LMFDB - Group of Dirichlet characters of modulus 145200

Show commands: PariGP / SageMath

sage: H = DirichletGroup(145200)

pari: g = idealstar(,145200,2)

Character group

sage: G.order() pari: g.no
Order	=	35200
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{20}\times C_{220}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{145200}(90751,\cdot)$, $\chi_{145200}(108901,\cdot)$, $\chi_{145200}(48401,\cdot)$, $\chi_{145200}(127777,\cdot)$, $\chi_{145200}(14401,\cdot)$

First 32 of 35200 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	$-1$	$1$	$7$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{145200}(1,\cdot)$	145200.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{145200}(7,\cdot)$	145200.blr	220	no	$-1$	$1$	$e\left(\frac{43}{220}\right)$	$e\left(\frac{149}{220}\right)$	$e\left(\frac{81}{220}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{93}{220}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{15}{44}\right)$
$\chi_{145200}(13,\cdot)$	145200.bot	220	no	$1$	$1$	$e\left(\frac{149}{220}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{123}{220}\right)$	$e\left(\frac{49}{220}\right)$	$e\left(\frac{167}{220}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{21}{22}\right)$
$\chi_{145200}(17,\cdot)$	145200.bme	220	no	$-1$	$1$	$e\left(\frac{81}{220}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{171}{220}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{183}{220}\right)$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{123}{220}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{39}{44}\right)$
$\chi_{145200}(19,\cdot)$	145200.bqh	220	no	$1$	$1$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{123}{220}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{127}{220}\right)$	$e\left(\frac{79}{110}\right)$	$e\left(\frac{193}{220}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{119}{220}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{27}{44}\right)$
$\chi_{145200}(23,\cdot)$	145200.bkf	220	no	$-1$	$1$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{49}{220}\right)$	$e\left(\frac{183}{220}\right)$	$e\left(\frac{79}{110}\right)$	$e\left(\frac{131}{220}\right)$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{39}{220}\right)$	$e\left(\frac{37}{110}\right)$	$e\left(\frac{7}{44}\right)$
$\chi_{145200}(29,\cdot)$	145200.bgo	220	yes	$1$	$1$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{167}{220}\right)$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{193}{220}\right)$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{127}{220}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{31}{220}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{5}{44}\right)$
$\chi_{145200}(31,\cdot)$	145200.bbz	110	no	$-1$	$1$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{1}{22}\right)$
$\chi_{145200}(37,\cdot)$	145200.bpc	220	no	$-1$	$1$	$e\left(\frac{93}{220}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{123}{220}\right)$	$e\left(\frac{119}{220}\right)$	$e\left(\frac{39}{220}\right)$	$e\left(\frac{31}{220}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{37}{110}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{6}{11}\right)$
$\chi_{145200}(41,\cdot)$	145200.bbp	110	no	$1$	$1$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{37}{110}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{8}{11}\right)$
$\chi_{145200}(43,\cdot)$	145200.ye	44	no	$-1$	$1$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{15}{22}\right)$
$\chi_{145200}(47,\cdot)$	145200.bmm	220	no	$-1$	$1$	$e\left(\frac{217}{220}\right)$	$e\left(\frac{29}{220}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{157}{220}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{43}{110}\right)$	$e\left(\frac{23}{44}\right)$
$\chi_{145200}(49,\cdot)$	145200.bag	110	no	$1$	$1$	$e\left(\frac{43}{110}\right)$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{15}{22}\right)$
$\chi_{145200}(53,\cdot)$	145200.bid	220	yes	$1$	$1$	$e\left(\frac{219}{220}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{59}{220}\right)$	$e\left(\frac{7}{220}\right)$	$e\left(\frac{67}{220}\right)$	$e\left(\frac{73}{220}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{13}{22}\right)$
$\chi_{145200}(59,\cdot)$	145200.bhm	220	yes	$1$	$1$	$e\left(\frac{59}{110}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{219}{220}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{131}{220}\right)$	$e\left(\frac{13}{110}\right)$	$e\left(\frac{169}{220}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{23}{44}\right)$
$\chi_{145200}(61,\cdot)$	145200.bqr	220	no	$-1$	$1$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{117}{220}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{197}{220}\right)$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{153}{220}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{23}{44}\right)$
$\chi_{145200}(67,\cdot)$	145200.bny	220	no	$1$	$1$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{219}{220}\right)$	$e\left(\frac{199}{220}\right)$	$e\left(\frac{173}{220}\right)$	$e\left(\frac{1}{220}\right)$	$e\left(\frac{97}{110}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{1}{110}\right)$	$e\left(\frac{8}{11}\right)$
$\chi_{145200}(71,\cdot)$	145200.zy	110	no	$1$	$1$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{23}{110}\right)$	$e\left(\frac{19}{110}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{4}{11}\right)$
$\chi_{145200}(73,\cdot)$	145200.bni	220	no	$1$	$1$	$e\left(\frac{23}{220}\right)$	$e\left(\frac{203}{220}\right)$	$e\left(\frac{139}{220}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{131}{220}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{127}{220}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{7}{44}\right)$
$\chi_{145200}(79,\cdot)$	145200.zs	110	no	$1$	$1$	$e\left(\frac{67}{110}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{59}{110}\right)$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{7}{22}\right)$
$\chi_{145200}(83,\cdot)$	145200.bhw	220	yes	$1$	$1$	$e\left(\frac{131}{220}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{81}{220}\right)$	$e\left(\frac{73}{220}\right)$	$e\left(\frac{133}{220}\right)$	$e\left(\frac{117}{220}\right)$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{19}{110}\right)$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{1}{11}\right)$
$\chi_{145200}(89,\cdot)$	145200.bfx	110	no	$-1$	$1$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{19}{110}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{27}{110}\right)$	$e\left(\frac{7}{11}\right)$
$\chi_{145200}(91,\cdot)$	145200.bqj	220	no	$-1$	$1$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{157}{220}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{59}{110}\right)$	$e\left(\frac{63}{220}\right)$	$e\left(\frac{97}{110}\right)$	$e\left(\frac{13}{44}\right)$
$\chi_{145200}(97,\cdot)$	145200.bko	220	no	$-1$	$1$	$e\left(\frac{119}{220}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{19}{220}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{57}{220}\right)$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{87}{220}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{41}{44}\right)$
$\chi_{145200}(101,\cdot)$	145200.bqb	220	no	$1$	$1$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{7}{220}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{131}{220}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{109}{220}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{59}{220}\right)$	$e\left(\frac{43}{110}\right)$	$e\left(\frac{1}{44}\right)$
$\chi_{145200}(103,\cdot)$	145200.blm	220	no	$1$	$1$	$e\left(\frac{3}{220}\right)$	$e\left(\frac{37}{220}\right)$	$e\left(\frac{197}{220}\right)$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{217}{220}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{51}{220}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{43}{44}\right)$
$\chi_{145200}(107,\cdot)$	145200.bnr	220	no	$1$	$1$	$e\left(\frac{57}{220}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{179}{220}\right)$	$e\left(\frac{63}{220}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{107}{220}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{19}{110}\right)$	$e\left(\frac{9}{11}\right)$
$\chi_{145200}(109,\cdot)$	145200.brb	220	no	$-1$	$1$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{151}{220}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{57}{220}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{13}{220}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{91}{220}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{9}{44}\right)$
$\chi_{145200}(113,\cdot)$	145200.bne	220	no	$1$	$1$	$e\left(\frac{97}{220}\right)$	$e\left(\frac{67}{220}\right)$	$e\left(\frac{151}{220}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{189}{220}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{153}{220}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{19}{44}\right)$
$\chi_{145200}(119,\cdot)$	145200.bep	110	no	$1$	$1$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{59}{110}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{5}{22}\right)$
$\chi_{145200}(127,\cdot)$	145200.bkw	220	no	$-1$	$1$	$e\left(\frac{91}{220}\right)$	$e\left(\frac{147}{220}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{151}{220}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{21}{44}\right)$
$\chi_{145200}(131,\cdot)$	145200.bqy	220	yes	$-1$	$1$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{157}{220}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{119}{220}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{31}{220}\right)$	$e\left(\frac{37}{110}\right)$	$e\left(\frac{217}{220}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{13}{44}\right)$

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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	$145200$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{20}\times C_{220}\)
Order	$35200$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(7\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\(\chi_{145200}(1,\cdot)\)	145200.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{145200}(7,\cdot)\)	145200.blr	220	no	\(-1\)	\(1\)	\(e\left(\frac{43}{220}\right)\)	\(e\left(\frac{149}{220}\right)\)	\(e\left(\frac{81}{220}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{107}{110}\right)\)	\(e\left(\frac{93}{220}\right)\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{15}{44}\right)\)
\(\chi_{145200}(13,\cdot)\)	145200.bot	220	no	\(1\)	\(1\)	\(e\left(\frac{149}{220}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{123}{220}\right)\)	\(e\left(\frac{49}{220}\right)\)	\(e\left(\frac{167}{220}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{21}{22}\right)\)
\(\chi_{145200}(17,\cdot)\)	145200.bme	220	no	\(-1\)	\(1\)	\(e\left(\frac{81}{220}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{171}{220}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{183}{220}\right)\)	\(e\left(\frac{41}{110}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{123}{220}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{39}{44}\right)\)
\(\chi_{145200}(19,\cdot)\)	145200.bqh	220	no	\(1\)	\(1\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{123}{220}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{127}{220}\right)\)	\(e\left(\frac{79}{110}\right)\)	\(e\left(\frac{193}{220}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{119}{220}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{27}{44}\right)\)
\(\chi_{145200}(23,\cdot)\)	145200.bkf	220	no	\(-1\)	\(1\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{49}{220}\right)\)	\(e\left(\frac{183}{220}\right)\)	\(e\left(\frac{79}{110}\right)\)	\(e\left(\frac{131}{220}\right)\)	\(e\left(\frac{101}{110}\right)\)	\(e\left(\frac{69}{110}\right)\)	\(e\left(\frac{39}{220}\right)\)	\(e\left(\frac{37}{110}\right)\)	\(e\left(\frac{7}{44}\right)\)
\(\chi_{145200}(29,\cdot)\)	145200.bgo	220	yes	\(1\)	\(1\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{167}{220}\right)\)	\(e\left(\frac{41}{110}\right)\)	\(e\left(\frac{193}{220}\right)\)	\(e\left(\frac{101}{110}\right)\)	\(e\left(\frac{127}{220}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{31}{220}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{5}{44}\right)\)
\(\chi_{145200}(31,\cdot)\)	145200.bbz	110	no	\(-1\)	\(1\)	\(e\left(\frac{107}{110}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{69}{110}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{1}{22}\right)\)
\(\chi_{145200}(37,\cdot)\)	145200.bpc	220	no	\(-1\)	\(1\)	\(e\left(\frac{93}{220}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{123}{220}\right)\)	\(e\left(\frac{119}{220}\right)\)	\(e\left(\frac{39}{220}\right)\)	\(e\left(\frac{31}{220}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{37}{110}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{6}{11}\right)\)
\(\chi_{145200}(41,\cdot)\)	145200.bbp	110	no	\(1\)	\(1\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{37}{110}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{8}{11}\right)\)
\(\chi_{145200}(43,\cdot)\)	145200.ye	44	no	\(-1\)	\(1\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)
\(\chi_{145200}(47,\cdot)\)	145200.bmm	220	no	\(-1\)	\(1\)	\(e\left(\frac{217}{220}\right)\)	\(e\left(\frac{29}{220}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{157}{220}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{101}{110}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{43}{110}\right)\)	\(e\left(\frac{23}{44}\right)\)
\(\chi_{145200}(49,\cdot)\)	145200.bag	110	no	\(1\)	\(1\)	\(e\left(\frac{43}{110}\right)\)	\(e\left(\frac{39}{110}\right)\)	\(e\left(\frac{81}{110}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{93}{110}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{15}{22}\right)\)
\(\chi_{145200}(53,\cdot)\)	145200.bid	220	yes	\(1\)	\(1\)	\(e\left(\frac{219}{220}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{59}{220}\right)\)	\(e\left(\frac{7}{220}\right)\)	\(e\left(\frac{67}{220}\right)\)	\(e\left(\frac{73}{220}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{13}{22}\right)\)
\(\chi_{145200}(59,\cdot)\)	145200.bhm	220	yes	\(1\)	\(1\)	\(e\left(\frac{59}{110}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{219}{220}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{131}{220}\right)\)	\(e\left(\frac{13}{110}\right)\)	\(e\left(\frac{169}{220}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{23}{44}\right)\)
\(\chi_{145200}(61,\cdot)\)	145200.bqr	220	no	\(-1\)	\(1\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{117}{220}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{197}{220}\right)\)	\(e\left(\frac{73}{110}\right)\)	\(e\left(\frac{153}{220}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{23}{44}\right)\)
\(\chi_{145200}(67,\cdot)\)	145200.bny	220	no	\(1\)	\(1\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{219}{220}\right)\)	\(e\left(\frac{199}{220}\right)\)	\(e\left(\frac{173}{220}\right)\)	\(e\left(\frac{1}{220}\right)\)	\(e\left(\frac{97}{110}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{1}{110}\right)\)	\(e\left(\frac{8}{11}\right)\)
\(\chi_{145200}(71,\cdot)\)	145200.zy	110	no	\(1\)	\(1\)	\(e\left(\frac{53}{110}\right)\)	\(e\left(\frac{23}{110}\right)\)	\(e\left(\frac{19}{110}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{87}{110}\right)\)	\(e\left(\frac{87}{110}\right)\)	\(e\left(\frac{61}{110}\right)\)	\(e\left(\frac{4}{11}\right)\)
\(\chi_{145200}(73,\cdot)\)	145200.bni	220	no	\(1\)	\(1\)	\(e\left(\frac{23}{220}\right)\)	\(e\left(\frac{203}{220}\right)\)	\(e\left(\frac{139}{220}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{131}{220}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{127}{220}\right)\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{7}{44}\right)\)
\(\chi_{145200}(79,\cdot)\)	145200.zs	110	no	\(1\)	\(1\)	\(e\left(\frac{67}{110}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{59}{110}\right)\)	\(e\left(\frac{39}{110}\right)\)	\(e\left(\frac{61}{110}\right)\)	\(e\left(\frac{107}{110}\right)\)	\(e\left(\frac{7}{22}\right)\)
\(\chi_{145200}(83,\cdot)\)	145200.bhw	220	yes	\(1\)	\(1\)	\(e\left(\frac{131}{220}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{81}{220}\right)\)	\(e\left(\frac{73}{220}\right)\)	\(e\left(\frac{133}{220}\right)\)	\(e\left(\frac{117}{220}\right)\)	\(e\left(\frac{41}{110}\right)\)	\(e\left(\frac{19}{110}\right)\)	\(e\left(\frac{73}{110}\right)\)	\(e\left(\frac{1}{11}\right)\)
\(\chi_{145200}(89,\cdot)\)	145200.bfx	110	no	\(-1\)	\(1\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{19}{110}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{27}{110}\right)\)	\(e\left(\frac{7}{11}\right)\)
\(\chi_{145200}(91,\cdot)\)	145200.bqj	220	no	\(-1\)	\(1\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{157}{220}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{59}{110}\right)\)	\(e\left(\frac{63}{220}\right)\)	\(e\left(\frac{97}{110}\right)\)	\(e\left(\frac{13}{44}\right)\)
\(\chi_{145200}(97,\cdot)\)	145200.bko	220	no	\(-1\)	\(1\)	\(e\left(\frac{119}{220}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{19}{220}\right)\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{57}{220}\right)\)	\(e\left(\frac{29}{110}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{87}{220}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{41}{44}\right)\)
\(\chi_{145200}(101,\cdot)\)	145200.bqb	220	no	\(1\)	\(1\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{7}{220}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{131}{220}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{109}{220}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{59}{220}\right)\)	\(e\left(\frac{43}{110}\right)\)	\(e\left(\frac{1}{44}\right)\)
\(\chi_{145200}(103,\cdot)\)	145200.blm	220	no	\(1\)	\(1\)	\(e\left(\frac{3}{220}\right)\)	\(e\left(\frac{37}{220}\right)\)	\(e\left(\frac{197}{220}\right)\)	\(e\left(\frac{39}{110}\right)\)	\(e\left(\frac{217}{220}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{51}{220}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{43}{44}\right)\)
\(\chi_{145200}(107,\cdot)\)	145200.bnr	220	no	\(1\)	\(1\)	\(e\left(\frac{57}{220}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{179}{220}\right)\)	\(e\left(\frac{63}{220}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{107}{220}\right)\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{61}{110}\right)\)	\(e\left(\frac{19}{110}\right)\)	\(e\left(\frac{9}{11}\right)\)
\(\chi_{145200}(109,\cdot)\)	145200.brb	220	no	\(-1\)	\(1\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{151}{220}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{57}{220}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{13}{220}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{91}{220}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{9}{44}\right)\)
\(\chi_{145200}(113,\cdot)\)	145200.bne	220	no	\(1\)	\(1\)	\(e\left(\frac{97}{220}\right)\)	\(e\left(\frac{67}{220}\right)\)	\(e\left(\frac{151}{220}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{189}{220}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{153}{220}\right)\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{19}{44}\right)\)
\(\chi_{145200}(119,\cdot)\)	145200.bep	110	no	\(1\)	\(1\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{59}{110}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{53}{110}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{89}{110}\right)\)	\(e\left(\frac{5}{22}\right)\)
\(\chi_{145200}(127,\cdot)\)	145200.bkw	220	no	\(-1\)	\(1\)	\(e\left(\frac{91}{220}\right)\)	\(e\left(\frac{147}{220}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{61}{110}\right)\)	\(e\left(\frac{151}{220}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{53}{110}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{89}{110}\right)\)	\(e\left(\frac{21}{44}\right)\)
\(\chi_{145200}(131,\cdot)\)	145200.bqy	220	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{157}{220}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{119}{220}\right)\)	\(e\left(\frac{69}{110}\right)\)	\(e\left(\frac{31}{220}\right)\)	\(e\left(\frac{37}{110}\right)\)	\(e\left(\frac{217}{220}\right)\)	\(e\left(\frac{31}{110}\right)\)	\(e\left(\frac{13}{44}\right)\)

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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.