LMFDB - Group of Dirichlet characters of modulus 735

Show commands: PariGP / SageMath

sage: H = DirichletGroup(735)

pari: g = idealstar(,735,2)

Character group

sage: G.order() pari: g.no
Order	=	336
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{84}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{735}(491,\cdot)$, $\chi_{735}(442,\cdot)$, $\chi_{735}(346,\cdot)$

First 32 of 336 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	$-1$	$1$	$2$	$4$	$8$	$11$	$13$	$16$	$17$	$19$	$22$	$23$
$\chi_{735}(1,\cdot)$	735.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{735}(2,\cdot)$	735.bt	84	yes	$1$	$1$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{65}{84}\right)$
$\chi_{735}(4,\cdot)$	735.bo	42	no	$1$	$1$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{23}{42}\right)$
$\chi_{735}(8,\cdot)$	735.bj	28	yes	$1$	$1$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{19}{28}\right)$	$-1$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{9}{28}\right)$
$\chi_{735}(11,\cdot)$	735.bl	42	no	$-1$	$1$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{29}{42}\right)$
$\chi_{735}(13,\cdot)$	735.bi	28	no	$1$	$1$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{11}{28}\right)$	$1$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{3}{28}\right)$
$\chi_{735}(16,\cdot)$	735.bg	21	no	$1$	$1$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{2}{21}\right)$
$\chi_{735}(17,\cdot)$	735.bs	84	yes	$-1$	$1$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{73}{84}\right)$
$\chi_{735}(19,\cdot)$	735.r	6	no	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{6}\right)$
$\chi_{735}(22,\cdot)$	735.bh	28	no	$-1$	$1$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{15}{28}\right)$	$-1$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{13}{28}\right)$
$\chi_{735}(23,\cdot)$	735.bt	84	yes	$1$	$1$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{11}{84}\right)$
$\chi_{735}(26,\cdot)$	735.bm	42	no	$1$	$1$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{37}{42}\right)$
$\chi_{735}(29,\cdot)$	735.bb	14	yes	$-1$	$1$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{5}{7}\right)$	$1$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{2}{7}\right)$
$\chi_{735}(31,\cdot)$	735.n	6	no	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$
$\chi_{735}(32,\cdot)$	735.bt	84	yes	$1$	$1$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{73}{84}\right)$
$\chi_{735}(34,\cdot)$	735.bc	14	no	$-1$	$1$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{6}{7}\right)$	$-1$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{9}{14}\right)$
$\chi_{735}(37,\cdot)$	735.bv	84	no	$-1$	$1$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{59}{84}\right)$
$\chi_{735}(38,\cdot)$	735.bs	84	yes	$-1$	$1$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{79}{84}\right)$
$\chi_{735}(41,\cdot)$	735.bf	14	no	$1$	$1$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{3}{7}\right)$	$-1$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{14}\right)$
$\chi_{735}(43,\cdot)$	735.bh	28	no	$-1$	$1$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{9}{28}\right)$	$-1$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{19}{28}\right)$
$\chi_{735}(44,\cdot)$	735.bq	42	yes	$-1$	$1$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{5}{21}\right)$
$\chi_{735}(46,\cdot)$	735.bg	21	no	$1$	$1$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{19}{21}\right)$
$\chi_{735}(47,\cdot)$	735.bs	84	yes	$-1$	$1$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{65}{84}\right)$
$\chi_{735}(52,\cdot)$	735.bu	84	no	$1$	$1$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{55}{84}\right)$
$\chi_{735}(53,\cdot)$	735.bt	84	yes	$1$	$1$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{67}{84}\right)$
$\chi_{735}(58,\cdot)$	735.bv	84	no	$-1$	$1$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{5}{84}\right)$
$\chi_{735}(59,\cdot)$	735.bp	42	yes	$1$	$1$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{16}{21}\right)$
$\chi_{735}(61,\cdot)$	735.br	42	no	$-1$	$1$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{20}{21}\right)$
$\chi_{735}(62,\cdot)$	735.bk	28	yes	$-1$	$1$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{11}{28}\right)$	$1$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{3}{28}\right)$
$\chi_{735}(64,\cdot)$	735.bd	14	no	$1$	$1$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{5}{14}\right)$	$1$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{9}{14}\right)$
$\chi_{735}(67,\cdot)$	735.w	12	no	$-1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$-i$	$e\left(\frac{2}{3}\right)$	$-i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$i$	$e\left(\frac{1}{12}\right)$
$\chi_{735}(68,\cdot)$	735.x	12	no	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$-i$	$e\left(\frac{5}{6}\right)$	$-i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$-i$	$e\left(\frac{5}{12}\right)$

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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	$735$
Structure	\(C_{2}\times C_{2}\times C_{84}\)
Order	$336$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(8\)	\(11\)	\(13\)	\(16\)	\(17\)	\(19\)	\(22\)	\(23\)
\(\chi_{735}(1,\cdot)\)	735.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{735}(2,\cdot)\)	735.bt	84	yes	\(1\)	\(1\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{65}{84}\right)\)
\(\chi_{735}(4,\cdot)\)	735.bo	42	no	\(1\)	\(1\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{23}{42}\right)\)
\(\chi_{735}(8,\cdot)\)	735.bj	28	yes	\(1\)	\(1\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(-1\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{9}{28}\right)\)
\(\chi_{735}(11,\cdot)\)	735.bl	42	no	\(-1\)	\(1\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{29}{42}\right)\)
\(\chi_{735}(13,\cdot)\)	735.bi	28	no	\(1\)	\(1\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(1\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{3}{28}\right)\)
\(\chi_{735}(16,\cdot)\)	735.bg	21	no	\(1\)	\(1\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{2}{21}\right)\)
\(\chi_{735}(17,\cdot)\)	735.bs	84	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{73}{84}\right)\)
\(\chi_{735}(19,\cdot)\)	735.r	6	no	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{735}(22,\cdot)\)	735.bh	28	no	\(-1\)	\(1\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(-1\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{13}{28}\right)\)
\(\chi_{735}(23,\cdot)\)	735.bt	84	yes	\(1\)	\(1\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{11}{84}\right)\)
\(\chi_{735}(26,\cdot)\)	735.bm	42	no	\(1\)	\(1\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{37}{42}\right)\)
\(\chi_{735}(29,\cdot)\)	735.bb	14	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(1\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)
\(\chi_{735}(31,\cdot)\)	735.n	6	no	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{735}(32,\cdot)\)	735.bt	84	yes	\(1\)	\(1\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{73}{84}\right)\)
\(\chi_{735}(34,\cdot)\)	735.bc	14	no	\(-1\)	\(1\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(-1\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{9}{14}\right)\)
\(\chi_{735}(37,\cdot)\)	735.bv	84	no	\(-1\)	\(1\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{59}{84}\right)\)
\(\chi_{735}(38,\cdot)\)	735.bs	84	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{79}{84}\right)\)
\(\chi_{735}(41,\cdot)\)	735.bf	14	no	\(1\)	\(1\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(-1\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)
\(\chi_{735}(43,\cdot)\)	735.bh	28	no	\(-1\)	\(1\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(-1\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{19}{28}\right)\)
\(\chi_{735}(44,\cdot)\)	735.bq	42	yes	\(-1\)	\(1\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{5}{21}\right)\)
\(\chi_{735}(46,\cdot)\)	735.bg	21	no	\(1\)	\(1\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{19}{21}\right)\)
\(\chi_{735}(47,\cdot)\)	735.bs	84	yes	\(-1\)	\(1\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{65}{84}\right)\)
\(\chi_{735}(52,\cdot)\)	735.bu	84	no	\(1\)	\(1\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{55}{84}\right)\)
\(\chi_{735}(53,\cdot)\)	735.bt	84	yes	\(1\)	\(1\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{67}{84}\right)\)
\(\chi_{735}(58,\cdot)\)	735.bv	84	no	\(-1\)	\(1\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{5}{84}\right)\)
\(\chi_{735}(59,\cdot)\)	735.bp	42	yes	\(1\)	\(1\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{16}{21}\right)\)
\(\chi_{735}(61,\cdot)\)	735.br	42	no	\(-1\)	\(1\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{20}{21}\right)\)
\(\chi_{735}(62,\cdot)\)	735.bk	28	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(1\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{3}{28}\right)\)
\(\chi_{735}(64,\cdot)\)	735.bd	14	no	\(1\)	\(1\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(1\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{9}{14}\right)\)
\(\chi_{735}(67,\cdot)\)	735.w	12	no	\(-1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-i\)	\(e\left(\frac{2}{3}\right)\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(i\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{735}(68,\cdot)\)	735.x	12	no	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-i\)	\(e\left(\frac{5}{6}\right)\)	\(-i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-i\)	\(e\left(\frac{5}{12}\right)\)

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