LMFDB - Group of Dirichlet characters of modulus 4600

Show commands: PariGP / SageMath

sage: H = DirichletGroup(4600)

pari: g = idealstar(,4600,2)

Character group

sage: G.order() pari: g.no
Order	=	1760
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{220}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{4600}(1151,\cdot)$, $\chi_{4600}(2301,\cdot)$, $\chi_{4600}(2577,\cdot)$, $\chi_{4600}(1201,\cdot)$

First 32 of 1760 characters

Each row describes a character. When available, the columns show the orbit label, order of the character, whether the character is primitive, and several values of the character.

Character	Orbit	Order	Primitive	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$27$	$29$
$\chi_{4600}(1,\cdot)$	4600.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{4600}(3,\cdot)$	4600.dp	220	yes	$1$	$1$	$e\left(\frac{19}{220}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{19}{110}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{73}{220}\right)$	$e\left(\frac{141}{220}\right)$	$e\left(\frac{23}{110}\right)$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{57}{220}\right)$	$e\left(\frac{16}{55}\right)$
$\chi_{4600}(7,\cdot)$	4600.cp	44	no	$-1$	$1$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{1}{22}\right)$
$\chi_{4600}(9,\cdot)$	4600.dc	110	no	$1$	$1$	$e\left(\frac{19}{110}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{32}{55}\right)$
$\chi_{4600}(11,\cdot)$	4600.dd	110	yes	$1$	$1$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{59}{110}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{51}{110}\right)$
$\chi_{4600}(13,\cdot)$	4600.dl	220	yes	$-1$	$1$	$e\left(\frac{73}{220}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{101}{220}\right)$	$e\left(\frac{177}{220}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{19}{110}\right)$	$e\left(\frac{219}{220}\right)$	$e\left(\frac{47}{55}\right)$
$\chi_{4600}(17,\cdot)$	4600.dk	220	no	$1$	$1$	$e\left(\frac{141}{220}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{177}{220}\right)$	$e\left(\frac{149}{220}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{203}{220}\right)$	$e\left(\frac{3}{110}\right)$
$\chi_{4600}(19,\cdot)$	4600.cz	110	yes	$1$	$1$	$e\left(\frac{23}{110}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{59}{110}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{63}{110}\right)$
$\chi_{4600}(21,\cdot)$	4600.db	110	yes	$-1$	$1$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{19}{110}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{37}{110}\right)$
$\chi_{4600}(27,\cdot)$	4600.dp	220	yes	$1$	$1$	$e\left(\frac{57}{220}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{219}{220}\right)$	$e\left(\frac{203}{220}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{171}{220}\right)$	$e\left(\frac{48}{55}\right)$
$\chi_{4600}(29,\cdot)$	4600.dg	110	yes	$1$	$1$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{37}{110}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{47}{110}\right)$
$\chi_{4600}(31,\cdot)$	4600.da	110	no	$-1$	$1$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{109}{110}\right)$	$e\left(\frac{39}{55}\right)$
$\chi_{4600}(33,\cdot)$	4600.dk	220	no	$1$	$1$	$e\left(\frac{51}{220}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{167}{220}\right)$	$e\left(\frac{199}{220}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{153}{220}\right)$	$e\left(\frac{83}{110}\right)$
$\chi_{4600}(37,\cdot)$	4600.dr	220	yes	$1$	$1$	$e\left(\frac{203}{220}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{91}{220}\right)$	$e\left(\frac{117}{220}\right)$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{169}{220}\right)$	$e\left(\frac{32}{55}\right)$
$\chi_{4600}(39,\cdot)$	4600.de	110	no	$-1$	$1$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{49}{110}\right)$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{8}{55}\right)$
$\chi_{4600}(41,\cdot)$	4600.cu	55	no	$1$	$1$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{12}{55}\right)$
$\chi_{4600}(43,\cdot)$	4600.cq	44	no	$-1$	$1$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{1}{11}\right)$
$\chi_{4600}(47,\cdot)$	4600.bu	20	no	$1$	$1$	$e\left(\frac{9}{20}\right)$	$-i$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{4600}(49,\cdot)$	4600.ci	22	no	$1$	$1$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{1}{11}\right)$
$\chi_{4600}(51,\cdot)$	4600.bz	22	no	$1$	$1$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{7}{22}\right)$
$\chi_{4600}(53,\cdot)$	4600.dr	220	yes	$1$	$1$	$e\left(\frac{169}{220}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{59}{110}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{53}{220}\right)$	$e\left(\frac{131}{220}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{67}{220}\right)$	$e\left(\frac{41}{55}\right)$
$\chi_{4600}(57,\cdot)$	4600.ct	44	no	$1$	$1$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{19}{22}\right)$
$\chi_{4600}(59,\cdot)$	4600.cx	110	yes	$-1$	$1$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{19}{110}\right)$	$e\left(\frac{27}{110}\right)$	$e\left(\frac{39}{110}\right)$
$\chi_{4600}(61,\cdot)$	4600.db	110	yes	$-1$	$1$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{43}{110}\right)$	$e\left(\frac{1}{110}\right)$
$\chi_{4600}(63,\cdot)$	4600.do	220	no	$-1$	$1$	$e\left(\frac{53}{220}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{111}{220}\right)$	$e\left(\frac{127}{220}\right)$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{59}{110}\right)$	$e\left(\frac{159}{220}\right)$	$e\left(\frac{69}{110}\right)$
$\chi_{4600}(67,\cdot)$	4600.dn	220	yes	$-1$	$1$	$e\left(\frac{1}{220}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{1}{110}\right)$	$e\left(\frac{79}{110}\right)$	$e\left(\frac{27}{220}\right)$	$e\left(\frac{129}{220}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{3}{220}\right)$	$e\left(\frac{24}{55}\right)$
$\chi_{4600}(71,\cdot)$	4600.da	110	no	$-1$	$1$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{46}{55}\right)$
$\chi_{4600}(73,\cdot)$	4600.dq	220	no	$-1$	$1$	$e\left(\frac{167}{220}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{219}{220}\right)$	$e\left(\frac{93}{220}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{61}{220}\right)$	$e\left(\frac{41}{110}\right)$
$\chi_{4600}(77,\cdot)$	4600.dl	220	yes	$-1$	$1$	$e\left(\frac{47}{220}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{59}{220}\right)$	$e\left(\frac{123}{220}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{71}{110}\right)$	$e\left(\frac{141}{220}\right)$	$e\left(\frac{28}{55}\right)$
$\chi_{4600}(79,\cdot)$	4600.dj	110	no	$1$	$1$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{36}{55}\right)$
$\chi_{4600}(81,\cdot)$	4600.cu	55	no	$1$	$1$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{9}{55}\right)$
$\chi_{4600}(83,\cdot)$	4600.dn	220	yes	$-1$	$1$	$e\left(\frac{71}{220}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{71}{110}\right)$	$e\left(\frac{109}{110}\right)$	$e\left(\frac{157}{220}\right)$	$e\left(\frac{139}{220}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{213}{220}\right)$	$e\left(\frac{54}{55}\right)$

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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	$4600$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{220}\)
Order	$1760$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(21\)	\(27\)	\(29\)
\(\chi_{4600}(1,\cdot)\)	4600.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{4600}(3,\cdot)\)	4600.dp	220	yes	\(1\)	\(1\)	\(e\left(\frac{19}{220}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{19}{110}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{73}{220}\right)\)	\(e\left(\frac{141}{220}\right)\)	\(e\left(\frac{23}{110}\right)\)	\(e\left(\frac{17}{110}\right)\)	\(e\left(\frac{57}{220}\right)\)	\(e\left(\frac{16}{55}\right)\)
\(\chi_{4600}(7,\cdot)\)	4600.cp	44	no	\(-1\)	\(1\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{1}{22}\right)\)
\(\chi_{4600}(9,\cdot)\)	4600.dc	110	no	\(1\)	\(1\)	\(e\left(\frac{19}{110}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{73}{110}\right)\)	\(e\left(\frac{31}{110}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{57}{110}\right)\)	\(e\left(\frac{32}{55}\right)\)
\(\chi_{4600}(11,\cdot)\)	4600.dd	110	yes	\(1\)	\(1\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{53}{110}\right)\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{29}{110}\right)\)	\(e\left(\frac{59}{110}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{51}{110}\right)\)
\(\chi_{4600}(13,\cdot)\)	4600.dl	220	yes	\(-1\)	\(1\)	\(e\left(\frac{73}{220}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{73}{110}\right)\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{101}{220}\right)\)	\(e\left(\frac{177}{220}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{19}{110}\right)\)	\(e\left(\frac{219}{220}\right)\)	\(e\left(\frac{47}{55}\right)\)
\(\chi_{4600}(17,\cdot)\)	4600.dk	220	no	\(1\)	\(1\)	\(e\left(\frac{141}{220}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{31}{110}\right)\)	\(e\left(\frac{29}{110}\right)\)	\(e\left(\frac{177}{220}\right)\)	\(e\left(\frac{149}{220}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{203}{220}\right)\)	\(e\left(\frac{3}{110}\right)\)
\(\chi_{4600}(19,\cdot)\)	4600.cz	110	yes	\(1\)	\(1\)	\(e\left(\frac{23}{110}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{59}{110}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{69}{110}\right)\)	\(e\left(\frac{63}{110}\right)\)
\(\chi_{4600}(21,\cdot)\)	4600.db	110	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{110}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{19}{110}\right)\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{37}{110}\right)\)
\(\chi_{4600}(27,\cdot)\)	4600.dp	220	yes	\(1\)	\(1\)	\(e\left(\frac{57}{220}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{57}{110}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{219}{220}\right)\)	\(e\left(\frac{203}{220}\right)\)	\(e\left(\frac{69}{110}\right)\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{171}{220}\right)\)	\(e\left(\frac{48}{55}\right)\)
\(\chi_{4600}(29,\cdot)\)	4600.dg	110	yes	\(1\)	\(1\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{3}{110}\right)\)	\(e\left(\frac{63}{110}\right)\)	\(e\left(\frac{37}{110}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{47}{110}\right)\)
\(\chi_{4600}(31,\cdot)\)	4600.da	110	no	\(-1\)	\(1\)	\(e\left(\frac{73}{110}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{39}{110}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{87}{110}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{109}{110}\right)\)	\(e\left(\frac{39}{55}\right)\)
\(\chi_{4600}(33,\cdot)\)	4600.dk	220	no	\(1\)	\(1\)	\(e\left(\frac{51}{220}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{69}{110}\right)\)	\(e\left(\frac{167}{220}\right)\)	\(e\left(\frac{199}{220}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{63}{110}\right)\)	\(e\left(\frac{153}{220}\right)\)	\(e\left(\frac{83}{110}\right)\)
\(\chi_{4600}(37,\cdot)\)	4600.dr	220	yes	\(1\)	\(1\)	\(e\left(\frac{203}{220}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{93}{110}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{91}{220}\right)\)	\(e\left(\frac{117}{220}\right)\)	\(e\left(\frac{101}{110}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{169}{220}\right)\)	\(e\left(\frac{32}{55}\right)\)
\(\chi_{4600}(39,\cdot)\)	4600.de	110	no	\(-1\)	\(1\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{63}{110}\right)\)	\(e\left(\frac{87}{110}\right)\)	\(e\left(\frac{49}{110}\right)\)	\(e\left(\frac{39}{110}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{8}{55}\right)\)
\(\chi_{4600}(41,\cdot)\)	4600.cu	55	no	\(1\)	\(1\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{12}{55}\right)\)
\(\chi_{4600}(43,\cdot)\)	4600.cq	44	no	\(-1\)	\(1\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{1}{11}\right)\)
\(\chi_{4600}(47,\cdot)\)	4600.bu	20	no	\(1\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(-i\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{4600}(49,\cdot)\)	4600.ci	22	no	\(1\)	\(1\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)
\(\chi_{4600}(51,\cdot)\)	4600.bz	22	no	\(1\)	\(1\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)
\(\chi_{4600}(53,\cdot)\)	4600.dr	220	yes	\(1\)	\(1\)	\(e\left(\frac{169}{220}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{59}{110}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{53}{220}\right)\)	\(e\left(\frac{131}{220}\right)\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{67}{220}\right)\)	\(e\left(\frac{41}{55}\right)\)
\(\chi_{4600}(57,\cdot)\)	4600.ct	44	no	\(1\)	\(1\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{19}{22}\right)\)
\(\chi_{4600}(59,\cdot)\)	4600.cx	110	yes	\(-1\)	\(1\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{61}{110}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{19}{110}\right)\)	\(e\left(\frac{27}{110}\right)\)	\(e\left(\frac{39}{110}\right)\)
\(\chi_{4600}(61,\cdot)\)	4600.db	110	yes	\(-1\)	\(1\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{57}{110}\right)\)	\(e\left(\frac{89}{110}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{43}{110}\right)\)	\(e\left(\frac{1}{110}\right)\)
\(\chi_{4600}(63,\cdot)\)	4600.do	220	no	\(-1\)	\(1\)	\(e\left(\frac{53}{220}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{53}{110}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{111}{220}\right)\)	\(e\left(\frac{127}{220}\right)\)	\(e\left(\frac{41}{110}\right)\)	\(e\left(\frac{59}{110}\right)\)	\(e\left(\frac{159}{220}\right)\)	\(e\left(\frac{69}{110}\right)\)
\(\chi_{4600}(67,\cdot)\)	4600.dn	220	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{220}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{1}{110}\right)\)	\(e\left(\frac{79}{110}\right)\)	\(e\left(\frac{27}{220}\right)\)	\(e\left(\frac{129}{220}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{3}{220}\right)\)	\(e\left(\frac{24}{55}\right)\)
\(\chi_{4600}(71,\cdot)\)	4600.da	110	no	\(-1\)	\(1\)	\(e\left(\frac{17}{110}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{101}{110}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{73}{110}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{46}{55}\right)\)
\(\chi_{4600}(73,\cdot)\)	4600.dq	220	no	\(-1\)	\(1\)	\(e\left(\frac{167}{220}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{57}{110}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{219}{220}\right)\)	\(e\left(\frac{93}{220}\right)\)	\(e\left(\frac{69}{110}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{61}{220}\right)\)	\(e\left(\frac{41}{110}\right)\)
\(\chi_{4600}(77,\cdot)\)	4600.dl	220	yes	\(-1\)	\(1\)	\(e\left(\frac{47}{220}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{59}{220}\right)\)	\(e\left(\frac{123}{220}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{71}{110}\right)\)	\(e\left(\frac{141}{220}\right)\)	\(e\left(\frac{28}{55}\right)\)
\(\chi_{4600}(79,\cdot)\)	4600.dj	110	no	\(1\)	\(1\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{89}{110}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{107}{110}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{36}{55}\right)\)
\(\chi_{4600}(81,\cdot)\)	4600.cu	55	no	\(1\)	\(1\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{9}{55}\right)\)
\(\chi_{4600}(83,\cdot)\)	4600.dn	220	yes	\(-1\)	\(1\)	\(e\left(\frac{71}{220}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{71}{110}\right)\)	\(e\left(\frac{109}{110}\right)\)	\(e\left(\frac{157}{220}\right)\)	\(e\left(\frac{139}{220}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{213}{220}\right)\)	\(e\left(\frac{54}{55}\right)\)

Introduction

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.