LMFDB - Group of Dirichlet characters of modulus 528

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(528)

gp:g = idealstar(,528,2)

magma:G = FullDirichletGroup(528);

Character group

Order	=	160	comment:Order sage:G.order() gp:g.no magma:Order(G);
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{20}$	comment:Group structure sage:sorted(g.order() for g in G.gens()) gp:g.cyc magma:PrimaryInvariants(G);
Generators	=	$\chi_{528}(463,\cdot)$, $\chi_{528}(133,\cdot)$, $\chi_{528}(353,\cdot)$, $\chi_{528}(145,\cdot)$	comment:Generators sage:G.gens() gp:g.gen magma:Generators(G);

First 32 of 160 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	$-1$	$1$	$5$	$7$	$13$	$17$	$19$	$23$	$25$	$29$	$31$	$35$
$\chi_{528}(1,\cdot)$	528.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{528}(5,\cdot)$	528.bu	20	yes	$-1$	$1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{19}{20}\right)$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{13}{20}\right)$
$\chi_{528}(7,\cdot)$	528.bh	10	no	$1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{10}\right)$	$-1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{528}(13,\cdot)$	528.bq	20	no	$-1$	$1$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{11}{20}\right)$	$-1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{20}\right)$
$\chi_{528}(17,\cdot)$	528.bn	10	no	$1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{10}\right)$	$-1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{528}(19,\cdot)$	528.bv	20	no	$1$	$1$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{13}{20}\right)$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{20}\right)$
$\chi_{528}(23,\cdot)$	528.k	2	no	$1$	$1$	$1$	$-1$	$-1$	$-1$	$1$	$1$	$1$	$1$	$-1$	$-1$
$\chi_{528}(25,\cdot)$	528.bj	10	no	$1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{9}{10}\right)$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{528}(29,\cdot)$	528.bo	20	yes	$1$	$1$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{20}\right)$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{9}{20}\right)$
$\chi_{528}(31,\cdot)$	528.bd	10	no	$-1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{10}\right)$	$-1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{528}(35,\cdot)$	528.bt	20	yes	$-1$	$1$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{20}\right)$	$-1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{20}\right)$
$\chi_{528}(37,\cdot)$	528.bs	20	no	$1$	$1$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{20}\right)$	$-1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{19}{20}\right)$
$\chi_{528}(41,\cdot)$	528.bc	10	no	$1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{5}\right)$	$-1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{528}(43,\cdot)$	528.q	4	no	$1$	$1$	$i$	$-1$	$i$	$-1$	$-i$	$1$	$-1$	$i$	$-1$	$-i$
$\chi_{528}(47,\cdot)$	528.bl	10	no	$1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{10}\right)$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{528}(49,\cdot)$	528.y	5	no	$1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{5}\right)$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{528}(53,\cdot)$	528.bu	20	yes	$-1$	$1$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{11}{20}\right)$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{17}{20}\right)$
$\chi_{528}(59,\cdot)$	528.br	20	yes	$1$	$1$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{17}{20}\right)$	$-1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{19}{20}\right)$
$\chi_{528}(61,\cdot)$	528.bq	20	no	$-1$	$1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{19}{20}\right)$	$-1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{20}\right)$
$\chi_{528}(65,\cdot)$	528.b	2	no	$1$	$1$	$-1$	$-1$	$-1$	$1$	$-1$	$-1$	$1$	$1$	$1$	$1$
$\chi_{528}(67,\cdot)$	528.w	4	no	$-1$	$1$	$-i$	$1$	$i$	$1$	$-i$	$1$	$-1$	$i$	$-1$	$-i$
$\chi_{528}(71,\cdot)$	528.be	10	no	$1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{5}\right)$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{528}(73,\cdot)$	528.bk	10	no	$-1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{5}\right)$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{528}(79,\cdot)$	528.ba	10	no	$1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{5}\right)$	$-1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{528}(83,\cdot)$	528.bt	20	yes	$-1$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{9}{20}\right)$	$-1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{20}\right)$
$\chi_{528}(85,\cdot)$	528.bq	20	no	$-1$	$1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{13}{20}\right)$	$-1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{20}\right)$
$\chi_{528}(89,\cdot)$	528.n	2	no	$-1$	$1$	$1$	$1$	$-1$	$-1$	$-1$	$-1$	$1$	$1$	$1$	$1$
$\chi_{528}(91,\cdot)$	528.bp	20	no	$-1$	$1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{13}{20}\right)$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{20}\right)$
$\chi_{528}(95,\cdot)$	528.bi	10	no	$-1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{528}(97,\cdot)$	528.y	5	no	$1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{528}(101,\cdot)$	528.bo	20	yes	$1$	$1$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{20}\right)$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{20}\right)$
$\chi_{528}(103,\cdot)$	528.bm	10	no	$-1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$	$-1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{5}\right)$

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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	$528$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{20}\)
Order	$160$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(7\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(35\)
\(\chi_{528}(1,\cdot)\)	528.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{528}(5,\cdot)\)	528.bu	20	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{13}{20}\right)\)
\(\chi_{528}(7,\cdot)\)	528.bh	10	no	\(1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(-1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{528}(13,\cdot)\)	528.bq	20	no	\(-1\)	\(1\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(-1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{20}\right)\)
\(\chi_{528}(17,\cdot)\)	528.bn	10	no	\(1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(-1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{528}(19,\cdot)\)	528.bv	20	no	\(1\)	\(1\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{20}\right)\)
\(\chi_{528}(23,\cdot)\)	528.k	2	no	\(1\)	\(1\)	\(1\)	\(-1\)	\(-1\)	\(-1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(-1\)	\(-1\)
\(\chi_{528}(25,\cdot)\)	528.bj	10	no	\(1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{528}(29,\cdot)\)	528.bo	20	yes	\(1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{9}{20}\right)\)
\(\chi_{528}(31,\cdot)\)	528.bd	10	no	\(-1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(-1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{528}(35,\cdot)\)	528.bt	20	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(-1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)
\(\chi_{528}(37,\cdot)\)	528.bs	20	no	\(1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(-1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{19}{20}\right)\)
\(\chi_{528}(41,\cdot)\)	528.bc	10	no	\(1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(-1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{528}(43,\cdot)\)	528.q	4	no	\(1\)	\(1\)	\(i\)	\(-1\)	\(i\)	\(-1\)	\(-i\)	\(1\)	\(-1\)	\(i\)	\(-1\)	\(-i\)
\(\chi_{528}(47,\cdot)\)	528.bl	10	no	\(1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{528}(49,\cdot)\)	528.y	5	no	\(1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{528}(53,\cdot)\)	528.bu	20	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{17}{20}\right)\)
\(\chi_{528}(59,\cdot)\)	528.br	20	yes	\(1\)	\(1\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(-1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)
\(\chi_{528}(61,\cdot)\)	528.bq	20	no	\(-1\)	\(1\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(-1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{20}\right)\)
\(\chi_{528}(65,\cdot)\)	528.b	2	no	\(1\)	\(1\)	\(-1\)	\(-1\)	\(-1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{528}(67,\cdot)\)	528.w	4	no	\(-1\)	\(1\)	\(-i\)	\(1\)	\(i\)	\(1\)	\(-i\)	\(1\)	\(-1\)	\(i\)	\(-1\)	\(-i\)
\(\chi_{528}(71,\cdot)\)	528.be	10	no	\(1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{528}(73,\cdot)\)	528.bk	10	no	\(-1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{528}(79,\cdot)\)	528.ba	10	no	\(1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(-1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{528}(83,\cdot)\)	528.bt	20	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(-1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{20}\right)\)
\(\chi_{528}(85,\cdot)\)	528.bq	20	no	\(-1\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(-1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{20}\right)\)
\(\chi_{528}(89,\cdot)\)	528.n	2	no	\(-1\)	\(1\)	\(1\)	\(1\)	\(-1\)	\(-1\)	\(-1\)	\(-1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{528}(91,\cdot)\)	528.bp	20	no	\(-1\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{20}\right)\)
\(\chi_{528}(95,\cdot)\)	528.bi	10	no	\(-1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{528}(97,\cdot)\)	528.y	5	no	\(1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{528}(101,\cdot)\)	528.bo	20	yes	\(1\)	\(1\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{20}\right)\)
\(\chi_{528}(103,\cdot)\)	528.bm	10	no	\(-1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(-1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)

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