LMFDB - Group of Dirichlet characters of modulus 44100

sage:H = DirichletGroup(44100)

pari:g = idealstar(,44100,2)

Character group

sage:G.order() pari:g.no
Order	=	10080
sage:H.invariants() pari:g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{6}\times C_{420}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{44100}(22051,\cdot)$, $\chi_{44100}(34301,\cdot)$, $\chi_{44100}(15877,\cdot)$, $\chi_{44100}(9901,\cdot)$

First 32 of 10080 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	$-1$	$1$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{44100}(1,\cdot)$	44100.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{44100}(11,\cdot)$	44100.pn	210	yes	$1$	$1$	$e\left(\frac{59}{105}\right)$	$e\left(\frac{101}{105}\right)$	$e\left(\frac{149}{210}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{34}{105}\right)$	$e\left(\frac{191}{210}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{71}{105}\right)$	$e\left(\frac{67}{210}\right)$	$e\left(\frac{37}{42}\right)$
$\chi_{44100}(13,\cdot)$	44100.rl	420	no	$1$	$1$	$e\left(\frac{101}{105}\right)$	$e\left(\frac{271}{420}\right)$	$e\left(\frac{139}{140}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{409}{420}\right)$	$e\left(\frac{79}{210}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{97}{140}\right)$	$e\left(\frac{53}{210}\right)$	$e\left(\frac{25}{84}\right)$
$\chi_{44100}(17,\cdot)$	44100.sf	420	no	$-1$	$1$	$e\left(\frac{149}{210}\right)$	$e\left(\frac{139}{140}\right)$	$e\left(\frac{349}{420}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{113}{420}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{377}{420}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{9}{28}\right)$
$\chi_{44100}(19,\cdot)$	44100.he	30	no	$1$	$1$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{1}{10}\right)$	$1$
$\chi_{44100}(23,\cdot)$	44100.rr	420	yes	$-1$	$1$	$e\left(\frac{34}{105}\right)$	$e\left(\frac{409}{420}\right)$	$e\left(\frac{113}{420}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{41}{420}\right)$	$e\left(\frac{23}{105}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{379}{420}\right)$	$e\left(\frac{197}{210}\right)$	$e\left(\frac{43}{84}\right)$
$\chi_{44100}(29,\cdot)$	44100.qt	210	no	$-1$	$1$	$e\left(\frac{191}{210}\right)$	$e\left(\frac{79}{210}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{23}{105}\right)$	$e\left(\frac{17}{210}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{139}{210}\right)$	$e\left(\frac{31}{42}\right)$
$\chi_{44100}(31,\cdot)$	44100.iv	30	no	$1$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{44100}(37,\cdot)$	44100.rm	420	no	$-1$	$1$	$e\left(\frac{71}{105}\right)$	$e\left(\frac{97}{140}\right)$	$e\left(\frac{377}{420}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{379}{420}\right)$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{181}{420}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{9}{28}\right)$
$\chi_{44100}(41,\cdot)$	44100.qu	210	no	$1$	$1$	$e\left(\frac{67}{210}\right)$	$e\left(\frac{53}{210}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{197}{210}\right)$	$e\left(\frac{139}{210}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{34}{105}\right)$	$e\left(\frac{10}{21}\right)$
$\chi_{44100}(43,\cdot)$	44100.nu	84	no	$1$	$1$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{9}{28}\right)$	$1$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{23}{84}\right)$
$\chi_{44100}(47,\cdot)$	44100.si	420	yes	$1$	$1$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{173}{420}\right)$	$e\left(\frac{221}{420}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{29}{140}\right)$	$e\left(\frac{1}{105}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{193}{420}\right)$	$e\left(\frac{2}{105}\right)$	$e\left(\frac{53}{84}\right)$
$\chi_{44100}(53,\cdot)$	44100.sb	420	no	$1$	$1$	$e\left(\frac{131}{210}\right)$	$e\left(\frac{71}{140}\right)$	$e\left(\frac{1}{420}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{167}{420}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{323}{420}\right)$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{19}{28}\right)$
$\chi_{44100}(59,\cdot)$	44100.rb	210	yes	$-1$	$1$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{19}{105}\right)$	$e\left(\frac{71}{210}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{169}{210}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{43}{210}\right)$	$e\left(\frac{64}{105}\right)$	$e\left(\frac{4}{21}\right)$
$\chi_{44100}(61,\cdot)$	44100.re	210	no	$-1$	$1$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{37}{210}\right)$	$e\left(\frac{199}{210}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{103}{105}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{61}{105}\right)$	$e\left(\frac{97}{210}\right)$	$e\left(\frac{5}{21}\right)$
$\chi_{44100}(67,\cdot)$	44100.mp	60	no	$1$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{44100}(71,\cdot)$	44100.ne	70	no	$1$	$1$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{13}{14}\right)$
$\chi_{44100}(73,\cdot)$	44100.rq	420	no	$1$	$1$	$e\left(\frac{4}{105}\right)$	$e\left(\frac{73}{140}\right)$	$e\left(\frac{73}{420}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{221}{420}\right)$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{59}{420}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{15}{28}\right)$
$\chi_{44100}(79,\cdot)$	44100.iu	30	no	$-1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{44100}(83,\cdot)$	44100.ru	420	yes	$1$	$1$	$e\left(\frac{67}{105}\right)$	$e\left(\frac{107}{420}\right)$	$e\left(\frac{113}{140}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{53}{420}\right)$	$e\left(\frac{34}{105}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{29}{140}\right)$	$e\left(\frac{68}{105}\right)$	$e\left(\frac{59}{84}\right)$
$\chi_{44100}(89,\cdot)$	44100.qx	210	no	$1$	$1$	$e\left(\frac{43}{210}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{19}{210}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{64}{105}\right)$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{47}{210}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{11}{14}\right)$
$\chi_{44100}(97,\cdot)$	44100.mb	60	no	$1$	$1$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{44100}(101,\cdot)$	44100.jt	42	no	$1$	$1$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{25}{42}\right)$	$-1$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{17}{21}\right)$
$\chi_{44100}(103,\cdot)$	44100.sa	420	yes	$-1$	$1$	$e\left(\frac{11}{210}\right)$	$e\left(\frac{43}{420}\right)$	$e\left(\frac{341}{420}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{107}{420}\right)$	$e\left(\frac{97}{210}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{103}{420}\right)$	$e\left(\frac{89}{210}\right)$	$e\left(\frac{19}{84}\right)$
$\chi_{44100}(107,\cdot)$	44100.ny	84	no	$-1$	$1$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{15}{28}\right)$
$\chi_{44100}(109,\cdot)$	44100.pj	210	no	$1$	$1$	$e\left(\frac{31}{105}\right)$	$e\left(\frac{51}{70}\right)$	$e\left(\frac{191}{210}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{187}{210}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{163}{210}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{3}{14}\right)$
$\chi_{44100}(113,\cdot)$	44100.sg	420	no	$1$	$1$	$e\left(\frac{127}{210}\right)$	$e\left(\frac{121}{420}\right)$	$e\left(\frac{99}{140}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{319}{420}\right)$	$e\left(\frac{62}{105}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{57}{140}\right)$	$e\left(\frac{143}{210}\right)$	$e\left(\frac{73}{84}\right)$
$\chi_{44100}(121,\cdot)$	44100.om	105	no	$1$	$1$	$e\left(\frac{13}{105}\right)$	$e\left(\frac{97}{105}\right)$	$e\left(\frac{44}{105}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{68}{105}\right)$	$e\left(\frac{86}{105}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{37}{105}\right)$	$e\left(\frac{67}{105}\right)$	$e\left(\frac{16}{21}\right)$
$\chi_{44100}(127,\cdot)$	44100.oq	140	no	$1$	$1$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{13}{140}\right)$	$e\left(\frac{51}{140}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{47}{140}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{23}{140}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{23}{28}\right)$
$\chi_{44100}(131,\cdot)$	44100.pt	210	yes	$-1$	$1$	$e\left(\frac{82}{105}\right)$	$e\left(\frac{101}{210}\right)$	$e\left(\frac{11}{105}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{17}{105}\right)$	$e\left(\frac{43}{210}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{88}{105}\right)$	$e\left(\frac{43}{105}\right)$	$e\left(\frac{29}{42}\right)$
$\chi_{44100}(137,\cdot)$	44100.rz	420	no	$1$	$1$	$e\left(\frac{157}{210}\right)$	$e\left(\frac{251}{420}\right)$	$e\left(\frac{247}{420}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{229}{420}\right)$	$e\left(\frac{67}{105}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{401}{420}\right)$	$e\left(\frac{163}{210}\right)$	$e\left(\frac{23}{84}\right)$
$\chi_{44100}(139,\cdot)$	44100.ql	210	yes	$1$	$1$	$e\left(\frac{193}{210}\right)$	$e\left(\frac{16}{105}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{105}\right)$	$e\left(\frac{38}{105}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{47}{210}\right)$	$e\left(\frac{10}{21}\right)$

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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 $\F_{q}$
Belyi maps

Modulus	$44100$
Structure	\(C_{2}\times C_{2}\times C_{6}\times C_{420}\)
Order	$10080$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\(\chi_{44100}(1,\cdot)\)	44100.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{44100}(11,\cdot)\)	44100.pn	210	yes	\(1\)	\(1\)	\(e\left(\frac{59}{105}\right)\)	\(e\left(\frac{101}{105}\right)\)	\(e\left(\frac{149}{210}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{34}{105}\right)\)	\(e\left(\frac{191}{210}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{71}{105}\right)\)	\(e\left(\frac{67}{210}\right)\)	\(e\left(\frac{37}{42}\right)\)
\(\chi_{44100}(13,\cdot)\)	44100.rl	420	no	\(1\)	\(1\)	\(e\left(\frac{101}{105}\right)\)	\(e\left(\frac{271}{420}\right)\)	\(e\left(\frac{139}{140}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{409}{420}\right)\)	\(e\left(\frac{79}{210}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{97}{140}\right)\)	\(e\left(\frac{53}{210}\right)\)	\(e\left(\frac{25}{84}\right)\)
\(\chi_{44100}(17,\cdot)\)	44100.sf	420	no	\(-1\)	\(1\)	\(e\left(\frac{149}{210}\right)\)	\(e\left(\frac{139}{140}\right)\)	\(e\left(\frac{349}{420}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{113}{420}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{377}{420}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{9}{28}\right)\)
\(\chi_{44100}(19,\cdot)\)	44100.he	30	no	\(1\)	\(1\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(1\)
\(\chi_{44100}(23,\cdot)\)	44100.rr	420	yes	\(-1\)	\(1\)	\(e\left(\frac{34}{105}\right)\)	\(e\left(\frac{409}{420}\right)\)	\(e\left(\frac{113}{420}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{41}{420}\right)\)	\(e\left(\frac{23}{105}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{379}{420}\right)\)	\(e\left(\frac{197}{210}\right)\)	\(e\left(\frac{43}{84}\right)\)
\(\chi_{44100}(29,\cdot)\)	44100.qt	210	no	\(-1\)	\(1\)	\(e\left(\frac{191}{210}\right)\)	\(e\left(\frac{79}{210}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{23}{105}\right)\)	\(e\left(\frac{17}{210}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{139}{210}\right)\)	\(e\left(\frac{31}{42}\right)\)
\(\chi_{44100}(31,\cdot)\)	44100.iv	30	no	\(1\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{44100}(37,\cdot)\)	44100.rm	420	no	\(-1\)	\(1\)	\(e\left(\frac{71}{105}\right)\)	\(e\left(\frac{97}{140}\right)\)	\(e\left(\frac{377}{420}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{379}{420}\right)\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{181}{420}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{9}{28}\right)\)
\(\chi_{44100}(41,\cdot)\)	44100.qu	210	no	\(1\)	\(1\)	\(e\left(\frac{67}{210}\right)\)	\(e\left(\frac{53}{210}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{197}{210}\right)\)	\(e\left(\frac{139}{210}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{34}{105}\right)\)	\(e\left(\frac{10}{21}\right)\)
\(\chi_{44100}(43,\cdot)\)	44100.nu	84	no	\(1\)	\(1\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(1\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{23}{84}\right)\)
\(\chi_{44100}(47,\cdot)\)	44100.si	420	yes	\(1\)	\(1\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{173}{420}\right)\)	\(e\left(\frac{221}{420}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{29}{140}\right)\)	\(e\left(\frac{1}{105}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{193}{420}\right)\)	\(e\left(\frac{2}{105}\right)\)	\(e\left(\frac{53}{84}\right)\)
\(\chi_{44100}(53,\cdot)\)	44100.sb	420	no	\(1\)	\(1\)	\(e\left(\frac{131}{210}\right)\)	\(e\left(\frac{71}{140}\right)\)	\(e\left(\frac{1}{420}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{167}{420}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{323}{420}\right)\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{19}{28}\right)\)
\(\chi_{44100}(59,\cdot)\)	44100.rb	210	yes	\(-1\)	\(1\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{19}{105}\right)\)	\(e\left(\frac{71}{210}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{169}{210}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{43}{210}\right)\)	\(e\left(\frac{64}{105}\right)\)	\(e\left(\frac{4}{21}\right)\)
\(\chi_{44100}(61,\cdot)\)	44100.re	210	no	\(-1\)	\(1\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{37}{210}\right)\)	\(e\left(\frac{199}{210}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{103}{105}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{61}{105}\right)\)	\(e\left(\frac{97}{210}\right)\)	\(e\left(\frac{5}{21}\right)\)
\(\chi_{44100}(67,\cdot)\)	44100.mp	60	no	\(1\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{44100}(71,\cdot)\)	44100.ne	70	no	\(1\)	\(1\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{13}{14}\right)\)
\(\chi_{44100}(73,\cdot)\)	44100.rq	420	no	\(1\)	\(1\)	\(e\left(\frac{4}{105}\right)\)	\(e\left(\frac{73}{140}\right)\)	\(e\left(\frac{73}{420}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{221}{420}\right)\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{59}{420}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{15}{28}\right)\)
\(\chi_{44100}(79,\cdot)\)	44100.iu	30	no	\(-1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{44100}(83,\cdot)\)	44100.ru	420	yes	\(1\)	\(1\)	\(e\left(\frac{67}{105}\right)\)	\(e\left(\frac{107}{420}\right)\)	\(e\left(\frac{113}{140}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{53}{420}\right)\)	\(e\left(\frac{34}{105}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{29}{140}\right)\)	\(e\left(\frac{68}{105}\right)\)	\(e\left(\frac{59}{84}\right)\)
\(\chi_{44100}(89,\cdot)\)	44100.qx	210	no	\(1\)	\(1\)	\(e\left(\frac{43}{210}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{19}{210}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{64}{105}\right)\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{47}{210}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{11}{14}\right)\)
\(\chi_{44100}(97,\cdot)\)	44100.mb	60	no	\(1\)	\(1\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{44100}(101,\cdot)\)	44100.jt	42	no	\(1\)	\(1\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(-1\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)
\(\chi_{44100}(103,\cdot)\)	44100.sa	420	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{210}\right)\)	\(e\left(\frac{43}{420}\right)\)	\(e\left(\frac{341}{420}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{107}{420}\right)\)	\(e\left(\frac{97}{210}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{103}{420}\right)\)	\(e\left(\frac{89}{210}\right)\)	\(e\left(\frac{19}{84}\right)\)
\(\chi_{44100}(107,\cdot)\)	44100.ny	84	no	\(-1\)	\(1\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{15}{28}\right)\)
\(\chi_{44100}(109,\cdot)\)	44100.pj	210	no	\(1\)	\(1\)	\(e\left(\frac{31}{105}\right)\)	\(e\left(\frac{51}{70}\right)\)	\(e\left(\frac{191}{210}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{187}{210}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{163}{210}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{3}{14}\right)\)
\(\chi_{44100}(113,\cdot)\)	44100.sg	420	no	\(1\)	\(1\)	\(e\left(\frac{127}{210}\right)\)	\(e\left(\frac{121}{420}\right)\)	\(e\left(\frac{99}{140}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{319}{420}\right)\)	\(e\left(\frac{62}{105}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{57}{140}\right)\)	\(e\left(\frac{143}{210}\right)\)	\(e\left(\frac{73}{84}\right)\)
\(\chi_{44100}(121,\cdot)\)	44100.om	105	no	\(1\)	\(1\)	\(e\left(\frac{13}{105}\right)\)	\(e\left(\frac{97}{105}\right)\)	\(e\left(\frac{44}{105}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{68}{105}\right)\)	\(e\left(\frac{86}{105}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{37}{105}\right)\)	\(e\left(\frac{67}{105}\right)\)	\(e\left(\frac{16}{21}\right)\)
\(\chi_{44100}(127,\cdot)\)	44100.oq	140	no	\(1\)	\(1\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{13}{140}\right)\)	\(e\left(\frac{51}{140}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{47}{140}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{23}{140}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{23}{28}\right)\)
\(\chi_{44100}(131,\cdot)\)	44100.pt	210	yes	\(-1\)	\(1\)	\(e\left(\frac{82}{105}\right)\)	\(e\left(\frac{101}{210}\right)\)	\(e\left(\frac{11}{105}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{17}{105}\right)\)	\(e\left(\frac{43}{210}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{88}{105}\right)\)	\(e\left(\frac{43}{105}\right)\)	\(e\left(\frac{29}{42}\right)\)
\(\chi_{44100}(137,\cdot)\)	44100.rz	420	no	\(1\)	\(1\)	\(e\left(\frac{157}{210}\right)\)	\(e\left(\frac{251}{420}\right)\)	\(e\left(\frac{247}{420}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{229}{420}\right)\)	\(e\left(\frac{67}{105}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{401}{420}\right)\)	\(e\left(\frac{163}{210}\right)\)	\(e\left(\frac{23}{84}\right)\)
\(\chi_{44100}(139,\cdot)\)	44100.ql	210	yes	\(1\)	\(1\)	\(e\left(\frac{193}{210}\right)\)	\(e\left(\frac{16}{105}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{105}\right)\)	\(e\left(\frac{38}{105}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{47}{210}\right)\)	\(e\left(\frac{10}{21}\right)\)

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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.