LMFDB - Group of Dirichlet characters of modulus 1267

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1267)

pari: g = idealstar(,1267,2)

Character group

sage: G.order() pari: g.no
Order	=	1080
sage: H.invariants() pari: g.cyc
Structure	=	$C_{6}\times C_{180}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{1267}(906,\cdot)$, $\chi_{1267}(183,\cdot)$

First 32 of 1080 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$8$	$9$	$10$	$11$	$12$
$\chi_{1267}(1,\cdot)$	1267.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1267}(2,\cdot)$	1267.dp	180	yes	$-1$	$1$	$e\left(\frac{121}{180}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{37}{180}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{89}{90}\right)$
$\chi_{1267}(3,\cdot)$	1267.df	90	yes	$-1$	$1$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{79}{90}\right)$
$\chi_{1267}(4,\cdot)$	1267.dj	90	yes	$1$	$1$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{44}{45}\right)$
$\chi_{1267}(5,\cdot)$	1267.ci	30	yes	$-1$	$1$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{13}{30}\right)$
$\chi_{1267}(6,\cdot)$	1267.cy	60	yes	$1$	$1$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{13}{15}\right)$
$\chi_{1267}(8,\cdot)$	1267.cz	60	no	$-1$	$1$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{29}{30}\right)$
$\chi_{1267}(9,\cdot)$	1267.ct	45	yes	$1$	$1$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{34}{45}\right)$
$\chi_{1267}(10,\cdot)$	1267.dr	180	yes	$1$	$1$	$e\left(\frac{37}{180}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{19}{180}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{19}{45}\right)$
$\chi_{1267}(11,\cdot)$	1267.dj	90	yes	$1$	$1$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{14}{45}\right)$
$\chi_{1267}(12,\cdot)$	1267.dg	90	yes	$-1$	$1$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{77}{90}\right)$
$\chi_{1267}(13,\cdot)$	1267.de	90	yes	$-1$	$1$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{31}{90}\right)$
$\chi_{1267}(15,\cdot)$	1267.cu	45	no	$1$	$1$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{14}{45}\right)$
$\chi_{1267}(16,\cdot)$	1267.ct	45	yes	$1$	$1$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{43}{45}\right)$
$\chi_{1267}(17,\cdot)$	1267.cm	36	yes	$1$	$1$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{11}{18}\right)$	$-1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{2}{9}\right)$
$\chi_{1267}(18,\cdot)$	1267.dp	180	yes	$-1$	$1$	$e\left(\frac{173}{180}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{41}{180}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{67}{90}\right)$
$\chi_{1267}(19,\cdot)$	1267.bi	12	yes	$1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$i$	$i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{1267}(20,\cdot)$	1267.dh	90	yes	$-1$	$1$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{37}{90}\right)$
$\chi_{1267}(22,\cdot)$	1267.by	20	no	$-1$	$1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{1267}(23,\cdot)$	1267.dm	180	yes	$-1$	$1$	$e\left(\frac{173}{180}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{101}{180}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{67}{90}\right)$
$\chi_{1267}(24,\cdot)$	1267.dn	180	yes	$1$	$1$	$e\left(\frac{119}{180}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{113}{180}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{38}{45}\right)$
$\chi_{1267}(25,\cdot)$	1267.bn	15	yes	$1$	$1$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{13}{15}\right)$
$\chi_{1267}(26,\cdot)$	1267.bj	12	yes	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$-i$	$-i$	$e\left(\frac{1}{3}\right)$	$-i$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{1267}(27,\cdot)$	1267.cj	30	yes	$-1$	$1$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{19}{30}\right)$
$\chi_{1267}(29,\cdot)$	1267.bm	15	no	$1$	$1$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{7}{15}\right)$
$\chi_{1267}(30,\cdot)$	1267.cv	60	yes	$-1$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{1267}(31,\cdot)$	1267.cx	60	yes	$1$	$1$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{11}{15}\right)$
$\chi_{1267}(32,\cdot)$	1267.co	36	yes	$-1$	$1$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{17}{18}\right)$
$\chi_{1267}(33,\cdot)$	1267.dg	90	yes	$-1$	$1$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{17}{90}\right)$
$\chi_{1267}(34,\cdot)$	1267.de	90	yes	$-1$	$1$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{19}{90}\right)$
$\chi_{1267}(36,\cdot)$	1267.ce	30	no	$1$	$1$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{11}{15}\right)$
$\chi_{1267}(37,\cdot)$	1267.dd	90	yes	$1$	$1$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{2}{45}\right)$

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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	$1267$
Structure	\(C_{6}\times C_{180}\)
Order	$1080$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(8\)	\(9\)	\(10\)	\(11\)	\(12\)
\(\chi_{1267}(1,\cdot)\)	1267.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1267}(2,\cdot)\)	1267.dp	180	yes	\(-1\)	\(1\)	\(e\left(\frac{121}{180}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{37}{180}\right)\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{89}{90}\right)\)
\(\chi_{1267}(3,\cdot)\)	1267.df	90	yes	\(-1\)	\(1\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{1}{90}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{79}{90}\right)\)
\(\chi_{1267}(4,\cdot)\)	1267.dj	90	yes	\(1\)	\(1\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{44}{45}\right)\)
\(\chi_{1267}(5,\cdot)\)	1267.ci	30	yes	\(-1\)	\(1\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{13}{30}\right)\)
\(\chi_{1267}(6,\cdot)\)	1267.cy	60	yes	\(1\)	\(1\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{13}{15}\right)\)
\(\chi_{1267}(8,\cdot)\)	1267.cz	60	no	\(-1\)	\(1\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{29}{30}\right)\)
\(\chi_{1267}(9,\cdot)\)	1267.ct	45	yes	\(1\)	\(1\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{34}{45}\right)\)
\(\chi_{1267}(10,\cdot)\)	1267.dr	180	yes	\(1\)	\(1\)	\(e\left(\frac{37}{180}\right)\)	\(e\left(\frac{1}{90}\right)\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{19}{180}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{19}{45}\right)\)
\(\chi_{1267}(11,\cdot)\)	1267.dj	90	yes	\(1\)	\(1\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{14}{45}\right)\)
\(\chi_{1267}(12,\cdot)\)	1267.dg	90	yes	\(-1\)	\(1\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{79}{90}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{77}{90}\right)\)
\(\chi_{1267}(13,\cdot)\)	1267.de	90	yes	\(-1\)	\(1\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{31}{90}\right)\)
\(\chi_{1267}(15,\cdot)\)	1267.cu	45	no	\(1\)	\(1\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{14}{45}\right)\)
\(\chi_{1267}(16,\cdot)\)	1267.ct	45	yes	\(1\)	\(1\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{43}{45}\right)\)
\(\chi_{1267}(17,\cdot)\)	1267.cm	36	yes	\(1\)	\(1\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(-1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)
\(\chi_{1267}(18,\cdot)\)	1267.dp	180	yes	\(-1\)	\(1\)	\(e\left(\frac{173}{180}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{41}{180}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{67}{90}\right)\)
\(\chi_{1267}(19,\cdot)\)	1267.bi	12	yes	\(1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(i\)	\(i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{1267}(20,\cdot)\)	1267.dh	90	yes	\(-1\)	\(1\)	\(e\left(\frac{79}{90}\right)\)	\(e\left(\frac{59}{90}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{37}{90}\right)\)
\(\chi_{1267}(22,\cdot)\)	1267.by	20	no	\(-1\)	\(1\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{1267}(23,\cdot)\)	1267.dm	180	yes	\(-1\)	\(1\)	\(e\left(\frac{173}{180}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{101}{180}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{67}{90}\right)\)
\(\chi_{1267}(24,\cdot)\)	1267.dn	180	yes	\(1\)	\(1\)	\(e\left(\frac{119}{180}\right)\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{113}{180}\right)\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{38}{45}\right)\)
\(\chi_{1267}(25,\cdot)\)	1267.bn	15	yes	\(1\)	\(1\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)
\(\chi_{1267}(26,\cdot)\)	1267.bj	12	yes	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-i\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)	\(-i\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{1267}(27,\cdot)\)	1267.cj	30	yes	\(-1\)	\(1\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{19}{30}\right)\)
\(\chi_{1267}(29,\cdot)\)	1267.bm	15	no	\(1\)	\(1\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)
\(\chi_{1267}(30,\cdot)\)	1267.cv	60	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{1267}(31,\cdot)\)	1267.cx	60	yes	\(1\)	\(1\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{11}{15}\right)\)
\(\chi_{1267}(32,\cdot)\)	1267.co	36	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{17}{18}\right)\)
\(\chi_{1267}(33,\cdot)\)	1267.dg	90	yes	\(-1\)	\(1\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{17}{90}\right)\)
\(\chi_{1267}(34,\cdot)\)	1267.de	90	yes	\(-1\)	\(1\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{1}{90}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{19}{90}\right)\)
\(\chi_{1267}(36,\cdot)\)	1267.ce	30	no	\(1\)	\(1\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)
\(\chi_{1267}(37,\cdot)\)	1267.dd	90	yes	\(1\)	\(1\)	\(e\left(\frac{73}{90}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{1}{90}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{2}{45}\right)\)

Introduction

L-functions

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First 32 of 1080 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.