LMFDB - Group of Dirichlet characters of modulus 6032

Show commands: PariGP / SageMath

sage: H = DirichletGroup(6032)

pari: g = idealstar(,6032,2)

Character group

sage: G.order() pari: g.no
Order	=	2688
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{4}\times C_{4}\times C_{84}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{6032}(5279,\cdot)$, $\chi_{6032}(1509,\cdot)$, $\chi_{6032}(1393,\cdot)$, $\chi_{6032}(1249,\cdot)$

First 32 of 2688 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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$15$	$17$	$19$	$21$	$23$
$\chi_{6032}(1,\cdot)$	6032.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{6032}(3,\cdot)$	6032.jh	84	yes	$1$	$1$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{19}{21}\right)$
$\chi_{6032}(5,\cdot)$	6032.gu	28	yes	$-1$	$1$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{27}{28}\right)$	$1$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{5}{7}\right)$
$\chi_{6032}(7,\cdot)$	6032.kx	84	no	$1$	$1$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{5}{21}\right)$
$\chi_{6032}(9,\cdot)$	6032.ix	42	no	$1$	$1$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{17}{21}\right)$
$\chi_{6032}(11,\cdot)$	6032.kq	84	yes	$-1$	$1$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{29}{42}\right)$
$\chi_{6032}(15,\cdot)$	6032.kd	84	no	$-1$	$1$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{13}{21}\right)$
$\chi_{6032}(17,\cdot)$	6032.fb	12	no	$-1$	$1$	$e\left(\frac{5}{12}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{12}\right)$	$i$	$e\left(\frac{2}{3}\right)$
$\chi_{6032}(19,\cdot)$	6032.iy	84	yes	$-1$	$1$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{25}{42}\right)$
$\chi_{6032}(21,\cdot)$	6032.hx	28	yes	$1$	$1$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{9}{14}\right)$	$i$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{1}{7}\right)$
$\chi_{6032}(23,\cdot)$	6032.it	42	no	$-1$	$1$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{5}{42}\right)$
$\chi_{6032}(25,\cdot)$	6032.fy	14	no	$1$	$1$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{13}{14}\right)$	$1$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{3}{7}\right)$
$\chi_{6032}(27,\cdot)$	6032.hz	28	no	$1$	$1$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{27}{28}\right)$	$i$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{5}{7}\right)$
$\chi_{6032}(31,\cdot)$	6032.hj	28	no	$-1$	$1$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{3}{14}\right)$	$i$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{5}{7}\right)$
$\chi_{6032}(33,\cdot)$	6032.jc	84	no	$-1$	$1$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{25}{42}\right)$
$\chi_{6032}(35,\cdot)$	6032.kh	84	yes	$-1$	$1$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{20}{21}\right)$
$\chi_{6032}(37,\cdot)$	6032.kr	84	yes	$1$	$1$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{10}{21}\right)$
$\chi_{6032}(41,\cdot)$	6032.em	12	no	$1$	$1$	$e\left(\frac{1}{12}\right)$	$-i$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{5}{6}\right)$
$\chi_{6032}(43,\cdot)$	6032.kt	84	yes	$1$	$1$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{20}{21}\right)$
$\chi_{6032}(45,\cdot)$	6032.kn	84	yes	$-1$	$1$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{11}{21}\right)$
$\chi_{6032}(47,\cdot)$	6032.hj	28	no	$-1$	$1$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{5}{14}\right)$	$-i$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{6}{7}\right)$
$\chi_{6032}(49,\cdot)$	6032.iu	42	no	$1$	$1$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{10}{21}\right)$
$\chi_{6032}(51,\cdot)$	6032.hn	28	yes	$-1$	$1$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{1}{14}\right)$	$-1$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{4}{7}\right)$
$\chi_{6032}(53,\cdot)$	6032.hm	28	no	$1$	$1$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{5}{7}\right)$	$1$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{3}{14}\right)$
$\chi_{6032}(55,\cdot)$	6032.jk	84	no	$1$	$1$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{17}{42}\right)$
$\chi_{6032}(57,\cdot)$	6032.cp	4	no	$-1$	$1$	$1$	$i$	$i$	$1$	$i$	$i$	$1$	$-i$	$i$	$-1$
$\chi_{6032}(59,\cdot)$	6032.ec	12	no	$1$	$1$	$e\left(\frac{11}{12}\right)$	$-1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{6}\right)$
$\chi_{6032}(61,\cdot)$	6032.ks	84	yes	$-1$	$1$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{31}{42}\right)$
$\chi_{6032}(63,\cdot)$	6032.kv	84	no	$1$	$1$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{1}{21}\right)$
$\chi_{6032}(67,\cdot)$	6032.km	84	yes	$1$	$1$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{41}{42}\right)$
$\chi_{6032}(69,\cdot)$	6032.jg	84	yes	$-1$	$1$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{1}{42}\right)$
$\chi_{6032}(71,\cdot)$	6032.jd	84	no	$1$	$1$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{11}{21}\right)$

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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	$6032$
Structure	\(C_{2}\times C_{4}\times C_{4}\times C_{84}\)
Order	$2688$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(15\)	\(17\)	\(19\)	\(21\)	\(23\)
\(\chi_{6032}(1,\cdot)\)	6032.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{6032}(3,\cdot)\)	6032.jh	84	yes	\(1\)	\(1\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{19}{21}\right)\)
\(\chi_{6032}(5,\cdot)\)	6032.gu	28	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(1\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{6032}(7,\cdot)\)	6032.kx	84	no	\(1\)	\(1\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{5}{21}\right)\)
\(\chi_{6032}(9,\cdot)\)	6032.ix	42	no	\(1\)	\(1\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{17}{21}\right)\)
\(\chi_{6032}(11,\cdot)\)	6032.kq	84	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{29}{42}\right)\)
\(\chi_{6032}(15,\cdot)\)	6032.kd	84	no	\(-1\)	\(1\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{13}{21}\right)\)
\(\chi_{6032}(17,\cdot)\)	6032.fb	12	no	\(-1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(i\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{6032}(19,\cdot)\)	6032.iy	84	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{25}{42}\right)\)
\(\chi_{6032}(21,\cdot)\)	6032.hx	28	yes	\(1\)	\(1\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(i\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{1}{7}\right)\)
\(\chi_{6032}(23,\cdot)\)	6032.it	42	no	\(-1\)	\(1\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{5}{42}\right)\)
\(\chi_{6032}(25,\cdot)\)	6032.fy	14	no	\(1\)	\(1\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(1\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)
\(\chi_{6032}(27,\cdot)\)	6032.hz	28	no	\(1\)	\(1\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(i\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{6032}(31,\cdot)\)	6032.hj	28	no	\(-1\)	\(1\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(i\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{6032}(33,\cdot)\)	6032.jc	84	no	\(-1\)	\(1\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{25}{42}\right)\)
\(\chi_{6032}(35,\cdot)\)	6032.kh	84	yes	\(-1\)	\(1\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{20}{21}\right)\)
\(\chi_{6032}(37,\cdot)\)	6032.kr	84	yes	\(1\)	\(1\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{10}{21}\right)\)
\(\chi_{6032}(41,\cdot)\)	6032.em	12	no	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(-i\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{6032}(43,\cdot)\)	6032.kt	84	yes	\(1\)	\(1\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{20}{21}\right)\)
\(\chi_{6032}(45,\cdot)\)	6032.kn	84	yes	\(-1\)	\(1\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{11}{21}\right)\)
\(\chi_{6032}(47,\cdot)\)	6032.hj	28	no	\(-1\)	\(1\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(-i\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)
\(\chi_{6032}(49,\cdot)\)	6032.iu	42	no	\(1\)	\(1\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{10}{21}\right)\)
\(\chi_{6032}(51,\cdot)\)	6032.hn	28	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(-1\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{4}{7}\right)\)
\(\chi_{6032}(53,\cdot)\)	6032.hm	28	no	\(1\)	\(1\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(1\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{3}{14}\right)\)
\(\chi_{6032}(55,\cdot)\)	6032.jk	84	no	\(1\)	\(1\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{17}{42}\right)\)
\(\chi_{6032}(57,\cdot)\)	6032.cp	4	no	\(-1\)	\(1\)	\(1\)	\(i\)	\(i\)	\(1\)	\(i\)	\(i\)	\(1\)	\(-i\)	\(i\)	\(-1\)
\(\chi_{6032}(59,\cdot)\)	6032.ec	12	no	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(-1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{6032}(61,\cdot)\)	6032.ks	84	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{31}{42}\right)\)
\(\chi_{6032}(63,\cdot)\)	6032.kv	84	no	\(1\)	\(1\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{1}{21}\right)\)
\(\chi_{6032}(67,\cdot)\)	6032.km	84	yes	\(1\)	\(1\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{41}{42}\right)\)
\(\chi_{6032}(69,\cdot)\)	6032.jg	84	yes	\(-1\)	\(1\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{1}{42}\right)\)
\(\chi_{6032}(71,\cdot)\)	6032.jd	84	no	\(1\)	\(1\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{11}{21}\right)\)

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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.