LMFDB - Group of Dirichlet characters of modulus 648

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(648)

gp:g = idealstar(,648,2)

magma:G := FullDirichletGroup(648);

Character group

Order	=	216	comment:Order sage:G.order() gp:g.no magma:Order(G);
Structure	=	$C_{2}\times C_{2}\times C_{54}$	comment:Group structure sage:sorted(g.order() for g in G.gens()) gp:g.cyc magma:PrimaryInvariants(AbelianGroup(G));
Generators	=	$\chi_{648}(487,\cdot)$, $\chi_{648}(325,\cdot)$, $\chi_{648}(569,\cdot)$	comment:Generators sage:G.gens() gp:g.gen magma:Generators(G);

First 32 of 216 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	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$
$\chi_{648}(1,\cdot)$	648.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{648}(5,\cdot)$	648.z	54	yes	$-1$	$1$	$e\left(\frac{8}{27}\right)$	$e\left(\frac{22}{27}\right)$	$e\left(\frac{1}{27}\right)$	$e\left(\frac{49}{54}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{37}{54}\right)$	$e\left(\frac{16}{27}\right)$	$e\left(\frac{7}{27}\right)$	$e\left(\frac{14}{27}\right)$
$\chi_{648}(7,\cdot)$	648.ba	54	no	$-1$	$1$	$e\left(\frac{22}{27}\right)$	$e\left(\frac{13}{54}\right)$	$e\left(\frac{19}{54}\right)$	$e\left(\frac{10}{27}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{41}{54}\right)$	$e\left(\frac{17}{27}\right)$	$e\left(\frac{26}{27}\right)$	$e\left(\frac{23}{54}\right)$
$\chi_{648}(11,\cdot)$	648.bb	54	yes	$1$	$1$	$e\left(\frac{1}{27}\right)$	$e\left(\frac{19}{54}\right)$	$e\left(\frac{7}{54}\right)$	$e\left(\frac{23}{54}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{4}{27}\right)$	$e\left(\frac{2}{27}\right)$	$e\left(\frac{11}{27}\right)$	$e\left(\frac{17}{54}\right)$
$\chi_{648}(13,\cdot)$	648.bd	54	yes	$1$	$1$	$e\left(\frac{49}{54}\right)$	$e\left(\frac{10}{27}\right)$	$e\left(\frac{23}{54}\right)$	$e\left(\frac{37}{54}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{17}{27}\right)$	$e\left(\frac{22}{27}\right)$	$e\left(\frac{53}{54}\right)$	$e\left(\frac{26}{27}\right)$
$\chi_{648}(17,\cdot)$	648.u	18	no	$-1$	$1$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{2}{9}\right)$
$\chi_{648}(19,\cdot)$	648.r	18	no	$-1$	$1$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{5}{18}\right)$
$\chi_{648}(23,\cdot)$	648.be	54	no	$1$	$1$	$e\left(\frac{37}{54}\right)$	$e\left(\frac{41}{54}\right)$	$e\left(\frac{4}{27}\right)$	$e\left(\frac{17}{27}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{20}{27}\right)$	$e\left(\frac{10}{27}\right)$	$e\left(\frac{29}{54}\right)$	$e\left(\frac{31}{54}\right)$
$\chi_{648}(25,\cdot)$	648.y	27	no	$1$	$1$	$e\left(\frac{16}{27}\right)$	$e\left(\frac{17}{27}\right)$	$e\left(\frac{2}{27}\right)$	$e\left(\frac{22}{27}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{10}{27}\right)$	$e\left(\frac{5}{27}\right)$	$e\left(\frac{14}{27}\right)$	$e\left(\frac{1}{27}\right)$
$\chi_{648}(29,\cdot)$	648.z	54	yes	$-1$	$1$	$e\left(\frac{7}{27}\right)$	$e\left(\frac{26}{27}\right)$	$e\left(\frac{11}{27}\right)$	$e\left(\frac{53}{54}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{29}{54}\right)$	$e\left(\frac{14}{27}\right)$	$e\left(\frac{23}{27}\right)$	$e\left(\frac{19}{27}\right)$
$\chi_{648}(31,\cdot)$	648.ba	54	no	$-1$	$1$	$e\left(\frac{14}{27}\right)$	$e\left(\frac{23}{54}\right)$	$e\left(\frac{17}{54}\right)$	$e\left(\frac{26}{27}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{31}{54}\right)$	$e\left(\frac{1}{27}\right)$	$e\left(\frac{19}{27}\right)$	$e\left(\frac{49}{54}\right)$
$\chi_{648}(35,\cdot)$	648.v	18	no	$1$	$1$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{17}{18}\right)$
$\chi_{648}(37,\cdot)$	648.t	18	no	$1$	$1$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{5}{9}\right)$
$\chi_{648}(41,\cdot)$	648.bc	54	no	$-1$	$1$	$e\left(\frac{31}{54}\right)$	$e\left(\frac{19}{27}\right)$	$e\left(\frac{41}{54}\right)$	$e\left(\frac{23}{27}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{43}{54}\right)$	$e\left(\frac{4}{27}\right)$	$e\left(\frac{17}{54}\right)$	$e\left(\frac{17}{27}\right)$
$\chi_{648}(43,\cdot)$	648.bf	54	yes	$-1$	$1$	$e\left(\frac{47}{54}\right)$	$e\left(\frac{1}{54}\right)$	$e\left(\frac{8}{27}\right)$	$e\left(\frac{41}{54}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{53}{54}\right)$	$e\left(\frac{20}{27}\right)$	$e\left(\frac{31}{54}\right)$	$e\left(\frac{35}{54}\right)$
$\chi_{648}(47,\cdot)$	648.be	54	no	$1$	$1$	$e\left(\frac{53}{54}\right)$	$e\left(\frac{31}{54}\right)$	$e\left(\frac{5}{27}\right)$	$e\left(\frac{1}{27}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{25}{27}\right)$	$e\left(\frac{26}{27}\right)$	$e\left(\frac{43}{54}\right)$	$e\left(\frac{5}{54}\right)$
$\chi_{648}(49,\cdot)$	648.y	27	no	$1$	$1$	$e\left(\frac{17}{27}\right)$	$e\left(\frac{13}{27}\right)$	$e\left(\frac{19}{27}\right)$	$e\left(\frac{20}{27}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{14}{27}\right)$	$e\left(\frac{7}{27}\right)$	$e\left(\frac{25}{27}\right)$	$e\left(\frac{23}{27}\right)$
$\chi_{648}(53,\cdot)$	648.j	6	no	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{648}(55,\cdot)$	648.k	6	no	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{648}(59,\cdot)$	648.bb	54	yes	$1$	$1$	$e\left(\frac{26}{27}\right)$	$e\left(\frac{35}{54}\right)$	$e\left(\frac{47}{54}\right)$	$e\left(\frac{31}{54}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{23}{27}\right)$	$e\left(\frac{25}{27}\right)$	$e\left(\frac{16}{27}\right)$	$e\left(\frac{37}{54}\right)$
$\chi_{648}(61,\cdot)$	648.bd	54	yes	$1$	$1$	$e\left(\frac{35}{54}\right)$	$e\left(\frac{11}{27}\right)$	$e\left(\frac{1}{54}\right)$	$e\left(\frac{11}{54}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{16}{27}\right)$	$e\left(\frac{8}{27}\right)$	$e\left(\frac{7}{54}\right)$	$e\left(\frac{7}{27}\right)$
$\chi_{648}(65,\cdot)$	648.bc	54	no	$-1$	$1$	$e\left(\frac{11}{54}\right)$	$e\left(\frac{5}{27}\right)$	$e\left(\frac{25}{54}\right)$	$e\left(\frac{16}{27}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{17}{54}\right)$	$e\left(\frac{11}{27}\right)$	$e\left(\frac{13}{54}\right)$	$e\left(\frac{13}{27}\right)$
$\chi_{648}(67,\cdot)$	648.bf	54	yes	$-1$	$1$	$e\left(\frac{13}{54}\right)$	$e\left(\frac{29}{54}\right)$	$e\left(\frac{16}{27}\right)$	$e\left(\frac{1}{54}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{25}{54}\right)$	$e\left(\frac{13}{27}\right)$	$e\left(\frac{35}{54}\right)$	$e\left(\frac{43}{54}\right)$
$\chi_{648}(71,\cdot)$	648.w	18	no	$1$	$1$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{7}{18}\right)$
$\chi_{648}(73,\cdot)$	648.q	9	no	$1$	$1$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{9}\right)$
$\chi_{648}(77,\cdot)$	648.z	54	yes	$-1$	$1$	$e\left(\frac{23}{27}\right)$	$e\left(\frac{16}{27}\right)$	$e\left(\frac{13}{27}\right)$	$e\left(\frac{43}{54}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{49}{54}\right)$	$e\left(\frac{19}{27}\right)$	$e\left(\frac{10}{27}\right)$	$e\left(\frac{20}{27}\right)$
$\chi_{648}(79,\cdot)$	648.ba	54	no	$-1$	$1$	$e\left(\frac{25}{27}\right)$	$e\left(\frac{43}{54}\right)$	$e\left(\frac{13}{54}\right)$	$e\left(\frac{4}{27}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{11}{54}\right)$	$e\left(\frac{23}{27}\right)$	$e\left(\frac{5}{27}\right)$	$e\left(\frac{47}{54}\right)$
$\chi_{648}(83,\cdot)$	648.bb	54	yes	$1$	$1$	$e\left(\frac{25}{27}\right)$	$e\left(\frac{43}{54}\right)$	$e\left(\frac{13}{54}\right)$	$e\left(\frac{35}{54}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{19}{27}\right)$	$e\left(\frac{23}{27}\right)$	$e\left(\frac{5}{27}\right)$	$e\left(\frac{47}{54}\right)$
$\chi_{648}(85,\cdot)$	648.bd	54	yes	$1$	$1$	$e\left(\frac{19}{54}\right)$	$e\left(\frac{16}{27}\right)$	$e\left(\frac{53}{54}\right)$	$e\left(\frac{43}{54}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{11}{27}\right)$	$e\left(\frac{19}{27}\right)$	$e\left(\frac{47}{54}\right)$	$e\left(\frac{20}{27}\right)$
$\chi_{648}(89,\cdot)$	648.u	18	no	$-1$	$1$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{1}{9}\right)$
$\chi_{648}(91,\cdot)$	648.r	18	no	$-1$	$1$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{7}{18}\right)$
$\chi_{648}(95,\cdot)$	648.be	54	no	$1$	$1$	$e\left(\frac{13}{54}\right)$	$e\left(\frac{29}{54}\right)$	$e\left(\frac{16}{27}\right)$	$e\left(\frac{14}{27}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{26}{27}\right)$	$e\left(\frac{13}{27}\right)$	$e\left(\frac{35}{54}\right)$	$e\left(\frac{43}{54}\right)$

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Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$ over number fields
Genus 2 curves
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Modulus	$648$
Structure	\(C_{2}\times C_{2}\times C_{54}\)
Order	$216$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)
\(\chi_{648}(1,\cdot)\)	648.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{648}(5,\cdot)\)	648.z	54	yes	\(-1\)	\(1\)	\(e\left(\frac{8}{27}\right)\)	\(e\left(\frac{22}{27}\right)\)	\(e\left(\frac{1}{27}\right)\)	\(e\left(\frac{49}{54}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{37}{54}\right)\)	\(e\left(\frac{16}{27}\right)\)	\(e\left(\frac{7}{27}\right)\)	\(e\left(\frac{14}{27}\right)\)
\(\chi_{648}(7,\cdot)\)	648.ba	54	no	\(-1\)	\(1\)	\(e\left(\frac{22}{27}\right)\)	\(e\left(\frac{13}{54}\right)\)	\(e\left(\frac{19}{54}\right)\)	\(e\left(\frac{10}{27}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{41}{54}\right)\)	\(e\left(\frac{17}{27}\right)\)	\(e\left(\frac{26}{27}\right)\)	\(e\left(\frac{23}{54}\right)\)
\(\chi_{648}(11,\cdot)\)	648.bb	54	yes	\(1\)	\(1\)	\(e\left(\frac{1}{27}\right)\)	\(e\left(\frac{19}{54}\right)\)	\(e\left(\frac{7}{54}\right)\)	\(e\left(\frac{23}{54}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{4}{27}\right)\)	\(e\left(\frac{2}{27}\right)\)	\(e\left(\frac{11}{27}\right)\)	\(e\left(\frac{17}{54}\right)\)
\(\chi_{648}(13,\cdot)\)	648.bd	54	yes	\(1\)	\(1\)	\(e\left(\frac{49}{54}\right)\)	\(e\left(\frac{10}{27}\right)\)	\(e\left(\frac{23}{54}\right)\)	\(e\left(\frac{37}{54}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{17}{27}\right)\)	\(e\left(\frac{22}{27}\right)\)	\(e\left(\frac{53}{54}\right)\)	\(e\left(\frac{26}{27}\right)\)
\(\chi_{648}(17,\cdot)\)	648.u	18	no	\(-1\)	\(1\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)
\(\chi_{648}(19,\cdot)\)	648.r	18	no	\(-1\)	\(1\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{5}{18}\right)\)
\(\chi_{648}(23,\cdot)\)	648.be	54	no	\(1\)	\(1\)	\(e\left(\frac{37}{54}\right)\)	\(e\left(\frac{41}{54}\right)\)	\(e\left(\frac{4}{27}\right)\)	\(e\left(\frac{17}{27}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{20}{27}\right)\)	\(e\left(\frac{10}{27}\right)\)	\(e\left(\frac{29}{54}\right)\)	\(e\left(\frac{31}{54}\right)\)
\(\chi_{648}(25,\cdot)\)	648.y	27	no	\(1\)	\(1\)	\(e\left(\frac{16}{27}\right)\)	\(e\left(\frac{17}{27}\right)\)	\(e\left(\frac{2}{27}\right)\)	\(e\left(\frac{22}{27}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{10}{27}\right)\)	\(e\left(\frac{5}{27}\right)\)	\(e\left(\frac{14}{27}\right)\)	\(e\left(\frac{1}{27}\right)\)
\(\chi_{648}(29,\cdot)\)	648.z	54	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{27}\right)\)	\(e\left(\frac{26}{27}\right)\)	\(e\left(\frac{11}{27}\right)\)	\(e\left(\frac{53}{54}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{29}{54}\right)\)	\(e\left(\frac{14}{27}\right)\)	\(e\left(\frac{23}{27}\right)\)	\(e\left(\frac{19}{27}\right)\)
\(\chi_{648}(31,\cdot)\)	648.ba	54	no	\(-1\)	\(1\)	\(e\left(\frac{14}{27}\right)\)	\(e\left(\frac{23}{54}\right)\)	\(e\left(\frac{17}{54}\right)\)	\(e\left(\frac{26}{27}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{31}{54}\right)\)	\(e\left(\frac{1}{27}\right)\)	\(e\left(\frac{19}{27}\right)\)	\(e\left(\frac{49}{54}\right)\)
\(\chi_{648}(35,\cdot)\)	648.v	18	no	\(1\)	\(1\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{17}{18}\right)\)
\(\chi_{648}(37,\cdot)\)	648.t	18	no	\(1\)	\(1\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{5}{9}\right)\)
\(\chi_{648}(41,\cdot)\)	648.bc	54	no	\(-1\)	\(1\)	\(e\left(\frac{31}{54}\right)\)	\(e\left(\frac{19}{27}\right)\)	\(e\left(\frac{41}{54}\right)\)	\(e\left(\frac{23}{27}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{43}{54}\right)\)	\(e\left(\frac{4}{27}\right)\)	\(e\left(\frac{17}{54}\right)\)	\(e\left(\frac{17}{27}\right)\)
\(\chi_{648}(43,\cdot)\)	648.bf	54	yes	\(-1\)	\(1\)	\(e\left(\frac{47}{54}\right)\)	\(e\left(\frac{1}{54}\right)\)	\(e\left(\frac{8}{27}\right)\)	\(e\left(\frac{41}{54}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{53}{54}\right)\)	\(e\left(\frac{20}{27}\right)\)	\(e\left(\frac{31}{54}\right)\)	\(e\left(\frac{35}{54}\right)\)
\(\chi_{648}(47,\cdot)\)	648.be	54	no	\(1\)	\(1\)	\(e\left(\frac{53}{54}\right)\)	\(e\left(\frac{31}{54}\right)\)	\(e\left(\frac{5}{27}\right)\)	\(e\left(\frac{1}{27}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{25}{27}\right)\)	\(e\left(\frac{26}{27}\right)\)	\(e\left(\frac{43}{54}\right)\)	\(e\left(\frac{5}{54}\right)\)
\(\chi_{648}(49,\cdot)\)	648.y	27	no	\(1\)	\(1\)	\(e\left(\frac{17}{27}\right)\)	\(e\left(\frac{13}{27}\right)\)	\(e\left(\frac{19}{27}\right)\)	\(e\left(\frac{20}{27}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{14}{27}\right)\)	\(e\left(\frac{7}{27}\right)\)	\(e\left(\frac{25}{27}\right)\)	\(e\left(\frac{23}{27}\right)\)
\(\chi_{648}(53,\cdot)\)	648.j	6	no	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{648}(55,\cdot)\)	648.k	6	no	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{648}(59,\cdot)\)	648.bb	54	yes	\(1\)	\(1\)	\(e\left(\frac{26}{27}\right)\)	\(e\left(\frac{35}{54}\right)\)	\(e\left(\frac{47}{54}\right)\)	\(e\left(\frac{31}{54}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{23}{27}\right)\)	\(e\left(\frac{25}{27}\right)\)	\(e\left(\frac{16}{27}\right)\)	\(e\left(\frac{37}{54}\right)\)
\(\chi_{648}(61,\cdot)\)	648.bd	54	yes	\(1\)	\(1\)	\(e\left(\frac{35}{54}\right)\)	\(e\left(\frac{11}{27}\right)\)	\(e\left(\frac{1}{54}\right)\)	\(e\left(\frac{11}{54}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{16}{27}\right)\)	\(e\left(\frac{8}{27}\right)\)	\(e\left(\frac{7}{54}\right)\)	\(e\left(\frac{7}{27}\right)\)
\(\chi_{648}(65,\cdot)\)	648.bc	54	no	\(-1\)	\(1\)	\(e\left(\frac{11}{54}\right)\)	\(e\left(\frac{5}{27}\right)\)	\(e\left(\frac{25}{54}\right)\)	\(e\left(\frac{16}{27}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{17}{54}\right)\)	\(e\left(\frac{11}{27}\right)\)	\(e\left(\frac{13}{54}\right)\)	\(e\left(\frac{13}{27}\right)\)
\(\chi_{648}(67,\cdot)\)	648.bf	54	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{54}\right)\)	\(e\left(\frac{29}{54}\right)\)	\(e\left(\frac{16}{27}\right)\)	\(e\left(\frac{1}{54}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{25}{54}\right)\)	\(e\left(\frac{13}{27}\right)\)	\(e\left(\frac{35}{54}\right)\)	\(e\left(\frac{43}{54}\right)\)
\(\chi_{648}(71,\cdot)\)	648.w	18	no	\(1\)	\(1\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{7}{18}\right)\)
\(\chi_{648}(73,\cdot)\)	648.q	9	no	\(1\)	\(1\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)
\(\chi_{648}(77,\cdot)\)	648.z	54	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{27}\right)\)	\(e\left(\frac{16}{27}\right)\)	\(e\left(\frac{13}{27}\right)\)	\(e\left(\frac{43}{54}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{49}{54}\right)\)	\(e\left(\frac{19}{27}\right)\)	\(e\left(\frac{10}{27}\right)\)	\(e\left(\frac{20}{27}\right)\)
\(\chi_{648}(79,\cdot)\)	648.ba	54	no	\(-1\)	\(1\)	\(e\left(\frac{25}{27}\right)\)	\(e\left(\frac{43}{54}\right)\)	\(e\left(\frac{13}{54}\right)\)	\(e\left(\frac{4}{27}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{11}{54}\right)\)	\(e\left(\frac{23}{27}\right)\)	\(e\left(\frac{5}{27}\right)\)	\(e\left(\frac{47}{54}\right)\)
\(\chi_{648}(83,\cdot)\)	648.bb	54	yes	\(1\)	\(1\)	\(e\left(\frac{25}{27}\right)\)	\(e\left(\frac{43}{54}\right)\)	\(e\left(\frac{13}{54}\right)\)	\(e\left(\frac{35}{54}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{19}{27}\right)\)	\(e\left(\frac{23}{27}\right)\)	\(e\left(\frac{5}{27}\right)\)	\(e\left(\frac{47}{54}\right)\)
\(\chi_{648}(85,\cdot)\)	648.bd	54	yes	\(1\)	\(1\)	\(e\left(\frac{19}{54}\right)\)	\(e\left(\frac{16}{27}\right)\)	\(e\left(\frac{53}{54}\right)\)	\(e\left(\frac{43}{54}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{11}{27}\right)\)	\(e\left(\frac{19}{27}\right)\)	\(e\left(\frac{47}{54}\right)\)	\(e\left(\frac{20}{27}\right)\)
\(\chi_{648}(89,\cdot)\)	648.u	18	no	\(-1\)	\(1\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)
\(\chi_{648}(91,\cdot)\)	648.r	18	no	\(-1\)	\(1\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{7}{18}\right)\)
\(\chi_{648}(95,\cdot)\)	648.be	54	no	\(1\)	\(1\)	\(e\left(\frac{13}{54}\right)\)	\(e\left(\frac{29}{54}\right)\)	\(e\left(\frac{16}{27}\right)\)	\(e\left(\frac{14}{27}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{26}{27}\right)\)	\(e\left(\frac{13}{27}\right)\)	\(e\left(\frac{35}{54}\right)\)	\(e\left(\frac{43}{54}\right)\)

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