LMFDB - Group of Dirichlet characters of modulus 61

Show commands: PariGP / SageMath

sage: H = DirichletGroup(61)

pari: g = idealstar(,61,2)

Character group

sage: G.order() pari: g.no
Order	=	60
sage: H.invariants() pari: g.cyc
Structure	=	$C_{60}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{61}(2,\cdot)$

First 32 of 60 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{61}(1,\cdot)$	61.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{61}(2,\cdot)$	61.l	60	yes	$-1$	$1$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{23}{60}\right)$	$i$
$\chi_{61}(3,\cdot)$	61.g	10	yes	$1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{10}\right)$	$-1$
$\chi_{61}(4,\cdot)$	61.k	30	yes	$1$	$1$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{23}{30}\right)$	$-1$
$\chi_{61}(5,\cdot)$	61.k	30	yes	$1$	$1$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{13}{30}\right)$	$-1$
$\chi_{61}(6,\cdot)$	61.l	60	yes	$-1$	$1$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{41}{60}\right)$	$-i$
$\chi_{61}(7,\cdot)$	61.l	60	yes	$-1$	$1$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{47}{60}\right)$	$i$
$\chi_{61}(8,\cdot)$	61.j	20	yes	$-1$	$1$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{20}\right)$	$-i$
$\chi_{61}(9,\cdot)$	61.e	5	yes	$1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{5}\right)$	$1$
$\chi_{61}(10,\cdot)$	61.l	60	yes	$-1$	$1$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{49}{60}\right)$	$-i$
$\chi_{61}(11,\cdot)$	61.d	4	yes	$-1$	$1$	$i$	$-1$	$-1$	$-1$	$-i$	$i$	$-i$	$1$	$-i$	$-i$
$\chi_{61}(12,\cdot)$	61.i	15	yes	$1$	$1$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{15}\right)$	$1$
$\chi_{61}(13,\cdot)$	61.c	3	yes	$1$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$1$
$\chi_{61}(14,\cdot)$	61.f	6	yes	$1$	$1$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$-1$
$\chi_{61}(15,\cdot)$	61.i	15	yes	$1$	$1$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{11}{15}\right)$	$1$
$\chi_{61}(16,\cdot)$	61.i	15	yes	$1$	$1$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{8}{15}\right)$	$1$
$\chi_{61}(17,\cdot)$	61.l	60	yes	$-1$	$1$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{60}\right)$	$-i$
$\chi_{61}(18,\cdot)$	61.l	60	yes	$-1$	$1$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{59}{60}\right)$	$i$
$\chi_{61}(19,\cdot)$	61.k	30	yes	$1$	$1$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{29}{30}\right)$	$-1$
$\chi_{61}(20,\cdot)$	61.e	5	yes	$1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{5}\right)$	$1$
$\chi_{61}(21,\cdot)$	61.h	12	yes	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{11}{12}\right)$	$-i$	$1$	$e\left(\frac{1}{12}\right)$	$-i$
$\chi_{61}(22,\cdot)$	61.i	15	yes	$1$	$1$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{15}\right)$	$1$
$\chi_{61}(23,\cdot)$	61.j	20	yes	$-1$	$1$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{17}{20}\right)$	$i$
$\chi_{61}(24,\cdot)$	61.j	20	yes	$-1$	$1$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{9}{20}\right)$	$i$
$\chi_{61}(25,\cdot)$	61.i	15	yes	$1$	$1$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{13}{15}\right)$	$1$
$\chi_{61}(26,\cdot)$	61.l	60	yes	$-1$	$1$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{43}{60}\right)$	$i$
$\chi_{61}(27,\cdot)$	61.g	10	yes	$1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{9}{10}\right)$	$-1$
$\chi_{61}(28,\cdot)$	61.j	20	yes	$-1$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{11}{20}\right)$	$-i$
$\chi_{61}(29,\cdot)$	61.h	12	yes	$-1$	$1$	$e\left(\frac{7}{12}\right)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{12}\right)$	$-i$	$1$	$e\left(\frac{5}{12}\right)$	$-i$
$\chi_{61}(30,\cdot)$	61.l	60	yes	$-1$	$1$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{60}\right)$	$i$
$\chi_{61}(31,\cdot)$	61.l	60	yes	$-1$	$1$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{37}{60}\right)$	$-i$
$\chi_{61}(32,\cdot)$	61.h	12	yes	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{12}\right)$	$i$	$1$	$e\left(\frac{11}{12}\right)$	$i$

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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	$61$
Structure	\(C_{60}\)
Order	$60$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{61}(1,\cdot)\)	61.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{61}(2,\cdot)\)	61.l	60	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(i\)
\(\chi_{61}(3,\cdot)\)	61.g	10	yes	\(1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(-1\)
\(\chi_{61}(4,\cdot)\)	61.k	30	yes	\(1\)	\(1\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(-1\)
\(\chi_{61}(5,\cdot)\)	61.k	30	yes	\(1\)	\(1\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(-1\)
\(\chi_{61}(6,\cdot)\)	61.l	60	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(-i\)
\(\chi_{61}(7,\cdot)\)	61.l	60	yes	\(-1\)	\(1\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(i\)
\(\chi_{61}(8,\cdot)\)	61.j	20	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(-i\)
\(\chi_{61}(9,\cdot)\)	61.e	5	yes	\(1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(1\)
\(\chi_{61}(10,\cdot)\)	61.l	60	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(-i\)
\(\chi_{61}(11,\cdot)\)	61.d	4	yes	\(-1\)	\(1\)	\(i\)	\(-1\)	\(-1\)	\(-1\)	\(-i\)	\(i\)	\(-i\)	\(1\)	\(-i\)	\(-i\)
\(\chi_{61}(12,\cdot)\)	61.i	15	yes	\(1\)	\(1\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(1\)
\(\chi_{61}(13,\cdot)\)	61.c	3	yes	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(1\)
\(\chi_{61}(14,\cdot)\)	61.f	6	yes	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)
\(\chi_{61}(15,\cdot)\)	61.i	15	yes	\(1\)	\(1\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(1\)
\(\chi_{61}(16,\cdot)\)	61.i	15	yes	\(1\)	\(1\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(1\)
\(\chi_{61}(17,\cdot)\)	61.l	60	yes	\(-1\)	\(1\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(-i\)
\(\chi_{61}(18,\cdot)\)	61.l	60	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(i\)
\(\chi_{61}(19,\cdot)\)	61.k	30	yes	\(1\)	\(1\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(-1\)
\(\chi_{61}(20,\cdot)\)	61.e	5	yes	\(1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(1\)
\(\chi_{61}(21,\cdot)\)	61.h	12	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(-i\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(-i\)
\(\chi_{61}(22,\cdot)\)	61.i	15	yes	\(1\)	\(1\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(1\)
\(\chi_{61}(23,\cdot)\)	61.j	20	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(i\)
\(\chi_{61}(24,\cdot)\)	61.j	20	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(i\)
\(\chi_{61}(25,\cdot)\)	61.i	15	yes	\(1\)	\(1\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(1\)
\(\chi_{61}(26,\cdot)\)	61.l	60	yes	\(-1\)	\(1\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(i\)
\(\chi_{61}(27,\cdot)\)	61.g	10	yes	\(1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(-1\)
\(\chi_{61}(28,\cdot)\)	61.j	20	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(-i\)
\(\chi_{61}(29,\cdot)\)	61.h	12	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-i\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(-i\)
\(\chi_{61}(30,\cdot)\)	61.l	60	yes	\(-1\)	\(1\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(i\)
\(\chi_{61}(31,\cdot)\)	61.l	60	yes	\(-1\)	\(1\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(-i\)
\(\chi_{61}(32,\cdot)\)	61.h	12	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(i\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(i\)

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First 32 of 60 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.