LMFDB - Group of Dirichlet characters of modulus 2541

Show commands: PariGP / SageMath

sage: H = DirichletGroup(2541)

pari: g = idealstar(,2541,2)

Character group

sage: G.order() pari: g.no
Order	=	1320
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{330}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{2541}(848,\cdot)$, $\chi_{2541}(1816,\cdot)$, $\chi_{2541}(2059,\cdot)$

First 32 of 1320 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	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$13$	$16$	$17$	$19$	$20$
$\chi_{2541}(1,\cdot)$	2541.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{2541}(2,\cdot)$	2541.cg	330	yes	$1$	$1$	$e\left(\frac{29}{165}\right)$	$e\left(\frac{58}{165}\right)$	$e\left(\frac{277}{330}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{116}{165}\right)$	$e\left(\frac{46}{165}\right)$	$e\left(\frac{139}{330}\right)$	$e\left(\frac{21}{110}\right)$
$\chi_{2541}(4,\cdot)$	2541.ce	165	no	$1$	$1$	$e\left(\frac{58}{165}\right)$	$e\left(\frac{116}{165}\right)$	$e\left(\frac{112}{165}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{67}{165}\right)$	$e\left(\frac{92}{165}\right)$	$e\left(\frac{139}{165}\right)$	$e\left(\frac{21}{55}\right)$
$\chi_{2541}(5,\cdot)$	2541.ci	330	yes	$1$	$1$	$e\left(\frac{277}{330}\right)$	$e\left(\frac{112}{165}\right)$	$e\left(\frac{74}{165}\right)$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{49}{110}\right)$	$e\left(\frac{59}{165}\right)$	$e\left(\frac{49}{165}\right)$	$e\left(\frac{1}{330}\right)$	$e\left(\frac{7}{55}\right)$
$\chi_{2541}(8,\cdot)$	2541.cc	110	no	$1$	$1$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{63}{110}\right)$
$\chi_{2541}(10,\cdot)$	2541.br	66	no	$1$	$1$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{7}{22}\right)$
$\chi_{2541}(13,\cdot)$	2541.by	110	no	$1$	$1$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{49}{110}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{31}{110}\right)$
$\chi_{2541}(16,\cdot)$	2541.ce	165	no	$1$	$1$	$e\left(\frac{116}{165}\right)$	$e\left(\frac{67}{165}\right)$	$e\left(\frac{59}{165}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{134}{165}\right)$	$e\left(\frac{19}{165}\right)$	$e\left(\frac{113}{165}\right)$	$e\left(\frac{42}{55}\right)$
$\chi_{2541}(17,\cdot)$	2541.cf	330	yes	$-1$	$1$	$e\left(\frac{46}{165}\right)$	$e\left(\frac{92}{165}\right)$	$e\left(\frac{49}{165}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{19}{165}\right)$	$e\left(\frac{163}{330}\right)$	$e\left(\frac{133}{165}\right)$	$e\left(\frac{47}{55}\right)$
$\chi_{2541}(19,\cdot)$	2541.ck	330	no	$1$	$1$	$e\left(\frac{139}{330}\right)$	$e\left(\frac{139}{165}\right)$	$e\left(\frac{1}{330}\right)$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{113}{165}\right)$	$e\left(\frac{133}{165}\right)$	$e\left(\frac{131}{165}\right)$	$e\left(\frac{93}{110}\right)$
$\chi_{2541}(20,\cdot)$	2541.ca	110	yes	$1$	$1$	$e\left(\frac{21}{110}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{28}{55}\right)$
$\chi_{2541}(23,\cdot)$	2541.bq	66	yes	$-1$	$1$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{19}{22}\right)$
$\chi_{2541}(25,\cdot)$	2541.ce	165	no	$1$	$1$	$e\left(\frac{112}{165}\right)$	$e\left(\frac{59}{165}\right)$	$e\left(\frac{148}{165}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{118}{165}\right)$	$e\left(\frac{98}{165}\right)$	$e\left(\frac{1}{165}\right)$	$e\left(\frac{14}{55}\right)$
$\chi_{2541}(26,\cdot)$	2541.ci	330	yes	$1$	$1$	$e\left(\frac{31}{330}\right)$	$e\left(\frac{31}{165}\right)$	$e\left(\frac{47}{165}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{62}{165}\right)$	$e\left(\frac{127}{165}\right)$	$e\left(\frac{43}{330}\right)$	$e\left(\frac{26}{55}\right)$
$\chi_{2541}(29,\cdot)$	2541.cc	110	no	$1$	$1$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{67}{110}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{27}{110}\right)$
$\chi_{2541}(31,\cdot)$	2541.ch	330	no	$-1$	$1$	$e\left(\frac{19}{165}\right)$	$e\left(\frac{38}{165}\right)$	$e\left(\frac{227}{330}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{76}{165}\right)$	$e\left(\frac{157}{330}\right)$	$e\left(\frac{239}{330}\right)$	$e\left(\frac{101}{110}\right)$
$\chi_{2541}(32,\cdot)$	2541.bv	66	yes	$1$	$1$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{21}{22}\right)$
$\chi_{2541}(34,\cdot)$	2541.bc	22	no	$-1$	$1$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{1}{22}\right)$
$\chi_{2541}(37,\cdot)$	2541.ce	165	no	$1$	$1$	$e\left(\frac{8}{165}\right)$	$e\left(\frac{16}{165}\right)$	$e\left(\frac{152}{165}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{32}{165}\right)$	$e\left(\frac{7}{165}\right)$	$e\left(\frac{59}{165}\right)$	$e\left(\frac{1}{55}\right)$
$\chi_{2541}(38,\cdot)$	2541.ci	330	yes	$1$	$1$	$e\left(\frac{197}{330}\right)$	$e\left(\frac{32}{165}\right)$	$e\left(\frac{139}{165}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{64}{165}\right)$	$e\left(\frac{14}{165}\right)$	$e\left(\frac{71}{330}\right)$	$e\left(\frac{2}{55}\right)$
$\chi_{2541}(40,\cdot)$	2541.bi	30	no	$1$	$1$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{2541}(41,\cdot)$	2541.cd	110	yes	$-1$	$1$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{27}{110}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{49}{55}\right)$
$\chi_{2541}(43,\cdot)$	2541.be	22	no	$-1$	$1$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{3}{11}\right)$
$\chi_{2541}(46,\cdot)$	2541.cj	330	no	$-1$	$1$	$e\left(\frac{323}{330}\right)$	$e\left(\frac{158}{165}\right)$	$e\left(\frac{16}{165}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{21}{110}\right)$	$e\left(\frac{151}{165}\right)$	$e\left(\frac{97}{330}\right)$	$e\left(\frac{299}{330}\right)$	$e\left(\frac{3}{55}\right)$
$\chi_{2541}(47,\cdot)$	2541.ci	330	yes	$1$	$1$	$e\left(\frac{19}{330}\right)$	$e\left(\frac{19}{165}\right)$	$e\left(\frac{98}{165}\right)$	$e\left(\frac{19}{110}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{38}{165}\right)$	$e\left(\frac{163}{165}\right)$	$e\left(\frac{37}{330}\right)$	$e\left(\frac{39}{55}\right)$
$\chi_{2541}(50,\cdot)$	2541.cc	110	no	$1$	$1$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{49}{110}\right)$
$\chi_{2541}(52,\cdot)$	2541.ck	330	no	$1$	$1$	$e\left(\frac{89}{330}\right)$	$e\left(\frac{89}{165}\right)$	$e\left(\frac{41}{330}\right)$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{13}{165}\right)$	$e\left(\frac{8}{165}\right)$	$e\left(\frac{91}{165}\right)$	$e\left(\frac{73}{110}\right)$
$\chi_{2541}(53,\cdot)$	2541.cl	330	yes	$-1$	$1$	$e\left(\frac{263}{330}\right)$	$e\left(\frac{98}{165}\right)$	$e\left(\frac{47}{330}\right)$	$e\left(\frac{43}{110}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{31}{165}\right)$	$e\left(\frac{127}{330}\right)$	$e\left(\frac{52}{165}\right)$	$e\left(\frac{81}{110}\right)$
$\chi_{2541}(58,\cdot)$	2541.ce	165	no	$1$	$1$	$e\left(\frac{137}{165}\right)$	$e\left(\frac{109}{165}\right)$	$e\left(\frac{128}{165}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{53}{165}\right)$	$e\left(\frac{58}{165}\right)$	$e\left(\frac{41}{165}\right)$	$e\left(\frac{24}{55}\right)$
$\chi_{2541}(59,\cdot)$	2541.ci	330	yes	$1$	$1$	$e\left(\frac{41}{330}\right)$	$e\left(\frac{41}{165}\right)$	$e\left(\frac{142}{165}\right)$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{97}{110}\right)$	$e\left(\frac{82}{165}\right)$	$e\left(\frac{152}{165}\right)$	$e\left(\frac{323}{330}\right)$	$e\left(\frac{6}{55}\right)$
$\chi_{2541}(61,\cdot)$	2541.ck	330	no	$1$	$1$	$e\left(\frac{217}{330}\right)$	$e\left(\frac{52}{165}\right)$	$e\left(\frac{163}{330}\right)$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{104}{165}\right)$	$e\left(\frac{64}{165}\right)$	$e\left(\frac{68}{165}\right)$	$e\left(\frac{89}{110}\right)$
$\chi_{2541}(62,\cdot)$	2541.cd	110	yes	$-1$	$1$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{6}{55}\right)$

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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	$2541$
Structure	\(C_{2}\times C_{2}\times C_{330}\)
Order	$1320$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(8\)	\(10\)	\(13\)	\(16\)	\(17\)	\(19\)	\(20\)
\(\chi_{2541}(1,\cdot)\)	2541.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{2541}(2,\cdot)\)	2541.cg	330	yes	\(1\)	\(1\)	\(e\left(\frac{29}{165}\right)\)	\(e\left(\frac{58}{165}\right)\)	\(e\left(\frac{277}{330}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{101}{110}\right)\)	\(e\left(\frac{116}{165}\right)\)	\(e\left(\frac{46}{165}\right)\)	\(e\left(\frac{139}{330}\right)\)	\(e\left(\frac{21}{110}\right)\)
\(\chi_{2541}(4,\cdot)\)	2541.ce	165	no	\(1\)	\(1\)	\(e\left(\frac{58}{165}\right)\)	\(e\left(\frac{116}{165}\right)\)	\(e\left(\frac{112}{165}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{67}{165}\right)\)	\(e\left(\frac{92}{165}\right)\)	\(e\left(\frac{139}{165}\right)\)	\(e\left(\frac{21}{55}\right)\)
\(\chi_{2541}(5,\cdot)\)	2541.ci	330	yes	\(1\)	\(1\)	\(e\left(\frac{277}{330}\right)\)	\(e\left(\frac{112}{165}\right)\)	\(e\left(\frac{74}{165}\right)\)	\(e\left(\frac{57}{110}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{49}{110}\right)\)	\(e\left(\frac{59}{165}\right)\)	\(e\left(\frac{49}{165}\right)\)	\(e\left(\frac{1}{330}\right)\)	\(e\left(\frac{7}{55}\right)\)
\(\chi_{2541}(8,\cdot)\)	2541.cc	110	no	\(1\)	\(1\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{57}{110}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{29}{110}\right)\)	\(e\left(\frac{63}{110}\right)\)
\(\chi_{2541}(10,\cdot)\)	2541.br	66	no	\(1\)	\(1\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{7}{22}\right)\)
\(\chi_{2541}(13,\cdot)\)	2541.by	110	no	\(1\)	\(1\)	\(e\left(\frac{101}{110}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{49}{110}\right)\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{31}{110}\right)\)
\(\chi_{2541}(16,\cdot)\)	2541.ce	165	no	\(1\)	\(1\)	\(e\left(\frac{116}{165}\right)\)	\(e\left(\frac{67}{165}\right)\)	\(e\left(\frac{59}{165}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{134}{165}\right)\)	\(e\left(\frac{19}{165}\right)\)	\(e\left(\frac{113}{165}\right)\)	\(e\left(\frac{42}{55}\right)\)
\(\chi_{2541}(17,\cdot)\)	2541.cf	330	yes	\(-1\)	\(1\)	\(e\left(\frac{46}{165}\right)\)	\(e\left(\frac{92}{165}\right)\)	\(e\left(\frac{49}{165}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{19}{165}\right)\)	\(e\left(\frac{163}{330}\right)\)	\(e\left(\frac{133}{165}\right)\)	\(e\left(\frac{47}{55}\right)\)
\(\chi_{2541}(19,\cdot)\)	2541.ck	330	no	\(1\)	\(1\)	\(e\left(\frac{139}{330}\right)\)	\(e\left(\frac{139}{165}\right)\)	\(e\left(\frac{1}{330}\right)\)	\(e\left(\frac{29}{110}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{113}{165}\right)\)	\(e\left(\frac{133}{165}\right)\)	\(e\left(\frac{131}{165}\right)\)	\(e\left(\frac{93}{110}\right)\)
\(\chi_{2541}(20,\cdot)\)	2541.ca	110	yes	\(1\)	\(1\)	\(e\left(\frac{21}{110}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{63}{110}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{31}{110}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{93}{110}\right)\)	\(e\left(\frac{28}{55}\right)\)
\(\chi_{2541}(23,\cdot)\)	2541.bq	66	yes	\(-1\)	\(1\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{19}{22}\right)\)
\(\chi_{2541}(25,\cdot)\)	2541.ce	165	no	\(1\)	\(1\)	\(e\left(\frac{112}{165}\right)\)	\(e\left(\frac{59}{165}\right)\)	\(e\left(\frac{148}{165}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{118}{165}\right)\)	\(e\left(\frac{98}{165}\right)\)	\(e\left(\frac{1}{165}\right)\)	\(e\left(\frac{14}{55}\right)\)
\(\chi_{2541}(26,\cdot)\)	2541.ci	330	yes	\(1\)	\(1\)	\(e\left(\frac{31}{330}\right)\)	\(e\left(\frac{31}{165}\right)\)	\(e\left(\frac{47}{165}\right)\)	\(e\left(\frac{31}{110}\right)\)	\(e\left(\frac{25}{66}\right)\)	\(e\left(\frac{17}{110}\right)\)	\(e\left(\frac{62}{165}\right)\)	\(e\left(\frac{127}{165}\right)\)	\(e\left(\frac{43}{330}\right)\)	\(e\left(\frac{26}{55}\right)\)
\(\chi_{2541}(29,\cdot)\)	2541.cc	110	no	\(1\)	\(1\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{67}{110}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{27}{110}\right)\)
\(\chi_{2541}(31,\cdot)\)	2541.ch	330	no	\(-1\)	\(1\)	\(e\left(\frac{19}{165}\right)\)	\(e\left(\frac{38}{165}\right)\)	\(e\left(\frac{227}{330}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{76}{165}\right)\)	\(e\left(\frac{157}{330}\right)\)	\(e\left(\frac{239}{330}\right)\)	\(e\left(\frac{101}{110}\right)\)
\(\chi_{2541}(32,\cdot)\)	2541.bv	66	yes	\(1\)	\(1\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{21}{22}\right)\)
\(\chi_{2541}(34,\cdot)\)	2541.bc	22	no	\(-1\)	\(1\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)
\(\chi_{2541}(37,\cdot)\)	2541.ce	165	no	\(1\)	\(1\)	\(e\left(\frac{8}{165}\right)\)	\(e\left(\frac{16}{165}\right)\)	\(e\left(\frac{152}{165}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{32}{165}\right)\)	\(e\left(\frac{7}{165}\right)\)	\(e\left(\frac{59}{165}\right)\)	\(e\left(\frac{1}{55}\right)\)
\(\chi_{2541}(38,\cdot)\)	2541.ci	330	yes	\(1\)	\(1\)	\(e\left(\frac{197}{330}\right)\)	\(e\left(\frac{32}{165}\right)\)	\(e\left(\frac{139}{165}\right)\)	\(e\left(\frac{87}{110}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{69}{110}\right)\)	\(e\left(\frac{64}{165}\right)\)	\(e\left(\frac{14}{165}\right)\)	\(e\left(\frac{71}{330}\right)\)	\(e\left(\frac{2}{55}\right)\)
\(\chi_{2541}(40,\cdot)\)	2541.bi	30	no	\(1\)	\(1\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{2541}(41,\cdot)\)	2541.cd	110	yes	\(-1\)	\(1\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{27}{110}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{49}{55}\right)\)
\(\chi_{2541}(43,\cdot)\)	2541.be	22	no	\(-1\)	\(1\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)
\(\chi_{2541}(46,\cdot)\)	2541.cj	330	no	\(-1\)	\(1\)	\(e\left(\frac{323}{330}\right)\)	\(e\left(\frac{158}{165}\right)\)	\(e\left(\frac{16}{165}\right)\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{21}{110}\right)\)	\(e\left(\frac{151}{165}\right)\)	\(e\left(\frac{97}{330}\right)\)	\(e\left(\frac{299}{330}\right)\)	\(e\left(\frac{3}{55}\right)\)
\(\chi_{2541}(47,\cdot)\)	2541.ci	330	yes	\(1\)	\(1\)	\(e\left(\frac{19}{330}\right)\)	\(e\left(\frac{19}{165}\right)\)	\(e\left(\frac{98}{165}\right)\)	\(e\left(\frac{19}{110}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{53}{110}\right)\)	\(e\left(\frac{38}{165}\right)\)	\(e\left(\frac{163}{165}\right)\)	\(e\left(\frac{37}{330}\right)\)	\(e\left(\frac{39}{55}\right)\)
\(\chi_{2541}(50,\cdot)\)	2541.cc	110	no	\(1\)	\(1\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{81}{110}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{89}{110}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{49}{110}\right)\)
\(\chi_{2541}(52,\cdot)\)	2541.ck	330	no	\(1\)	\(1\)	\(e\left(\frac{89}{330}\right)\)	\(e\left(\frac{89}{165}\right)\)	\(e\left(\frac{41}{330}\right)\)	\(e\left(\frac{89}{110}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{13}{165}\right)\)	\(e\left(\frac{8}{165}\right)\)	\(e\left(\frac{91}{165}\right)\)	\(e\left(\frac{73}{110}\right)\)
\(\chi_{2541}(53,\cdot)\)	2541.cl	330	yes	\(-1\)	\(1\)	\(e\left(\frac{263}{330}\right)\)	\(e\left(\frac{98}{165}\right)\)	\(e\left(\frac{47}{330}\right)\)	\(e\left(\frac{43}{110}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{31}{165}\right)\)	\(e\left(\frac{127}{330}\right)\)	\(e\left(\frac{52}{165}\right)\)	\(e\left(\frac{81}{110}\right)\)
\(\chi_{2541}(58,\cdot)\)	2541.ce	165	no	\(1\)	\(1\)	\(e\left(\frac{137}{165}\right)\)	\(e\left(\frac{109}{165}\right)\)	\(e\left(\frac{128}{165}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{53}{165}\right)\)	\(e\left(\frac{58}{165}\right)\)	\(e\left(\frac{41}{165}\right)\)	\(e\left(\frac{24}{55}\right)\)
\(\chi_{2541}(59,\cdot)\)	2541.ci	330	yes	\(1\)	\(1\)	\(e\left(\frac{41}{330}\right)\)	\(e\left(\frac{41}{165}\right)\)	\(e\left(\frac{142}{165}\right)\)	\(e\left(\frac{41}{110}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{97}{110}\right)\)	\(e\left(\frac{82}{165}\right)\)	\(e\left(\frac{152}{165}\right)\)	\(e\left(\frac{323}{330}\right)\)	\(e\left(\frac{6}{55}\right)\)
\(\chi_{2541}(61,\cdot)\)	2541.ck	330	no	\(1\)	\(1\)	\(e\left(\frac{217}{330}\right)\)	\(e\left(\frac{52}{165}\right)\)	\(e\left(\frac{163}{330}\right)\)	\(e\left(\frac{107}{110}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{104}{165}\right)\)	\(e\left(\frac{64}{165}\right)\)	\(e\left(\frac{68}{165}\right)\)	\(e\left(\frac{89}{110}\right)\)
\(\chi_{2541}(62,\cdot)\)	2541.cd	110	yes	\(-1\)	\(1\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{6}{55}\right)\)

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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.