LMFDB - Group of Dirichlet characters of modulus 2183

Show commands: PariGP / SageMath

sage: H = DirichletGroup(2183)

pari: g = idealstar(,2183,2)

Character group

sage: G.order() pari: g.no
Order	=	2088
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{1044}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{2183}(1889,\cdot)$, $\chi_{2183}(297,\cdot)$

First 32 of 2088 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{2183}(1,\cdot)$	2183.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{2183}(2,\cdot)$	2183.bi	1044	yes	$1$	$1$	$e\left(\frac{47}{1044}\right)$	$e\left(\frac{305}{522}\right)$	$e\left(\frac{47}{522}\right)$	$e\left(\frac{775}{1044}\right)$	$e\left(\frac{73}{116}\right)$	$e\left(\frac{52}{261}\right)$	$e\left(\frac{47}{348}\right)$	$e\left(\frac{44}{261}\right)$	$e\left(\frac{137}{174}\right)$	$e\left(\frac{23}{87}\right)$
$\chi_{2183}(3,\cdot)$	2183.bh	522	yes	$1$	$1$	$e\left(\frac{305}{522}\right)$	$e\left(\frac{230}{261}\right)$	$e\left(\frac{44}{261}\right)$	$e\left(\frac{409}{522}\right)$	$e\left(\frac{27}{58}\right)$	$e\left(\frac{164}{261}\right)$	$e\left(\frac{131}{174}\right)$	$e\left(\frac{199}{261}\right)$	$e\left(\frac{32}{87}\right)$	$e\left(\frac{19}{87}\right)$
$\chi_{2183}(4,\cdot)$	2183.bh	522	yes	$1$	$1$	$e\left(\frac{47}{522}\right)$	$e\left(\frac{44}{261}\right)$	$e\left(\frac{47}{261}\right)$	$e\left(\frac{253}{522}\right)$	$e\left(\frac{15}{58}\right)$	$e\left(\frac{104}{261}\right)$	$e\left(\frac{47}{174}\right)$	$e\left(\frac{88}{261}\right)$	$e\left(\frac{50}{87}\right)$	$e\left(\frac{46}{87}\right)$
$\chi_{2183}(5,\cdot)$	2183.bj	1044	yes	$-1$	$1$	$e\left(\frac{775}{1044}\right)$	$e\left(\frac{409}{522}\right)$	$e\left(\frac{253}{522}\right)$	$e\left(\frac{329}{1044}\right)$	$e\left(\frac{61}{116}\right)$	$e\left(\frac{80}{261}\right)$	$e\left(\frac{79}{348}\right)$	$e\left(\frac{148}{261}\right)$	$e\left(\frac{5}{87}\right)$	$e\left(\frac{131}{174}\right)$
$\chi_{2183}(6,\cdot)$	2183.y	116	yes	$1$	$1$	$e\left(\frac{73}{116}\right)$	$e\left(\frac{27}{58}\right)$	$e\left(\frac{15}{58}\right)$	$e\left(\frac{61}{116}\right)$	$e\left(\frac{11}{116}\right)$	$e\left(\frac{24}{29}\right)$	$e\left(\frac{103}{116}\right)$	$e\left(\frac{27}{29}\right)$	$e\left(\frac{9}{58}\right)$	$e\left(\frac{14}{29}\right)$
$\chi_{2183}(7,\cdot)$	2183.bc	261	yes	$1$	$1$	$e\left(\frac{52}{261}\right)$	$e\left(\frac{164}{261}\right)$	$e\left(\frac{104}{261}\right)$	$e\left(\frac{80}{261}\right)$	$e\left(\frac{24}{29}\right)$	$e\left(\frac{8}{261}\right)$	$e\left(\frac{52}{87}\right)$	$e\left(\frac{67}{261}\right)$	$e\left(\frac{44}{87}\right)$	$e\left(\frac{37}{87}\right)$
$\chi_{2183}(8,\cdot)$	2183.be	348	yes	$1$	$1$	$e\left(\frac{47}{348}\right)$	$e\left(\frac{131}{174}\right)$	$e\left(\frac{47}{174}\right)$	$e\left(\frac{79}{348}\right)$	$e\left(\frac{103}{116}\right)$	$e\left(\frac{52}{87}\right)$	$e\left(\frac{47}{116}\right)$	$e\left(\frac{44}{87}\right)$	$e\left(\frac{21}{58}\right)$	$e\left(\frac{23}{29}\right)$
$\chi_{2183}(9,\cdot)$	2183.bc	261	yes	$1$	$1$	$e\left(\frac{44}{261}\right)$	$e\left(\frac{199}{261}\right)$	$e\left(\frac{88}{261}\right)$	$e\left(\frac{148}{261}\right)$	$e\left(\frac{27}{29}\right)$	$e\left(\frac{67}{261}\right)$	$e\left(\frac{44}{87}\right)$	$e\left(\frac{137}{261}\right)$	$e\left(\frac{64}{87}\right)$	$e\left(\frac{38}{87}\right)$
$\chi_{2183}(10,\cdot)$	2183.ba	174	yes	$-1$	$1$	$e\left(\frac{137}{174}\right)$	$e\left(\frac{32}{87}\right)$	$e\left(\frac{50}{87}\right)$	$e\left(\frac{5}{87}\right)$	$e\left(\frac{9}{58}\right)$	$e\left(\frac{44}{87}\right)$	$e\left(\frac{21}{58}\right)$	$e\left(\frac{64}{87}\right)$	$e\left(\frac{49}{58}\right)$	$e\left(\frac{1}{58}\right)$
$\chi_{2183}(11,\cdot)$	2183.bb	174	yes	$-1$	$1$	$e\left(\frac{23}{87}\right)$	$e\left(\frac{19}{87}\right)$	$e\left(\frac{46}{87}\right)$	$e\left(\frac{131}{174}\right)$	$e\left(\frac{14}{29}\right)$	$e\left(\frac{37}{87}\right)$	$e\left(\frac{23}{29}\right)$	$e\left(\frac{38}{87}\right)$	$e\left(\frac{1}{58}\right)$	$e\left(\frac{45}{58}\right)$
$\chi_{2183}(12,\cdot)$	2183.bc	261	yes	$1$	$1$	$e\left(\frac{176}{261}\right)$	$e\left(\frac{13}{261}\right)$	$e\left(\frac{91}{261}\right)$	$e\left(\frac{70}{261}\right)$	$e\left(\frac{21}{29}\right)$	$e\left(\frac{7}{261}\right)$	$e\left(\frac{2}{87}\right)$	$e\left(\frac{26}{261}\right)$	$e\left(\frac{82}{87}\right)$	$e\left(\frac{65}{87}\right)$
$\chi_{2183}(13,\cdot)$	2183.bi	1044	yes	$1$	$1$	$e\left(\frac{85}{1044}\right)$	$e\left(\frac{385}{522}\right)$	$e\left(\frac{85}{522}\right)$	$e\left(\frac{713}{1044}\right)$	$e\left(\frac{95}{116}\right)$	$e\left(\frac{194}{261}\right)$	$e\left(\frac{85}{348}\right)$	$e\left(\frac{124}{261}\right)$	$e\left(\frac{133}{174}\right)$	$e\left(\frac{49}{87}\right)$
$\chi_{2183}(14,\cdot)$	2183.be	348	yes	$1$	$1$	$e\left(\frac{85}{348}\right)$	$e\left(\frac{37}{174}\right)$	$e\left(\frac{85}{174}\right)$	$e\left(\frac{17}{348}\right)$	$e\left(\frac{53}{116}\right)$	$e\left(\frac{20}{87}\right)$	$e\left(\frac{85}{116}\right)$	$e\left(\frac{37}{87}\right)$	$e\left(\frac{17}{58}\right)$	$e\left(\frac{20}{29}\right)$
$\chi_{2183}(15,\cdot)$	2183.bj	1044	yes	$-1$	$1$	$e\left(\frac{341}{1044}\right)$	$e\left(\frac{347}{522}\right)$	$e\left(\frac{341}{522}\right)$	$e\left(\frac{103}{1044}\right)$	$e\left(\frac{115}{116}\right)$	$e\left(\frac{244}{261}\right)$	$e\left(\frac{341}{348}\right)$	$e\left(\frac{86}{261}\right)$	$e\left(\frac{37}{87}\right)$	$e\left(\frac{169}{174}\right)$
$\chi_{2183}(16,\cdot)$	2183.bc	261	yes	$1$	$1$	$e\left(\frac{47}{261}\right)$	$e\left(\frac{88}{261}\right)$	$e\left(\frac{94}{261}\right)$	$e\left(\frac{253}{261}\right)$	$e\left(\frac{15}{29}\right)$	$e\left(\frac{208}{261}\right)$	$e\left(\frac{47}{87}\right)$	$e\left(\frac{176}{261}\right)$	$e\left(\frac{13}{87}\right)$	$e\left(\frac{5}{87}\right)$
$\chi_{2183}(17,\cdot)$	2183.bj	1044	yes	$-1$	$1$	$e\left(\frac{923}{1044}\right)$	$e\left(\frac{281}{522}\right)$	$e\left(\frac{401}{522}\right)$	$e\left(\frac{637}{1044}\right)$	$e\left(\frac{49}{116}\right)$	$e\left(\frac{166}{261}\right)$	$e\left(\frac{227}{348}\right)$	$e\left(\frac{20}{261}\right)$	$e\left(\frac{43}{87}\right)$	$e\left(\frac{13}{174}\right)$
$\chi_{2183}(18,\cdot)$	2183.bi	1044	yes	$1$	$1$	$e\left(\frac{223}{1044}\right)$	$e\left(\frac{181}{522}\right)$	$e\left(\frac{223}{522}\right)$	$e\left(\frac{323}{1044}\right)$	$e\left(\frac{65}{116}\right)$	$e\left(\frac{119}{261}\right)$	$e\left(\frac{223}{348}\right)$	$e\left(\frac{181}{261}\right)$	$e\left(\frac{91}{174}\right)$	$e\left(\frac{61}{87}\right)$
$\chi_{2183}(19,\cdot)$	2183.bj	1044	yes	$-1$	$1$	$e\left(\frac{655}{1044}\right)$	$e\left(\frac{19}{522}\right)$	$e\left(\frac{133}{522}\right)$	$e\left(\frac{305}{1044}\right)$	$e\left(\frac{77}{116}\right)$	$e\left(\frac{236}{261}\right)$	$e\left(\frac{307}{348}\right)$	$e\left(\frac{19}{261}\right)$	$e\left(\frac{80}{87}\right)$	$e\left(\frac{95}{174}\right)$
$\chi_{2183}(20,\cdot)$	2183.bj	1044	yes	$-1$	$1$	$e\left(\frac{869}{1044}\right)$	$e\left(\frac{497}{522}\right)$	$e\left(\frac{347}{522}\right)$	$e\left(\frac{835}{1044}\right)$	$e\left(\frac{91}{116}\right)$	$e\left(\frac{184}{261}\right)$	$e\left(\frac{173}{348}\right)$	$e\left(\frac{236}{261}\right)$	$e\left(\frac{55}{87}\right)$	$e\left(\frac{49}{174}\right)$
$\chi_{2183}(21,\cdot)$	2183.bh	522	yes	$1$	$1$	$e\left(\frac{409}{522}\right)$	$e\left(\frac{133}{261}\right)$	$e\left(\frac{148}{261}\right)$	$e\left(\frac{47}{522}\right)$	$e\left(\frac{17}{58}\right)$	$e\left(\frac{172}{261}\right)$	$e\left(\frac{61}{174}\right)$	$e\left(\frac{5}{261}\right)$	$e\left(\frac{76}{87}\right)$	$e\left(\frac{56}{87}\right)$
$\chi_{2183}(22,\cdot)$	2183.bj	1044	yes	$-1$	$1$	$e\left(\frac{323}{1044}\right)$	$e\left(\frac{419}{522}\right)$	$e\left(\frac{323}{522}\right)$	$e\left(\frac{517}{1044}\right)$	$e\left(\frac{13}{116}\right)$	$e\left(\frac{163}{261}\right)$	$e\left(\frac{323}{348}\right)$	$e\left(\frac{158}{261}\right)$	$e\left(\frac{70}{87}\right)$	$e\left(\frac{7}{174}\right)$
$\chi_{2183}(23,\cdot)$	2183.be	348	yes	$1$	$1$	$e\left(\frac{235}{348}\right)$	$e\left(\frac{133}{174}\right)$	$e\left(\frac{61}{174}\right)$	$e\left(\frac{47}{348}\right)$	$e\left(\frac{51}{116}\right)$	$e\left(\frac{86}{87}\right)$	$e\left(\frac{3}{116}\right)$	$e\left(\frac{46}{87}\right)$	$e\left(\frac{47}{58}\right)$	$e\left(\frac{28}{29}\right)$
$\chi_{2183}(24,\cdot)$	2183.bi	1044	yes	$1$	$1$	$e\left(\frac{751}{1044}\right)$	$e\left(\frac{331}{522}\right)$	$e\left(\frac{229}{522}\right)$	$e\left(\frac{11}{1044}\right)$	$e\left(\frac{41}{116}\right)$	$e\left(\frac{59}{261}\right)$	$e\left(\frac{55}{348}\right)$	$e\left(\frac{70}{261}\right)$	$e\left(\frac{127}{174}\right)$	$e\left(\frac{1}{87}\right)$
$\chi_{2183}(25,\cdot)$	2183.bh	522	yes	$1$	$1$	$e\left(\frac{253}{522}\right)$	$e\left(\frac{148}{261}\right)$	$e\left(\frac{253}{261}\right)$	$e\left(\frac{329}{522}\right)$	$e\left(\frac{3}{58}\right)$	$e\left(\frac{160}{261}\right)$	$e\left(\frac{79}{174}\right)$	$e\left(\frac{35}{261}\right)$	$e\left(\frac{10}{87}\right)$	$e\left(\frac{44}{87}\right)$
$\chi_{2183}(26,\cdot)$	2183.w	87	yes	$1$	$1$	$e\left(\frac{11}{87}\right)$	$e\left(\frac{28}{87}\right)$	$e\left(\frac{22}{87}\right)$	$e\left(\frac{37}{87}\right)$	$e\left(\frac{13}{29}\right)$	$e\left(\frac{82}{87}\right)$	$e\left(\frac{11}{29}\right)$	$e\left(\frac{56}{87}\right)$	$e\left(\frac{16}{29}\right)$	$e\left(\frac{24}{29}\right)$
$\chi_{2183}(27,\cdot)$	2183.z	174	yes	$1$	$1$	$e\left(\frac{131}{174}\right)$	$e\left(\frac{56}{87}\right)$	$e\left(\frac{44}{87}\right)$	$e\left(\frac{61}{174}\right)$	$e\left(\frac{23}{58}\right)$	$e\left(\frac{77}{87}\right)$	$e\left(\frac{15}{58}\right)$	$e\left(\frac{25}{87}\right)$	$e\left(\frac{3}{29}\right)$	$e\left(\frac{19}{29}\right)$
$\chi_{2183}(28,\cdot)$	2183.bh	522	yes	$1$	$1$	$e\left(\frac{151}{522}\right)$	$e\left(\frac{208}{261}\right)$	$e\left(\frac{151}{261}\right)$	$e\left(\frac{413}{522}\right)$	$e\left(\frac{5}{58}\right)$	$e\left(\frac{112}{261}\right)$	$e\left(\frac{151}{174}\right)$	$e\left(\frac{155}{261}\right)$	$e\left(\frac{7}{87}\right)$	$e\left(\frac{83}{87}\right)$
$\chi_{2183}(29,\cdot)$	2183.bd	348	yes	$-1$	$1$	$e\left(\frac{23}{348}\right)$	$e\left(\frac{53}{174}\right)$	$e\left(\frac{23}{174}\right)$	$e\left(\frac{109}{348}\right)$	$e\left(\frac{43}{116}\right)$	$e\left(\frac{31}{87}\right)$	$e\left(\frac{23}{116}\right)$	$e\left(\frac{53}{87}\right)$	$e\left(\frac{11}{29}\right)$	$e\left(\frac{33}{58}\right)$
$\chi_{2183}(30,\cdot)$	2183.bf	522	yes	$-1$	$1$	$e\left(\frac{97}{261}\right)$	$e\left(\frac{65}{261}\right)$	$e\left(\frac{194}{261}\right)$	$e\left(\frac{439}{522}\right)$	$e\left(\frac{18}{29}\right)$	$e\left(\frac{35}{261}\right)$	$e\left(\frac{10}{87}\right)$	$e\left(\frac{130}{261}\right)$	$e\left(\frac{37}{174}\right)$	$e\left(\frac{41}{174}\right)$
$\chi_{2183}(31,\cdot)$	2183.y	116	yes	$1$	$1$	$e\left(\frac{11}{116}\right)$	$e\left(\frac{43}{58}\right)$	$e\left(\frac{11}{58}\right)$	$e\left(\frac{95}{116}\right)$	$e\left(\frac{97}{116}\right)$	$e\left(\frac{6}{29}\right)$	$e\left(\frac{33}{116}\right)$	$e\left(\frac{14}{29}\right)$	$e\left(\frac{53}{58}\right)$	$e\left(\frac{18}{29}\right)$
$\chi_{2183}(32,\cdot)$	2183.bi	1044	yes	$1$	$1$	$e\left(\frac{235}{1044}\right)$	$e\left(\frac{481}{522}\right)$	$e\left(\frac{235}{522}\right)$	$e\left(\frac{743}{1044}\right)$	$e\left(\frac{17}{116}\right)$	$e\left(\frac{260}{261}\right)$	$e\left(\frac{235}{348}\right)$	$e\left(\frac{220}{261}\right)$	$e\left(\frac{163}{174}\right)$	$e\left(\frac{28}{87}\right)$

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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	$2183$
Structure	\(C_{2}\times C_{1044}\)
Order	$2088$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{2183}(1,\cdot)\)	2183.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{2183}(2,\cdot)\)	2183.bi	1044	yes	\(1\)	\(1\)	\(e\left(\frac{47}{1044}\right)\)	\(e\left(\frac{305}{522}\right)\)	\(e\left(\frac{47}{522}\right)\)	\(e\left(\frac{775}{1044}\right)\)	\(e\left(\frac{73}{116}\right)\)	\(e\left(\frac{52}{261}\right)\)	\(e\left(\frac{47}{348}\right)\)	\(e\left(\frac{44}{261}\right)\)	\(e\left(\frac{137}{174}\right)\)	\(e\left(\frac{23}{87}\right)\)
\(\chi_{2183}(3,\cdot)\)	2183.bh	522	yes	\(1\)	\(1\)	\(e\left(\frac{305}{522}\right)\)	\(e\left(\frac{230}{261}\right)\)	\(e\left(\frac{44}{261}\right)\)	\(e\left(\frac{409}{522}\right)\)	\(e\left(\frac{27}{58}\right)\)	\(e\left(\frac{164}{261}\right)\)	\(e\left(\frac{131}{174}\right)\)	\(e\left(\frac{199}{261}\right)\)	\(e\left(\frac{32}{87}\right)\)	\(e\left(\frac{19}{87}\right)\)
\(\chi_{2183}(4,\cdot)\)	2183.bh	522	yes	\(1\)	\(1\)	\(e\left(\frac{47}{522}\right)\)	\(e\left(\frac{44}{261}\right)\)	\(e\left(\frac{47}{261}\right)\)	\(e\left(\frac{253}{522}\right)\)	\(e\left(\frac{15}{58}\right)\)	\(e\left(\frac{104}{261}\right)\)	\(e\left(\frac{47}{174}\right)\)	\(e\left(\frac{88}{261}\right)\)	\(e\left(\frac{50}{87}\right)\)	\(e\left(\frac{46}{87}\right)\)
\(\chi_{2183}(5,\cdot)\)	2183.bj	1044	yes	\(-1\)	\(1\)	\(e\left(\frac{775}{1044}\right)\)	\(e\left(\frac{409}{522}\right)\)	\(e\left(\frac{253}{522}\right)\)	\(e\left(\frac{329}{1044}\right)\)	\(e\left(\frac{61}{116}\right)\)	\(e\left(\frac{80}{261}\right)\)	\(e\left(\frac{79}{348}\right)\)	\(e\left(\frac{148}{261}\right)\)	\(e\left(\frac{5}{87}\right)\)	\(e\left(\frac{131}{174}\right)\)
\(\chi_{2183}(6,\cdot)\)	2183.y	116	yes	\(1\)	\(1\)	\(e\left(\frac{73}{116}\right)\)	\(e\left(\frac{27}{58}\right)\)	\(e\left(\frac{15}{58}\right)\)	\(e\left(\frac{61}{116}\right)\)	\(e\left(\frac{11}{116}\right)\)	\(e\left(\frac{24}{29}\right)\)	\(e\left(\frac{103}{116}\right)\)	\(e\left(\frac{27}{29}\right)\)	\(e\left(\frac{9}{58}\right)\)	\(e\left(\frac{14}{29}\right)\)
\(\chi_{2183}(7,\cdot)\)	2183.bc	261	yes	\(1\)	\(1\)	\(e\left(\frac{52}{261}\right)\)	\(e\left(\frac{164}{261}\right)\)	\(e\left(\frac{104}{261}\right)\)	\(e\left(\frac{80}{261}\right)\)	\(e\left(\frac{24}{29}\right)\)	\(e\left(\frac{8}{261}\right)\)	\(e\left(\frac{52}{87}\right)\)	\(e\left(\frac{67}{261}\right)\)	\(e\left(\frac{44}{87}\right)\)	\(e\left(\frac{37}{87}\right)\)
\(\chi_{2183}(8,\cdot)\)	2183.be	348	yes	\(1\)	\(1\)	\(e\left(\frac{47}{348}\right)\)	\(e\left(\frac{131}{174}\right)\)	\(e\left(\frac{47}{174}\right)\)	\(e\left(\frac{79}{348}\right)\)	\(e\left(\frac{103}{116}\right)\)	\(e\left(\frac{52}{87}\right)\)	\(e\left(\frac{47}{116}\right)\)	\(e\left(\frac{44}{87}\right)\)	\(e\left(\frac{21}{58}\right)\)	\(e\left(\frac{23}{29}\right)\)
\(\chi_{2183}(9,\cdot)\)	2183.bc	261	yes	\(1\)	\(1\)	\(e\left(\frac{44}{261}\right)\)	\(e\left(\frac{199}{261}\right)\)	\(e\left(\frac{88}{261}\right)\)	\(e\left(\frac{148}{261}\right)\)	\(e\left(\frac{27}{29}\right)\)	\(e\left(\frac{67}{261}\right)\)	\(e\left(\frac{44}{87}\right)\)	\(e\left(\frac{137}{261}\right)\)	\(e\left(\frac{64}{87}\right)\)	\(e\left(\frac{38}{87}\right)\)
\(\chi_{2183}(10,\cdot)\)	2183.ba	174	yes	\(-1\)	\(1\)	\(e\left(\frac{137}{174}\right)\)	\(e\left(\frac{32}{87}\right)\)	\(e\left(\frac{50}{87}\right)\)	\(e\left(\frac{5}{87}\right)\)	\(e\left(\frac{9}{58}\right)\)	\(e\left(\frac{44}{87}\right)\)	\(e\left(\frac{21}{58}\right)\)	\(e\left(\frac{64}{87}\right)\)	\(e\left(\frac{49}{58}\right)\)	\(e\left(\frac{1}{58}\right)\)
\(\chi_{2183}(11,\cdot)\)	2183.bb	174	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{87}\right)\)	\(e\left(\frac{19}{87}\right)\)	\(e\left(\frac{46}{87}\right)\)	\(e\left(\frac{131}{174}\right)\)	\(e\left(\frac{14}{29}\right)\)	\(e\left(\frac{37}{87}\right)\)	\(e\left(\frac{23}{29}\right)\)	\(e\left(\frac{38}{87}\right)\)	\(e\left(\frac{1}{58}\right)\)	\(e\left(\frac{45}{58}\right)\)
\(\chi_{2183}(12,\cdot)\)	2183.bc	261	yes	\(1\)	\(1\)	\(e\left(\frac{176}{261}\right)\)	\(e\left(\frac{13}{261}\right)\)	\(e\left(\frac{91}{261}\right)\)	\(e\left(\frac{70}{261}\right)\)	\(e\left(\frac{21}{29}\right)\)	\(e\left(\frac{7}{261}\right)\)	\(e\left(\frac{2}{87}\right)\)	\(e\left(\frac{26}{261}\right)\)	\(e\left(\frac{82}{87}\right)\)	\(e\left(\frac{65}{87}\right)\)
\(\chi_{2183}(13,\cdot)\)	2183.bi	1044	yes	\(1\)	\(1\)	\(e\left(\frac{85}{1044}\right)\)	\(e\left(\frac{385}{522}\right)\)	\(e\left(\frac{85}{522}\right)\)	\(e\left(\frac{713}{1044}\right)\)	\(e\left(\frac{95}{116}\right)\)	\(e\left(\frac{194}{261}\right)\)	\(e\left(\frac{85}{348}\right)\)	\(e\left(\frac{124}{261}\right)\)	\(e\left(\frac{133}{174}\right)\)	\(e\left(\frac{49}{87}\right)\)
\(\chi_{2183}(14,\cdot)\)	2183.be	348	yes	\(1\)	\(1\)	\(e\left(\frac{85}{348}\right)\)	\(e\left(\frac{37}{174}\right)\)	\(e\left(\frac{85}{174}\right)\)	\(e\left(\frac{17}{348}\right)\)	\(e\left(\frac{53}{116}\right)\)	\(e\left(\frac{20}{87}\right)\)	\(e\left(\frac{85}{116}\right)\)	\(e\left(\frac{37}{87}\right)\)	\(e\left(\frac{17}{58}\right)\)	\(e\left(\frac{20}{29}\right)\)
\(\chi_{2183}(15,\cdot)\)	2183.bj	1044	yes	\(-1\)	\(1\)	\(e\left(\frac{341}{1044}\right)\)	\(e\left(\frac{347}{522}\right)\)	\(e\left(\frac{341}{522}\right)\)	\(e\left(\frac{103}{1044}\right)\)	\(e\left(\frac{115}{116}\right)\)	\(e\left(\frac{244}{261}\right)\)	\(e\left(\frac{341}{348}\right)\)	\(e\left(\frac{86}{261}\right)\)	\(e\left(\frac{37}{87}\right)\)	\(e\left(\frac{169}{174}\right)\)
\(\chi_{2183}(16,\cdot)\)	2183.bc	261	yes	\(1\)	\(1\)	\(e\left(\frac{47}{261}\right)\)	\(e\left(\frac{88}{261}\right)\)	\(e\left(\frac{94}{261}\right)\)	\(e\left(\frac{253}{261}\right)\)	\(e\left(\frac{15}{29}\right)\)	\(e\left(\frac{208}{261}\right)\)	\(e\left(\frac{47}{87}\right)\)	\(e\left(\frac{176}{261}\right)\)	\(e\left(\frac{13}{87}\right)\)	\(e\left(\frac{5}{87}\right)\)
\(\chi_{2183}(17,\cdot)\)	2183.bj	1044	yes	\(-1\)	\(1\)	\(e\left(\frac{923}{1044}\right)\)	\(e\left(\frac{281}{522}\right)\)	\(e\left(\frac{401}{522}\right)\)	\(e\left(\frac{637}{1044}\right)\)	\(e\left(\frac{49}{116}\right)\)	\(e\left(\frac{166}{261}\right)\)	\(e\left(\frac{227}{348}\right)\)	\(e\left(\frac{20}{261}\right)\)	\(e\left(\frac{43}{87}\right)\)	\(e\left(\frac{13}{174}\right)\)
\(\chi_{2183}(18,\cdot)\)	2183.bi	1044	yes	\(1\)	\(1\)	\(e\left(\frac{223}{1044}\right)\)	\(e\left(\frac{181}{522}\right)\)	\(e\left(\frac{223}{522}\right)\)	\(e\left(\frac{323}{1044}\right)\)	\(e\left(\frac{65}{116}\right)\)	\(e\left(\frac{119}{261}\right)\)	\(e\left(\frac{223}{348}\right)\)	\(e\left(\frac{181}{261}\right)\)	\(e\left(\frac{91}{174}\right)\)	\(e\left(\frac{61}{87}\right)\)
\(\chi_{2183}(19,\cdot)\)	2183.bj	1044	yes	\(-1\)	\(1\)	\(e\left(\frac{655}{1044}\right)\)	\(e\left(\frac{19}{522}\right)\)	\(e\left(\frac{133}{522}\right)\)	\(e\left(\frac{305}{1044}\right)\)	\(e\left(\frac{77}{116}\right)\)	\(e\left(\frac{236}{261}\right)\)	\(e\left(\frac{307}{348}\right)\)	\(e\left(\frac{19}{261}\right)\)	\(e\left(\frac{80}{87}\right)\)	\(e\left(\frac{95}{174}\right)\)
\(\chi_{2183}(20,\cdot)\)	2183.bj	1044	yes	\(-1\)	\(1\)	\(e\left(\frac{869}{1044}\right)\)	\(e\left(\frac{497}{522}\right)\)	\(e\left(\frac{347}{522}\right)\)	\(e\left(\frac{835}{1044}\right)\)	\(e\left(\frac{91}{116}\right)\)	\(e\left(\frac{184}{261}\right)\)	\(e\left(\frac{173}{348}\right)\)	\(e\left(\frac{236}{261}\right)\)	\(e\left(\frac{55}{87}\right)\)	\(e\left(\frac{49}{174}\right)\)
\(\chi_{2183}(21,\cdot)\)	2183.bh	522	yes	\(1\)	\(1\)	\(e\left(\frac{409}{522}\right)\)	\(e\left(\frac{133}{261}\right)\)	\(e\left(\frac{148}{261}\right)\)	\(e\left(\frac{47}{522}\right)\)	\(e\left(\frac{17}{58}\right)\)	\(e\left(\frac{172}{261}\right)\)	\(e\left(\frac{61}{174}\right)\)	\(e\left(\frac{5}{261}\right)\)	\(e\left(\frac{76}{87}\right)\)	\(e\left(\frac{56}{87}\right)\)
\(\chi_{2183}(22,\cdot)\)	2183.bj	1044	yes	\(-1\)	\(1\)	\(e\left(\frac{323}{1044}\right)\)	\(e\left(\frac{419}{522}\right)\)	\(e\left(\frac{323}{522}\right)\)	\(e\left(\frac{517}{1044}\right)\)	\(e\left(\frac{13}{116}\right)\)	\(e\left(\frac{163}{261}\right)\)	\(e\left(\frac{323}{348}\right)\)	\(e\left(\frac{158}{261}\right)\)	\(e\left(\frac{70}{87}\right)\)	\(e\left(\frac{7}{174}\right)\)
\(\chi_{2183}(23,\cdot)\)	2183.be	348	yes	\(1\)	\(1\)	\(e\left(\frac{235}{348}\right)\)	\(e\left(\frac{133}{174}\right)\)	\(e\left(\frac{61}{174}\right)\)	\(e\left(\frac{47}{348}\right)\)	\(e\left(\frac{51}{116}\right)\)	\(e\left(\frac{86}{87}\right)\)	\(e\left(\frac{3}{116}\right)\)	\(e\left(\frac{46}{87}\right)\)	\(e\left(\frac{47}{58}\right)\)	\(e\left(\frac{28}{29}\right)\)
\(\chi_{2183}(24,\cdot)\)	2183.bi	1044	yes	\(1\)	\(1\)	\(e\left(\frac{751}{1044}\right)\)	\(e\left(\frac{331}{522}\right)\)	\(e\left(\frac{229}{522}\right)\)	\(e\left(\frac{11}{1044}\right)\)	\(e\left(\frac{41}{116}\right)\)	\(e\left(\frac{59}{261}\right)\)	\(e\left(\frac{55}{348}\right)\)	\(e\left(\frac{70}{261}\right)\)	\(e\left(\frac{127}{174}\right)\)	\(e\left(\frac{1}{87}\right)\)
\(\chi_{2183}(25,\cdot)\)	2183.bh	522	yes	\(1\)	\(1\)	\(e\left(\frac{253}{522}\right)\)	\(e\left(\frac{148}{261}\right)\)	\(e\left(\frac{253}{261}\right)\)	\(e\left(\frac{329}{522}\right)\)	\(e\left(\frac{3}{58}\right)\)	\(e\left(\frac{160}{261}\right)\)	\(e\left(\frac{79}{174}\right)\)	\(e\left(\frac{35}{261}\right)\)	\(e\left(\frac{10}{87}\right)\)	\(e\left(\frac{44}{87}\right)\)
\(\chi_{2183}(26,\cdot)\)	2183.w	87	yes	\(1\)	\(1\)	\(e\left(\frac{11}{87}\right)\)	\(e\left(\frac{28}{87}\right)\)	\(e\left(\frac{22}{87}\right)\)	\(e\left(\frac{37}{87}\right)\)	\(e\left(\frac{13}{29}\right)\)	\(e\left(\frac{82}{87}\right)\)	\(e\left(\frac{11}{29}\right)\)	\(e\left(\frac{56}{87}\right)\)	\(e\left(\frac{16}{29}\right)\)	\(e\left(\frac{24}{29}\right)\)
\(\chi_{2183}(27,\cdot)\)	2183.z	174	yes	\(1\)	\(1\)	\(e\left(\frac{131}{174}\right)\)	\(e\left(\frac{56}{87}\right)\)	\(e\left(\frac{44}{87}\right)\)	\(e\left(\frac{61}{174}\right)\)	\(e\left(\frac{23}{58}\right)\)	\(e\left(\frac{77}{87}\right)\)	\(e\left(\frac{15}{58}\right)\)	\(e\left(\frac{25}{87}\right)\)	\(e\left(\frac{3}{29}\right)\)	\(e\left(\frac{19}{29}\right)\)
\(\chi_{2183}(28,\cdot)\)	2183.bh	522	yes	\(1\)	\(1\)	\(e\left(\frac{151}{522}\right)\)	\(e\left(\frac{208}{261}\right)\)	\(e\left(\frac{151}{261}\right)\)	\(e\left(\frac{413}{522}\right)\)	\(e\left(\frac{5}{58}\right)\)	\(e\left(\frac{112}{261}\right)\)	\(e\left(\frac{151}{174}\right)\)	\(e\left(\frac{155}{261}\right)\)	\(e\left(\frac{7}{87}\right)\)	\(e\left(\frac{83}{87}\right)\)
\(\chi_{2183}(29,\cdot)\)	2183.bd	348	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{348}\right)\)	\(e\left(\frac{53}{174}\right)\)	\(e\left(\frac{23}{174}\right)\)	\(e\left(\frac{109}{348}\right)\)	\(e\left(\frac{43}{116}\right)\)	\(e\left(\frac{31}{87}\right)\)	\(e\left(\frac{23}{116}\right)\)	\(e\left(\frac{53}{87}\right)\)	\(e\left(\frac{11}{29}\right)\)	\(e\left(\frac{33}{58}\right)\)
\(\chi_{2183}(30,\cdot)\)	2183.bf	522	yes	\(-1\)	\(1\)	\(e\left(\frac{97}{261}\right)\)	\(e\left(\frac{65}{261}\right)\)	\(e\left(\frac{194}{261}\right)\)	\(e\left(\frac{439}{522}\right)\)	\(e\left(\frac{18}{29}\right)\)	\(e\left(\frac{35}{261}\right)\)	\(e\left(\frac{10}{87}\right)\)	\(e\left(\frac{130}{261}\right)\)	\(e\left(\frac{37}{174}\right)\)	\(e\left(\frac{41}{174}\right)\)
\(\chi_{2183}(31,\cdot)\)	2183.y	116	yes	\(1\)	\(1\)	\(e\left(\frac{11}{116}\right)\)	\(e\left(\frac{43}{58}\right)\)	\(e\left(\frac{11}{58}\right)\)	\(e\left(\frac{95}{116}\right)\)	\(e\left(\frac{97}{116}\right)\)	\(e\left(\frac{6}{29}\right)\)	\(e\left(\frac{33}{116}\right)\)	\(e\left(\frac{14}{29}\right)\)	\(e\left(\frac{53}{58}\right)\)	\(e\left(\frac{18}{29}\right)\)
\(\chi_{2183}(32,\cdot)\)	2183.bi	1044	yes	\(1\)	\(1\)	\(e\left(\frac{235}{1044}\right)\)	\(e\left(\frac{481}{522}\right)\)	\(e\left(\frac{235}{522}\right)\)	\(e\left(\frac{743}{1044}\right)\)	\(e\left(\frac{17}{116}\right)\)	\(e\left(\frac{260}{261}\right)\)	\(e\left(\frac{235}{348}\right)\)	\(e\left(\frac{220}{261}\right)\)	\(e\left(\frac{163}{174}\right)\)	\(e\left(\frac{28}{87}\right)\)

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.