LMFDB - Group of Dirichlet characters of modulus 338

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(338)

gp:g = idealstar(,338,2)

magma:G = FullDirichletGroup(338);

Character group

Order	=	156	comment:Order sage:G.order() gp:g.no magma:Order(G);
Structure	=	$C_{156}$	comment:Group structure sage:sorted(g.order() for g in G.gens()) gp:g.cyc magma:PrimaryInvariants(G);
Generators	=	$\chi_{338}(171,\cdot)$	comment:Generators sage:G.gens() gp:g.gen magma:Generators(G);

First 32 of 156 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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$15$	$17$	$19$	$21$	$23$
$\chi_{338}(1,\cdot)$	338.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{338}(3,\cdot)$	338.i	39	no	$1$	$1$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{338}(5,\cdot)$	338.j	52	no	$-1$	$1$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{11}{26}\right)$	$-i$	$e\left(\frac{17}{52}\right)$	$-1$
$\chi_{338}(7,\cdot)$	338.l	156	no	$-1$	$1$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{61}{156}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{101}{156}\right)$	$e\left(\frac{35}{156}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{338}(9,\cdot)$	338.i	39	no	$1$	$1$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{338}(11,\cdot)$	338.l	156	no	$-1$	$1$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{101}{156}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{1}{156}\right)$	$e\left(\frac{127}{156}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{338}(15,\cdot)$	338.l	156	no	$-1$	$1$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{35}{156}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{127}{156}\right)$	$e\left(\frac{61}{156}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{338}(17,\cdot)$	338.k	78	no	$1$	$1$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{338}(19,\cdot)$	338.f	12	no	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$-i$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{12}\right)$	$i$	$e\left(\frac{1}{6}\right)$
$\chi_{338}(21,\cdot)$	338.j	52	no	$-1$	$1$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{5}{26}\right)$	$i$	$e\left(\frac{3}{52}\right)$	$-1$
$\chi_{338}(23,\cdot)$	338.e	6	no	$1$	$1$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{3}\right)$
$\chi_{338}(25,\cdot)$	338.h	26	no	$1$	$1$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{11}{13}\right)$	$-1$	$e\left(\frac{17}{26}\right)$	$1$
$\chi_{338}(27,\cdot)$	338.g	13	no	$1$	$1$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{2}{13}\right)$	$1$	$e\left(\frac{11}{13}\right)$	$1$
$\chi_{338}(29,\cdot)$	338.i	39	no	$1$	$1$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{338}(31,\cdot)$	338.j	52	no	$-1$	$1$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{17}{26}\right)$	$-i$	$e\left(\frac{5}{52}\right)$	$-1$
$\chi_{338}(33,\cdot)$	338.l	156	no	$-1$	$1$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{109}{156}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{137}{156}\right)$	$e\left(\frac{83}{156}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{338}(35,\cdot)$	338.i	39	no	$1$	$1$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{338}(37,\cdot)$	338.l	156	no	$-1$	$1$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{89}{156}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{109}{156}\right)$	$e\left(\frac{115}{156}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{338}(41,\cdot)$	338.l	156	no	$-1$	$1$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{47}{156}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{19}{156}\right)$	$e\left(\frac{73}{156}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{338}(43,\cdot)$	338.k	78	no	$1$	$1$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{338}(45,\cdot)$	338.l	156	no	$-1$	$1$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{43}{156}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{107}{156}\right)$	$e\left(\frac{17}{156}\right)$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{338}(47,\cdot)$	338.j	52	no	$-1$	$1$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{25}{26}\right)$	$i$	$e\left(\frac{15}{52}\right)$	$-1$
$\chi_{338}(49,\cdot)$	338.k	78	no	$1$	$1$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{338}(51,\cdot)$	338.h	26	no	$1$	$1$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{9}{13}\right)$	$-1$	$e\left(\frac{21}{26}\right)$	$1$
$\chi_{338}(53,\cdot)$	338.g	13	no	$1$	$1$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{4}{13}\right)$	$1$	$e\left(\frac{9}{13}\right)$	$1$
$\chi_{338}(55,\cdot)$	338.i	39	no	$1$	$1$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{338}(57,\cdot)$	338.j	52	no	$-1$	$1$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{23}{26}\right)$	$-i$	$e\left(\frac{45}{52}\right)$	$-1$
$\chi_{338}(59,\cdot)$	338.l	156	no	$-1$	$1$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{1}{156}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{17}{156}\right)$	$e\left(\frac{131}{156}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{338}(61,\cdot)$	338.i	39	no	$1$	$1$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{338}(63,\cdot)$	338.l	156	no	$-1$	$1$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{77}{156}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{61}{156}\right)$	$e\left(\frac{103}{156}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{338}(67,\cdot)$	338.l	156	no	$-1$	$1$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{59}{156}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{67}{156}\right)$	$e\left(\frac{85}{156}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{338}(69,\cdot)$	338.k	78	no	$1$	$1$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{2}{3}\right)$

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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	$338$
Structure	\(C_{156}\)
Order	$156$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(15\)	\(17\)	\(19\)	\(21\)	\(23\)
\(\chi_{338}(1,\cdot)\)	338.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{338}(3,\cdot)\)	338.i	39	no	\(1\)	\(1\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{338}(5,\cdot)\)	338.j	52	no	\(-1\)	\(1\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(-i\)	\(e\left(\frac{17}{52}\right)\)	\(-1\)
\(\chi_{338}(7,\cdot)\)	338.l	156	no	\(-1\)	\(1\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{61}{156}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{101}{156}\right)\)	\(e\left(\frac{35}{156}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{338}(9,\cdot)\)	338.i	39	no	\(1\)	\(1\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{338}(11,\cdot)\)	338.l	156	no	\(-1\)	\(1\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{101}{156}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{1}{156}\right)\)	\(e\left(\frac{127}{156}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{338}(15,\cdot)\)	338.l	156	no	\(-1\)	\(1\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{35}{156}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{127}{156}\right)\)	\(e\left(\frac{61}{156}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{338}(17,\cdot)\)	338.k	78	no	\(1\)	\(1\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{338}(19,\cdot)\)	338.f	12	no	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(-i\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(i\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{338}(21,\cdot)\)	338.j	52	no	\(-1\)	\(1\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(i\)	\(e\left(\frac{3}{52}\right)\)	\(-1\)
\(\chi_{338}(23,\cdot)\)	338.e	6	no	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{338}(25,\cdot)\)	338.h	26	no	\(1\)	\(1\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(-1\)	\(e\left(\frac{17}{26}\right)\)	\(1\)
\(\chi_{338}(27,\cdot)\)	338.g	13	no	\(1\)	\(1\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(1\)	\(e\left(\frac{11}{13}\right)\)	\(1\)
\(\chi_{338}(29,\cdot)\)	338.i	39	no	\(1\)	\(1\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{338}(31,\cdot)\)	338.j	52	no	\(-1\)	\(1\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(-i\)	\(e\left(\frac{5}{52}\right)\)	\(-1\)
\(\chi_{338}(33,\cdot)\)	338.l	156	no	\(-1\)	\(1\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{109}{156}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{137}{156}\right)\)	\(e\left(\frac{83}{156}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{338}(35,\cdot)\)	338.i	39	no	\(1\)	\(1\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{338}(37,\cdot)\)	338.l	156	no	\(-1\)	\(1\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{89}{156}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{109}{156}\right)\)	\(e\left(\frac{115}{156}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{338}(41,\cdot)\)	338.l	156	no	\(-1\)	\(1\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{47}{156}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{19}{156}\right)\)	\(e\left(\frac{73}{156}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{338}(43,\cdot)\)	338.k	78	no	\(1\)	\(1\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{338}(45,\cdot)\)	338.l	156	no	\(-1\)	\(1\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{43}{156}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{107}{156}\right)\)	\(e\left(\frac{17}{156}\right)\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{338}(47,\cdot)\)	338.j	52	no	\(-1\)	\(1\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(i\)	\(e\left(\frac{15}{52}\right)\)	\(-1\)
\(\chi_{338}(49,\cdot)\)	338.k	78	no	\(1\)	\(1\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{338}(51,\cdot)\)	338.h	26	no	\(1\)	\(1\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(-1\)	\(e\left(\frac{21}{26}\right)\)	\(1\)
\(\chi_{338}(53,\cdot)\)	338.g	13	no	\(1\)	\(1\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(1\)	\(e\left(\frac{9}{13}\right)\)	\(1\)
\(\chi_{338}(55,\cdot)\)	338.i	39	no	\(1\)	\(1\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{338}(57,\cdot)\)	338.j	52	no	\(-1\)	\(1\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(-i\)	\(e\left(\frac{45}{52}\right)\)	\(-1\)
\(\chi_{338}(59,\cdot)\)	338.l	156	no	\(-1\)	\(1\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{1}{156}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{17}{156}\right)\)	\(e\left(\frac{131}{156}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{338}(61,\cdot)\)	338.i	39	no	\(1\)	\(1\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{338}(63,\cdot)\)	338.l	156	no	\(-1\)	\(1\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{77}{156}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{61}{156}\right)\)	\(e\left(\frac{103}{156}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{338}(67,\cdot)\)	338.l	156	no	\(-1\)	\(1\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{59}{156}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{67}{156}\right)\)	\(e\left(\frac{85}{156}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{338}(69,\cdot)\)	338.k	78	no	\(1\)	\(1\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{2}{3}\right)\)

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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.