LMFDB - Group of Dirichlet characters of modulus 241

Show commands: PariGP / SageMath

sage: H = DirichletGroup(241)

pari: g = idealstar(,241,2)

Character group

sage: G.order() pari: g.no
Order	=	240
sage: H.invariants() pari: g.cyc
Structure	=	$C_{240}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{241}(7,\cdot)$

First 32 of 240 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{241}(1,\cdot)$	241.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{241}(2,\cdot)$	241.m	24	yes	$1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{6}\right)$	$i$	$-1$	$e\left(\frac{19}{24}\right)$	$i$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{19}{24}\right)$
$\chi_{241}(3,\cdot)$	241.s	120	yes	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{91}{120}\right)$	$i$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{23}{24}\right)$
$\chi_{241}(4,\cdot)$	241.i	12	yes	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$1$	$e\left(\frac{7}{12}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{241}(5,\cdot)$	241.o	40	yes	$1$	$1$	$i$	$e\left(\frac{13}{20}\right)$	$-1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{23}{40}\right)$	$-i$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{241}(6,\cdot)$	241.l	20	yes	$1$	$1$	$-1$	$e\left(\frac{1}{10}\right)$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{11}{20}\right)$	$-1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{5}\right)$	$-i$
$\chi_{241}(7,\cdot)$	241.t	240	yes	$-1$	$1$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{91}{120}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{240}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{5}{48}\right)$
$\chi_{241}(8,\cdot)$	241.g	8	yes	$1$	$1$	$i$	$i$	$-1$	$-i$	$-1$	$e\left(\frac{3}{8}\right)$	$-i$	$-1$	$1$	$e\left(\frac{3}{8}\right)$
$\chi_{241}(9,\cdot)$	241.q	60	yes	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{31}{60}\right)$	$-1$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{241}(10,\cdot)$	241.n	30	yes	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{11}{30}\right)$	$1$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{241}(11,\cdot)$	241.p	48	yes	$-1$	$1$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{3}{8}\right)$	$-i$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{29}{48}\right)$
$\chi_{241}(12,\cdot)$	241.s	120	yes	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{41}{120}\right)$	$-i$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{13}{24}\right)$
$\chi_{241}(13,\cdot)$	241.t	240	yes	$-1$	$1$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{77}{120}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{47}{240}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{43}{48}\right)$
$\chi_{241}(14,\cdot)$	241.t	240	yes	$-1$	$1$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{101}{120}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{191}{240}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{43}{48}\right)$
$\chi_{241}(15,\cdot)$	241.c	3	yes	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{241}(16,\cdot)$	241.f	6	yes	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$1$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{241}(17,\cdot)$	241.r	80	yes	$-1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{40}\right)$	$-i$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{16}\right)$
$\chi_{241}(18,\cdot)$	241.s	120	yes	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{37}{120}\right)$	$-i$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{17}{24}\right)$
$\chi_{241}(19,\cdot)$	241.p	48	yes	$-1$	$1$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{8}\right)$	$-i$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{41}{48}\right)$
$\chi_{241}(20,\cdot)$	241.s	120	yes	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{19}{120}\right)$	$i$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{23}{24}\right)$
$\chi_{241}(21,\cdot)$	241.r	80	yes	$-1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{31}{40}\right)$	$-i$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{16}\right)$
$\chi_{241}(22,\cdot)$	241.p	48	yes	$-1$	$1$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{8}\right)$	$i$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{19}{48}\right)$
$\chi_{241}(23,\cdot)$	241.r	80	yes	$-1$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{9}{40}\right)$	$i$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{15}{16}\right)$
$\chi_{241}(24,\cdot)$	241.j	15	yes	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{15}\right)$	$1$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{241}(25,\cdot)$	241.l	20	yes	$1$	$1$	$-1$	$e\left(\frac{3}{10}\right)$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{20}\right)$	$-1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{5}\right)$	$-i$
$\chi_{241}(26,\cdot)$	241.r	80	yes	$-1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{29}{40}\right)$	$i$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{11}{16}\right)$
$\chi_{241}(27,\cdot)$	241.o	40	yes	$1$	$1$	$i$	$e\left(\frac{1}{20}\right)$	$-1$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{11}{40}\right)$	$-i$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{241}(28,\cdot)$	241.r	80	yes	$-1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{37}{40}\right)$	$i$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{11}{16}\right)$
$\chi_{241}(29,\cdot)$	241.s	120	yes	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{77}{120}\right)$	$-i$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{24}\right)$
$\chi_{241}(30,\cdot)$	241.g	8	yes	$1$	$1$	$-i$	$-i$	$-1$	$i$	$-1$	$e\left(\frac{1}{8}\right)$	$i$	$-1$	$1$	$e\left(\frac{1}{8}\right)$
$\chi_{241}(31,\cdot)$	241.t	240	yes	$-1$	$1$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{61}{120}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{151}{240}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{35}{48}\right)$
$\chi_{241}(32,\cdot)$	241.m	24	yes	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$	$i$	$-1$	$e\left(\frac{23}{24}\right)$	$i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{23}{24}\right)$

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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	$241$
Structure	\(C_{240}\)
Order	$240$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{241}(1,\cdot)\)	241.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{241}(2,\cdot)\)	241.m	24	yes	\(1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{19}{24}\right)\)	\(i\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{19}{24}\right)\)
\(\chi_{241}(3,\cdot)\)	241.s	120	yes	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{91}{120}\right)\)	\(i\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{23}{24}\right)\)
\(\chi_{241}(4,\cdot)\)	241.i	12	yes	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{241}(5,\cdot)\)	241.o	40	yes	\(1\)	\(1\)	\(i\)	\(e\left(\frac{13}{20}\right)\)	\(-1\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(-i\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{241}(6,\cdot)\)	241.l	20	yes	\(1\)	\(1\)	\(-1\)	\(e\left(\frac{1}{10}\right)\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(-1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(-i\)
\(\chi_{241}(7,\cdot)\)	241.t	240	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{91}{120}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{1}{240}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{5}{48}\right)\)
\(\chi_{241}(8,\cdot)\)	241.g	8	yes	\(1\)	\(1\)	\(i\)	\(i\)	\(-1\)	\(-i\)	\(-1\)	\(e\left(\frac{3}{8}\right)\)	\(-i\)	\(-1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{241}(9,\cdot)\)	241.q	60	yes	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(-1\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{241}(10,\cdot)\)	241.n	30	yes	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(1\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{241}(11,\cdot)\)	241.p	48	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(-i\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{29}{48}\right)\)
\(\chi_{241}(12,\cdot)\)	241.s	120	yes	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{41}{120}\right)\)	\(-i\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{13}{24}\right)\)
\(\chi_{241}(13,\cdot)\)	241.t	240	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{77}{120}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{47}{240}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{43}{48}\right)\)
\(\chi_{241}(14,\cdot)\)	241.t	240	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{101}{120}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{191}{240}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{43}{48}\right)\)
\(\chi_{241}(15,\cdot)\)	241.c	3	yes	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{241}(16,\cdot)\)	241.f	6	yes	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{241}(17,\cdot)\)	241.r	80	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(-i\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{16}\right)\)
\(\chi_{241}(18,\cdot)\)	241.s	120	yes	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{37}{120}\right)\)	\(-i\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{17}{24}\right)\)
\(\chi_{241}(19,\cdot)\)	241.p	48	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(-i\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{41}{48}\right)\)
\(\chi_{241}(20,\cdot)\)	241.s	120	yes	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{19}{120}\right)\)	\(i\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{23}{24}\right)\)
\(\chi_{241}(21,\cdot)\)	241.r	80	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(-i\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{16}\right)\)
\(\chi_{241}(22,\cdot)\)	241.p	48	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(i\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{19}{48}\right)\)
\(\chi_{241}(23,\cdot)\)	241.r	80	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(i\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{15}{16}\right)\)
\(\chi_{241}(24,\cdot)\)	241.j	15	yes	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(1\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{241}(25,\cdot)\)	241.l	20	yes	\(1\)	\(1\)	\(-1\)	\(e\left(\frac{3}{10}\right)\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(-1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(-i\)
\(\chi_{241}(26,\cdot)\)	241.r	80	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(i\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{11}{16}\right)\)
\(\chi_{241}(27,\cdot)\)	241.o	40	yes	\(1\)	\(1\)	\(i\)	\(e\left(\frac{1}{20}\right)\)	\(-1\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(-i\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{241}(28,\cdot)\)	241.r	80	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(i\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{11}{16}\right)\)
\(\chi_{241}(29,\cdot)\)	241.s	120	yes	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{77}{120}\right)\)	\(-i\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{1}{24}\right)\)
\(\chi_{241}(30,\cdot)\)	241.g	8	yes	\(1\)	\(1\)	\(-i\)	\(-i\)	\(-1\)	\(i\)	\(-1\)	\(e\left(\frac{1}{8}\right)\)	\(i\)	\(-1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{241}(31,\cdot)\)	241.t	240	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{61}{120}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{151}{240}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{35}{48}\right)\)
\(\chi_{241}(32,\cdot)\)	241.m	24	yes	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{23}{24}\right)\)	\(i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{23}{24}\right)\)

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L-functions

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Character group

First 32 of 240 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.