LMFDB - Group of Dirichlet characters of modulus 547

Show commands: PariGP / SageMath

sage: H = DirichletGroup(547)

pari: g = idealstar(,547,2)

Character group

sage: G.order() pari: g.no
Order	=	546
sage: H.invariants() pari: g.cyc
Structure	=	$C_{546}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{547}(2,\cdot)$

First 32 of 546 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{547}(1,\cdot)$	547.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{547}(2,\cdot)$	547.p	546	yes	$-1$	$1$	$e\left(\frac{1}{546}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{1}{273}\right)$	$e\left(\frac{179}{546}\right)$	$e\left(\frac{215}{273}\right)$	$e\left(\frac{103}{546}\right)$	$e\left(\frac{1}{182}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{30}{91}\right)$	$e\left(\frac{5}{39}\right)$
$\chi_{547}(3,\cdot)$	547.g	14	yes	$-1$	$1$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{3}{7}\right)$	$1$
$\chi_{547}(4,\cdot)$	547.o	273	yes	$1$	$1$	$e\left(\frac{1}{273}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{2}{273}\right)$	$e\left(\frac{179}{273}\right)$	$e\left(\frac{157}{273}\right)$	$e\left(\frac{103}{273}\right)$	$e\left(\frac{1}{91}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{60}{91}\right)$	$e\left(\frac{10}{39}\right)$
$\chi_{547}(5,\cdot)$	547.p	546	yes	$-1$	$1$	$e\left(\frac{179}{546}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{179}{273}\right)$	$e\left(\frac{373}{546}\right)$	$e\left(\frac{265}{273}\right)$	$e\left(\frac{419}{546}\right)$	$e\left(\frac{179}{182}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{1}{91}\right)$	$e\left(\frac{37}{39}\right)$
$\chi_{547}(6,\cdot)$	547.o	273	yes	$1$	$1$	$e\left(\frac{215}{273}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{157}{273}\right)$	$e\left(\frac{265}{273}\right)$	$e\left(\frac{176}{273}\right)$	$e\left(\frac{32}{273}\right)$	$e\left(\frac{33}{91}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{69}{91}\right)$	$e\left(\frac{5}{39}\right)$
$\chi_{547}(7,\cdot)$	547.p	546	yes	$-1$	$1$	$e\left(\frac{103}{546}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{103}{273}\right)$	$e\left(\frac{419}{546}\right)$	$e\left(\frac{32}{273}\right)$	$e\left(\frac{235}{546}\right)$	$e\left(\frac{103}{182}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{87}{91}\right)$	$e\left(\frac{8}{39}\right)$
$\chi_{547}(8,\cdot)$	547.n	182	yes	$-1$	$1$	$e\left(\frac{1}{182}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{1}{91}\right)$	$e\left(\frac{179}{182}\right)$	$e\left(\frac{33}{91}\right)$	$e\left(\frac{103}{182}\right)$	$e\left(\frac{3}{182}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{90}{91}\right)$	$e\left(\frac{5}{13}\right)$
$\chi_{547}(9,\cdot)$	547.e	7	yes	$1$	$1$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{6}{7}\right)$	$1$
$\chi_{547}(10,\cdot)$	547.m	91	yes	$1$	$1$	$e\left(\frac{30}{91}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{60}{91}\right)$	$e\left(\frac{1}{91}\right)$	$e\left(\frac{69}{91}\right)$	$e\left(\frac{87}{91}\right)$	$e\left(\frac{90}{91}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{31}{91}\right)$	$e\left(\frac{1}{13}\right)$
$\chi_{547}(11,\cdot)$	547.j	39	yes	$1$	$1$	$e\left(\frac{5}{39}\right)$	$1$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{5}{13}\right)$	$1$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{38}{39}\right)$
$\chi_{547}(12,\cdot)$	547.p	546	yes	$-1$	$1$	$e\left(\frac{431}{546}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{158}{273}\right)$	$e\left(\frac{163}{546}\right)$	$e\left(\frac{118}{273}\right)$	$e\left(\frac{167}{546}\right)$	$e\left(\frac{67}{182}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{8}{91}\right)$	$e\left(\frac{10}{39}\right)$
$\chi_{547}(13,\cdot)$	547.h	21	yes	$1$	$1$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{547}(14,\cdot)$	547.h	21	yes	$1$	$1$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{547}(15,\cdot)$	547.o	273	yes	$1$	$1$	$e\left(\frac{31}{273}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{62}{273}\right)$	$e\left(\frac{89}{273}\right)$	$e\left(\frac{226}{273}\right)$	$e\left(\frac{190}{273}\right)$	$e\left(\frac{31}{91}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{40}{91}\right)$	$e\left(\frac{37}{39}\right)$
$\chi_{547}(16,\cdot)$	547.o	273	yes	$1$	$1$	$e\left(\frac{2}{273}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{4}{273}\right)$	$e\left(\frac{85}{273}\right)$	$e\left(\frac{41}{273}\right)$	$e\left(\frac{206}{273}\right)$	$e\left(\frac{2}{91}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{29}{91}\right)$	$e\left(\frac{20}{39}\right)$
$\chi_{547}(17,\cdot)$	547.p	546	yes	$-1$	$1$	$e\left(\frac{151}{546}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{151}{273}\right)$	$e\left(\frac{275}{546}\right)$	$e\left(\frac{251}{273}\right)$	$e\left(\frac{265}{546}\right)$	$e\left(\frac{151}{182}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{71}{91}\right)$	$e\left(\frac{14}{39}\right)$
$\chi_{547}(18,\cdot)$	547.p	546	yes	$-1$	$1$	$e\left(\frac{313}{546}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{40}{273}\right)$	$e\left(\frac{335}{546}\right)$	$e\left(\frac{137}{273}\right)$	$e\left(\frac{25}{546}\right)$	$e\left(\frac{131}{182}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{17}{91}\right)$	$e\left(\frac{5}{39}\right)$
$\chi_{547}(19,\cdot)$	547.o	273	yes	$1$	$1$	$e\left(\frac{115}{273}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{230}{273}\right)$	$e\left(\frac{110}{273}\right)$	$e\left(\frac{37}{273}\right)$	$e\left(\frac{106}{273}\right)$	$e\left(\frac{24}{91}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{75}{91}\right)$	$e\left(\frac{19}{39}\right)$
$\chi_{547}(20,\cdot)$	547.p	546	yes	$-1$	$1$	$e\left(\frac{181}{546}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{181}{273}\right)$	$e\left(\frac{185}{546}\right)$	$e\left(\frac{149}{273}\right)$	$e\left(\frac{79}{546}\right)$	$e\left(\frac{181}{182}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{61}{91}\right)$	$e\left(\frac{8}{39}\right)$
$\chi_{547}(21,\cdot)$	547.j	39	yes	$1$	$1$	$e\left(\frac{38}{39}\right)$	$1$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{12}{13}\right)$	$1$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{8}{39}\right)$
$\chi_{547}(22,\cdot)$	547.p	546	yes	$-1$	$1$	$e\left(\frac{71}{546}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{71}{273}\right)$	$e\left(\frac{151}{546}\right)$	$e\left(\frac{250}{273}\right)$	$e\left(\frac{215}{546}\right)$	$e\left(\frac{71}{182}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{37}{91}\right)$	$e\left(\frac{4}{39}\right)$
$\chi_{547}(23,\cdot)$	547.p	546	yes	$-1$	$1$	$e\left(\frac{293}{546}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{20}{273}\right)$	$e\left(\frac{31}{546}\right)$	$e\left(\frac{205}{273}\right)$	$e\left(\frac{149}{546}\right)$	$e\left(\frac{111}{182}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{54}{91}\right)$	$e\left(\frac{22}{39}\right)$
$\chi_{547}(24,\cdot)$	547.m	91	yes	$1$	$1$	$e\left(\frac{72}{91}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{53}{91}\right)$	$e\left(\frac{57}{91}\right)$	$e\left(\frac{20}{91}\right)$	$e\left(\frac{45}{91}\right)$	$e\left(\frac{34}{91}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{38}{91}\right)$	$e\left(\frac{5}{13}\right)$
$\chi_{547}(25,\cdot)$	547.o	273	yes	$1$	$1$	$e\left(\frac{179}{273}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{85}{273}\right)$	$e\left(\frac{100}{273}\right)$	$e\left(\frac{257}{273}\right)$	$e\left(\frac{146}{273}\right)$	$e\left(\frac{88}{91}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{2}{91}\right)$	$e\left(\frac{35}{39}\right)$
$\chi_{547}(26,\cdot)$	547.l	78	yes	$-1$	$1$	$e\left(\frac{41}{78}\right)$	$-1$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{15}{26}\right)$	$1$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{31}{39}\right)$
$\chi_{547}(27,\cdot)$	547.g	14	yes	$-1$	$1$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{2}{7}\right)$	$1$
$\chi_{547}(28,\cdot)$	547.i	26	yes	$-1$	$1$	$e\left(\frac{5}{26}\right)$	$-1$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{15}{26}\right)$	$1$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{6}{13}\right)$
$\chi_{547}(29,\cdot)$	547.m	91	yes	$1$	$1$	$e\left(\frac{53}{91}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{15}{91}\right)$	$e\left(\frac{23}{91}\right)$	$e\left(\frac{40}{91}\right)$	$e\left(\frac{90}{91}\right)$	$e\left(\frac{68}{91}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{76}{91}\right)$	$e\left(\frac{10}{13}\right)$
$\chi_{547}(30,\cdot)$	547.i	26	yes	$-1$	$1$	$e\left(\frac{3}{26}\right)$	$-1$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{9}{26}\right)$	$1$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{1}{13}\right)$
$\chi_{547}(31,\cdot)$	547.n	182	yes	$-1$	$1$	$e\left(\frac{101}{182}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{10}{91}\right)$	$e\left(\frac{61}{182}\right)$	$e\left(\frac{57}{91}\right)$	$e\left(\frac{29}{182}\right)$	$e\left(\frac{121}{182}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{81}{91}\right)$	$e\left(\frac{11}{13}\right)$
$\chi_{547}(32,\cdot)$	547.p	546	yes	$-1$	$1$	$e\left(\frac{5}{546}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{5}{273}\right)$	$e\left(\frac{349}{546}\right)$	$e\left(\frac{256}{273}\right)$	$e\left(\frac{515}{546}\right)$	$e\left(\frac{5}{182}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{59}{91}\right)$	$e\left(\frac{25}{39}\right)$

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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	$547$
Structure	\(C_{546}\)
Order	$546$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{547}(1,\cdot)\)	547.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{547}(2,\cdot)\)	547.p	546	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{546}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{1}{273}\right)\)	\(e\left(\frac{179}{546}\right)\)	\(e\left(\frac{215}{273}\right)\)	\(e\left(\frac{103}{546}\right)\)	\(e\left(\frac{1}{182}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{30}{91}\right)\)	\(e\left(\frac{5}{39}\right)\)
\(\chi_{547}(3,\cdot)\)	547.g	14	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(1\)
\(\chi_{547}(4,\cdot)\)	547.o	273	yes	\(1\)	\(1\)	\(e\left(\frac{1}{273}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{2}{273}\right)\)	\(e\left(\frac{179}{273}\right)\)	\(e\left(\frac{157}{273}\right)\)	\(e\left(\frac{103}{273}\right)\)	\(e\left(\frac{1}{91}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{60}{91}\right)\)	\(e\left(\frac{10}{39}\right)\)
\(\chi_{547}(5,\cdot)\)	547.p	546	yes	\(-1\)	\(1\)	\(e\left(\frac{179}{546}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{179}{273}\right)\)	\(e\left(\frac{373}{546}\right)\)	\(e\left(\frac{265}{273}\right)\)	\(e\left(\frac{419}{546}\right)\)	\(e\left(\frac{179}{182}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{1}{91}\right)\)	\(e\left(\frac{37}{39}\right)\)
\(\chi_{547}(6,\cdot)\)	547.o	273	yes	\(1\)	\(1\)	\(e\left(\frac{215}{273}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{157}{273}\right)\)	\(e\left(\frac{265}{273}\right)\)	\(e\left(\frac{176}{273}\right)\)	\(e\left(\frac{32}{273}\right)\)	\(e\left(\frac{33}{91}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{69}{91}\right)\)	\(e\left(\frac{5}{39}\right)\)
\(\chi_{547}(7,\cdot)\)	547.p	546	yes	\(-1\)	\(1\)	\(e\left(\frac{103}{546}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{103}{273}\right)\)	\(e\left(\frac{419}{546}\right)\)	\(e\left(\frac{32}{273}\right)\)	\(e\left(\frac{235}{546}\right)\)	\(e\left(\frac{103}{182}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{87}{91}\right)\)	\(e\left(\frac{8}{39}\right)\)
\(\chi_{547}(8,\cdot)\)	547.n	182	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{182}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{1}{91}\right)\)	\(e\left(\frac{179}{182}\right)\)	\(e\left(\frac{33}{91}\right)\)	\(e\left(\frac{103}{182}\right)\)	\(e\left(\frac{3}{182}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{90}{91}\right)\)	\(e\left(\frac{5}{13}\right)\)
\(\chi_{547}(9,\cdot)\)	547.e	7	yes	\(1\)	\(1\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(1\)
\(\chi_{547}(10,\cdot)\)	547.m	91	yes	\(1\)	\(1\)	\(e\left(\frac{30}{91}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{60}{91}\right)\)	\(e\left(\frac{1}{91}\right)\)	\(e\left(\frac{69}{91}\right)\)	\(e\left(\frac{87}{91}\right)\)	\(e\left(\frac{90}{91}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{31}{91}\right)\)	\(e\left(\frac{1}{13}\right)\)
\(\chi_{547}(11,\cdot)\)	547.j	39	yes	\(1\)	\(1\)	\(e\left(\frac{5}{39}\right)\)	\(1\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(1\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{38}{39}\right)\)
\(\chi_{547}(12,\cdot)\)	547.p	546	yes	\(-1\)	\(1\)	\(e\left(\frac{431}{546}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{158}{273}\right)\)	\(e\left(\frac{163}{546}\right)\)	\(e\left(\frac{118}{273}\right)\)	\(e\left(\frac{167}{546}\right)\)	\(e\left(\frac{67}{182}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{8}{91}\right)\)	\(e\left(\frac{10}{39}\right)\)
\(\chi_{547}(13,\cdot)\)	547.h	21	yes	\(1\)	\(1\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{547}(14,\cdot)\)	547.h	21	yes	\(1\)	\(1\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{547}(15,\cdot)\)	547.o	273	yes	\(1\)	\(1\)	\(e\left(\frac{31}{273}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{62}{273}\right)\)	\(e\left(\frac{89}{273}\right)\)	\(e\left(\frac{226}{273}\right)\)	\(e\left(\frac{190}{273}\right)\)	\(e\left(\frac{31}{91}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{40}{91}\right)\)	\(e\left(\frac{37}{39}\right)\)
\(\chi_{547}(16,\cdot)\)	547.o	273	yes	\(1\)	\(1\)	\(e\left(\frac{2}{273}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{4}{273}\right)\)	\(e\left(\frac{85}{273}\right)\)	\(e\left(\frac{41}{273}\right)\)	\(e\left(\frac{206}{273}\right)\)	\(e\left(\frac{2}{91}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{29}{91}\right)\)	\(e\left(\frac{20}{39}\right)\)
\(\chi_{547}(17,\cdot)\)	547.p	546	yes	\(-1\)	\(1\)	\(e\left(\frac{151}{546}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{151}{273}\right)\)	\(e\left(\frac{275}{546}\right)\)	\(e\left(\frac{251}{273}\right)\)	\(e\left(\frac{265}{546}\right)\)	\(e\left(\frac{151}{182}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{71}{91}\right)\)	\(e\left(\frac{14}{39}\right)\)
\(\chi_{547}(18,\cdot)\)	547.p	546	yes	\(-1\)	\(1\)	\(e\left(\frac{313}{546}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{40}{273}\right)\)	\(e\left(\frac{335}{546}\right)\)	\(e\left(\frac{137}{273}\right)\)	\(e\left(\frac{25}{546}\right)\)	\(e\left(\frac{131}{182}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{17}{91}\right)\)	\(e\left(\frac{5}{39}\right)\)
\(\chi_{547}(19,\cdot)\)	547.o	273	yes	\(1\)	\(1\)	\(e\left(\frac{115}{273}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{230}{273}\right)\)	\(e\left(\frac{110}{273}\right)\)	\(e\left(\frac{37}{273}\right)\)	\(e\left(\frac{106}{273}\right)\)	\(e\left(\frac{24}{91}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{75}{91}\right)\)	\(e\left(\frac{19}{39}\right)\)
\(\chi_{547}(20,\cdot)\)	547.p	546	yes	\(-1\)	\(1\)	\(e\left(\frac{181}{546}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{181}{273}\right)\)	\(e\left(\frac{185}{546}\right)\)	\(e\left(\frac{149}{273}\right)\)	\(e\left(\frac{79}{546}\right)\)	\(e\left(\frac{181}{182}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{61}{91}\right)\)	\(e\left(\frac{8}{39}\right)\)
\(\chi_{547}(21,\cdot)\)	547.j	39	yes	\(1\)	\(1\)	\(e\left(\frac{38}{39}\right)\)	\(1\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(1\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{8}{39}\right)\)
\(\chi_{547}(22,\cdot)\)	547.p	546	yes	\(-1\)	\(1\)	\(e\left(\frac{71}{546}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{71}{273}\right)\)	\(e\left(\frac{151}{546}\right)\)	\(e\left(\frac{250}{273}\right)\)	\(e\left(\frac{215}{546}\right)\)	\(e\left(\frac{71}{182}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{37}{91}\right)\)	\(e\left(\frac{4}{39}\right)\)
\(\chi_{547}(23,\cdot)\)	547.p	546	yes	\(-1\)	\(1\)	\(e\left(\frac{293}{546}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{20}{273}\right)\)	\(e\left(\frac{31}{546}\right)\)	\(e\left(\frac{205}{273}\right)\)	\(e\left(\frac{149}{546}\right)\)	\(e\left(\frac{111}{182}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{54}{91}\right)\)	\(e\left(\frac{22}{39}\right)\)
\(\chi_{547}(24,\cdot)\)	547.m	91	yes	\(1\)	\(1\)	\(e\left(\frac{72}{91}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{53}{91}\right)\)	\(e\left(\frac{57}{91}\right)\)	\(e\left(\frac{20}{91}\right)\)	\(e\left(\frac{45}{91}\right)\)	\(e\left(\frac{34}{91}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{38}{91}\right)\)	\(e\left(\frac{5}{13}\right)\)
\(\chi_{547}(25,\cdot)\)	547.o	273	yes	\(1\)	\(1\)	\(e\left(\frac{179}{273}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{85}{273}\right)\)	\(e\left(\frac{100}{273}\right)\)	\(e\left(\frac{257}{273}\right)\)	\(e\left(\frac{146}{273}\right)\)	\(e\left(\frac{88}{91}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{2}{91}\right)\)	\(e\left(\frac{35}{39}\right)\)
\(\chi_{547}(26,\cdot)\)	547.l	78	yes	\(-1\)	\(1\)	\(e\left(\frac{41}{78}\right)\)	\(-1\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(1\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{31}{39}\right)\)
\(\chi_{547}(27,\cdot)\)	547.g	14	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(1\)
\(\chi_{547}(28,\cdot)\)	547.i	26	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{26}\right)\)	\(-1\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(1\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{6}{13}\right)\)
\(\chi_{547}(29,\cdot)\)	547.m	91	yes	\(1\)	\(1\)	\(e\left(\frac{53}{91}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{15}{91}\right)\)	\(e\left(\frac{23}{91}\right)\)	\(e\left(\frac{40}{91}\right)\)	\(e\left(\frac{90}{91}\right)\)	\(e\left(\frac{68}{91}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{76}{91}\right)\)	\(e\left(\frac{10}{13}\right)\)
\(\chi_{547}(30,\cdot)\)	547.i	26	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{26}\right)\)	\(-1\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(1\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{1}{13}\right)\)
\(\chi_{547}(31,\cdot)\)	547.n	182	yes	\(-1\)	\(1\)	\(e\left(\frac{101}{182}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{10}{91}\right)\)	\(e\left(\frac{61}{182}\right)\)	\(e\left(\frac{57}{91}\right)\)	\(e\left(\frac{29}{182}\right)\)	\(e\left(\frac{121}{182}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{81}{91}\right)\)	\(e\left(\frac{11}{13}\right)\)
\(\chi_{547}(32,\cdot)\)	547.p	546	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{546}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{5}{273}\right)\)	\(e\left(\frac{349}{546}\right)\)	\(e\left(\frac{256}{273}\right)\)	\(e\left(\frac{515}{546}\right)\)	\(e\left(\frac{5}{182}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{59}{91}\right)\)	\(e\left(\frac{25}{39}\right)\)

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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.