LMFDB - Group of Dirichlet characters of modulus 2898

Show commands: PariGP / SageMath

sage: H = DirichletGroup(2898)

pari: g = idealstar(,2898,2)

Character group

sage: G.order() pari: g.no
Order	=	792
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{6}\times C_{66}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{2898}(1289,\cdot)$, $\chi_{2898}(829,\cdot)$, $\chi_{2898}(1891,\cdot)$

First 32 of 792 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	$-1$	$1$	$5$	$11$	$13$	$17$	$19$	$25$	$29$	$31$	$37$	$41$
$\chi_{2898}(1,\cdot)$	2898.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{2898}(5,\cdot)$	2898.ck	66	no	$-1$	$1$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{7}{33}\right)$
$\chi_{2898}(11,\cdot)$	2898.cx	66	no	$1$	$1$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{49}{66}\right)$
$\chi_{2898}(13,\cdot)$	2898.cm	66	no	$-1$	$1$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{53}{66}\right)$
$\chi_{2898}(17,\cdot)$	2898.co	66	no	$-1$	$1$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{9}{11}\right)$
$\chi_{2898}(19,\cdot)$	2898.cu	66	no	$1$	$1$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{15}{22}\right)$
$\chi_{2898}(25,\cdot)$	2898.bz	33	no	$1$	$1$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{14}{33}\right)$
$\chi_{2898}(29,\cdot)$	2898.ch	66	no	$-1$	$1$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{43}{66}\right)$
$\chi_{2898}(31,\cdot)$	2898.cy	66	no	$-1$	$1$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{29}{66}\right)$
$\chi_{2898}(37,\cdot)$	2898.cd	66	no	$-1$	$1$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{5}{11}\right)$
$\chi_{2898}(41,\cdot)$	2898.cq	66	no	$1$	$1$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{7}{33}\right)$
$\chi_{2898}(43,\cdot)$	2898.ci	66	no	$-1$	$1$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{2}{33}\right)$
$\chi_{2898}(47,\cdot)$	2898.bm	6	no	$1$	$1$	$1$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{2898}(53,\cdot)$	2898.cv	66	no	$1$	$1$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{19}{22}\right)$
$\chi_{2898}(55,\cdot)$	2898.bt	22	no	$-1$	$1$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{21}{22}\right)$
$\chi_{2898}(59,\cdot)$	2898.cb	66	no	$1$	$1$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{10}{33}\right)$
$\chi_{2898}(61,\cdot)$	2898.cc	66	no	$1$	$1$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{7}{66}\right)$
$\chi_{2898}(65,\cdot)$	2898.ca	66	no	$1$	$1$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{1}{66}\right)$
$\chi_{2898}(67,\cdot)$	2898.da	66	no	$-1$	$1$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{25}{33}\right)$
$\chi_{2898}(71,\cdot)$	2898.bu	22	no	$-1$	$1$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{13}{22}\right)$
$\chi_{2898}(73,\cdot)$	2898.cn	66	no	$-1$	$1$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{15}{22}\right)$
$\chi_{2898}(79,\cdot)$	2898.da	66	no	$-1$	$1$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{32}{33}\right)$
$\chi_{2898}(83,\cdot)$	2898.cl	66	no	$-1$	$1$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{26}{33}\right)$
$\chi_{2898}(85,\cdot)$	2898.by	33	no	$1$	$1$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{1}{33}\right)$
$\chi_{2898}(89,\cdot)$	2898.co	66	no	$-1$	$1$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{8}{11}\right)$
$\chi_{2898}(95,\cdot)$	2898.db	66	no	$-1$	$1$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{59}{66}\right)$
$\chi_{2898}(97,\cdot)$	2898.cp	66	no	$1$	$1$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{25}{66}\right)$
$\chi_{2898}(101,\cdot)$	2898.cr	66	no	$1$	$1$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{26}{33}\right)$
$\chi_{2898}(103,\cdot)$	2898.cs	66	no	$1$	$1$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{5}{66}\right)$
$\chi_{2898}(107,\cdot)$	2898.cv	66	no	$1$	$1$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{17}{22}\right)$
$\chi_{2898}(109,\cdot)$	2898.cd	66	no	$-1$	$1$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{9}{11}\right)$
$\chi_{2898}(113,\cdot)$	2898.cw	66	no	$1$	$1$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{17}{66}\right)$

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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	$2898$
Structure	\(C_{2}\times C_{6}\times C_{66}\)
Order	$792$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(11\)	\(13\)	\(17\)	\(19\)	\(25\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{2898}(1,\cdot)\)	2898.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{2898}(5,\cdot)\)	2898.ck	66	no	\(-1\)	\(1\)	\(e\left(\frac{25}{66}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{7}{33}\right)\)
\(\chi_{2898}(11,\cdot)\)	2898.cx	66	no	\(1\)	\(1\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{49}{66}\right)\)
\(\chi_{2898}(13,\cdot)\)	2898.cm	66	no	\(-1\)	\(1\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{53}{66}\right)\)
\(\chi_{2898}(17,\cdot)\)	2898.co	66	no	\(-1\)	\(1\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{9}{11}\right)\)
\(\chi_{2898}(19,\cdot)\)	2898.cu	66	no	\(1\)	\(1\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{15}{22}\right)\)
\(\chi_{2898}(25,\cdot)\)	2898.bz	33	no	\(1\)	\(1\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{14}{33}\right)\)
\(\chi_{2898}(29,\cdot)\)	2898.ch	66	no	\(-1\)	\(1\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{43}{66}\right)\)
\(\chi_{2898}(31,\cdot)\)	2898.cy	66	no	\(-1\)	\(1\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{29}{66}\right)\)
\(\chi_{2898}(37,\cdot)\)	2898.cd	66	no	\(-1\)	\(1\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{5}{11}\right)\)
\(\chi_{2898}(41,\cdot)\)	2898.cq	66	no	\(1\)	\(1\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{7}{33}\right)\)
\(\chi_{2898}(43,\cdot)\)	2898.ci	66	no	\(-1\)	\(1\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{2}{33}\right)\)
\(\chi_{2898}(47,\cdot)\)	2898.bm	6	no	\(1\)	\(1\)	\(1\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{2898}(53,\cdot)\)	2898.cv	66	no	\(1\)	\(1\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{19}{22}\right)\)
\(\chi_{2898}(55,\cdot)\)	2898.bt	22	no	\(-1\)	\(1\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{21}{22}\right)\)
\(\chi_{2898}(59,\cdot)\)	2898.cb	66	no	\(1\)	\(1\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{25}{66}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{10}{33}\right)\)
\(\chi_{2898}(61,\cdot)\)	2898.cc	66	no	\(1\)	\(1\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{7}{66}\right)\)
\(\chi_{2898}(65,\cdot)\)	2898.ca	66	no	\(1\)	\(1\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{1}{66}\right)\)
\(\chi_{2898}(67,\cdot)\)	2898.da	66	no	\(-1\)	\(1\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{25}{33}\right)\)
\(\chi_{2898}(71,\cdot)\)	2898.bu	22	no	\(-1\)	\(1\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{13}{22}\right)\)
\(\chi_{2898}(73,\cdot)\)	2898.cn	66	no	\(-1\)	\(1\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{15}{22}\right)\)
\(\chi_{2898}(79,\cdot)\)	2898.da	66	no	\(-1\)	\(1\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{32}{33}\right)\)
\(\chi_{2898}(83,\cdot)\)	2898.cl	66	no	\(-1\)	\(1\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{26}{33}\right)\)
\(\chi_{2898}(85,\cdot)\)	2898.by	33	no	\(1\)	\(1\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{1}{33}\right)\)
\(\chi_{2898}(89,\cdot)\)	2898.co	66	no	\(-1\)	\(1\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{8}{11}\right)\)
\(\chi_{2898}(95,\cdot)\)	2898.db	66	no	\(-1\)	\(1\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{59}{66}\right)\)
\(\chi_{2898}(97,\cdot)\)	2898.cp	66	no	\(1\)	\(1\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{25}{66}\right)\)
\(\chi_{2898}(101,\cdot)\)	2898.cr	66	no	\(1\)	\(1\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{26}{33}\right)\)
\(\chi_{2898}(103,\cdot)\)	2898.cs	66	no	\(1\)	\(1\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{5}{66}\right)\)
\(\chi_{2898}(107,\cdot)\)	2898.cv	66	no	\(1\)	\(1\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{17}{22}\right)\)
\(\chi_{2898}(109,\cdot)\)	2898.cd	66	no	\(-1\)	\(1\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{9}{11}\right)\)
\(\chi_{2898}(113,\cdot)\)	2898.cw	66	no	\(1\)	\(1\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{17}{66}\right)\)

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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.