LMFDB - Group of Dirichlet characters of modulus 1815

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1815)

pari: g = idealstar(,1815,2)

Character group

sage: G.order() pari: g.no
Order	=	880
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{220}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{1815}(1211,\cdot)$, $\chi_{1815}(727,\cdot)$, $\chi_{1815}(1696,\cdot)$

First 32 of 880 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	$-1$	$1$	$2$	$4$	$7$	$8$	$13$	$14$	$16$	$17$	$19$	$23$
$\chi_{1815}(1,\cdot)$	1815.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1815}(2,\cdot)$	1815.bv	220	yes	$-1$	$1$	$e\left(\frac{167}{220}\right)$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{69}{220}\right)$	$e\left(\frac{61}{220}\right)$	$e\left(\frac{147}{220}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{43}{220}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{39}{44}\right)$
$\chi_{1815}(4,\cdot)$	1815.bm	110	no	$1$	$1$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{37}{110}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{43}{110}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{17}{22}\right)$
$\chi_{1815}(7,\cdot)$	1815.bt	220	no	$1$	$1$	$e\left(\frac{69}{220}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{153}{220}\right)$	$e\left(\frac{207}{220}\right)$	$e\left(\frac{39}{220}\right)$	$e\left(\frac{1}{110}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{81}{220}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{9}{44}\right)$
$\chi_{1815}(8,\cdot)$	1815.bv	220	yes	$-1$	$1$	$e\left(\frac{61}{220}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{207}{220}\right)$	$e\left(\frac{183}{220}\right)$	$e\left(\frac{1}{220}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{129}{220}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{29}{44}\right)$
$\chi_{1815}(13,\cdot)$	1815.bt	220	no	$1$	$1$	$e\left(\frac{147}{220}\right)$	$e\left(\frac{37}{110}\right)$	$e\left(\frac{39}{220}\right)$	$e\left(\frac{1}{220}\right)$	$e\left(\frac{217}{220}\right)$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{163}{220}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{23}{44}\right)$
$\chi_{1815}(14,\cdot)$	1815.bq	110	yes	$-1$	$1$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{1}{110}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{1}{11}\right)$
$\chi_{1815}(16,\cdot)$	1815.bk	55	no	$1$	$1$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{6}{11}\right)$
$\chi_{1815}(17,\cdot)$	1815.bv	220	yes	$-1$	$1$	$e\left(\frac{43}{220}\right)$	$e\left(\frac{43}{110}\right)$	$e\left(\frac{81}{220}\right)$	$e\left(\frac{129}{220}\right)$	$e\left(\frac{163}{220}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{127}{220}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{19}{44}\right)$
$\chi_{1815}(19,\cdot)$	1815.br	110	no	$-1$	$1$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{7}{22}\right)$
$\chi_{1815}(23,\cdot)$	1815.bh	44	yes	$1$	$1$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{13}{44}\right)$
$\chi_{1815}(26,\cdot)$	1815.bo	110	no	$-1$	$1$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{9}{22}\right)$
$\chi_{1815}(28,\cdot)$	1815.bt	220	no	$1$	$1$	$e\left(\frac{183}{220}\right)$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{71}{220}\right)$	$e\left(\frac{109}{220}\right)$	$e\left(\frac{113}{220}\right)$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{167}{220}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{43}{44}\right)$
$\chi_{1815}(29,\cdot)$	1815.bn	110	yes	$1$	$1$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{9}{11}\right)$
$\chi_{1815}(31,\cdot)$	1815.bk	55	no	$1$	$1$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{8}{11}\right)$
$\chi_{1815}(32,\cdot)$	1815.bg	44	yes	$-1$	$1$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{19}{44}\right)$
$\chi_{1815}(34,\cdot)$	1815.be	22	no	$1$	$1$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{7}{22}\right)$
$\chi_{1815}(37,\cdot)$	1815.bs	220	no	$-1$	$1$	$e\left(\frac{139}{220}\right)$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{203}{220}\right)$	$e\left(\frac{197}{220}\right)$	$e\left(\frac{69}{220}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{211}{220}\right)$	$e\left(\frac{21}{110}\right)$	$e\left(\frac{21}{44}\right)$
$\chi_{1815}(38,\cdot)$	1815.bu	220	yes	$1$	$1$	$e\left(\frac{3}{220}\right)$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{21}{220}\right)$	$e\left(\frac{9}{220}\right)$	$e\left(\frac{83}{220}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{147}{220}\right)$	$e\left(\frac{97}{110}\right)$	$e\left(\frac{9}{44}\right)$
$\chi_{1815}(41,\cdot)$	1815.bp	110	no	$1$	$1$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{13}{110}\right)$	$e\left(\frac{19}{110}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{3}{22}\right)$
$\chi_{1815}(43,\cdot)$	1815.bi	44	no	$1$	$1$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{7}{44}\right)$
$\chi_{1815}(46,\cdot)$	1815.bl	110	no	$-1$	$1$	$e\left(\frac{71}{110}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{21}{110}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{2}{11}\right)$
$\chi_{1815}(47,\cdot)$	1815.bu	220	yes	$1$	$1$	$e\left(\frac{141}{220}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{107}{220}\right)$	$e\left(\frac{203}{220}\right)$	$e\left(\frac{161}{220}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{89}{220}\right)$	$e\left(\frac{49}{110}\right)$	$e\left(\frac{27}{44}\right)$
$\chi_{1815}(49,\cdot)$	1815.bm	110	no	$1$	$1$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{43}{110}\right)$	$e\left(\frac{97}{110}\right)$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{9}{22}\right)$
$\chi_{1815}(52,\cdot)$	1815.bt	220	no	$1$	$1$	$e\left(\frac{41}{220}\right)$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{177}{220}\right)$	$e\left(\frac{123}{220}\right)$	$e\left(\frac{71}{220}\right)$	$e\left(\frac{109}{110}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{29}{220}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{13}{44}\right)$
$\chi_{1815}(53,\cdot)$	1815.bu	220	yes	$1$	$1$	$e\left(\frac{47}{220}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{109}{220}\right)$	$e\left(\frac{141}{220}\right)$	$e\left(\frac{127}{220}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{103}{220}\right)$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{9}{44}\right)$
$\chi_{1815}(56,\cdot)$	1815.bc	22	no	$-1$	$1$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{19}{22}\right)$
$\chi_{1815}(58,\cdot)$	1815.bs	220	no	$-1$	$1$	$e\left(\frac{201}{220}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{197}{220}\right)$	$e\left(\frac{163}{220}\right)$	$e\left(\frac{171}{220}\right)$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{169}{220}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{31}{44}\right)$
$\chi_{1815}(59,\cdot)$	1815.bq	110	yes	$-1$	$1$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{59}{110}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{97}{110}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{4}{11}\right)$
$\chi_{1815}(61,\cdot)$	1815.bl	110	no	$-1$	$1$	$e\left(\frac{109}{110}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{27}{110}\right)$	$e\left(\frac{4}{11}\right)$
$\chi_{1815}(62,\cdot)$	1815.bv	220	yes	$-1$	$1$	$e\left(\frac{119}{220}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{173}{220}\right)$	$e\left(\frac{137}{220}\right)$	$e\left(\frac{139}{220}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{111}{220}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{27}{44}\right)$
$\chi_{1815}(64,\cdot)$	1815.bm	110	no	$1$	$1$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{97}{110}\right)$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{1}{110}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{19}{110}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{7}{22}\right)$

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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	$1815$
Structure	\(C_{2}\times C_{2}\times C_{220}\)
Order	$880$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(7\)	\(8\)	\(13\)	\(14\)	\(16\)	\(17\)	\(19\)	\(23\)
\(\chi_{1815}(1,\cdot)\)	1815.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1815}(2,\cdot)\)	1815.bv	220	yes	\(-1\)	\(1\)	\(e\left(\frac{167}{220}\right)\)	\(e\left(\frac{57}{110}\right)\)	\(e\left(\frac{69}{220}\right)\)	\(e\left(\frac{61}{220}\right)\)	\(e\left(\frac{147}{220}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{43}{220}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{39}{44}\right)\)
\(\chi_{1815}(4,\cdot)\)	1815.bm	110	no	\(1\)	\(1\)	\(e\left(\frac{57}{110}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{69}{110}\right)\)	\(e\left(\frac{61}{110}\right)\)	\(e\left(\frac{37}{110}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{43}{110}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{17}{22}\right)\)
\(\chi_{1815}(7,\cdot)\)	1815.bt	220	no	\(1\)	\(1\)	\(e\left(\frac{69}{220}\right)\)	\(e\left(\frac{69}{110}\right)\)	\(e\left(\frac{153}{220}\right)\)	\(e\left(\frac{207}{220}\right)\)	\(e\left(\frac{39}{220}\right)\)	\(e\left(\frac{1}{110}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{81}{220}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{9}{44}\right)\)
\(\chi_{1815}(8,\cdot)\)	1815.bv	220	yes	\(-1\)	\(1\)	\(e\left(\frac{61}{220}\right)\)	\(e\left(\frac{61}{110}\right)\)	\(e\left(\frac{207}{220}\right)\)	\(e\left(\frac{183}{220}\right)\)	\(e\left(\frac{1}{220}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{129}{220}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{29}{44}\right)\)
\(\chi_{1815}(13,\cdot)\)	1815.bt	220	no	\(1\)	\(1\)	\(e\left(\frac{147}{220}\right)\)	\(e\left(\frac{37}{110}\right)\)	\(e\left(\frac{39}{220}\right)\)	\(e\left(\frac{1}{220}\right)\)	\(e\left(\frac{217}{220}\right)\)	\(e\left(\frac{93}{110}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{163}{220}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{23}{44}\right)\)
\(\chi_{1815}(14,\cdot)\)	1815.bq	110	yes	\(-1\)	\(1\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{1}{110}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{93}{110}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{1}{11}\right)\)
\(\chi_{1815}(16,\cdot)\)	1815.bk	55	no	\(1\)	\(1\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{6}{11}\right)\)
\(\chi_{1815}(17,\cdot)\)	1815.bv	220	yes	\(-1\)	\(1\)	\(e\left(\frac{43}{220}\right)\)	\(e\left(\frac{43}{110}\right)\)	\(e\left(\frac{81}{220}\right)\)	\(e\left(\frac{129}{220}\right)\)	\(e\left(\frac{163}{220}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{127}{220}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{19}{44}\right)\)
\(\chi_{1815}(19,\cdot)\)	1815.br	110	no	\(-1\)	\(1\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{69}{110}\right)\)	\(e\left(\frac{7}{22}\right)\)
\(\chi_{1815}(23,\cdot)\)	1815.bh	44	yes	\(1\)	\(1\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{13}{44}\right)\)
\(\chi_{1815}(26,\cdot)\)	1815.bo	110	no	\(-1\)	\(1\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{31}{110}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{101}{110}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{9}{22}\right)\)
\(\chi_{1815}(28,\cdot)\)	1815.bt	220	no	\(1\)	\(1\)	\(e\left(\frac{183}{220}\right)\)	\(e\left(\frac{73}{110}\right)\)	\(e\left(\frac{71}{220}\right)\)	\(e\left(\frac{109}{220}\right)\)	\(e\left(\frac{113}{220}\right)\)	\(e\left(\frac{17}{110}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{167}{220}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{43}{44}\right)\)
\(\chi_{1815}(29,\cdot)\)	1815.bn	110	yes	\(1\)	\(1\)	\(e\left(\frac{17}{110}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{81}{110}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{63}{110}\right)\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{9}{11}\right)\)
\(\chi_{1815}(31,\cdot)\)	1815.bk	55	no	\(1\)	\(1\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{8}{11}\right)\)
\(\chi_{1815}(32,\cdot)\)	1815.bg	44	yes	\(-1\)	\(1\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{19}{44}\right)\)
\(\chi_{1815}(34,\cdot)\)	1815.be	22	no	\(1\)	\(1\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)
\(\chi_{1815}(37,\cdot)\)	1815.bs	220	no	\(-1\)	\(1\)	\(e\left(\frac{139}{220}\right)\)	\(e\left(\frac{29}{110}\right)\)	\(e\left(\frac{203}{220}\right)\)	\(e\left(\frac{197}{220}\right)\)	\(e\left(\frac{69}{220}\right)\)	\(e\left(\frac{61}{110}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{211}{220}\right)\)	\(e\left(\frac{21}{110}\right)\)	\(e\left(\frac{21}{44}\right)\)
\(\chi_{1815}(38,\cdot)\)	1815.bu	220	yes	\(1\)	\(1\)	\(e\left(\frac{3}{220}\right)\)	\(e\left(\frac{3}{110}\right)\)	\(e\left(\frac{21}{220}\right)\)	\(e\left(\frac{9}{220}\right)\)	\(e\left(\frac{83}{220}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{147}{220}\right)\)	\(e\left(\frac{97}{110}\right)\)	\(e\left(\frac{9}{44}\right)\)
\(\chi_{1815}(41,\cdot)\)	1815.bp	110	no	\(1\)	\(1\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{13}{110}\right)\)	\(e\left(\frac{19}{110}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{39}{110}\right)\)	\(e\left(\frac{3}{22}\right)\)
\(\chi_{1815}(43,\cdot)\)	1815.bi	44	no	\(1\)	\(1\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{7}{44}\right)\)
\(\chi_{1815}(46,\cdot)\)	1815.bl	110	no	\(-1\)	\(1\)	\(e\left(\frac{71}{110}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{57}{110}\right)\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{21}{110}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{69}{110}\right)\)	\(e\left(\frac{63}{110}\right)\)	\(e\left(\frac{2}{11}\right)\)
\(\chi_{1815}(47,\cdot)\)	1815.bu	220	yes	\(1\)	\(1\)	\(e\left(\frac{141}{220}\right)\)	\(e\left(\frac{31}{110}\right)\)	\(e\left(\frac{107}{220}\right)\)	\(e\left(\frac{203}{220}\right)\)	\(e\left(\frac{161}{220}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{89}{220}\right)\)	\(e\left(\frac{49}{110}\right)\)	\(e\left(\frac{27}{44}\right)\)
\(\chi_{1815}(49,\cdot)\)	1815.bm	110	no	\(1\)	\(1\)	\(e\left(\frac{69}{110}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{43}{110}\right)\)	\(e\left(\frac{97}{110}\right)\)	\(e\left(\frac{39}{110}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{81}{110}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{9}{22}\right)\)
\(\chi_{1815}(52,\cdot)\)	1815.bt	220	no	\(1\)	\(1\)	\(e\left(\frac{41}{220}\right)\)	\(e\left(\frac{41}{110}\right)\)	\(e\left(\frac{177}{220}\right)\)	\(e\left(\frac{123}{220}\right)\)	\(e\left(\frac{71}{220}\right)\)	\(e\left(\frac{109}{110}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{29}{220}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{13}{44}\right)\)
\(\chi_{1815}(53,\cdot)\)	1815.bu	220	yes	\(1\)	\(1\)	\(e\left(\frac{47}{220}\right)\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{109}{220}\right)\)	\(e\left(\frac{141}{220}\right)\)	\(e\left(\frac{127}{220}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{103}{220}\right)\)	\(e\left(\frac{53}{110}\right)\)	\(e\left(\frac{9}{44}\right)\)
\(\chi_{1815}(56,\cdot)\)	1815.bc	22	no	\(-1\)	\(1\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{19}{22}\right)\)
\(\chi_{1815}(58,\cdot)\)	1815.bs	220	no	\(-1\)	\(1\)	\(e\left(\frac{201}{220}\right)\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{197}{220}\right)\)	\(e\left(\frac{163}{220}\right)\)	\(e\left(\frac{171}{220}\right)\)	\(e\left(\frac{89}{110}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{169}{220}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{31}{44}\right)\)
\(\chi_{1815}(59,\cdot)\)	1815.bq	110	yes	\(-1\)	\(1\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{59}{110}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{97}{110}\right)\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{4}{11}\right)\)
\(\chi_{1815}(61,\cdot)\)	1815.bl	110	no	\(-1\)	\(1\)	\(e\left(\frac{109}{110}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{107}{110}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{61}{110}\right)\)	\(e\left(\frac{27}{110}\right)\)	\(e\left(\frac{4}{11}\right)\)
\(\chi_{1815}(62,\cdot)\)	1815.bv	220	yes	\(-1\)	\(1\)	\(e\left(\frac{119}{220}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{173}{220}\right)\)	\(e\left(\frac{137}{220}\right)\)	\(e\left(\frac{139}{220}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{111}{220}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{27}{44}\right)\)
\(\chi_{1815}(64,\cdot)\)	1815.bm	110	no	\(1\)	\(1\)	\(e\left(\frac{61}{110}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{97}{110}\right)\)	\(e\left(\frac{73}{110}\right)\)	\(e\left(\frac{1}{110}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{19}{110}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{7}{22}\right)\)

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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.