LMFDB - Group of Dirichlet characters of modulus 921

Show commands: PariGP / SageMath

sage: H = DirichletGroup(921)

pari: g = idealstar(,921,2)

Character group

sage: G.order() pari: g.no
Order	=	612
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{306}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{921}(308,\cdot)$, $\chi_{921}(619,\cdot)$

First 32 of 612 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	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$13$	$14$	$16$
$\chi_{921}(1,\cdot)$	921.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{921}(2,\cdot)$	921.r	102	yes	$1$	$1$	$e\left(\frac{13}{17}\right)$	$e\left(\frac{9}{17}\right)$	$e\left(\frac{41}{51}\right)$	$e\left(\frac{13}{51}\right)$	$e\left(\frac{5}{17}\right)$	$e\left(\frac{29}{51}\right)$	$e\left(\frac{73}{102}\right)$	$e\left(\frac{91}{102}\right)$	$e\left(\frac{1}{51}\right)$	$e\left(\frac{1}{17}\right)$
$\chi_{921}(4,\cdot)$	921.q	51	no	$1$	$1$	$e\left(\frac{9}{17}\right)$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{31}{51}\right)$	$e\left(\frac{26}{51}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{7}{51}\right)$	$e\left(\frac{22}{51}\right)$	$e\left(\frac{40}{51}\right)$	$e\left(\frac{2}{51}\right)$	$e\left(\frac{2}{17}\right)$
$\chi_{921}(5,\cdot)$	921.x	306	yes	$1$	$1$	$e\left(\frac{41}{51}\right)$	$e\left(\frac{31}{51}\right)$	$e\left(\frac{77}{153}\right)$	$e\left(\frac{58}{153}\right)$	$e\left(\frac{7}{17}\right)$	$e\left(\frac{47}{153}\right)$	$e\left(\frac{157}{306}\right)$	$e\left(\frac{253}{306}\right)$	$e\left(\frac{28}{153}\right)$	$e\left(\frac{11}{51}\right)$
$\chi_{921}(7,\cdot)$	921.u	153	no	$1$	$1$	$e\left(\frac{13}{51}\right)$	$e\left(\frac{26}{51}\right)$	$e\left(\frac{58}{153}\right)$	$e\left(\frac{149}{153}\right)$	$e\left(\frac{13}{17}\right)$	$e\left(\frac{97}{153}\right)$	$e\left(\frac{79}{153}\right)$	$e\left(\frac{139}{153}\right)$	$e\left(\frac{35}{153}\right)$	$e\left(\frac{1}{51}\right)$
$\chi_{921}(8,\cdot)$	921.n	34	yes	$1$	$1$	$e\left(\frac{5}{17}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{7}{17}\right)$	$e\left(\frac{13}{17}\right)$	$e\left(\frac{15}{17}\right)$	$e\left(\frac{12}{17}\right)$	$e\left(\frac{5}{34}\right)$	$e\left(\frac{23}{34}\right)$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{3}{17}\right)$
$\chi_{921}(10,\cdot)$	921.u	153	no	$1$	$1$	$e\left(\frac{29}{51}\right)$	$e\left(\frac{7}{51}\right)$	$e\left(\frac{47}{153}\right)$	$e\left(\frac{97}{153}\right)$	$e\left(\frac{12}{17}\right)$	$e\left(\frac{134}{153}\right)$	$e\left(\frac{35}{153}\right)$	$e\left(\frac{110}{153}\right)$	$e\left(\frac{31}{153}\right)$	$e\left(\frac{14}{51}\right)$
$\chi_{921}(11,\cdot)$	921.w	306	yes	$-1$	$1$	$e\left(\frac{73}{102}\right)$	$e\left(\frac{22}{51}\right)$	$e\left(\frac{157}{306}\right)$	$e\left(\frac{79}{153}\right)$	$e\left(\frac{5}{34}\right)$	$e\left(\frac{35}{153}\right)$	$e\left(\frac{169}{306}\right)$	$e\left(\frac{47}{153}\right)$	$e\left(\frac{71}{306}\right)$	$e\left(\frac{44}{51}\right)$
$\chi_{921}(13,\cdot)$	921.v	306	no	$-1$	$1$	$e\left(\frac{91}{102}\right)$	$e\left(\frac{40}{51}\right)$	$e\left(\frac{253}{306}\right)$	$e\left(\frac{139}{153}\right)$	$e\left(\frac{23}{34}\right)$	$e\left(\frac{110}{153}\right)$	$e\left(\frac{47}{153}\right)$	$e\left(\frac{55}{306}\right)$	$e\left(\frac{245}{306}\right)$	$e\left(\frac{29}{51}\right)$
$\chi_{921}(14,\cdot)$	921.x	306	yes	$1$	$1$	$e\left(\frac{1}{51}\right)$	$e\left(\frac{2}{51}\right)$	$e\left(\frac{28}{153}\right)$	$e\left(\frac{35}{153}\right)$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{31}{153}\right)$	$e\left(\frac{71}{306}\right)$	$e\left(\frac{245}{306}\right)$	$e\left(\frac{38}{153}\right)$	$e\left(\frac{4}{51}\right)$
$\chi_{921}(16,\cdot)$	921.q	51	no	$1$	$1$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{11}{51}\right)$	$e\left(\frac{1}{51}\right)$	$e\left(\frac{3}{17}\right)$	$e\left(\frac{14}{51}\right)$	$e\left(\frac{44}{51}\right)$	$e\left(\frac{29}{51}\right)$	$e\left(\frac{4}{51}\right)$	$e\left(\frac{4}{17}\right)$
$\chi_{921}(17,\cdot)$	921.g	6	yes	$-1$	$1$	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$1$
$\chi_{921}(19,\cdot)$	921.q	51	no	$1$	$1$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{28}{51}\right)$	$e\left(\frac{35}{51}\right)$	$e\left(\frac{3}{17}\right)$	$e\left(\frac{31}{51}\right)$	$e\left(\frac{10}{51}\right)$	$e\left(\frac{46}{51}\right)$	$e\left(\frac{38}{51}\right)$	$e\left(\frac{4}{17}\right)$
$\chi_{921}(20,\cdot)$	921.k	18	yes	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{8}{9}\right)$	$1$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{921}(22,\cdot)$	921.v	306	no	$-1$	$1$	$e\left(\frac{49}{102}\right)$	$e\left(\frac{49}{51}\right)$	$e\left(\frac{97}{306}\right)$	$e\left(\frac{118}{153}\right)$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{122}{153}\right)$	$e\left(\frac{41}{153}\right)$	$e\left(\frac{61}{306}\right)$	$e\left(\frac{77}{306}\right)$	$e\left(\frac{47}{51}\right)$
$\chi_{921}(23,\cdot)$	921.x	306	yes	$1$	$1$	$e\left(\frac{46}{51}\right)$	$e\left(\frac{41}{51}\right)$	$e\left(\frac{13}{153}\right)$	$e\left(\frac{131}{153}\right)$	$e\left(\frac{12}{17}\right)$	$e\left(\frac{151}{153}\right)$	$e\left(\frac{257}{306}\right)$	$e\left(\frac{305}{306}\right)$	$e\left(\frac{116}{153}\right)$	$e\left(\frac{31}{51}\right)$
$\chi_{921}(25,\cdot)$	921.u	153	no	$1$	$1$	$e\left(\frac{31}{51}\right)$	$e\left(\frac{11}{51}\right)$	$e\left(\frac{1}{153}\right)$	$e\left(\frac{116}{153}\right)$	$e\left(\frac{14}{17}\right)$	$e\left(\frac{94}{153}\right)$	$e\left(\frac{4}{153}\right)$	$e\left(\frac{100}{153}\right)$	$e\left(\frac{56}{153}\right)$	$e\left(\frac{22}{51}\right)$
$\chi_{921}(26,\cdot)$	921.w	306	yes	$-1$	$1$	$e\left(\frac{67}{102}\right)$	$e\left(\frac{16}{51}\right)$	$e\left(\frac{193}{306}\right)$	$e\left(\frac{25}{153}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{44}{153}\right)$	$e\left(\frac{7}{306}\right)$	$e\left(\frac{11}{153}\right)$	$e\left(\frac{251}{306}\right)$	$e\left(\frac{32}{51}\right)$
$\chi_{921}(28,\cdot)$	921.u	153	no	$1$	$1$	$e\left(\frac{40}{51}\right)$	$e\left(\frac{29}{51}\right)$	$e\left(\frac{151}{153}\right)$	$e\left(\frac{74}{153}\right)$	$e\left(\frac{6}{17}\right)$	$e\left(\frac{118}{153}\right)$	$e\left(\frac{145}{153}\right)$	$e\left(\frac{106}{153}\right)$	$e\left(\frac{41}{153}\right)$	$e\left(\frac{7}{51}\right)$
$\chi_{921}(29,\cdot)$	921.x	306	yes	$1$	$1$	$e\left(\frac{22}{51}\right)$	$e\left(\frac{44}{51}\right)$	$e\left(\frac{55}{153}\right)$	$e\left(\frac{107}{153}\right)$	$e\left(\frac{5}{17}\right)$	$e\left(\frac{121}{153}\right)$	$e\left(\frac{287}{306}\right)$	$e\left(\frac{137}{306}\right)$	$e\left(\frac{20}{153}\right)$	$e\left(\frac{37}{51}\right)$
$\chi_{921}(31,\cdot)$	921.v	306	no	$-1$	$1$	$e\left(\frac{5}{102}\right)$	$e\left(\frac{5}{51}\right)$	$e\left(\frac{293}{306}\right)$	$e\left(\frac{11}{153}\right)$	$e\left(\frac{5}{34}\right)$	$e\left(\frac{1}{153}\right)$	$e\left(\frac{127}{153}\right)$	$e\left(\frac{77}{306}\right)$	$e\left(\frac{37}{306}\right)$	$e\left(\frac{10}{51}\right)$
$\chi_{921}(32,\cdot)$	921.r	102	yes	$1$	$1$	$e\left(\frac{14}{17}\right)$	$e\left(\frac{11}{17}\right)$	$e\left(\frac{1}{51}\right)$	$e\left(\frac{14}{51}\right)$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{43}{51}\right)$	$e\left(\frac{59}{102}\right)$	$e\left(\frac{47}{102}\right)$	$e\left(\frac{5}{51}\right)$	$e\left(\frac{5}{17}\right)$
$\chi_{921}(34,\cdot)$	921.o	34	no	$-1$	$1$	$e\left(\frac{9}{34}\right)$	$e\left(\frac{9}{17}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{27}{34}\right)$	$e\left(\frac{4}{17}\right)$	$e\left(\frac{15}{17}\right)$	$e\left(\frac{19}{34}\right)$	$e\left(\frac{29}{34}\right)$	$e\left(\frac{1}{17}\right)$
$\chi_{921}(35,\cdot)$	921.n	34	yes	$1$	$1$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{15}{17}\right)$	$e\left(\frac{6}{17}\right)$	$e\left(\frac{3}{17}\right)$	$e\left(\frac{16}{17}\right)$	$e\left(\frac{1}{34}\right)$	$e\left(\frac{25}{34}\right)$	$e\left(\frac{7}{17}\right)$	$e\left(\frac{4}{17}\right)$
$\chi_{921}(37,\cdot)$	921.u	153	no	$1$	$1$	$e\left(\frac{47}{51}\right)$	$e\left(\frac{43}{51}\right)$	$e\left(\frac{92}{153}\right)$	$e\left(\frac{115}{153}\right)$	$e\left(\frac{13}{17}\right)$	$e\left(\frac{80}{153}\right)$	$e\left(\frac{62}{153}\right)$	$e\left(\frac{20}{153}\right)$	$e\left(\frac{103}{153}\right)$	$e\left(\frac{35}{51}\right)$
$\chi_{921}(38,\cdot)$	921.n	34	yes	$1$	$1$	$e\left(\frac{14}{17}\right)$	$e\left(\frac{11}{17}\right)$	$e\left(\frac{6}{17}\right)$	$e\left(\frac{16}{17}\right)$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{3}{17}\right)$	$e\left(\frac{31}{34}\right)$	$e\left(\frac{27}{34}\right)$	$e\left(\frac{13}{17}\right)$	$e\left(\frac{5}{17}\right)$
$\chi_{921}(40,\cdot)$	921.u	153	no	$1$	$1$	$e\left(\frac{5}{51}\right)$	$e\left(\frac{10}{51}\right)$	$e\left(\frac{140}{153}\right)$	$e\left(\frac{22}{153}\right)$	$e\left(\frac{5}{17}\right)$	$e\left(\frac{2}{153}\right)$	$e\left(\frac{101}{153}\right)$	$e\left(\frac{77}{153}\right)$	$e\left(\frac{37}{153}\right)$	$e\left(\frac{20}{51}\right)$
$\chi_{921}(41,\cdot)$	921.w	306	yes	$-1$	$1$	$e\left(\frac{59}{102}\right)$	$e\left(\frac{8}{51}\right)$	$e\left(\frac{71}{306}\right)$	$e\left(\frac{140}{153}\right)$	$e\left(\frac{25}{34}\right)$	$e\left(\frac{124}{153}\right)$	$e\left(\frac{131}{306}\right)$	$e\left(\frac{31}{153}\right)$	$e\left(\frac{151}{306}\right)$	$e\left(\frac{16}{51}\right)$
$\chi_{921}(43,\cdot)$	921.v	306	no	$-1$	$1$	$e\left(\frac{13}{102}\right)$	$e\left(\frac{13}{51}\right)$	$e\left(\frac{211}{306}\right)$	$e\left(\frac{151}{153}\right)$	$e\left(\frac{13}{34}\right)$	$e\left(\frac{125}{153}\right)$	$e\left(\frac{116}{153}\right)$	$e\left(\frac{139}{306}\right)$	$e\left(\frac{35}{306}\right)$	$e\left(\frac{26}{51}\right)$
$\chi_{921}(44,\cdot)$	921.w	306	yes	$-1$	$1$	$e\left(\frac{25}{102}\right)$	$e\left(\frac{25}{51}\right)$	$e\left(\frac{37}{306}\right)$	$e\left(\frac{4}{153}\right)$	$e\left(\frac{25}{34}\right)$	$e\left(\frac{56}{153}\right)$	$e\left(\frac{301}{306}\right)$	$e\left(\frac{14}{153}\right)$	$e\left(\frac{83}{306}\right)$	$e\left(\frac{50}{51}\right)$
$\chi_{921}(46,\cdot)$	921.i	9	no	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{9}\right)$	$1$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{921}(47,\cdot)$	921.x	306	yes	$1$	$1$	$e\left(\frac{37}{51}\right)$	$e\left(\frac{23}{51}\right)$	$e\left(\frac{67}{153}\right)$	$e\left(\frac{122}{153}\right)$	$e\left(\frac{3}{17}\right)$	$e\left(\frac{25}{153}\right)$	$e\left(\frac{77}{306}\right)$	$e\left(\frac{89}{306}\right)$	$e\left(\frac{80}{153}\right)$	$e\left(\frac{46}{51}\right)$

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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	$921$
Structure	\(C_{2}\times C_{306}\)
Order	$612$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(13\)	\(14\)	\(16\)
\(\chi_{921}(1,\cdot)\)	921.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{921}(2,\cdot)\)	921.r	102	yes	\(1\)	\(1\)	\(e\left(\frac{13}{17}\right)\)	\(e\left(\frac{9}{17}\right)\)	\(e\left(\frac{41}{51}\right)\)	\(e\left(\frac{13}{51}\right)\)	\(e\left(\frac{5}{17}\right)\)	\(e\left(\frac{29}{51}\right)\)	\(e\left(\frac{73}{102}\right)\)	\(e\left(\frac{91}{102}\right)\)	\(e\left(\frac{1}{51}\right)\)	\(e\left(\frac{1}{17}\right)\)
\(\chi_{921}(4,\cdot)\)	921.q	51	no	\(1\)	\(1\)	\(e\left(\frac{9}{17}\right)\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{31}{51}\right)\)	\(e\left(\frac{26}{51}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{7}{51}\right)\)	\(e\left(\frac{22}{51}\right)\)	\(e\left(\frac{40}{51}\right)\)	\(e\left(\frac{2}{51}\right)\)	\(e\left(\frac{2}{17}\right)\)
\(\chi_{921}(5,\cdot)\)	921.x	306	yes	\(1\)	\(1\)	\(e\left(\frac{41}{51}\right)\)	\(e\left(\frac{31}{51}\right)\)	\(e\left(\frac{77}{153}\right)\)	\(e\left(\frac{58}{153}\right)\)	\(e\left(\frac{7}{17}\right)\)	\(e\left(\frac{47}{153}\right)\)	\(e\left(\frac{157}{306}\right)\)	\(e\left(\frac{253}{306}\right)\)	\(e\left(\frac{28}{153}\right)\)	\(e\left(\frac{11}{51}\right)\)
\(\chi_{921}(7,\cdot)\)	921.u	153	no	\(1\)	\(1\)	\(e\left(\frac{13}{51}\right)\)	\(e\left(\frac{26}{51}\right)\)	\(e\left(\frac{58}{153}\right)\)	\(e\left(\frac{149}{153}\right)\)	\(e\left(\frac{13}{17}\right)\)	\(e\left(\frac{97}{153}\right)\)	\(e\left(\frac{79}{153}\right)\)	\(e\left(\frac{139}{153}\right)\)	\(e\left(\frac{35}{153}\right)\)	\(e\left(\frac{1}{51}\right)\)
\(\chi_{921}(8,\cdot)\)	921.n	34	yes	\(1\)	\(1\)	\(e\left(\frac{5}{17}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{7}{17}\right)\)	\(e\left(\frac{13}{17}\right)\)	\(e\left(\frac{15}{17}\right)\)	\(e\left(\frac{12}{17}\right)\)	\(e\left(\frac{5}{34}\right)\)	\(e\left(\frac{23}{34}\right)\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{3}{17}\right)\)
\(\chi_{921}(10,\cdot)\)	921.u	153	no	\(1\)	\(1\)	\(e\left(\frac{29}{51}\right)\)	\(e\left(\frac{7}{51}\right)\)	\(e\left(\frac{47}{153}\right)\)	\(e\left(\frac{97}{153}\right)\)	\(e\left(\frac{12}{17}\right)\)	\(e\left(\frac{134}{153}\right)\)	\(e\left(\frac{35}{153}\right)\)	\(e\left(\frac{110}{153}\right)\)	\(e\left(\frac{31}{153}\right)\)	\(e\left(\frac{14}{51}\right)\)
\(\chi_{921}(11,\cdot)\)	921.w	306	yes	\(-1\)	\(1\)	\(e\left(\frac{73}{102}\right)\)	\(e\left(\frac{22}{51}\right)\)	\(e\left(\frac{157}{306}\right)\)	\(e\left(\frac{79}{153}\right)\)	\(e\left(\frac{5}{34}\right)\)	\(e\left(\frac{35}{153}\right)\)	\(e\left(\frac{169}{306}\right)\)	\(e\left(\frac{47}{153}\right)\)	\(e\left(\frac{71}{306}\right)\)	\(e\left(\frac{44}{51}\right)\)
\(\chi_{921}(13,\cdot)\)	921.v	306	no	\(-1\)	\(1\)	\(e\left(\frac{91}{102}\right)\)	\(e\left(\frac{40}{51}\right)\)	\(e\left(\frac{253}{306}\right)\)	\(e\left(\frac{139}{153}\right)\)	\(e\left(\frac{23}{34}\right)\)	\(e\left(\frac{110}{153}\right)\)	\(e\left(\frac{47}{153}\right)\)	\(e\left(\frac{55}{306}\right)\)	\(e\left(\frac{245}{306}\right)\)	\(e\left(\frac{29}{51}\right)\)
\(\chi_{921}(14,\cdot)\)	921.x	306	yes	\(1\)	\(1\)	\(e\left(\frac{1}{51}\right)\)	\(e\left(\frac{2}{51}\right)\)	\(e\left(\frac{28}{153}\right)\)	\(e\left(\frac{35}{153}\right)\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{31}{153}\right)\)	\(e\left(\frac{71}{306}\right)\)	\(e\left(\frac{245}{306}\right)\)	\(e\left(\frac{38}{153}\right)\)	\(e\left(\frac{4}{51}\right)\)
\(\chi_{921}(16,\cdot)\)	921.q	51	no	\(1\)	\(1\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{2}{17}\right)\)	\(e\left(\frac{11}{51}\right)\)	\(e\left(\frac{1}{51}\right)\)	\(e\left(\frac{3}{17}\right)\)	\(e\left(\frac{14}{51}\right)\)	\(e\left(\frac{44}{51}\right)\)	\(e\left(\frac{29}{51}\right)\)	\(e\left(\frac{4}{51}\right)\)	\(e\left(\frac{4}{17}\right)\)
\(\chi_{921}(17,\cdot)\)	921.g	6	yes	\(-1\)	\(1\)	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)
\(\chi_{921}(19,\cdot)\)	921.q	51	no	\(1\)	\(1\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{2}{17}\right)\)	\(e\left(\frac{28}{51}\right)\)	\(e\left(\frac{35}{51}\right)\)	\(e\left(\frac{3}{17}\right)\)	\(e\left(\frac{31}{51}\right)\)	\(e\left(\frac{10}{51}\right)\)	\(e\left(\frac{46}{51}\right)\)	\(e\left(\frac{38}{51}\right)\)	\(e\left(\frac{4}{17}\right)\)
\(\chi_{921}(20,\cdot)\)	921.k	18	yes	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(1\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{921}(22,\cdot)\)	921.v	306	no	\(-1\)	\(1\)	\(e\left(\frac{49}{102}\right)\)	\(e\left(\frac{49}{51}\right)\)	\(e\left(\frac{97}{306}\right)\)	\(e\left(\frac{118}{153}\right)\)	\(e\left(\frac{15}{34}\right)\)	\(e\left(\frac{122}{153}\right)\)	\(e\left(\frac{41}{153}\right)\)	\(e\left(\frac{61}{306}\right)\)	\(e\left(\frac{77}{306}\right)\)	\(e\left(\frac{47}{51}\right)\)
\(\chi_{921}(23,\cdot)\)	921.x	306	yes	\(1\)	\(1\)	\(e\left(\frac{46}{51}\right)\)	\(e\left(\frac{41}{51}\right)\)	\(e\left(\frac{13}{153}\right)\)	\(e\left(\frac{131}{153}\right)\)	\(e\left(\frac{12}{17}\right)\)	\(e\left(\frac{151}{153}\right)\)	\(e\left(\frac{257}{306}\right)\)	\(e\left(\frac{305}{306}\right)\)	\(e\left(\frac{116}{153}\right)\)	\(e\left(\frac{31}{51}\right)\)
\(\chi_{921}(25,\cdot)\)	921.u	153	no	\(1\)	\(1\)	\(e\left(\frac{31}{51}\right)\)	\(e\left(\frac{11}{51}\right)\)	\(e\left(\frac{1}{153}\right)\)	\(e\left(\frac{116}{153}\right)\)	\(e\left(\frac{14}{17}\right)\)	\(e\left(\frac{94}{153}\right)\)	\(e\left(\frac{4}{153}\right)\)	\(e\left(\frac{100}{153}\right)\)	\(e\left(\frac{56}{153}\right)\)	\(e\left(\frac{22}{51}\right)\)
\(\chi_{921}(26,\cdot)\)	921.w	306	yes	\(-1\)	\(1\)	\(e\left(\frac{67}{102}\right)\)	\(e\left(\frac{16}{51}\right)\)	\(e\left(\frac{193}{306}\right)\)	\(e\left(\frac{25}{153}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{44}{153}\right)\)	\(e\left(\frac{7}{306}\right)\)	\(e\left(\frac{11}{153}\right)\)	\(e\left(\frac{251}{306}\right)\)	\(e\left(\frac{32}{51}\right)\)
\(\chi_{921}(28,\cdot)\)	921.u	153	no	\(1\)	\(1\)	\(e\left(\frac{40}{51}\right)\)	\(e\left(\frac{29}{51}\right)\)	\(e\left(\frac{151}{153}\right)\)	\(e\left(\frac{74}{153}\right)\)	\(e\left(\frac{6}{17}\right)\)	\(e\left(\frac{118}{153}\right)\)	\(e\left(\frac{145}{153}\right)\)	\(e\left(\frac{106}{153}\right)\)	\(e\left(\frac{41}{153}\right)\)	\(e\left(\frac{7}{51}\right)\)
\(\chi_{921}(29,\cdot)\)	921.x	306	yes	\(1\)	\(1\)	\(e\left(\frac{22}{51}\right)\)	\(e\left(\frac{44}{51}\right)\)	\(e\left(\frac{55}{153}\right)\)	\(e\left(\frac{107}{153}\right)\)	\(e\left(\frac{5}{17}\right)\)	\(e\left(\frac{121}{153}\right)\)	\(e\left(\frac{287}{306}\right)\)	\(e\left(\frac{137}{306}\right)\)	\(e\left(\frac{20}{153}\right)\)	\(e\left(\frac{37}{51}\right)\)
\(\chi_{921}(31,\cdot)\)	921.v	306	no	\(-1\)	\(1\)	\(e\left(\frac{5}{102}\right)\)	\(e\left(\frac{5}{51}\right)\)	\(e\left(\frac{293}{306}\right)\)	\(e\left(\frac{11}{153}\right)\)	\(e\left(\frac{5}{34}\right)\)	\(e\left(\frac{1}{153}\right)\)	\(e\left(\frac{127}{153}\right)\)	\(e\left(\frac{77}{306}\right)\)	\(e\left(\frac{37}{306}\right)\)	\(e\left(\frac{10}{51}\right)\)
\(\chi_{921}(32,\cdot)\)	921.r	102	yes	\(1\)	\(1\)	\(e\left(\frac{14}{17}\right)\)	\(e\left(\frac{11}{17}\right)\)	\(e\left(\frac{1}{51}\right)\)	\(e\left(\frac{14}{51}\right)\)	\(e\left(\frac{8}{17}\right)\)	\(e\left(\frac{43}{51}\right)\)	\(e\left(\frac{59}{102}\right)\)	\(e\left(\frac{47}{102}\right)\)	\(e\left(\frac{5}{51}\right)\)	\(e\left(\frac{5}{17}\right)\)
\(\chi_{921}(34,\cdot)\)	921.o	34	no	\(-1\)	\(1\)	\(e\left(\frac{9}{34}\right)\)	\(e\left(\frac{9}{17}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{27}{34}\right)\)	\(e\left(\frac{4}{17}\right)\)	\(e\left(\frac{15}{17}\right)\)	\(e\left(\frac{19}{34}\right)\)	\(e\left(\frac{29}{34}\right)\)	\(e\left(\frac{1}{17}\right)\)
\(\chi_{921}(35,\cdot)\)	921.n	34	yes	\(1\)	\(1\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{2}{17}\right)\)	\(e\left(\frac{15}{17}\right)\)	\(e\left(\frac{6}{17}\right)\)	\(e\left(\frac{3}{17}\right)\)	\(e\left(\frac{16}{17}\right)\)	\(e\left(\frac{1}{34}\right)\)	\(e\left(\frac{25}{34}\right)\)	\(e\left(\frac{7}{17}\right)\)	\(e\left(\frac{4}{17}\right)\)
\(\chi_{921}(37,\cdot)\)	921.u	153	no	\(1\)	\(1\)	\(e\left(\frac{47}{51}\right)\)	\(e\left(\frac{43}{51}\right)\)	\(e\left(\frac{92}{153}\right)\)	\(e\left(\frac{115}{153}\right)\)	\(e\left(\frac{13}{17}\right)\)	\(e\left(\frac{80}{153}\right)\)	\(e\left(\frac{62}{153}\right)\)	\(e\left(\frac{20}{153}\right)\)	\(e\left(\frac{103}{153}\right)\)	\(e\left(\frac{35}{51}\right)\)
\(\chi_{921}(38,\cdot)\)	921.n	34	yes	\(1\)	\(1\)	\(e\left(\frac{14}{17}\right)\)	\(e\left(\frac{11}{17}\right)\)	\(e\left(\frac{6}{17}\right)\)	\(e\left(\frac{16}{17}\right)\)	\(e\left(\frac{8}{17}\right)\)	\(e\left(\frac{3}{17}\right)\)	\(e\left(\frac{31}{34}\right)\)	\(e\left(\frac{27}{34}\right)\)	\(e\left(\frac{13}{17}\right)\)	\(e\left(\frac{5}{17}\right)\)
\(\chi_{921}(40,\cdot)\)	921.u	153	no	\(1\)	\(1\)	\(e\left(\frac{5}{51}\right)\)	\(e\left(\frac{10}{51}\right)\)	\(e\left(\frac{140}{153}\right)\)	\(e\left(\frac{22}{153}\right)\)	\(e\left(\frac{5}{17}\right)\)	\(e\left(\frac{2}{153}\right)\)	\(e\left(\frac{101}{153}\right)\)	\(e\left(\frac{77}{153}\right)\)	\(e\left(\frac{37}{153}\right)\)	\(e\left(\frac{20}{51}\right)\)
\(\chi_{921}(41,\cdot)\)	921.w	306	yes	\(-1\)	\(1\)	\(e\left(\frac{59}{102}\right)\)	\(e\left(\frac{8}{51}\right)\)	\(e\left(\frac{71}{306}\right)\)	\(e\left(\frac{140}{153}\right)\)	\(e\left(\frac{25}{34}\right)\)	\(e\left(\frac{124}{153}\right)\)	\(e\left(\frac{131}{306}\right)\)	\(e\left(\frac{31}{153}\right)\)	\(e\left(\frac{151}{306}\right)\)	\(e\left(\frac{16}{51}\right)\)
\(\chi_{921}(43,\cdot)\)	921.v	306	no	\(-1\)	\(1\)	\(e\left(\frac{13}{102}\right)\)	\(e\left(\frac{13}{51}\right)\)	\(e\left(\frac{211}{306}\right)\)	\(e\left(\frac{151}{153}\right)\)	\(e\left(\frac{13}{34}\right)\)	\(e\left(\frac{125}{153}\right)\)	\(e\left(\frac{116}{153}\right)\)	\(e\left(\frac{139}{306}\right)\)	\(e\left(\frac{35}{306}\right)\)	\(e\left(\frac{26}{51}\right)\)
\(\chi_{921}(44,\cdot)\)	921.w	306	yes	\(-1\)	\(1\)	\(e\left(\frac{25}{102}\right)\)	\(e\left(\frac{25}{51}\right)\)	\(e\left(\frac{37}{306}\right)\)	\(e\left(\frac{4}{153}\right)\)	\(e\left(\frac{25}{34}\right)\)	\(e\left(\frac{56}{153}\right)\)	\(e\left(\frac{301}{306}\right)\)	\(e\left(\frac{14}{153}\right)\)	\(e\left(\frac{83}{306}\right)\)	\(e\left(\frac{50}{51}\right)\)
\(\chi_{921}(46,\cdot)\)	921.i	9	no	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(1\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{921}(47,\cdot)\)	921.x	306	yes	\(1\)	\(1\)	\(e\left(\frac{37}{51}\right)\)	\(e\left(\frac{23}{51}\right)\)	\(e\left(\frac{67}{153}\right)\)	\(e\left(\frac{122}{153}\right)\)	\(e\left(\frac{3}{17}\right)\)	\(e\left(\frac{25}{153}\right)\)	\(e\left(\frac{77}{306}\right)\)	\(e\left(\frac{89}{306}\right)\)	\(e\left(\frac{80}{153}\right)\)	\(e\left(\frac{46}{51}\right)\)

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L-functions

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First 32 of 612 characters

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.