LMFDB - Group of Dirichlet characters of modulus 2156

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(2156)

gp:g = idealstar(,2156,2)

magma:G = FullDirichletGroup(2156);

Character group

Order	=	840	comment:Order sage:G.order() gp:g.no magma:Order(G);
Structure	=	$C_{2}\times C_{2}\times C_{210}$	comment:Group structure sage:sorted(g.order() for g in G.gens()) gp:g.cyc magma:PrimaryInvariants(G);
Generators	=	$\chi_{2156}(1079,\cdot)$, $\chi_{2156}(1277,\cdot)$, $\chi_{2156}(981,\cdot)$	comment:Generators sage:G.gens() gp:g.gen magma:Generators(G);

First 32 of 840 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	$-1$	$1$	$3$	$5$	$9$	$13$	$15$	$17$	$19$	$23$	$25$	$27$
$\chi_{2156}(1,\cdot)$	2156.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{2156}(3,\cdot)$	2156.cg	210	yes	$1$	$1$	$e\left(\frac{97}{105}\right)$	$e\left(\frac{187}{210}\right)$	$e\left(\frac{89}{105}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{167}{210}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{82}{105}\right)$	$e\left(\frac{27}{35}\right)$
$\chi_{2156}(5,\cdot)$	2156.ck	210	no	$-1$	$1$	$e\left(\frac{187}{210}\right)$	$e\left(\frac{131}{210}\right)$	$e\left(\frac{82}{105}\right)$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{181}{210}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{26}{105}\right)$	$e\left(\frac{47}{70}\right)$
$\chi_{2156}(9,\cdot)$	2156.ce	105	no	$1$	$1$	$e\left(\frac{89}{105}\right)$	$e\left(\frac{82}{105}\right)$	$e\left(\frac{73}{105}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{62}{105}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{59}{105}\right)$	$e\left(\frac{19}{35}\right)$
$\chi_{2156}(13,\cdot)$	2156.by	70	no	$1$	$1$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{53}{70}\right)$
$\chi_{2156}(15,\cdot)$	2156.ca	70	yes	$-1$	$1$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{31}{70}\right)$
$\chi_{2156}(17,\cdot)$	2156.cl	210	no	$1$	$1$	$e\left(\frac{167}{210}\right)$	$e\left(\frac{181}{210}\right)$	$e\left(\frac{62}{105}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{103}{105}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{27}{70}\right)$
$\chi_{2156}(19,\cdot)$	2156.bm	30	no	$-1$	$1$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{2156}(23,\cdot)$	2156.bs	42	no	$-1$	$1$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{3}{14}\right)$
$\chi_{2156}(25,\cdot)$	2156.ce	105	no	$1$	$1$	$e\left(\frac{82}{105}\right)$	$e\left(\frac{26}{105}\right)$	$e\left(\frac{59}{105}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{52}{105}\right)$	$e\left(\frac{12}{35}\right)$
$\chi_{2156}(27,\cdot)$	2156.cb	70	yes	$1$	$1$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{11}{35}\right)$
$\chi_{2156}(29,\cdot)$	2156.cd	70	no	$-1$	$1$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{3}{35}\right)$
$\chi_{2156}(31,\cdot)$	2156.bn	30	no	$1$	$1$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{2156}(37,\cdot)$	2156.ce	105	no	$1$	$1$	$e\left(\frac{38}{105}\right)$	$e\left(\frac{94}{105}\right)$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{89}{105}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{83}{105}\right)$	$e\left(\frac{3}{35}\right)$
$\chi_{2156}(39,\cdot)$	2156.ci	210	yes	$1$	$1$	$e\left(\frac{107}{210}\right)$	$e\left(\frac{8}{105}\right)$	$e\left(\frac{2}{105}\right)$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{71}{210}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{16}{105}\right)$	$e\left(\frac{37}{70}\right)$
$\chi_{2156}(41,\cdot)$	2156.by	70	no	$1$	$1$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{19}{70}\right)$
$\chi_{2156}(43,\cdot)$	2156.bd	14	yes	$1$	$1$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{1}{14}\right)$	$1$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{13}{14}\right)$
$\chi_{2156}(45,\cdot)$	2156.br	42	no	$-1$	$1$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{3}{14}\right)$
$\chi_{2156}(47,\cdot)$	2156.cg	210	yes	$1$	$1$	$e\left(\frac{2}{105}\right)$	$e\left(\frac{137}{210}\right)$	$e\left(\frac{4}{105}\right)$	$e\left(\frac{51}{70}\right)$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{37}{210}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{32}{105}\right)$	$e\left(\frac{2}{35}\right)$
$\chi_{2156}(51,\cdot)$	2156.ci	210	yes	$1$	$1$	$e\left(\frac{151}{210}\right)$	$e\left(\frac{79}{105}\right)$	$e\left(\frac{46}{105}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{163}{210}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{53}{105}\right)$	$e\left(\frac{11}{70}\right)$
$\chi_{2156}(53,\cdot)$	2156.ce	105	no	$1$	$1$	$e\left(\frac{4}{105}\right)$	$e\left(\frac{32}{105}\right)$	$e\left(\frac{8}{105}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{37}{105}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{64}{105}\right)$	$e\left(\frac{4}{35}\right)$
$\chi_{2156}(57,\cdot)$	2156.cd	70	no	$-1$	$1$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{34}{35}\right)$
$\chi_{2156}(59,\cdot)$	2156.cg	210	yes	$1$	$1$	$e\left(\frac{43}{105}\right)$	$e\left(\frac{163}{210}\right)$	$e\left(\frac{86}{105}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{113}{210}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{58}{105}\right)$	$e\left(\frac{8}{35}\right)$
$\chi_{2156}(61,\cdot)$	2156.cl	210	no	$1$	$1$	$e\left(\frac{97}{210}\right)$	$e\left(\frac{41}{210}\right)$	$e\left(\frac{97}{105}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{68}{105}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{41}{105}\right)$	$e\left(\frac{27}{70}\right)$
$\chi_{2156}(65,\cdot)$	2156.bw	42	no	$-1$	$1$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{3}{7}\right)$
$\chi_{2156}(67,\cdot)$	2156.o	6	no	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$-1$
$\chi_{2156}(69,\cdot)$	2156.bx	70	no	$-1$	$1$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{69}{70}\right)$
$\chi_{2156}(71,\cdot)$	2156.ca	70	yes	$-1$	$1$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{57}{70}\right)$
$\chi_{2156}(73,\cdot)$	2156.cl	210	no	$1$	$1$	$e\left(\frac{101}{210}\right)$	$e\left(\frac{73}{210}\right)$	$e\left(\frac{101}{105}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{34}{105}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{73}{105}\right)$	$e\left(\frac{31}{70}\right)$
$\chi_{2156}(75,\cdot)$	2156.cg	210	yes	$1$	$1$	$e\left(\frac{74}{105}\right)$	$e\left(\frac{29}{210}\right)$	$e\left(\frac{43}{105}\right)$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{109}{210}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{29}{105}\right)$	$e\left(\frac{4}{35}\right)$
$\chi_{2156}(79,\cdot)$	2156.bl	30	no	$1$	$1$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{2156}(81,\cdot)$	2156.ce	105	no	$1$	$1$	$e\left(\frac{73}{105}\right)$	$e\left(\frac{59}{105}\right)$	$e\left(\frac{41}{105}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{19}{105}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{13}{105}\right)$	$e\left(\frac{3}{35}\right)$

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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	$2156$
Structure	\(C_{2}\times C_{2}\times C_{210}\)
Order	$840$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(9\)	\(13\)	\(15\)	\(17\)	\(19\)	\(23\)	\(25\)	\(27\)
\(\chi_{2156}(1,\cdot)\)	2156.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{2156}(3,\cdot)\)	2156.cg	210	yes	\(1\)	\(1\)	\(e\left(\frac{97}{105}\right)\)	\(e\left(\frac{187}{210}\right)\)	\(e\left(\frac{89}{105}\right)\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{167}{210}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{82}{105}\right)\)	\(e\left(\frac{27}{35}\right)\)
\(\chi_{2156}(5,\cdot)\)	2156.ck	210	no	\(-1\)	\(1\)	\(e\left(\frac{187}{210}\right)\)	\(e\left(\frac{131}{210}\right)\)	\(e\left(\frac{82}{105}\right)\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{181}{210}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{26}{105}\right)\)	\(e\left(\frac{47}{70}\right)\)
\(\chi_{2156}(9,\cdot)\)	2156.ce	105	no	\(1\)	\(1\)	\(e\left(\frac{89}{105}\right)\)	\(e\left(\frac{82}{105}\right)\)	\(e\left(\frac{73}{105}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{62}{105}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{59}{105}\right)\)	\(e\left(\frac{19}{35}\right)\)
\(\chi_{2156}(13,\cdot)\)	2156.by	70	no	\(1\)	\(1\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{53}{70}\right)\)
\(\chi_{2156}(15,\cdot)\)	2156.ca	70	yes	\(-1\)	\(1\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{31}{70}\right)\)
\(\chi_{2156}(17,\cdot)\)	2156.cl	210	no	\(1\)	\(1\)	\(e\left(\frac{167}{210}\right)\)	\(e\left(\frac{181}{210}\right)\)	\(e\left(\frac{62}{105}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{103}{105}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{27}{70}\right)\)
\(\chi_{2156}(19,\cdot)\)	2156.bm	30	no	\(-1\)	\(1\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{2156}(23,\cdot)\)	2156.bs	42	no	\(-1\)	\(1\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{3}{14}\right)\)
\(\chi_{2156}(25,\cdot)\)	2156.ce	105	no	\(1\)	\(1\)	\(e\left(\frac{82}{105}\right)\)	\(e\left(\frac{26}{105}\right)\)	\(e\left(\frac{59}{105}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{52}{105}\right)\)	\(e\left(\frac{12}{35}\right)\)
\(\chi_{2156}(27,\cdot)\)	2156.cb	70	yes	\(1\)	\(1\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{11}{35}\right)\)
\(\chi_{2156}(29,\cdot)\)	2156.cd	70	no	\(-1\)	\(1\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{3}{35}\right)\)
\(\chi_{2156}(31,\cdot)\)	2156.bn	30	no	\(1\)	\(1\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{2156}(37,\cdot)\)	2156.ce	105	no	\(1\)	\(1\)	\(e\left(\frac{38}{105}\right)\)	\(e\left(\frac{94}{105}\right)\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{89}{105}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{83}{105}\right)\)	\(e\left(\frac{3}{35}\right)\)
\(\chi_{2156}(39,\cdot)\)	2156.ci	210	yes	\(1\)	\(1\)	\(e\left(\frac{107}{210}\right)\)	\(e\left(\frac{8}{105}\right)\)	\(e\left(\frac{2}{105}\right)\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{71}{210}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{16}{105}\right)\)	\(e\left(\frac{37}{70}\right)\)
\(\chi_{2156}(41,\cdot)\)	2156.by	70	no	\(1\)	\(1\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{19}{70}\right)\)
\(\chi_{2156}(43,\cdot)\)	2156.bd	14	yes	\(1\)	\(1\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(1\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)
\(\chi_{2156}(45,\cdot)\)	2156.br	42	no	\(-1\)	\(1\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{3}{14}\right)\)
\(\chi_{2156}(47,\cdot)\)	2156.cg	210	yes	\(1\)	\(1\)	\(e\left(\frac{2}{105}\right)\)	\(e\left(\frac{137}{210}\right)\)	\(e\left(\frac{4}{105}\right)\)	\(e\left(\frac{51}{70}\right)\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{37}{210}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{32}{105}\right)\)	\(e\left(\frac{2}{35}\right)\)
\(\chi_{2156}(51,\cdot)\)	2156.ci	210	yes	\(1\)	\(1\)	\(e\left(\frac{151}{210}\right)\)	\(e\left(\frac{79}{105}\right)\)	\(e\left(\frac{46}{105}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{163}{210}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{53}{105}\right)\)	\(e\left(\frac{11}{70}\right)\)
\(\chi_{2156}(53,\cdot)\)	2156.ce	105	no	\(1\)	\(1\)	\(e\left(\frac{4}{105}\right)\)	\(e\left(\frac{32}{105}\right)\)	\(e\left(\frac{8}{105}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{37}{105}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{64}{105}\right)\)	\(e\left(\frac{4}{35}\right)\)
\(\chi_{2156}(57,\cdot)\)	2156.cd	70	no	\(-1\)	\(1\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{34}{35}\right)\)
\(\chi_{2156}(59,\cdot)\)	2156.cg	210	yes	\(1\)	\(1\)	\(e\left(\frac{43}{105}\right)\)	\(e\left(\frac{163}{210}\right)\)	\(e\left(\frac{86}{105}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{113}{210}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{58}{105}\right)\)	\(e\left(\frac{8}{35}\right)\)
\(\chi_{2156}(61,\cdot)\)	2156.cl	210	no	\(1\)	\(1\)	\(e\left(\frac{97}{210}\right)\)	\(e\left(\frac{41}{210}\right)\)	\(e\left(\frac{97}{105}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{68}{105}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{41}{105}\right)\)	\(e\left(\frac{27}{70}\right)\)
\(\chi_{2156}(65,\cdot)\)	2156.bw	42	no	\(-1\)	\(1\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{3}{7}\right)\)
\(\chi_{2156}(67,\cdot)\)	2156.o	6	no	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)
\(\chi_{2156}(69,\cdot)\)	2156.bx	70	no	\(-1\)	\(1\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{69}{70}\right)\)
\(\chi_{2156}(71,\cdot)\)	2156.ca	70	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{57}{70}\right)\)
\(\chi_{2156}(73,\cdot)\)	2156.cl	210	no	\(1\)	\(1\)	\(e\left(\frac{101}{210}\right)\)	\(e\left(\frac{73}{210}\right)\)	\(e\left(\frac{101}{105}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{34}{105}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{73}{105}\right)\)	\(e\left(\frac{31}{70}\right)\)
\(\chi_{2156}(75,\cdot)\)	2156.cg	210	yes	\(1\)	\(1\)	\(e\left(\frac{74}{105}\right)\)	\(e\left(\frac{29}{210}\right)\)	\(e\left(\frac{43}{105}\right)\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{109}{210}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{29}{105}\right)\)	\(e\left(\frac{4}{35}\right)\)
\(\chi_{2156}(79,\cdot)\)	2156.bl	30	no	\(1\)	\(1\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{2156}(81,\cdot)\)	2156.ce	105	no	\(1\)	\(1\)	\(e\left(\frac{73}{105}\right)\)	\(e\left(\frac{59}{105}\right)\)	\(e\left(\frac{41}{105}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{19}{105}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{13}{105}\right)\)	\(e\left(\frac{3}{35}\right)\)

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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.