LMFDB - Group of Dirichlet characters of modulus 1155

sage:H = DirichletGroup(1155)

pari:g = idealstar(,1155,2)

Character group

sage:G.order() pari:g.no
Order	=	480
sage:H.invariants() pari:g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{60}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{1155}(386,\cdot)$, $\chi_{1155}(232,\cdot)$, $\chi_{1155}(661,\cdot)$, $\chi_{1155}(211,\cdot)$

First 32 of 480 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	$-1$	$1$	$2$	$4$	$8$	$13$	$16$	$17$	$19$	$23$	$26$	$29$
$\chi_{1155}(1,\cdot)$	1155.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1155}(2,\cdot)$	1155.dp	60	yes	$-1$	$1$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{1155}(4,\cdot)$	1155.da	30	no	$1$	$1$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{1155}(8,\cdot)$	1155.cp	20	no	$-1$	$1$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{2}{5}\right)$	$-i$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{1155}(13,\cdot)$	1155.cu	20	no	$-1$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{3}{10}\right)$	$i$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{1155}(16,\cdot)$	1155.cm	15	no	$1$	$1$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{1155}(17,\cdot)$	1155.dm	60	yes	$1$	$1$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{1155}(19,\cdot)$	1155.dh	30	no	$1$	$1$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{1155}(23,\cdot)$	1155.ck	12	no	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$-i$	$i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$	$1$
$\chi_{1155}(26,\cdot)$	1155.db	30	no	$1$	$1$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{1155}(29,\cdot)$	1155.bz	10	no	$1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{10}\right)$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{1155}(31,\cdot)$	1155.dg	30	no	$-1$	$1$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{1155}(32,\cdot)$	1155.cg	12	yes	$-1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$-i$	$i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{6}\right)$	$-1$
$\chi_{1155}(34,\cdot)$	1155.h	2	no	$-1$	$1$	$-1$	$1$	$-1$	$1$	$1$	$1$	$-1$	$-1$	$-1$	$1$
$\chi_{1155}(37,\cdot)$	1155.dn	60	no	$-1$	$1$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{1155}(38,\cdot)$	1155.dq	60	yes	$-1$	$1$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{1155}(41,\cdot)$	1155.bq	10	no	$-1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{5}\right)$	$-1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{1155}(43,\cdot)$	1155.y	4	no	$1$	$1$	$i$	$-1$	$-i$	$-i$	$1$	$i$	$1$	$i$	$1$	$1$
$\chi_{1155}(46,\cdot)$	1155.cz	30	no	$-1$	$1$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{1155}(47,\cdot)$	1155.dq	60	yes	$-1$	$1$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{1155}(52,\cdot)$	1155.dk	60	no	$-1$	$1$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{1155}(53,\cdot)$	1155.dl	60	yes	$1$	$1$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{1155}(58,\cdot)$	1155.dn	60	no	$-1$	$1$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{1155}(59,\cdot)$	1155.dd	30	yes	$1$	$1$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{1155}(61,\cdot)$	1155.cy	30	no	$1$	$1$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{1155}(62,\cdot)$	1155.cs	20	yes	$1$	$1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{10}\right)$	$i$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{1155}(64,\cdot)$	1155.cc	10	no	$1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{5}\right)$	$-1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{1155}(67,\cdot)$	1155.ci	12	no	$-1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$-i$	$-i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{3}\right)$	$-1$
$\chi_{1155}(68,\cdot)$	1155.dm	60	yes	$1$	$1$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{1155}(71,\cdot)$	1155.by	10	no	$-1$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{5}\right)$	$-1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{1155}(73,\cdot)$	1155.dk	60	no	$-1$	$1$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{1155}(74,\cdot)$	1155.cv	30	yes	$1$	$1$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{3}{5}\right)$

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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 $\F_{q}$
Belyi maps

Modulus	$1155$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{60}\)
Order	$480$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(8\)	\(13\)	\(16\)	\(17\)	\(19\)	\(23\)	\(26\)	\(29\)
\(\chi_{1155}(1,\cdot)\)	1155.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1155}(2,\cdot)\)	1155.dp	60	yes	\(-1\)	\(1\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{1155}(4,\cdot)\)	1155.da	30	no	\(1\)	\(1\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{1155}(8,\cdot)\)	1155.cp	20	no	\(-1\)	\(1\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(-i\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{1155}(13,\cdot)\)	1155.cu	20	no	\(-1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(i\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{1155}(16,\cdot)\)	1155.cm	15	no	\(1\)	\(1\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{1155}(17,\cdot)\)	1155.dm	60	yes	\(1\)	\(1\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{1155}(19,\cdot)\)	1155.dh	30	no	\(1\)	\(1\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{1155}(23,\cdot)\)	1155.ck	12	no	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-i\)	\(i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)
\(\chi_{1155}(26,\cdot)\)	1155.db	30	no	\(1\)	\(1\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{1155}(29,\cdot)\)	1155.bz	10	no	\(1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{1155}(31,\cdot)\)	1155.dg	30	no	\(-1\)	\(1\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{1155}(32,\cdot)\)	1155.cg	12	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-i\)	\(i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)
\(\chi_{1155}(34,\cdot)\)	1155.h	2	no	\(-1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(1\)	\(1\)	\(1\)	\(-1\)	\(-1\)	\(-1\)	\(1\)
\(\chi_{1155}(37,\cdot)\)	1155.dn	60	no	\(-1\)	\(1\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{1155}(38,\cdot)\)	1155.dq	60	yes	\(-1\)	\(1\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{1155}(41,\cdot)\)	1155.bq	10	no	\(-1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(-1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{1155}(43,\cdot)\)	1155.y	4	no	\(1\)	\(1\)	\(i\)	\(-1\)	\(-i\)	\(-i\)	\(1\)	\(i\)	\(1\)	\(i\)	\(1\)	\(1\)
\(\chi_{1155}(46,\cdot)\)	1155.cz	30	no	\(-1\)	\(1\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{1155}(47,\cdot)\)	1155.dq	60	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{1155}(52,\cdot)\)	1155.dk	60	no	\(-1\)	\(1\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{1155}(53,\cdot)\)	1155.dl	60	yes	\(1\)	\(1\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{1155}(58,\cdot)\)	1155.dn	60	no	\(-1\)	\(1\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{1155}(59,\cdot)\)	1155.dd	30	yes	\(1\)	\(1\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{1155}(61,\cdot)\)	1155.cy	30	no	\(1\)	\(1\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{1155}(62,\cdot)\)	1155.cs	20	yes	\(1\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(i\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{1155}(64,\cdot)\)	1155.cc	10	no	\(1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(-1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{1155}(67,\cdot)\)	1155.ci	12	no	\(-1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-i\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)
\(\chi_{1155}(68,\cdot)\)	1155.dm	60	yes	\(1\)	\(1\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{1155}(71,\cdot)\)	1155.by	10	no	\(-1\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(-1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{1155}(73,\cdot)\)	1155.dk	60	no	\(-1\)	\(1\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{1155}(74,\cdot)\)	1155.cv	30	yes	\(1\)	\(1\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{3}{5}\right)\)

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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.