LMFDB - Group of Dirichlet characters of modulus 29040

Show commands: PariGP / SageMath

sage: H = DirichletGroup(29040)

pari: g = idealstar(,29040,2)

Character group

sage: G.order() pari: g.no
Order	=	7040
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{4}\times C_{220}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{29040}(3631,\cdot)$, $\chi_{29040}(21781,\cdot)$, $\chi_{29040}(19361,\cdot)$, $\chi_{29040}(11617,\cdot)$, $\chi_{29040}(14401,\cdot)$

First 32 of 7040 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	$-1$	$1$	$7$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{29040}(1,\cdot)$	29040.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{29040}(7,\cdot)$	29040.lk	220	no	$-1$	$1$	$e\left(\frac{43}{220}\right)$	$e\left(\frac{149}{220}\right)$	$e\left(\frac{81}{220}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{93}{220}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{15}{44}\right)$
$\chi_{29040}(13,\cdot)$	29040.lx	220	no	$1$	$1$	$e\left(\frac{149}{220}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{163}{220}\right)$	$e\left(\frac{211}{220}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{79}{220}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{7}{110}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{21}{22}\right)$
$\chi_{29040}(17,\cdot)$	29040.ln	220	no	$-1$	$1$	$e\left(\frac{81}{220}\right)$	$e\left(\frac{163}{220}\right)$	$e\left(\frac{127}{220}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{211}{220}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{39}{44}\right)$
$\chi_{29040}(19,\cdot)$	29040.mg	220	no	$1$	$1$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{211}{220}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{83}{220}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{17}{220}\right)$	$e\left(\frac{43}{110}\right)$	$e\left(\frac{207}{220}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{27}{44}\right)$
$\chi_{29040}(23,\cdot)$	29040.ip	44	no	$-1$	$1$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{7}{44}\right)$
$\chi_{29040}(29,\cdot)$	29040.kp	220	yes	$1$	$1$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{79}{220}\right)$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{17}{220}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{83}{220}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{163}{220}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{5}{44}\right)$
$\chi_{29040}(31,\cdot)$	29040.ju	110	no	$-1$	$1$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{43}{110}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{1}{22}\right)$
$\chi_{29040}(37,\cdot)$	29040.ky	220	no	$-1$	$1$	$e\left(\frac{93}{220}\right)$	$e\left(\frac{7}{110}\right)$	$e\left(\frac{211}{220}\right)$	$e\left(\frac{207}{220}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{163}{220}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{59}{110}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{6}{11}\right)$
$\chi_{29040}(41,\cdot)$	29040.jw	110	no	$1$	$1$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{8}{11}\right)$
$\chi_{29040}(43,\cdot)$	29040.iu	44	no	$-1$	$1$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{15}{22}\right)$
$\chi_{29040}(47,\cdot)$	29040.lo	220	no	$-1$	$1$	$e\left(\frac{217}{220}\right)$	$e\left(\frac{161}{220}\right)$	$e\left(\frac{89}{220}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{13}{110}\right)$	$e\left(\frac{147}{220}\right)$	$e\left(\frac{109}{110}\right)$	$e\left(\frac{23}{44}\right)$
$\chi_{29040}(49,\cdot)$	29040.jk	110	no	$1$	$1$	$e\left(\frac{43}{110}\right)$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{15}{22}\right)$
$\chi_{29040}(53,\cdot)$	29040.lz	220	yes	$1$	$1$	$e\left(\frac{219}{220}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{103}{220}\right)$	$e\left(\frac{51}{220}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{29}{220}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{13}{22}\right)$
$\chi_{29040}(59,\cdot)$	29040.kq	220	yes	$1$	$1$	$e\left(\frac{59}{110}\right)$	$e\left(\frac{139}{220}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{87}{220}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{43}{220}\right)$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{213}{220}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{23}{44}\right)$
$\chi_{29040}(61,\cdot)$	29040.md	220	no	$-1$	$1$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{73}{220}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{109}{220}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{21}{220}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{81}{220}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{23}{44}\right)$
$\chi_{29040}(67,\cdot)$	29040.hx	44	no	$1$	$1$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{8}{11}\right)$
$\chi_{29040}(71,\cdot)$	29040.jj	110	no	$1$	$1$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{109}{110}\right)$	$e\left(\frac{43}{110}\right)$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{4}{11}\right)$
$\chi_{29040}(73,\cdot)$	29040.le	220	no	$1$	$1$	$e\left(\frac{23}{220}\right)$	$e\left(\frac{159}{220}\right)$	$e\left(\frac{51}{220}\right)$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{79}{110}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{83}{220}\right)$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{7}{44}\right)$
$\chi_{29040}(79,\cdot)$	29040.jv	110	no	$1$	$1$	$e\left(\frac{67}{110}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{37}{110}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{7}{22}\right)$
$\chi_{29040}(83,\cdot)$	29040.ls	220	yes	$1$	$1$	$e\left(\frac{131}{220}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{37}{220}\right)$	$e\left(\frac{29}{220}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{161}{220}\right)$	$e\left(\frac{19}{110}\right)$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{7}{110}\right)$	$e\left(\frac{1}{11}\right)$
$\chi_{29040}(89,\cdot)$	29040.gw	22	no	$-1$	$1$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{7}{11}\right)$
$\chi_{29040}(91,\cdot)$	29040.me	220	no	$-1$	$1$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{201}{220}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{163}{220}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{97}{220}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{107}{220}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{13}{44}\right)$
$\chi_{29040}(97,\cdot)$	29040.lf	220	no	$-1$	$1$	$e\left(\frac{119}{220}\right)$	$e\left(\frac{177}{220}\right)$	$e\left(\frac{63}{220}\right)$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{7}{110}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{219}{220}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{41}{44}\right)$
$\chi_{29040}(101,\cdot)$	29040.mf	220	no	$1$	$1$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{7}{220}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{131}{220}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{109}{220}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{59}{220}\right)$	$e\left(\frac{43}{110}\right)$	$e\left(\frac{1}{44}\right)$
$\chi_{29040}(103,\cdot)$	29040.lh	220	no	$1$	$1$	$e\left(\frac{3}{220}\right)$	$e\left(\frac{169}{220}\right)$	$e\left(\frac{21}{220}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{97}{110}\right)$	$e\left(\frac{183}{220}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{43}{44}\right)$
$\chi_{29040}(107,\cdot)$	29040.ls	220	yes	$1$	$1$	$e\left(\frac{57}{220}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{179}{220}\right)$	$e\left(\frac{63}{220}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{107}{220}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{19}{110}\right)$	$e\left(\frac{9}{11}\right)$
$\chi_{29040}(109,\cdot)$	29040.iy	44	no	$-1$	$1$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{9}{44}\right)$
$\chi_{29040}(113,\cdot)$	29040.li	220	no	$1$	$1$	$e\left(\frac{97}{220}\right)$	$e\left(\frac{111}{220}\right)$	$e\left(\frac{19}{220}\right)$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{197}{220}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{19}{44}\right)$
$\chi_{29040}(119,\cdot)$	29040.kl	110	no	$1$	$1$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{23}{110}\right)$	$e\left(\frac{5}{22}\right)$
$\chi_{29040}(127,\cdot)$	29040.lg	220	no	$-1$	$1$	$e\left(\frac{91}{220}\right)$	$e\left(\frac{103}{220}\right)$	$e\left(\frac{197}{220}\right)$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{51}{220}\right)$	$e\left(\frac{67}{110}\right)$	$e\left(\frac{21}{44}\right)$
$\chi_{29040}(131,\cdot)$	29040.jb	44	no	$-1$	$1$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{13}{44}\right)$

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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	$29040$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{4}\times C_{220}\)
Order	$7040$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(7\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\(\chi_{29040}(1,\cdot)\)	29040.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{29040}(7,\cdot)\)	29040.lk	220	no	\(-1\)	\(1\)	\(e\left(\frac{43}{220}\right)\)	\(e\left(\frac{149}{220}\right)\)	\(e\left(\frac{81}{220}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{107}{110}\right)\)	\(e\left(\frac{93}{220}\right)\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{15}{44}\right)\)
\(\chi_{29040}(13,\cdot)\)	29040.lx	220	no	\(1\)	\(1\)	\(e\left(\frac{149}{220}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{163}{220}\right)\)	\(e\left(\frac{211}{220}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{79}{220}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{7}{110}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{21}{22}\right)\)
\(\chi_{29040}(17,\cdot)\)	29040.ln	220	no	\(-1\)	\(1\)	\(e\left(\frac{81}{220}\right)\)	\(e\left(\frac{163}{220}\right)\)	\(e\left(\frac{127}{220}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{63}{110}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{211}{220}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{39}{44}\right)\)
\(\chi_{29040}(19,\cdot)\)	29040.mg	220	no	\(1\)	\(1\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{211}{220}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{83}{220}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{17}{220}\right)\)	\(e\left(\frac{43}{110}\right)\)	\(e\left(\frac{207}{220}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{27}{44}\right)\)
\(\chi_{29040}(23,\cdot)\)	29040.ip	44	no	\(-1\)	\(1\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{7}{44}\right)\)
\(\chi_{29040}(29,\cdot)\)	29040.kp	220	yes	\(1\)	\(1\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{79}{220}\right)\)	\(e\left(\frac{63}{110}\right)\)	\(e\left(\frac{17}{220}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{83}{220}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{163}{220}\right)\)	\(e\left(\frac{61}{110}\right)\)	\(e\left(\frac{5}{44}\right)\)
\(\chi_{29040}(31,\cdot)\)	29040.ju	110	no	\(-1\)	\(1\)	\(e\left(\frac{107}{110}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{43}{110}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{81}{110}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{1}{22}\right)\)
\(\chi_{29040}(37,\cdot)\)	29040.ky	220	no	\(-1\)	\(1\)	\(e\left(\frac{93}{220}\right)\)	\(e\left(\frac{7}{110}\right)\)	\(e\left(\frac{211}{220}\right)\)	\(e\left(\frac{207}{220}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{163}{220}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{59}{110}\right)\)	\(e\left(\frac{31}{110}\right)\)	\(e\left(\frac{6}{11}\right)\)
\(\chi_{29040}(41,\cdot)\)	29040.jw	110	no	\(1\)	\(1\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{61}{110}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{31}{110}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{8}{11}\right)\)
\(\chi_{29040}(43,\cdot)\)	29040.iu	44	no	\(-1\)	\(1\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)
\(\chi_{29040}(47,\cdot)\)	29040.lo	220	no	\(-1\)	\(1\)	\(e\left(\frac{217}{220}\right)\)	\(e\left(\frac{161}{220}\right)\)	\(e\left(\frac{89}{220}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{13}{110}\right)\)	\(e\left(\frac{147}{220}\right)\)	\(e\left(\frac{109}{110}\right)\)	\(e\left(\frac{23}{44}\right)\)
\(\chi_{29040}(49,\cdot)\)	29040.jk	110	no	\(1\)	\(1\)	\(e\left(\frac{43}{110}\right)\)	\(e\left(\frac{39}{110}\right)\)	\(e\left(\frac{81}{110}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{93}{110}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{15}{22}\right)\)
\(\chi_{29040}(53,\cdot)\)	29040.lz	220	yes	\(1\)	\(1\)	\(e\left(\frac{219}{220}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{103}{220}\right)\)	\(e\left(\frac{51}{220}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{29}{220}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{13}{22}\right)\)
\(\chi_{29040}(59,\cdot)\)	29040.kq	220	yes	\(1\)	\(1\)	\(e\left(\frac{59}{110}\right)\)	\(e\left(\frac{139}{220}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{87}{220}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{43}{220}\right)\)	\(e\left(\frac{57}{110}\right)\)	\(e\left(\frac{213}{220}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{23}{44}\right)\)
\(\chi_{29040}(61,\cdot)\)	29040.md	220	no	\(-1\)	\(1\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{73}{220}\right)\)	\(e\left(\frac{61}{110}\right)\)	\(e\left(\frac{109}{220}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{21}{220}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{81}{220}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{23}{44}\right)\)
\(\chi_{29040}(67,\cdot)\)	29040.hx	44	no	\(1\)	\(1\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)
\(\chi_{29040}(71,\cdot)\)	29040.jj	110	no	\(1\)	\(1\)	\(e\left(\frac{53}{110}\right)\)	\(e\left(\frac{89}{110}\right)\)	\(e\left(\frac{41}{110}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{109}{110}\right)\)	\(e\left(\frac{43}{110}\right)\)	\(e\left(\frac{17}{110}\right)\)	\(e\left(\frac{4}{11}\right)\)
\(\chi_{29040}(73,\cdot)\)	29040.le	220	no	\(1\)	\(1\)	\(e\left(\frac{23}{220}\right)\)	\(e\left(\frac{159}{220}\right)\)	\(e\left(\frac{51}{220}\right)\)	\(e\left(\frac{101}{110}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{79}{110}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{83}{220}\right)\)	\(e\left(\frac{81}{110}\right)\)	\(e\left(\frac{7}{44}\right)\)
\(\chi_{29040}(79,\cdot)\)	29040.jv	110	no	\(1\)	\(1\)	\(e\left(\frac{67}{110}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{37}{110}\right)\)	\(e\left(\frac{61}{110}\right)\)	\(e\left(\frac{17}{110}\right)\)	\(e\left(\frac{63}{110}\right)\)	\(e\left(\frac{7}{22}\right)\)
\(\chi_{29040}(83,\cdot)\)	29040.ls	220	yes	\(1\)	\(1\)	\(e\left(\frac{131}{220}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{37}{220}\right)\)	\(e\left(\frac{29}{220}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{161}{220}\right)\)	\(e\left(\frac{19}{110}\right)\)	\(e\left(\frac{63}{110}\right)\)	\(e\left(\frac{7}{110}\right)\)	\(e\left(\frac{1}{11}\right)\)
\(\chi_{29040}(89,\cdot)\)	29040.gw	22	no	\(-1\)	\(1\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{7}{11}\right)\)
\(\chi_{29040}(91,\cdot)\)	29040.me	220	no	\(-1\)	\(1\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{201}{220}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{163}{220}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{97}{220}\right)\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{107}{220}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{13}{44}\right)\)
\(\chi_{29040}(97,\cdot)\)	29040.lf	220	no	\(-1\)	\(1\)	\(e\left(\frac{119}{220}\right)\)	\(e\left(\frac{177}{220}\right)\)	\(e\left(\frac{63}{220}\right)\)	\(e\left(\frac{73}{110}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{7}{110}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{219}{220}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{41}{44}\right)\)
\(\chi_{29040}(101,\cdot)\)	29040.mf	220	no	\(1\)	\(1\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{7}{220}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{131}{220}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{109}{220}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{59}{220}\right)\)	\(e\left(\frac{43}{110}\right)\)	\(e\left(\frac{1}{44}\right)\)
\(\chi_{29040}(103,\cdot)\)	29040.lh	220	no	\(1\)	\(1\)	\(e\left(\frac{3}{220}\right)\)	\(e\left(\frac{169}{220}\right)\)	\(e\left(\frac{21}{220}\right)\)	\(e\left(\frac{61}{110}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{97}{110}\right)\)	\(e\left(\frac{183}{220}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{43}{44}\right)\)
\(\chi_{29040}(107,\cdot)\)	29040.ls	220	yes	\(1\)	\(1\)	\(e\left(\frac{57}{220}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{179}{220}\right)\)	\(e\left(\frac{63}{220}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{107}{220}\right)\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{61}{110}\right)\)	\(e\left(\frac{19}{110}\right)\)	\(e\left(\frac{9}{11}\right)\)
\(\chi_{29040}(109,\cdot)\)	29040.iy	44	no	\(-1\)	\(1\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{9}{44}\right)\)
\(\chi_{29040}(113,\cdot)\)	29040.li	220	no	\(1\)	\(1\)	\(e\left(\frac{97}{220}\right)\)	\(e\left(\frac{111}{220}\right)\)	\(e\left(\frac{19}{220}\right)\)	\(e\left(\frac{29}{110}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{197}{220}\right)\)	\(e\left(\frac{69}{110}\right)\)	\(e\left(\frac{19}{44}\right)\)
\(\chi_{29040}(119,\cdot)\)	29040.kl	110	no	\(1\)	\(1\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{31}{110}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{23}{110}\right)\)	\(e\left(\frac{5}{22}\right)\)
\(\chi_{29040}(127,\cdot)\)	29040.lg	220	no	\(-1\)	\(1\)	\(e\left(\frac{91}{220}\right)\)	\(e\left(\frac{103}{220}\right)\)	\(e\left(\frac{197}{220}\right)\)	\(e\left(\frac{17}{110}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{51}{220}\right)\)	\(e\left(\frac{67}{110}\right)\)	\(e\left(\frac{21}{44}\right)\)
\(\chi_{29040}(131,\cdot)\)	29040.jb	44	no	\(-1\)	\(1\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{13}{44}\right)\)

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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.