LMFDB - Group of Dirichlet characters of modulus 2450

Show commands: PariGP / SageMath

sage: H = DirichletGroup(2450)

pari: g = idealstar(,2450,2)

Character group

sage: G.order() pari: g.no
Order	=	840
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{420}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{2450}(1177,\cdot)$, $\chi_{2450}(101,\cdot)$

First 32 of 840 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	$-1$	$1$	$3$	$9$	$11$	$13$	$17$	$19$	$23$	$27$	$29$	$31$
$\chi_{2450}(1,\cdot)$	2450.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{2450}(3,\cdot)$	2450.bv	420	no	$1$	$1$	$e\left(\frac{199}{420}\right)$	$e\left(\frac{199}{210}\right)$	$e\left(\frac{58}{105}\right)$	$e\left(\frac{61}{140}\right)$	$e\left(\frac{61}{420}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{317}{420}\right)$	$e\left(\frac{59}{140}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{29}{30}\right)$
$\chi_{2450}(9,\cdot)$	2450.bt	210	no	$1$	$1$	$e\left(\frac{199}{210}\right)$	$e\left(\frac{94}{105}\right)$	$e\left(\frac{11}{105}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{61}{210}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{107}{210}\right)$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{14}{15}\right)$
$\chi_{2450}(11,\cdot)$	2450.bo	105	no	$1$	$1$	$e\left(\frac{58}{105}\right)$	$e\left(\frac{11}{105}\right)$	$e\left(\frac{94}{105}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{22}{105}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{104}{105}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{1}{15}\right)$
$\chi_{2450}(13,\cdot)$	2450.bp	140	no	$1$	$1$	$e\left(\frac{61}{140}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{137}{140}\right)$	$e\left(\frac{139}{140}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{43}{140}\right)$	$e\left(\frac{43}{140}\right)$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{2450}(17,\cdot)$	2450.bv	420	no	$1$	$1$	$e\left(\frac{61}{420}\right)$	$e\left(\frac{61}{210}\right)$	$e\left(\frac{22}{105}\right)$	$e\left(\frac{139}{140}\right)$	$e\left(\frac{139}{420}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{323}{420}\right)$	$e\left(\frac{61}{140}\right)$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{11}{30}\right)$
$\chi_{2450}(19,\cdot)$	2450.bc	30	no	$-1$	$1$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{30}\right)$
$\chi_{2450}(23,\cdot)$	2450.bu	420	no	$-1$	$1$	$e\left(\frac{317}{420}\right)$	$e\left(\frac{107}{210}\right)$	$e\left(\frac{104}{105}\right)$	$e\left(\frac{43}{140}\right)$	$e\left(\frac{323}{420}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{181}{420}\right)$	$e\left(\frac{37}{140}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{11}{15}\right)$
$\chi_{2450}(27,\cdot)$	2450.bp	140	no	$1$	$1$	$e\left(\frac{59}{140}\right)$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{43}{140}\right)$	$e\left(\frac{61}{140}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{37}{140}\right)$	$e\left(\frac{37}{140}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{2450}(29,\cdot)$	2450.bj	70	no	$1$	$1$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{2450}(31,\cdot)$	2450.ba	30	no	$-1$	$1$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{11}{30}\right)$
$\chi_{2450}(33,\cdot)$	2450.bv	420	no	$1$	$1$	$e\left(\frac{11}{420}\right)$	$e\left(\frac{11}{210}\right)$	$e\left(\frac{47}{105}\right)$	$e\left(\frac{9}{140}\right)$	$e\left(\frac{149}{420}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{313}{420}\right)$	$e\left(\frac{11}{140}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{1}{30}\right)$
$\chi_{2450}(37,\cdot)$	2450.bu	420	no	$-1$	$1$	$e\left(\frac{383}{420}\right)$	$e\left(\frac{173}{210}\right)$	$e\left(\frac{71}{105}\right)$	$e\left(\frac{97}{140}\right)$	$e\left(\frac{377}{420}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{379}{420}\right)$	$e\left(\frac{103}{140}\right)$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{14}{15}\right)$
$\chi_{2450}(39,\cdot)$	2450.bt	210	no	$1$	$1$	$e\left(\frac{191}{210}\right)$	$e\left(\frac{86}{105}\right)$	$e\left(\frac{19}{105}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{29}{210}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{13}{210}\right)$	$e\left(\frac{51}{70}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{1}{15}\right)$
$\chi_{2450}(41,\cdot)$	2450.bk	70	no	$-1$	$1$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{2450}(43,\cdot)$	2450.y	28	no	$-1$	$1$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{9}{28}\right)$	$-1$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{1}{14}\right)$	$1$
$\chi_{2450}(47,\cdot)$	2450.bv	420	no	$1$	$1$	$e\left(\frac{29}{420}\right)$	$e\left(\frac{29}{210}\right)$	$e\left(\frac{38}{105}\right)$	$e\left(\frac{11}{140}\right)$	$e\left(\frac{11}{420}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{367}{420}\right)$	$e\left(\frac{29}{140}\right)$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{19}{30}\right)$
$\chi_{2450}(51,\cdot)$	2450.x	21	no	$1$	$1$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{2450}(53,\cdot)$	2450.bu	420	no	$-1$	$1$	$e\left(\frac{289}{420}\right)$	$e\left(\frac{79}{210}\right)$	$e\left(\frac{13}{105}\right)$	$e\left(\frac{71}{140}\right)$	$e\left(\frac{211}{420}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{377}{420}\right)$	$e\left(\frac{9}{140}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{7}{15}\right)$
$\chi_{2450}(57,\cdot)$	2450.y	28	no	$-1$	$1$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{19}{28}\right)$	$-1$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{13}{14}\right)$	$1$
$\chi_{2450}(59,\cdot)$	2450.br	210	no	$-1$	$1$	$e\left(\frac{22}{105}\right)$	$e\left(\frac{44}{105}\right)$	$e\left(\frac{61}{105}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{88}{105}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{97}{210}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{23}{30}\right)$
$\chi_{2450}(61,\cdot)$	2450.bs	210	no	$-1$	$1$	$e\left(\frac{181}{210}\right)$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{29}{105}\right)$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{199}{210}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{79}{105}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{7}{30}\right)$
$\chi_{2450}(67,\cdot)$	2450.bh	60	no	$-1$	$1$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{13}{15}\right)$
$\chi_{2450}(69,\cdot)$	2450.bl	70	no	$-1$	$1$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{2450}(71,\cdot)$	2450.bd	35	no	$1$	$1$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{2450}(73,\cdot)$	2450.bv	420	no	$1$	$1$	$e\left(\frac{307}{420}\right)$	$e\left(\frac{97}{210}\right)$	$e\left(\frac{4}{105}\right)$	$e\left(\frac{73}{140}\right)$	$e\left(\frac{73}{420}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{221}{420}\right)$	$e\left(\frac{27}{140}\right)$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{17}{30}\right)$
$\chi_{2450}(79,\cdot)$	2450.bb	30	no	$1$	$1$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{15}\right)$
$\chi_{2450}(81,\cdot)$	2450.bo	105	no	$1$	$1$	$e\left(\frac{94}{105}\right)$	$e\left(\frac{83}{105}\right)$	$e\left(\frac{22}{105}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{61}{105}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{2}{105}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{13}{15}\right)$
$\chi_{2450}(83,\cdot)$	2450.bp	140	no	$1$	$1$	$e\left(\frac{37}{140}\right)$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{129}{140}\right)$	$e\left(\frac{43}{140}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{111}{140}\right)$	$e\left(\frac{111}{140}\right)$	$e\left(\frac{11}{70}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{2450}(87,\cdot)$	2450.bv	420	no	$1$	$1$	$e\left(\frac{253}{420}\right)$	$e\left(\frac{43}{210}\right)$	$e\left(\frac{31}{105}\right)$	$e\left(\frac{67}{140}\right)$	$e\left(\frac{67}{420}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{59}{420}\right)$	$e\left(\frac{113}{140}\right)$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{23}{30}\right)$
$\chi_{2450}(89,\cdot)$	2450.br	210	no	$-1$	$1$	$e\left(\frac{68}{105}\right)$	$e\left(\frac{31}{105}\right)$	$e\left(\frac{74}{105}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{62}{105}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{23}{210}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{7}{30}\right)$
$\chi_{2450}(93,\cdot)$	2450.bn	84	no	$-1$	$1$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{1}{3}\right)$

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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	$2450$
Structure	\(C_{2}\times C_{420}\)
Order	$840$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(27\)	\(29\)	\(31\)
\(\chi_{2450}(1,\cdot)\)	2450.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{2450}(3,\cdot)\)	2450.bv	420	no	\(1\)	\(1\)	\(e\left(\frac{199}{420}\right)\)	\(e\left(\frac{199}{210}\right)\)	\(e\left(\frac{58}{105}\right)\)	\(e\left(\frac{61}{140}\right)\)	\(e\left(\frac{61}{420}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{317}{420}\right)\)	\(e\left(\frac{59}{140}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{29}{30}\right)\)
\(\chi_{2450}(9,\cdot)\)	2450.bt	210	no	\(1\)	\(1\)	\(e\left(\frac{199}{210}\right)\)	\(e\left(\frac{94}{105}\right)\)	\(e\left(\frac{11}{105}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{61}{210}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{107}{210}\right)\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{14}{15}\right)\)
\(\chi_{2450}(11,\cdot)\)	2450.bo	105	no	\(1\)	\(1\)	\(e\left(\frac{58}{105}\right)\)	\(e\left(\frac{11}{105}\right)\)	\(e\left(\frac{94}{105}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{22}{105}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{104}{105}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{1}{15}\right)\)
\(\chi_{2450}(13,\cdot)\)	2450.bp	140	no	\(1\)	\(1\)	\(e\left(\frac{61}{140}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{137}{140}\right)\)	\(e\left(\frac{139}{140}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{43}{140}\right)\)	\(e\left(\frac{43}{140}\right)\)	\(e\left(\frac{3}{70}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{2450}(17,\cdot)\)	2450.bv	420	no	\(1\)	\(1\)	\(e\left(\frac{61}{420}\right)\)	\(e\left(\frac{61}{210}\right)\)	\(e\left(\frac{22}{105}\right)\)	\(e\left(\frac{139}{140}\right)\)	\(e\left(\frac{139}{420}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{323}{420}\right)\)	\(e\left(\frac{61}{140}\right)\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{11}{30}\right)\)
\(\chi_{2450}(19,\cdot)\)	2450.bc	30	no	\(-1\)	\(1\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{30}\right)\)
\(\chi_{2450}(23,\cdot)\)	2450.bu	420	no	\(-1\)	\(1\)	\(e\left(\frac{317}{420}\right)\)	\(e\left(\frac{107}{210}\right)\)	\(e\left(\frac{104}{105}\right)\)	\(e\left(\frac{43}{140}\right)\)	\(e\left(\frac{323}{420}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{181}{420}\right)\)	\(e\left(\frac{37}{140}\right)\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{11}{15}\right)\)
\(\chi_{2450}(27,\cdot)\)	2450.bp	140	no	\(1\)	\(1\)	\(e\left(\frac{59}{140}\right)\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{43}{140}\right)\)	\(e\left(\frac{61}{140}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{37}{140}\right)\)	\(e\left(\frac{37}{140}\right)\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{2450}(29,\cdot)\)	2450.bj	70	no	\(1\)	\(1\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{3}{70}\right)\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{2450}(31,\cdot)\)	2450.ba	30	no	\(-1\)	\(1\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{11}{30}\right)\)
\(\chi_{2450}(33,\cdot)\)	2450.bv	420	no	\(1\)	\(1\)	\(e\left(\frac{11}{420}\right)\)	\(e\left(\frac{11}{210}\right)\)	\(e\left(\frac{47}{105}\right)\)	\(e\left(\frac{9}{140}\right)\)	\(e\left(\frac{149}{420}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{313}{420}\right)\)	\(e\left(\frac{11}{140}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{1}{30}\right)\)
\(\chi_{2450}(37,\cdot)\)	2450.bu	420	no	\(-1\)	\(1\)	\(e\left(\frac{383}{420}\right)\)	\(e\left(\frac{173}{210}\right)\)	\(e\left(\frac{71}{105}\right)\)	\(e\left(\frac{97}{140}\right)\)	\(e\left(\frac{377}{420}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{379}{420}\right)\)	\(e\left(\frac{103}{140}\right)\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{14}{15}\right)\)
\(\chi_{2450}(39,\cdot)\)	2450.bt	210	no	\(1\)	\(1\)	\(e\left(\frac{191}{210}\right)\)	\(e\left(\frac{86}{105}\right)\)	\(e\left(\frac{19}{105}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{29}{210}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{13}{210}\right)\)	\(e\left(\frac{51}{70}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{1}{15}\right)\)
\(\chi_{2450}(41,\cdot)\)	2450.bk	70	no	\(-1\)	\(1\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{2450}(43,\cdot)\)	2450.y	28	no	\(-1\)	\(1\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(-1\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(1\)
\(\chi_{2450}(47,\cdot)\)	2450.bv	420	no	\(1\)	\(1\)	\(e\left(\frac{29}{420}\right)\)	\(e\left(\frac{29}{210}\right)\)	\(e\left(\frac{38}{105}\right)\)	\(e\left(\frac{11}{140}\right)\)	\(e\left(\frac{11}{420}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{367}{420}\right)\)	\(e\left(\frac{29}{140}\right)\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{19}{30}\right)\)
\(\chi_{2450}(51,\cdot)\)	2450.x	21	no	\(1\)	\(1\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{2450}(53,\cdot)\)	2450.bu	420	no	\(-1\)	\(1\)	\(e\left(\frac{289}{420}\right)\)	\(e\left(\frac{79}{210}\right)\)	\(e\left(\frac{13}{105}\right)\)	\(e\left(\frac{71}{140}\right)\)	\(e\left(\frac{211}{420}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{377}{420}\right)\)	\(e\left(\frac{9}{140}\right)\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{7}{15}\right)\)
\(\chi_{2450}(57,\cdot)\)	2450.y	28	no	\(-1\)	\(1\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(-1\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(1\)
\(\chi_{2450}(59,\cdot)\)	2450.br	210	no	\(-1\)	\(1\)	\(e\left(\frac{22}{105}\right)\)	\(e\left(\frac{44}{105}\right)\)	\(e\left(\frac{61}{105}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{88}{105}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{97}{210}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{23}{30}\right)\)
\(\chi_{2450}(61,\cdot)\)	2450.bs	210	no	\(-1\)	\(1\)	\(e\left(\frac{181}{210}\right)\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{29}{105}\right)\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{199}{210}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{79}{105}\right)\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{7}{30}\right)\)
\(\chi_{2450}(67,\cdot)\)	2450.bh	60	no	\(-1\)	\(1\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{13}{15}\right)\)
\(\chi_{2450}(69,\cdot)\)	2450.bl	70	no	\(-1\)	\(1\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{2450}(71,\cdot)\)	2450.bd	35	no	\(1\)	\(1\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{2450}(73,\cdot)\)	2450.bv	420	no	\(1\)	\(1\)	\(e\left(\frac{307}{420}\right)\)	\(e\left(\frac{97}{210}\right)\)	\(e\left(\frac{4}{105}\right)\)	\(e\left(\frac{73}{140}\right)\)	\(e\left(\frac{73}{420}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{221}{420}\right)\)	\(e\left(\frac{27}{140}\right)\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{17}{30}\right)\)
\(\chi_{2450}(79,\cdot)\)	2450.bb	30	no	\(1\)	\(1\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{15}\right)\)
\(\chi_{2450}(81,\cdot)\)	2450.bo	105	no	\(1\)	\(1\)	\(e\left(\frac{94}{105}\right)\)	\(e\left(\frac{83}{105}\right)\)	\(e\left(\frac{22}{105}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{61}{105}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{2}{105}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{13}{15}\right)\)
\(\chi_{2450}(83,\cdot)\)	2450.bp	140	no	\(1\)	\(1\)	\(e\left(\frac{37}{140}\right)\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{129}{140}\right)\)	\(e\left(\frac{43}{140}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{111}{140}\right)\)	\(e\left(\frac{111}{140}\right)\)	\(e\left(\frac{11}{70}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{2450}(87,\cdot)\)	2450.bv	420	no	\(1\)	\(1\)	\(e\left(\frac{253}{420}\right)\)	\(e\left(\frac{43}{210}\right)\)	\(e\left(\frac{31}{105}\right)\)	\(e\left(\frac{67}{140}\right)\)	\(e\left(\frac{67}{420}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{59}{420}\right)\)	\(e\left(\frac{113}{140}\right)\)	\(e\left(\frac{3}{70}\right)\)	\(e\left(\frac{23}{30}\right)\)
\(\chi_{2450}(89,\cdot)\)	2450.br	210	no	\(-1\)	\(1\)	\(e\left(\frac{68}{105}\right)\)	\(e\left(\frac{31}{105}\right)\)	\(e\left(\frac{74}{105}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{62}{105}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{23}{210}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{7}{30}\right)\)
\(\chi_{2450}(93,\cdot)\)	2450.bn	84	no	\(-1\)	\(1\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{1}{3}\right)\)

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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.