac{253}{419}\right)\)	\(e\left(\frac{86}{419}\right)\)	\(e\left(\frac{329}{419}\right)\)	\(e\left(\frac{147}{419}\right)\)	\(e\left(\frac{110}{419}\right)\)	\(e\left(\frac{243}{838}\right)\)
\(\chi_{839}(30,\cdot)\)	839.c	419	yes	\(1\)	\(1\)	\(e\left(\frac{367}{419}\right)\)	\(e\left(\frac{295}{419}\right)\)	\(e\left(\frac{315}{419}\right)\)	\(e\left(\frac{103}{419}\right)\)	\(e\left(\frac{243}{419}\right)\)	\(e\left(\frac{177}{419}\right)\)	\(e\left(\frac{263}{419}\right)\)	\(e\left(\frac{171}{419}\right)\)	\(e\left(\frac{51}{419}\right)\)	\(e\left(\frac{43}{419}\right)\)
\(\chi_{839}(31,\cdot)\)	839.d	838	yes	\(-1\)	\(1\)	\(e\left(\frac{337}{419}\right)\)	\(e\left(\frac{159}{419}\right)\)	\(e\left(\frac{255}{419}\right)\)	\(e\left(\frac{243}{419}\right)\)	\(e\left(\frac{77}{419}\right)\)	\(e\left(\frac{263}{419}\right)\)	\(e\left(\frac{173}{419}\right)\)	\(e\left(\frac{318}{419}\right)\)	\(e\left(\frac{161}{419}\right)\)	\(e\left(\frac{329}{838}\right)\)
\(\chi_{839}(32,\cdot)\)	839.c	419	yes	\(1\)	\(1\)	\(e\left(\frac{119}{419}\right)\)	\(e\left(\frac{316}{419}\right)\)	\(e\left(\frac{238}{419}\right)\)	\(e\left(\frac{143}{419}\right)\)	\(e\left(\frac{16}{419}\right)\)	\(e\left(\frac{22}{419}\right)\)	\(e\left(\frac{357}{419}\right)\)	\(e\left(\frac{213}{419}\right)\)	\(e\left(\frac{262}{419}\right)\)	\(e\left(\frac{377}{419}\right)\)

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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.