LMFDB - Group of Dirichlet characters of modulus 4592

Show commands: PariGP / SageMath

sage: H = DirichletGroup(4592)

pari: g = idealstar(,4592,2)

Character group

sage: G.order() pari: g.no
Order	=	1920
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{4}\times C_{120}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{4592}(575,\cdot)$, $\chi_{4592}(3445,\cdot)$, $\chi_{4592}(3937,\cdot)$, $\chi_{4592}(785,\cdot)$

First 32 of 1920 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	$-1$	$1$	$3$	$5$	$9$	$11$	$13$	$15$	$17$	$19$	$23$	$25$
$\chi_{4592}(1,\cdot)$	4592.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{4592}(3,\cdot)$	4592.fw	24	yes	$-1$	$1$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{4592}(5,\cdot)$	4592.hx	60	yes	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{1}{30}\right)$
$\chi_{4592}(9,\cdot)$	4592.do	12	no	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{12}\right)$	$-i$	$-i$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{4592}(11,\cdot)$	4592.ib	120	yes	$1$	$1$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{77}{120}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{17}{120}\right)$	$e\left(\frac{31}{120}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{7}{15}\right)$
$\chi_{4592}(13,\cdot)$	4592.gy	40	yes	$1$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{10}\right)$	$-i$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{4592}(15,\cdot)$	4592.gq	40	no	$1$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{7}{20}\right)$	$-i$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{4592}(17,\cdot)$	4592.ih	120	no	$1$	$1$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{17}{120}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{47}{120}\right)$	$e\left(\frac{31}{120}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{29}{30}\right)$
$\chi_{4592}(19,\cdot)$	4592.im	120	yes	$-1$	$1$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{31}{120}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{31}{120}\right)$	$e\left(\frac{113}{120}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{11}{15}\right)$
$\chi_{4592}(23,\cdot)$	4592.ge	30	no	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{14}{15}\right)$
$\chi_{4592}(25,\cdot)$	4592.fz	30	no	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{15}\right)$
$\chi_{4592}(27,\cdot)$	4592.cf	8	yes	$-1$	$1$	$e\left(\frac{5}{8}\right)$	$-1$	$i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{8}\right)$	$-1$	$1$
$\chi_{4592}(29,\cdot)$	4592.gn	40	no	$-1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{5}\right)$	$-i$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{4592}(31,\cdot)$	4592.gg	30	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{7}{15}\right)$
$\chi_{4592}(33,\cdot)$	4592.hu	60	no	$-1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{2}{15}\right)$
$\chi_{4592}(37,\cdot)$	4592.hm	60	yes	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{1}{30}\right)$
$\chi_{4592}(39,\cdot)$	4592.hs	60	no	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{4}{15}\right)$
$\chi_{4592}(43,\cdot)$	4592.fg	20	no	$-1$	$1$	$1$	$e\left(\frac{11}{20}\right)$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{4592}(45,\cdot)$	4592.hq	60	yes	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{11}{30}\right)$
$\chi_{4592}(47,\cdot)$	4592.ij	120	no	$-1$	$1$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{109}{120}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{79}{120}\right)$	$e\left(\frac{107}{120}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{13}{30}\right)$
$\chi_{4592}(51,\cdot)$	4592.hr	60	yes	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{19}{30}\right)$
$\chi_{4592}(53,\cdot)$	4592.ic	120	yes	$-1$	$1$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{113}{120}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{113}{120}\right)$	$e\left(\frac{19}{120}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{13}{15}\right)$
$\chi_{4592}(55,\cdot)$	4592.cn	8	no	$-1$	$1$	$e\left(\frac{7}{8}\right)$	$-i$	$-i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{8}\right)$	$1$	$-1$
$\chi_{4592}(57,\cdot)$	4592.dc	10	no	$1$	$1$	$-1$	$e\left(\frac{7}{10}\right)$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{4592}(59,\cdot)$	4592.hp	60	yes	$1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{23}{30}\right)$
$\chi_{4592}(61,\cdot)$	4592.hx	60	yes	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{7}{30}\right)$
$\chi_{4592}(65,\cdot)$	4592.if	120	no	$-1$	$1$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{37}{120}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{7}{120}\right)$	$e\left(\frac{71}{120}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{19}{30}\right)$
$\chi_{4592}(67,\cdot)$	4592.ib	120	yes	$1$	$1$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{23}{120}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{83}{120}\right)$	$e\left(\frac{109}{120}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{13}{15}\right)$
$\chi_{4592}(69,\cdot)$	4592.gm	40	yes	$1$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{4}{5}\right)$	$-i$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{4592}(71,\cdot)$	4592.gr	40	no	$1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{20}\right)$	$i$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{4592}(73,\cdot)$	4592.eb	12	no	$-1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{12}\right)$	$-i$	$i$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{4592}(75,\cdot)$	4592.im	120	yes	$-1$	$1$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{61}{120}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{61}{120}\right)$	$e\left(\frac{83}{120}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{11}{15}\right)$

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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	$4592$
Structure	\(C_{2}\times C_{2}\times C_{4}\times C_{120}\)
Order	$1920$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(23\)	\(25\)
\(\chi_{4592}(1,\cdot)\)	4592.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{4592}(3,\cdot)\)	4592.fw	24	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{4592}(5,\cdot)\)	4592.hx	60	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{1}{30}\right)\)
\(\chi_{4592}(9,\cdot)\)	4592.do	12	no	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-i\)	\(-i\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{4592}(11,\cdot)\)	4592.ib	120	yes	\(1\)	\(1\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{77}{120}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{17}{120}\right)\)	\(e\left(\frac{31}{120}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)
\(\chi_{4592}(13,\cdot)\)	4592.gy	40	yes	\(1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(-i\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{4592}(15,\cdot)\)	4592.gq	40	no	\(1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(-i\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{4592}(17,\cdot)\)	4592.ih	120	no	\(1\)	\(1\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{17}{120}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{47}{120}\right)\)	\(e\left(\frac{31}{120}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{29}{30}\right)\)
\(\chi_{4592}(19,\cdot)\)	4592.im	120	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{31}{120}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{31}{120}\right)\)	\(e\left(\frac{113}{120}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{11}{15}\right)\)
\(\chi_{4592}(23,\cdot)\)	4592.ge	30	no	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)
\(\chi_{4592}(25,\cdot)\)	4592.fz	30	no	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)
\(\chi_{4592}(27,\cdot)\)	4592.cf	8	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(-1\)	\(i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(-1\)	\(1\)
\(\chi_{4592}(29,\cdot)\)	4592.gn	40	no	\(-1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(-i\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{4592}(31,\cdot)\)	4592.gg	30	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)
\(\chi_{4592}(33,\cdot)\)	4592.hu	60	no	\(-1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)
\(\chi_{4592}(37,\cdot)\)	4592.hm	60	yes	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{1}{30}\right)\)
\(\chi_{4592}(39,\cdot)\)	4592.hs	60	no	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{4}{15}\right)\)
\(\chi_{4592}(43,\cdot)\)	4592.fg	20	no	\(-1\)	\(1\)	\(1\)	\(e\left(\frac{11}{20}\right)\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{4592}(45,\cdot)\)	4592.hq	60	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{11}{30}\right)\)
\(\chi_{4592}(47,\cdot)\)	4592.ij	120	no	\(-1\)	\(1\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{109}{120}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{79}{120}\right)\)	\(e\left(\frac{107}{120}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{13}{30}\right)\)
\(\chi_{4592}(51,\cdot)\)	4592.hr	60	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{19}{30}\right)\)
\(\chi_{4592}(53,\cdot)\)	4592.ic	120	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{113}{120}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{113}{120}\right)\)	\(e\left(\frac{19}{120}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)
\(\chi_{4592}(55,\cdot)\)	4592.cn	8	no	\(-1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(-i\)	\(-i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(1\)	\(-1\)
\(\chi_{4592}(57,\cdot)\)	4592.dc	10	no	\(1\)	\(1\)	\(-1\)	\(e\left(\frac{7}{10}\right)\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{4592}(59,\cdot)\)	4592.hp	60	yes	\(1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{23}{30}\right)\)
\(\chi_{4592}(61,\cdot)\)	4592.hx	60	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{7}{30}\right)\)
\(\chi_{4592}(65,\cdot)\)	4592.if	120	no	\(-1\)	\(1\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{37}{120}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{7}{120}\right)\)	\(e\left(\frac{71}{120}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{19}{30}\right)\)
\(\chi_{4592}(67,\cdot)\)	4592.ib	120	yes	\(1\)	\(1\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{23}{120}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{83}{120}\right)\)	\(e\left(\frac{109}{120}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{13}{15}\right)\)
\(\chi_{4592}(69,\cdot)\)	4592.gm	40	yes	\(1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(-i\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{4592}(71,\cdot)\)	4592.gr	40	no	\(1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(i\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{4592}(73,\cdot)\)	4592.eb	12	no	\(-1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(-i\)	\(i\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{4592}(75,\cdot)\)	4592.im	120	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{61}{120}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{61}{120}\right)\)	\(e\left(\frac{83}{120}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{11}{15}\right)\)

Introduction

L-functions

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Character group

First 32 of 1920 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.