LMFDB - Group of Dirichlet characters of modulus 1305

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(1305)

gp:g = idealstar(,1305,2)

magma:G = FullDirichletGroup(1305);

Character group

Order	=	672	comment:Order sage:G.order() gp:g.no magma:Order(G);
Structure	=	$C_{2}\times C_{4}\times C_{84}$	comment:Group structure sage:sorted(g.order() for g in G.gens()) gp:g.cyc magma:PrimaryInvariants(G);
Generators	=	$\chi_{1305}(146,\cdot)$, $\chi_{1305}(262,\cdot)$, $\chi_{1305}(901,\cdot)$	comment:Generators sage:G.gens() gp:g.gen magma:Generators(G);

First 32 of 672 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	$-1$	$1$	$2$	$4$	$7$	$8$	$11$	$13$	$14$	$16$	$17$	$19$
$\chi_{1305}(1,\cdot)$	1305.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1305}(2,\cdot)$	1305.cr	84	yes	$-1$	$1$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{17}{21}\right)$	$-1$	$e\left(\frac{23}{28}\right)$
$\chi_{1305}(4,\cdot)$	1305.co	42	yes	$1$	$1$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{13}{21}\right)$	$1$	$e\left(\frac{9}{14}\right)$
$\chi_{1305}(7,\cdot)$	1305.cx	84	yes	$-1$	$1$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{8}{21}\right)$	$i$	$e\left(\frac{5}{14}\right)$
$\chi_{1305}(8,\cdot)$	1305.ci	28	no	$-1$	$1$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{3}{7}\right)$	$-1$	$e\left(\frac{13}{28}\right)$
$\chi_{1305}(11,\cdot)$	1305.cy	84	no	$1$	$1$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{5}{21}\right)$	$i$	$e\left(\frac{1}{28}\right)$
$\chi_{1305}(13,\cdot)$	1305.cu	84	yes	$-1$	$1$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{19}{21}\right)$	$i$	$e\left(\frac{2}{7}\right)$
$\chi_{1305}(14,\cdot)$	1305.ct	84	yes	$1$	$1$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{4}{21}\right)$	$-i$	$e\left(\frac{5}{28}\right)$
$\chi_{1305}(16,\cdot)$	1305.bw	21	no	$1$	$1$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{5}{21}\right)$	$1$	$e\left(\frac{2}{7}\right)$
$\chi_{1305}(17,\cdot)$	1305.j	4	no	$-1$	$1$	$-1$	$1$	$i$	$-1$	$i$	$i$	$-i$	$1$	$-1$	$i$
$\chi_{1305}(19,\cdot)$	1305.cg	28	no	$-1$	$1$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{2}{7}\right)$	$i$	$e\left(\frac{25}{28}\right)$
$\chi_{1305}(22,\cdot)$	1305.cu	84	yes	$-1$	$1$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{1}{21}\right)$	$-i$	$e\left(\frac{6}{7}\right)$
$\chi_{1305}(23,\cdot)$	1305.cv	84	yes	$1$	$1$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{4}{21}\right)$	$i$	$e\left(\frac{13}{14}\right)$
$\chi_{1305}(26,\cdot)$	1305.ca	28	no	$1$	$1$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{5}{7}\right)$	$-i$	$e\left(\frac{3}{28}\right)$
$\chi_{1305}(28,\cdot)$	1305.o	4	no	$-1$	$1$	$i$	$-1$	$-i$	$-i$	$-1$	$i$	$1$	$1$	$i$	$1$
$\chi_{1305}(31,\cdot)$	1305.cz	84	no	$-1$	$1$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{10}{21}\right)$	$-i$	$e\left(\frac{9}{28}\right)$
$\chi_{1305}(32,\cdot)$	1305.cr	84	yes	$-1$	$1$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{1}{21}\right)$	$-1$	$e\left(\frac{3}{28}\right)$
$\chi_{1305}(34,\cdot)$	1305.co	42	yes	$1$	$1$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{17}{21}\right)$	$1$	$e\left(\frac{1}{14}\right)$
$\chi_{1305}(37,\cdot)$	1305.ch	28	no	$1$	$1$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{3}{7}\right)$	$-1$	$e\left(\frac{13}{28}\right)$
$\chi_{1305}(38,\cdot)$	1305.cw	84	yes	$1$	$1$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{2}{21}\right)$	$-i$	$e\left(\frac{5}{7}\right)$
$\chi_{1305}(41,\cdot)$	1305.bg	12	no	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$i$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$-i$	$i$
$\chi_{1305}(43,\cdot)$	1305.cq	84	yes	$1$	$1$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{11}{21}\right)$	$-1$	$e\left(\frac{19}{28}\right)$
$\chi_{1305}(44,\cdot)$	1305.cf	28	no	$1$	$1$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{6}{7}\right)$	$i$	$e\left(\frac{19}{28}\right)$
$\chi_{1305}(46,\cdot)$	1305.s	4	no	$-1$	$1$	$-i$	$-1$	$1$	$i$	$-i$	$-1$	$-i$	$1$	$-i$	$-i$
$\chi_{1305}(47,\cdot)$	1305.da	84	yes	$-1$	$1$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{5}{21}\right)$	$1$	$e\left(\frac{1}{28}\right)$
$\chi_{1305}(49,\cdot)$	1305.cj	42	yes	$1$	$1$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{16}{21}\right)$	$-1$	$e\left(\frac{5}{7}\right)$
$\chi_{1305}(52,\cdot)$	1305.cx	84	yes	$-1$	$1$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{11}{21}\right)$	$i$	$e\left(\frac{13}{14}\right)$
$\chi_{1305}(53,\cdot)$	1305.ce	28	no	$1$	$1$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{1}{7}\right)$	$i$	$e\left(\frac{1}{14}\right)$
$\chi_{1305}(56,\cdot)$	1305.cy	84	no	$1$	$1$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{17}{21}\right)$	$-i$	$e\left(\frac{23}{28}\right)$
$\chi_{1305}(59,\cdot)$	1305.x	6	no	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$1$
$\chi_{1305}(61,\cdot)$	1305.cz	84	no	$-1$	$1$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{8}{21}\right)$	$-i$	$e\left(\frac{17}{28}\right)$
$\chi_{1305}(62,\cdot)$	1305.cb	28	no	$1$	$1$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{2}{7}\right)$	$i$	$e\left(\frac{1}{7}\right)$

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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 $\F_{q}$
Belyi maps

Modulus	$1305$
Structure	\(C_{2}\times C_{4}\times C_{84}\)
Order	$672$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(7\)	\(8\)	\(11\)	\(13\)	\(14\)	\(16\)	\(17\)	\(19\)
\(\chi_{1305}(1,\cdot)\)	1305.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1305}(2,\cdot)\)	1305.cr	84	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(-1\)	\(e\left(\frac{23}{28}\right)\)
\(\chi_{1305}(4,\cdot)\)	1305.co	42	yes	\(1\)	\(1\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(1\)	\(e\left(\frac{9}{14}\right)\)
\(\chi_{1305}(7,\cdot)\)	1305.cx	84	yes	\(-1\)	\(1\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(i\)	\(e\left(\frac{5}{14}\right)\)
\(\chi_{1305}(8,\cdot)\)	1305.ci	28	no	\(-1\)	\(1\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(-1\)	\(e\left(\frac{13}{28}\right)\)
\(\chi_{1305}(11,\cdot)\)	1305.cy	84	no	\(1\)	\(1\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(i\)	\(e\left(\frac{1}{28}\right)\)
\(\chi_{1305}(13,\cdot)\)	1305.cu	84	yes	\(-1\)	\(1\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(i\)	\(e\left(\frac{2}{7}\right)\)
\(\chi_{1305}(14,\cdot)\)	1305.ct	84	yes	\(1\)	\(1\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(-i\)	\(e\left(\frac{5}{28}\right)\)
\(\chi_{1305}(16,\cdot)\)	1305.bw	21	no	\(1\)	\(1\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(1\)	\(e\left(\frac{2}{7}\right)\)
\(\chi_{1305}(17,\cdot)\)	1305.j	4	no	\(-1\)	\(1\)	\(-1\)	\(1\)	\(i\)	\(-1\)	\(i\)	\(i\)	\(-i\)	\(1\)	\(-1\)	\(i\)
\(\chi_{1305}(19,\cdot)\)	1305.cg	28	no	\(-1\)	\(1\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(i\)	\(e\left(\frac{25}{28}\right)\)
\(\chi_{1305}(22,\cdot)\)	1305.cu	84	yes	\(-1\)	\(1\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(-i\)	\(e\left(\frac{6}{7}\right)\)
\(\chi_{1305}(23,\cdot)\)	1305.cv	84	yes	\(1\)	\(1\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(i\)	\(e\left(\frac{13}{14}\right)\)
\(\chi_{1305}(26,\cdot)\)	1305.ca	28	no	\(1\)	\(1\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(-i\)	\(e\left(\frac{3}{28}\right)\)
\(\chi_{1305}(28,\cdot)\)	1305.o	4	no	\(-1\)	\(1\)	\(i\)	\(-1\)	\(-i\)	\(-i\)	\(-1\)	\(i\)	\(1\)	\(1\)	\(i\)	\(1\)
\(\chi_{1305}(31,\cdot)\)	1305.cz	84	no	\(-1\)	\(1\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(-i\)	\(e\left(\frac{9}{28}\right)\)
\(\chi_{1305}(32,\cdot)\)	1305.cr	84	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(-1\)	\(e\left(\frac{3}{28}\right)\)
\(\chi_{1305}(34,\cdot)\)	1305.co	42	yes	\(1\)	\(1\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(1\)	\(e\left(\frac{1}{14}\right)\)
\(\chi_{1305}(37,\cdot)\)	1305.ch	28	no	\(1\)	\(1\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(-1\)	\(e\left(\frac{13}{28}\right)\)
\(\chi_{1305}(38,\cdot)\)	1305.cw	84	yes	\(1\)	\(1\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(-i\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{1305}(41,\cdot)\)	1305.bg	12	no	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(i\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-i\)	\(i\)
\(\chi_{1305}(43,\cdot)\)	1305.cq	84	yes	\(1\)	\(1\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(-1\)	\(e\left(\frac{19}{28}\right)\)
\(\chi_{1305}(44,\cdot)\)	1305.cf	28	no	\(1\)	\(1\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(i\)	\(e\left(\frac{19}{28}\right)\)
\(\chi_{1305}(46,\cdot)\)	1305.s	4	no	\(-1\)	\(1\)	\(-i\)	\(-1\)	\(1\)	\(i\)	\(-i\)	\(-1\)	\(-i\)	\(1\)	\(-i\)	\(-i\)
\(\chi_{1305}(47,\cdot)\)	1305.da	84	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(1\)	\(e\left(\frac{1}{28}\right)\)
\(\chi_{1305}(49,\cdot)\)	1305.cj	42	yes	\(1\)	\(1\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(-1\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{1305}(52,\cdot)\)	1305.cx	84	yes	\(-1\)	\(1\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(i\)	\(e\left(\frac{13}{14}\right)\)
\(\chi_{1305}(53,\cdot)\)	1305.ce	28	no	\(1\)	\(1\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(i\)	\(e\left(\frac{1}{14}\right)\)
\(\chi_{1305}(56,\cdot)\)	1305.cy	84	no	\(1\)	\(1\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(-i\)	\(e\left(\frac{23}{28}\right)\)
\(\chi_{1305}(59,\cdot)\)	1305.x	6	no	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(1\)
\(\chi_{1305}(61,\cdot)\)	1305.cz	84	no	\(-1\)	\(1\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(-i\)	\(e\left(\frac{17}{28}\right)\)
\(\chi_{1305}(62,\cdot)\)	1305.cb	28	no	\(1\)	\(1\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(i\)	\(e\left(\frac{1}{7}\right)\)

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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.