LMFDB - Group of Dirichlet characters of modulus 3940

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(3940)

gp:g = idealstar(,3940,2)

magma:G = FullDirichletGroup(3940);

Character group

Order	=	1568	comment:Order sage:G.order() gp:g.no magma:Order(G);
Structure	=	$C_{2}\times C_{4}\times C_{196}$	comment:Group structure sage:sorted(g.order() for g in G.gens()) gp:g.cyc magma:PrimaryInvariants(G);
Generators	=	$\chi_{3940}(1971,\cdot)$, $\chi_{3940}(1577,\cdot)$, $\chi_{3940}(1381,\cdot)$	comment:Generators sage:G.gens() gp:g.gen magma:Generators(G);

First 32 of 1568 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	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{3940}(1,\cdot)$	3940.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{3940}(3,\cdot)$	3940.cf	196	yes	$-1$	$1$	$e\left(\frac{44}{49}\right)$	$e\left(\frac{15}{196}\right)$	$e\left(\frac{39}{49}\right)$	$e\left(\frac{55}{196}\right)$	$e\left(\frac{33}{98}\right)$	$e\left(\frac{57}{98}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{191}{196}\right)$	$e\left(\frac{111}{196}\right)$	$e\left(\frac{34}{49}\right)$
$\chi_{3940}(7,\cdot)$	3940.bx	196	yes	$1$	$1$	$e\left(\frac{15}{196}\right)$	$e\left(\frac{99}{196}\right)$	$e\left(\frac{15}{98}\right)$	$e\left(\frac{5}{49}\right)$	$e\left(\frac{73}{196}\right)$	$e\left(\frac{135}{196}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{57}{98}\right)$	$e\left(\frac{125}{196}\right)$	$e\left(\frac{45}{196}\right)$
$\chi_{3940}(9,\cdot)$	3940.br	98	no	$1$	$1$	$e\left(\frac{39}{49}\right)$	$e\left(\frac{15}{98}\right)$	$e\left(\frac{29}{49}\right)$	$e\left(\frac{55}{98}\right)$	$e\left(\frac{33}{49}\right)$	$e\left(\frac{8}{49}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{93}{98}\right)$	$e\left(\frac{13}{98}\right)$	$e\left(\frac{19}{49}\right)$
$\chi_{3940}(11,\cdot)$	3940.cb	196	no	$1$	$1$	$e\left(\frac{55}{196}\right)$	$e\left(\frac{5}{49}\right)$	$e\left(\frac{55}{98}\right)$	$e\left(\frac{155}{196}\right)$	$e\left(\frac{137}{196}\right)$	$e\left(\frac{103}{196}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{75}{196}\right)$	$e\left(\frac{25}{98}\right)$	$e\left(\frac{165}{196}\right)$
$\chi_{3940}(13,\cdot)$	3940.bz	196	no	$1$	$1$	$e\left(\frac{33}{98}\right)$	$e\left(\frac{73}{196}\right)$	$e\left(\frac{33}{49}\right)$	$e\left(\frac{137}{196}\right)$	$e\left(\frac{43}{98}\right)$	$e\left(\frac{3}{98}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{139}{196}\right)$	$e\left(\frac{109}{196}\right)$	$e\left(\frac{1}{98}\right)$
$\chi_{3940}(17,\cdot)$	3940.bz	196	no	$1$	$1$	$e\left(\frac{57}{98}\right)$	$e\left(\frac{135}{196}\right)$	$e\left(\frac{8}{49}\right)$	$e\left(\frac{103}{196}\right)$	$e\left(\frac{3}{98}\right)$	$e\left(\frac{23}{98}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{53}{196}\right)$	$e\left(\frac{19}{196}\right)$	$e\left(\frac{73}{98}\right)$
$\chi_{3940}(19,\cdot)$	3940.y	14	yes	$-1$	$1$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{3}{7}\right)$	$-1$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{9}{14}\right)$
$\chi_{3940}(21,\cdot)$	3940.ch	196	no	$-1$	$1$	$e\left(\frac{191}{196}\right)$	$e\left(\frac{57}{98}\right)$	$e\left(\frac{93}{98}\right)$	$e\left(\frac{75}{196}\right)$	$e\left(\frac{139}{196}\right)$	$e\left(\frac{53}{196}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{109}{196}\right)$	$e\left(\frac{10}{49}\right)$	$e\left(\frac{181}{196}\right)$
$\chi_{3940}(23,\cdot)$	3940.ca	196	yes	$1$	$1$	$e\left(\frac{111}{196}\right)$	$e\left(\frac{125}{196}\right)$	$e\left(\frac{13}{98}\right)$	$e\left(\frac{25}{98}\right)$	$e\left(\frac{109}{196}\right)$	$e\left(\frac{19}{196}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{10}{49}\right)$	$e\left(\frac{43}{196}\right)$	$e\left(\frac{137}{196}\right)$
$\chi_{3940}(27,\cdot)$	3940.cf	196	yes	$-1$	$1$	$e\left(\frac{34}{49}\right)$	$e\left(\frac{45}{196}\right)$	$e\left(\frac{19}{49}\right)$	$e\left(\frac{165}{196}\right)$	$e\left(\frac{1}{98}\right)$	$e\left(\frac{73}{98}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{181}{196}\right)$	$e\left(\frac{137}{196}\right)$	$e\left(\frac{4}{49}\right)$
$\chi_{3940}(29,\cdot)$	3940.bq	98	no	$1$	$1$	$e\left(\frac{73}{98}\right)$	$e\left(\frac{31}{98}\right)$	$e\left(\frac{24}{49}\right)$	$e\left(\frac{16}{49}\right)$	$e\left(\frac{9}{98}\right)$	$e\left(\frac{69}{98}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{3}{49}\right)$	$e\left(\frac{53}{98}\right)$	$e\left(\frac{23}{98}\right)$
$\chi_{3940}(31,\cdot)$	3940.cb	196	no	$1$	$1$	$e\left(\frac{139}{196}\right)$	$e\left(\frac{26}{49}\right)$	$e\left(\frac{41}{98}\right)$	$e\left(\frac{71}{196}\right)$	$e\left(\frac{193}{196}\right)$	$e\left(\frac{75}{196}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{47}{196}\right)$	$e\left(\frac{81}{98}\right)$	$e\left(\frac{25}{196}\right)$
$\chi_{3940}(33,\cdot)$	3940.bi	28	no	$-1$	$1$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{3}{28}\right)$	$-1$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{15}{28}\right)$
$\chi_{3940}(37,\cdot)$	3940.cg	196	no	$-1$	$1$	$e\left(\frac{11}{196}\right)$	$e\left(\frac{53}{196}\right)$	$e\left(\frac{11}{98}\right)$	$e\left(\frac{20}{49}\right)$	$e\left(\frac{47}{196}\right)$	$e\left(\frac{1}{196}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{16}{49}\right)$	$e\left(\frac{59}{196}\right)$	$e\left(\frac{33}{196}\right)$
$\chi_{3940}(39,\cdot)$	3940.bv	98	yes	$-1$	$1$	$e\left(\frac{23}{98}\right)$	$e\left(\frac{22}{49}\right)$	$e\left(\frac{23}{49}\right)$	$e\left(\frac{48}{49}\right)$	$e\left(\frac{38}{49}\right)$	$e\left(\frac{30}{49}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{67}{98}\right)$	$e\left(\frac{6}{49}\right)$	$e\left(\frac{69}{98}\right)$
$\chi_{3940}(41,\cdot)$	3940.bp	98	no	$1$	$1$	$e\left(\frac{57}{98}\right)$	$e\left(\frac{46}{49}\right)$	$e\left(\frac{8}{49}\right)$	$e\left(\frac{27}{98}\right)$	$e\left(\frac{3}{98}\right)$	$e\left(\frac{23}{98}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{51}{98}\right)$	$e\left(\frac{17}{49}\right)$	$e\left(\frac{73}{98}\right)$
$\chi_{3940}(43,\cdot)$	3940.bx	196	yes	$1$	$1$	$e\left(\frac{153}{196}\right)$	$e\left(\frac{69}{196}\right)$	$e\left(\frac{55}{98}\right)$	$e\left(\frac{2}{49}\right)$	$e\left(\frac{39}{196}\right)$	$e\left(\frac{5}{196}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{13}{98}\right)$	$e\left(\frac{99}{196}\right)$	$e\left(\frac{67}{196}\right)$
$\chi_{3940}(47,\cdot)$	3940.bx	196	yes	$1$	$1$	$e\left(\frac{39}{196}\right)$	$e\left(\frac{179}{196}\right)$	$e\left(\frac{39}{98}\right)$	$e\left(\frac{13}{49}\right)$	$e\left(\frac{33}{196}\right)$	$e\left(\frac{155}{196}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{11}{98}\right)$	$e\left(\frac{129}{196}\right)$	$e\left(\frac{117}{196}\right)$
$\chi_{3940}(49,\cdot)$	3940.bq	98	no	$1$	$1$	$e\left(\frac{15}{98}\right)$	$e\left(\frac{1}{98}\right)$	$e\left(\frac{15}{49}\right)$	$e\left(\frac{10}{49}\right)$	$e\left(\frac{73}{98}\right)$	$e\left(\frac{37}{98}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{8}{49}\right)$	$e\left(\frac{27}{98}\right)$	$e\left(\frac{45}{98}\right)$
$\chi_{3940}(51,\cdot)$	3940.bs	98	no	$-1$	$1$	$e\left(\frac{47}{98}\right)$	$e\left(\frac{75}{98}\right)$	$e\left(\frac{47}{49}\right)$	$e\left(\frac{79}{98}\right)$	$e\left(\frac{18}{49}\right)$	$e\left(\frac{40}{49}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{12}{49}\right)$	$e\left(\frac{65}{98}\right)$	$e\left(\frac{43}{98}\right)$
$\chi_{3940}(53,\cdot)$	3940.cg	196	no	$-1$	$1$	$e\left(\frac{145}{196}\right)$	$e\left(\frac{75}{196}\right)$	$e\left(\frac{47}{98}\right)$	$e\left(\frac{32}{49}\right)$	$e\left(\frac{85}{196}\right)$	$e\left(\frac{31}{196}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{6}{49}\right)$	$e\left(\frac{65}{196}\right)$	$e\left(\frac{43}{196}\right)$
$\chi_{3940}(57,\cdot)$	3940.bz	196	no	$1$	$1$	$e\left(\frac{11}{98}\right)$	$e\left(\frac{155}{196}\right)$	$e\left(\frac{11}{49}\right)$	$e\left(\frac{111}{196}\right)$	$e\left(\frac{47}{98}\right)$	$e\left(\frac{1}{98}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{177}{196}\right)$	$e\left(\frac{167}{196}\right)$	$e\left(\frac{33}{98}\right)$
$\chi_{3940}(59,\cdot)$	3940.bu	98	yes	$-1$	$1$	$e\left(\frac{19}{49}\right)$	$e\left(\frac{47}{49}\right)$	$e\left(\frac{38}{49}\right)$	$e\left(\frac{67}{98}\right)$	$e\left(\frac{51}{98}\right)$	$e\left(\frac{97}{98}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{17}{49}\right)$	$e\left(\frac{44}{49}\right)$	$e\left(\frac{8}{49}\right)$
$\chi_{3940}(61,\cdot)$	3940.bo	49	no	$1$	$1$	$e\left(\frac{5}{49}\right)$	$e\left(\frac{33}{49}\right)$	$e\left(\frac{10}{49}\right)$	$e\left(\frac{23}{49}\right)$	$e\left(\frac{8}{49}\right)$	$e\left(\frac{45}{49}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{38}{49}\right)$	$e\left(\frac{9}{49}\right)$	$e\left(\frac{15}{49}\right)$
$\chi_{3940}(63,\cdot)$	3940.ca	196	yes	$1$	$1$	$e\left(\frac{171}{196}\right)$	$e\left(\frac{129}{196}\right)$	$e\left(\frac{73}{98}\right)$	$e\left(\frac{65}{98}\right)$	$e\left(\frac{9}{196}\right)$	$e\left(\frac{167}{196}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{26}{49}\right)$	$e\left(\frac{151}{196}\right)$	$e\left(\frac{121}{196}\right)$
$\chi_{3940}(67,\cdot)$	3940.ce	196	yes	$-1$	$1$	$e\left(\frac{93}{98}\right)$	$e\left(\frac{81}{196}\right)$	$e\left(\frac{44}{49}\right)$	$e\left(\frac{3}{196}\right)$	$e\left(\frac{45}{49}\right)$	$e\left(\frac{2}{49}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{71}{196}\right)$	$e\left(\frac{129}{196}\right)$	$e\left(\frac{83}{98}\right)$
$\chi_{3940}(69,\cdot)$	3940.be	28	no	$-1$	$1$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{19}{28}\right)$	$-1$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{11}{28}\right)$
$\chi_{3940}(71,\cdot)$	3940.cb	196	no	$1$	$1$	$e\left(\frac{9}{196}\right)$	$e\left(\frac{32}{49}\right)$	$e\left(\frac{9}{98}\right)$	$e\left(\frac{61}{196}\right)$	$e\left(\frac{83}{196}\right)$	$e\left(\frac{81}{196}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{137}{196}\right)$	$e\left(\frac{13}{98}\right)$	$e\left(\frac{27}{196}\right)$
$\chi_{3940}(73,\cdot)$	3940.bz	196	no	$1$	$1$	$e\left(\frac{79}{98}\right)$	$e\left(\frac{53}{196}\right)$	$e\left(\frac{30}{49}\right)$	$e\left(\frac{129}{196}\right)$	$e\left(\frac{97}{98}\right)$	$e\left(\frac{25}{98}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{15}{196}\right)$	$e\left(\frac{157}{196}\right)$	$e\left(\frac{41}{98}\right)$
$\chi_{3940}(77,\cdot)$	3940.bn	28	no	$1$	$1$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{3}{14}\right)$	$1$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{1}{14}\right)$
$\chi_{3940}(79,\cdot)$	3940.bw	196	yes	$1$	$1$	$e\left(\frac{159}{196}\right)$	$e\left(\frac{69}{98}\right)$	$e\left(\frac{61}{98}\right)$	$e\left(\frac{65}{196}\right)$	$e\left(\frac{29}{196}\right)$	$e\left(\frac{59}{196}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{101}{196}\right)$	$e\left(\frac{25}{49}\right)$	$e\left(\frac{85}{196}\right)$

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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	$3940$
Structure	\(C_{2}\times C_{4}\times C_{196}\)
Order	$1568$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)
\(\chi_{3940}(1,\cdot)\)	3940.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{3940}(3,\cdot)\)	3940.cf	196	yes	\(-1\)	\(1\)	\(e\left(\frac{44}{49}\right)\)	\(e\left(\frac{15}{196}\right)\)	\(e\left(\frac{39}{49}\right)\)	\(e\left(\frac{55}{196}\right)\)	\(e\left(\frac{33}{98}\right)\)	\(e\left(\frac{57}{98}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{191}{196}\right)\)	\(e\left(\frac{111}{196}\right)\)	\(e\left(\frac{34}{49}\right)\)
\(\chi_{3940}(7,\cdot)\)	3940.bx	196	yes	\(1\)	\(1\)	\(e\left(\frac{15}{196}\right)\)	\(e\left(\frac{99}{196}\right)\)	\(e\left(\frac{15}{98}\right)\)	\(e\left(\frac{5}{49}\right)\)	\(e\left(\frac{73}{196}\right)\)	\(e\left(\frac{135}{196}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{57}{98}\right)\)	\(e\left(\frac{125}{196}\right)\)	\(e\left(\frac{45}{196}\right)\)
\(\chi_{3940}(9,\cdot)\)	3940.br	98	no	\(1\)	\(1\)	\(e\left(\frac{39}{49}\right)\)	\(e\left(\frac{15}{98}\right)\)	\(e\left(\frac{29}{49}\right)\)	\(e\left(\frac{55}{98}\right)\)	\(e\left(\frac{33}{49}\right)\)	\(e\left(\frac{8}{49}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{93}{98}\right)\)	\(e\left(\frac{13}{98}\right)\)	\(e\left(\frac{19}{49}\right)\)
\(\chi_{3940}(11,\cdot)\)	3940.cb	196	no	\(1\)	\(1\)	\(e\left(\frac{55}{196}\right)\)	\(e\left(\frac{5}{49}\right)\)	\(e\left(\frac{55}{98}\right)\)	\(e\left(\frac{155}{196}\right)\)	\(e\left(\frac{137}{196}\right)\)	\(e\left(\frac{103}{196}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{75}{196}\right)\)	\(e\left(\frac{25}{98}\right)\)	\(e\left(\frac{165}{196}\right)\)
\(\chi_{3940}(13,\cdot)\)	3940.bz	196	no	\(1\)	\(1\)	\(e\left(\frac{33}{98}\right)\)	\(e\left(\frac{73}{196}\right)\)	\(e\left(\frac{33}{49}\right)\)	\(e\left(\frac{137}{196}\right)\)	\(e\left(\frac{43}{98}\right)\)	\(e\left(\frac{3}{98}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{139}{196}\right)\)	\(e\left(\frac{109}{196}\right)\)	\(e\left(\frac{1}{98}\right)\)
\(\chi_{3940}(17,\cdot)\)	3940.bz	196	no	\(1\)	\(1\)	\(e\left(\frac{57}{98}\right)\)	\(e\left(\frac{135}{196}\right)\)	\(e\left(\frac{8}{49}\right)\)	\(e\left(\frac{103}{196}\right)\)	\(e\left(\frac{3}{98}\right)\)	\(e\left(\frac{23}{98}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{53}{196}\right)\)	\(e\left(\frac{19}{196}\right)\)	\(e\left(\frac{73}{98}\right)\)
\(\chi_{3940}(19,\cdot)\)	3940.y	14	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(-1\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)
\(\chi_{3940}(21,\cdot)\)	3940.ch	196	no	\(-1\)	\(1\)	\(e\left(\frac{191}{196}\right)\)	\(e\left(\frac{57}{98}\right)\)	\(e\left(\frac{93}{98}\right)\)	\(e\left(\frac{75}{196}\right)\)	\(e\left(\frac{139}{196}\right)\)	\(e\left(\frac{53}{196}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{109}{196}\right)\)	\(e\left(\frac{10}{49}\right)\)	\(e\left(\frac{181}{196}\right)\)
\(\chi_{3940}(23,\cdot)\)	3940.ca	196	yes	\(1\)	\(1\)	\(e\left(\frac{111}{196}\right)\)	\(e\left(\frac{125}{196}\right)\)	\(e\left(\frac{13}{98}\right)\)	\(e\left(\frac{25}{98}\right)\)	\(e\left(\frac{109}{196}\right)\)	\(e\left(\frac{19}{196}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{10}{49}\right)\)	\(e\left(\frac{43}{196}\right)\)	\(e\left(\frac{137}{196}\right)\)
\(\chi_{3940}(27,\cdot)\)	3940.cf	196	yes	\(-1\)	\(1\)	\(e\left(\frac{34}{49}\right)\)	\(e\left(\frac{45}{196}\right)\)	\(e\left(\frac{19}{49}\right)\)	\(e\left(\frac{165}{196}\right)\)	\(e\left(\frac{1}{98}\right)\)	\(e\left(\frac{73}{98}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{181}{196}\right)\)	\(e\left(\frac{137}{196}\right)\)	\(e\left(\frac{4}{49}\right)\)
\(\chi_{3940}(29,\cdot)\)	3940.bq	98	no	\(1\)	\(1\)	\(e\left(\frac{73}{98}\right)\)	\(e\left(\frac{31}{98}\right)\)	\(e\left(\frac{24}{49}\right)\)	\(e\left(\frac{16}{49}\right)\)	\(e\left(\frac{9}{98}\right)\)	\(e\left(\frac{69}{98}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{3}{49}\right)\)	\(e\left(\frac{53}{98}\right)\)	\(e\left(\frac{23}{98}\right)\)
\(\chi_{3940}(31,\cdot)\)	3940.cb	196	no	\(1\)	\(1\)	\(e\left(\frac{139}{196}\right)\)	\(e\left(\frac{26}{49}\right)\)	\(e\left(\frac{41}{98}\right)\)	\(e\left(\frac{71}{196}\right)\)	\(e\left(\frac{193}{196}\right)\)	\(e\left(\frac{75}{196}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{47}{196}\right)\)	\(e\left(\frac{81}{98}\right)\)	\(e\left(\frac{25}{196}\right)\)
\(\chi_{3940}(33,\cdot)\)	3940.bi	28	no	\(-1\)	\(1\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(-1\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{15}{28}\right)\)
\(\chi_{3940}(37,\cdot)\)	3940.cg	196	no	\(-1\)	\(1\)	\(e\left(\frac{11}{196}\right)\)	\(e\left(\frac{53}{196}\right)\)	\(e\left(\frac{11}{98}\right)\)	\(e\left(\frac{20}{49}\right)\)	\(e\left(\frac{47}{196}\right)\)	\(e\left(\frac{1}{196}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{16}{49}\right)\)	\(e\left(\frac{59}{196}\right)\)	\(e\left(\frac{33}{196}\right)\)
\(\chi_{3940}(39,\cdot)\)	3940.bv	98	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{98}\right)\)	\(e\left(\frac{22}{49}\right)\)	\(e\left(\frac{23}{49}\right)\)	\(e\left(\frac{48}{49}\right)\)	\(e\left(\frac{38}{49}\right)\)	\(e\left(\frac{30}{49}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{67}{98}\right)\)	\(e\left(\frac{6}{49}\right)\)	\(e\left(\frac{69}{98}\right)\)
\(\chi_{3940}(41,\cdot)\)	3940.bp	98	no	\(1\)	\(1\)	\(e\left(\frac{57}{98}\right)\)	\(e\left(\frac{46}{49}\right)\)	\(e\left(\frac{8}{49}\right)\)	\(e\left(\frac{27}{98}\right)\)	\(e\left(\frac{3}{98}\right)\)	\(e\left(\frac{23}{98}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{51}{98}\right)\)	\(e\left(\frac{17}{49}\right)\)	\(e\left(\frac{73}{98}\right)\)
\(\chi_{3940}(43,\cdot)\)	3940.bx	196	yes	\(1\)	\(1\)	\(e\left(\frac{153}{196}\right)\)	\(e\left(\frac{69}{196}\right)\)	\(e\left(\frac{55}{98}\right)\)	\(e\left(\frac{2}{49}\right)\)	\(e\left(\frac{39}{196}\right)\)	\(e\left(\frac{5}{196}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{13}{98}\right)\)	\(e\left(\frac{99}{196}\right)\)	\(e\left(\frac{67}{196}\right)\)
\(\chi_{3940}(47,\cdot)\)	3940.bx	196	yes	\(1\)	\(1\)	\(e\left(\frac{39}{196}\right)\)	\(e\left(\frac{179}{196}\right)\)	\(e\left(\frac{39}{98}\right)\)	\(e\left(\frac{13}{49}\right)\)	\(e\left(\frac{33}{196}\right)\)	\(e\left(\frac{155}{196}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{11}{98}\right)\)	\(e\left(\frac{129}{196}\right)\)	\(e\left(\frac{117}{196}\right)\)
\(\chi_{3940}(49,\cdot)\)	3940.bq	98	no	\(1\)	\(1\)	\(e\left(\frac{15}{98}\right)\)	\(e\left(\frac{1}{98}\right)\)	\(e\left(\frac{15}{49}\right)\)	\(e\left(\frac{10}{49}\right)\)	\(e\left(\frac{73}{98}\right)\)	\(e\left(\frac{37}{98}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{8}{49}\right)\)	\(e\left(\frac{27}{98}\right)\)	\(e\left(\frac{45}{98}\right)\)
\(\chi_{3940}(51,\cdot)\)	3940.bs	98	no	\(-1\)	\(1\)	\(e\left(\frac{47}{98}\right)\)	\(e\left(\frac{75}{98}\right)\)	\(e\left(\frac{47}{49}\right)\)	\(e\left(\frac{79}{98}\right)\)	\(e\left(\frac{18}{49}\right)\)	\(e\left(\frac{40}{49}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{12}{49}\right)\)	\(e\left(\frac{65}{98}\right)\)	\(e\left(\frac{43}{98}\right)\)
\(\chi_{3940}(53,\cdot)\)	3940.cg	196	no	\(-1\)	\(1\)	\(e\left(\frac{145}{196}\right)\)	\(e\left(\frac{75}{196}\right)\)	\(e\left(\frac{47}{98}\right)\)	\(e\left(\frac{32}{49}\right)\)	\(e\left(\frac{85}{196}\right)\)	\(e\left(\frac{31}{196}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{6}{49}\right)\)	\(e\left(\frac{65}{196}\right)\)	\(e\left(\frac{43}{196}\right)\)
\(\chi_{3940}(57,\cdot)\)	3940.bz	196	no	\(1\)	\(1\)	\(e\left(\frac{11}{98}\right)\)	\(e\left(\frac{155}{196}\right)\)	\(e\left(\frac{11}{49}\right)\)	\(e\left(\frac{111}{196}\right)\)	\(e\left(\frac{47}{98}\right)\)	\(e\left(\frac{1}{98}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{177}{196}\right)\)	\(e\left(\frac{167}{196}\right)\)	\(e\left(\frac{33}{98}\right)\)
\(\chi_{3940}(59,\cdot)\)	3940.bu	98	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{49}\right)\)	\(e\left(\frac{47}{49}\right)\)	\(e\left(\frac{38}{49}\right)\)	\(e\left(\frac{67}{98}\right)\)	\(e\left(\frac{51}{98}\right)\)	\(e\left(\frac{97}{98}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{17}{49}\right)\)	\(e\left(\frac{44}{49}\right)\)	\(e\left(\frac{8}{49}\right)\)
\(\chi_{3940}(61,\cdot)\)	3940.bo	49	no	\(1\)	\(1\)	\(e\left(\frac{5}{49}\right)\)	\(e\left(\frac{33}{49}\right)\)	\(e\left(\frac{10}{49}\right)\)	\(e\left(\frac{23}{49}\right)\)	\(e\left(\frac{8}{49}\right)\)	\(e\left(\frac{45}{49}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{38}{49}\right)\)	\(e\left(\frac{9}{49}\right)\)	\(e\left(\frac{15}{49}\right)\)
\(\chi_{3940}(63,\cdot)\)	3940.ca	196	yes	\(1\)	\(1\)	\(e\left(\frac{171}{196}\right)\)	\(e\left(\frac{129}{196}\right)\)	\(e\left(\frac{73}{98}\right)\)	\(e\left(\frac{65}{98}\right)\)	\(e\left(\frac{9}{196}\right)\)	\(e\left(\frac{167}{196}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{26}{49}\right)\)	\(e\left(\frac{151}{196}\right)\)	\(e\left(\frac{121}{196}\right)\)
\(\chi_{3940}(67,\cdot)\)	3940.ce	196	yes	\(-1\)	\(1\)	\(e\left(\frac{93}{98}\right)\)	\(e\left(\frac{81}{196}\right)\)	\(e\left(\frac{44}{49}\right)\)	\(e\left(\frac{3}{196}\right)\)	\(e\left(\frac{45}{49}\right)\)	\(e\left(\frac{2}{49}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{71}{196}\right)\)	\(e\left(\frac{129}{196}\right)\)	\(e\left(\frac{83}{98}\right)\)
\(\chi_{3940}(69,\cdot)\)	3940.be	28	no	\(-1\)	\(1\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(-1\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{11}{28}\right)\)
\(\chi_{3940}(71,\cdot)\)	3940.cb	196	no	\(1\)	\(1\)	\(e\left(\frac{9}{196}\right)\)	\(e\left(\frac{32}{49}\right)\)	\(e\left(\frac{9}{98}\right)\)	\(e\left(\frac{61}{196}\right)\)	\(e\left(\frac{83}{196}\right)\)	\(e\left(\frac{81}{196}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{137}{196}\right)\)	\(e\left(\frac{13}{98}\right)\)	\(e\left(\frac{27}{196}\right)\)
\(\chi_{3940}(73,\cdot)\)	3940.bz	196	no	\(1\)	\(1\)	\(e\left(\frac{79}{98}\right)\)	\(e\left(\frac{53}{196}\right)\)	\(e\left(\frac{30}{49}\right)\)	\(e\left(\frac{129}{196}\right)\)	\(e\left(\frac{97}{98}\right)\)	\(e\left(\frac{25}{98}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{15}{196}\right)\)	\(e\left(\frac{157}{196}\right)\)	\(e\left(\frac{41}{98}\right)\)
\(\chi_{3940}(77,\cdot)\)	3940.bn	28	no	\(1\)	\(1\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(1\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{1}{14}\right)\)
\(\chi_{3940}(79,\cdot)\)	3940.bw	196	yes	\(1\)	\(1\)	\(e\left(\frac{159}{196}\right)\)	\(e\left(\frac{69}{98}\right)\)	\(e\left(\frac{61}{98}\right)\)	\(e\left(\frac{65}{196}\right)\)	\(e\left(\frac{29}{196}\right)\)	\(e\left(\frac{59}{196}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{101}{196}\right)\)	\(e\left(\frac{25}{49}\right)\)	\(e\left(\frac{85}{196}\right)\)

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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.