LMFDB - Group of Dirichlet characters of modulus 2850

Show commands: PariGP / SageMath

sage: H = DirichletGroup(2850)

pari: g = idealstar(,2850,2)

Character group

sage: G.order() pari: g.no
Order	=	720
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{180}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{2850}(1901,\cdot)$, $\chi_{2850}(1027,\cdot)$, $\chi_{2850}(1351,\cdot)$

First 32 of 720 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	$-1$	$1$	$7$	$11$	$13$	$17$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{2850}(1,\cdot)$	2850.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{2850}(7,\cdot)$	2850.bg	12	no	$-1$	$1$	$i$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{2850}(11,\cdot)$	2850.bz	30	no	$-1$	$1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{2850}(13,\cdot)$	2850.cs	180	no	$1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{79}{180}\right)$	$e\left(\frac{23}{180}\right)$	$e\left(\frac{1}{180}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{25}{36}\right)$
$\chi_{2850}(17,\cdot)$	2850.cr	180	no	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{23}{180}\right)$	$e\left(\frac{91}{180}\right)$	$e\left(\frac{137}{180}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{23}{36}\right)$
$\chi_{2850}(23,\cdot)$	2850.cr	180	no	$1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{180}\right)$	$e\left(\frac{137}{180}\right)$	$e\left(\frac{139}{180}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{1}{36}\right)$
$\chi_{2850}(29,\cdot)$	2850.cm	90	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{11}{18}\right)$
$\chi_{2850}(31,\cdot)$	2850.bx	30	no	$-1$	$1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{2850}(37,\cdot)$	2850.bp	20	no	$1$	$1$	$i$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{3}{10}\right)$	$-i$
$\chi_{2850}(41,\cdot)$	2850.cj	90	no	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{5}{9}\right)$
$\chi_{2850}(43,\cdot)$	2850.ca	36	no	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{1}{3}\right)$	$-i$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{17}{36}\right)$
$\chi_{2850}(47,\cdot)$	2850.cr	180	no	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{67}{180}\right)$	$e\left(\frac{179}{180}\right)$	$e\left(\frac{133}{180}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{31}{36}\right)$
$\chi_{2850}(49,\cdot)$	2850.r	6	no	$1$	$1$	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{2850}(53,\cdot)$	2850.cq	180	no	$-1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{127}{180}\right)$	$e\left(\frac{29}{180}\right)$	$e\left(\frac{103}{180}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{1}{36}\right)$
$\chi_{2850}(59,\cdot)$	2850.cm	90	no	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{7}{18}\right)$
$\chi_{2850}(61,\cdot)$	2850.ce	45	no	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{7}{9}\right)$
$\chi_{2850}(67,\cdot)$	2850.cs	180	no	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{13}{180}\right)$	$e\left(\frac{161}{180}\right)$	$e\left(\frac{7}{180}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{31}{36}\right)$
$\chi_{2850}(71,\cdot)$	2850.cj	90	no	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{2}{9}\right)$
$\chi_{2850}(73,\cdot)$	2850.ct	180	no	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{101}{180}\right)$	$e\left(\frac{67}{180}\right)$	$e\left(\frac{89}{180}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{29}{36}\right)$
$\chi_{2850}(77,\cdot)$	2850.br	20	no	$1$	$1$	$i$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{7}{10}\right)$	$-i$
$\chi_{2850}(79,\cdot)$	2850.co	90	no	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{1}{18}\right)$
$\chi_{2850}(83,\cdot)$	2850.ci	60	no	$1$	$1$	$-i$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{2850}(89,\cdot)$	2850.cm	90	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{17}{18}\right)$
$\chi_{2850}(91,\cdot)$	2850.cl	90	no	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{7}{9}\right)$
$\chi_{2850}(97,\cdot)$	2850.cs	180	no	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{77}{180}\right)$	$e\left(\frac{109}{180}\right)$	$e\left(\frac{83}{180}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{23}{36}\right)$
$\chi_{2850}(101,\cdot)$	2850.bj	18	no	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{4}{9}\right)$
$\chi_{2850}(103,\cdot)$	2850.cg	60	no	$1$	$1$	$-i$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{2850}(107,\cdot)$	2850.be	12	no	$-1$	$1$	$i$	$-1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$-i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{2850}(109,\cdot)$	2850.co	90	no	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{13}{18}\right)$
$\chi_{2850}(113,\cdot)$	2850.bs	20	no	$-1$	$1$	$-i$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{4}{5}\right)$	$i$
$\chi_{2850}(119,\cdot)$	2850.cn	90	no	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{13}{18}\right)$
$\chi_{2850}(121,\cdot)$	2850.bh	15	no	$1$	$1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{1}{3}\right)$

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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	$2850$
Structure	\(C_{2}\times C_{2}\times C_{180}\)
Order	$720$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(17\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\(\chi_{2850}(1,\cdot)\)	2850.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{2850}(7,\cdot)\)	2850.bg	12	no	\(-1\)	\(1\)	\(i\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{2850}(11,\cdot)\)	2850.bz	30	no	\(-1\)	\(1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{2850}(13,\cdot)\)	2850.cs	180	no	\(1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{79}{180}\right)\)	\(e\left(\frac{23}{180}\right)\)	\(e\left(\frac{1}{180}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{25}{36}\right)\)
\(\chi_{2850}(17,\cdot)\)	2850.cr	180	no	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{23}{180}\right)\)	\(e\left(\frac{91}{180}\right)\)	\(e\left(\frac{137}{180}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{23}{36}\right)\)
\(\chi_{2850}(23,\cdot)\)	2850.cr	180	no	\(1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{180}\right)\)	\(e\left(\frac{137}{180}\right)\)	\(e\left(\frac{139}{180}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{1}{36}\right)\)
\(\chi_{2850}(29,\cdot)\)	2850.cm	90	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{11}{18}\right)\)
\(\chi_{2850}(31,\cdot)\)	2850.bx	30	no	\(-1\)	\(1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{2850}(37,\cdot)\)	2850.bp	20	no	\(1\)	\(1\)	\(i\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(-i\)
\(\chi_{2850}(41,\cdot)\)	2850.cj	90	no	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{5}{9}\right)\)
\(\chi_{2850}(43,\cdot)\)	2850.ca	36	no	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-i\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{17}{36}\right)\)
\(\chi_{2850}(47,\cdot)\)	2850.cr	180	no	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{67}{180}\right)\)	\(e\left(\frac{179}{180}\right)\)	\(e\left(\frac{133}{180}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{31}{36}\right)\)
\(\chi_{2850}(49,\cdot)\)	2850.r	6	no	\(1\)	\(1\)	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{2850}(53,\cdot)\)	2850.cq	180	no	\(-1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{127}{180}\right)\)	\(e\left(\frac{29}{180}\right)\)	\(e\left(\frac{103}{180}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{1}{36}\right)\)
\(\chi_{2850}(59,\cdot)\)	2850.cm	90	no	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{7}{18}\right)\)
\(\chi_{2850}(61,\cdot)\)	2850.ce	45	no	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{7}{9}\right)\)
\(\chi_{2850}(67,\cdot)\)	2850.cs	180	no	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{13}{180}\right)\)	\(e\left(\frac{161}{180}\right)\)	\(e\left(\frac{7}{180}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{79}{90}\right)\)	\(e\left(\frac{31}{36}\right)\)
\(\chi_{2850}(71,\cdot)\)	2850.cj	90	no	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{79}{90}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{2}{9}\right)\)
\(\chi_{2850}(73,\cdot)\)	2850.ct	180	no	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{101}{180}\right)\)	\(e\left(\frac{67}{180}\right)\)	\(e\left(\frac{89}{180}\right)\)	\(e\left(\frac{79}{90}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{29}{36}\right)\)
\(\chi_{2850}(77,\cdot)\)	2850.br	20	no	\(1\)	\(1\)	\(i\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(-i\)
\(\chi_{2850}(79,\cdot)\)	2850.co	90	no	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{71}{90}\right)\)	\(e\left(\frac{1}{18}\right)\)
\(\chi_{2850}(83,\cdot)\)	2850.ci	60	no	\(1\)	\(1\)	\(-i\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{2850}(89,\cdot)\)	2850.cm	90	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{17}{18}\right)\)
\(\chi_{2850}(91,\cdot)\)	2850.cl	90	no	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{77}{90}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{71}{90}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{7}{9}\right)\)
\(\chi_{2850}(97,\cdot)\)	2850.cs	180	no	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{77}{180}\right)\)	\(e\left(\frac{109}{180}\right)\)	\(e\left(\frac{83}{180}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{23}{36}\right)\)
\(\chi_{2850}(101,\cdot)\)	2850.bj	18	no	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{4}{9}\right)\)
\(\chi_{2850}(103,\cdot)\)	2850.cg	60	no	\(1\)	\(1\)	\(-i\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{2850}(107,\cdot)\)	2850.be	12	no	\(-1\)	\(1\)	\(i\)	\(-1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{2850}(109,\cdot)\)	2850.co	90	no	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{1}{90}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{77}{90}\right)\)	\(e\left(\frac{13}{18}\right)\)
\(\chi_{2850}(113,\cdot)\)	2850.bs	20	no	\(-1\)	\(1\)	\(-i\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(i\)
\(\chi_{2850}(119,\cdot)\)	2850.cn	90	no	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{59}{90}\right)\)	\(e\left(\frac{13}{18}\right)\)
\(\chi_{2850}(121,\cdot)\)	2850.bh	15	no	\(1\)	\(1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{1}{3}\right)\)

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.