LMFDB - Group of Dirichlet characters of modulus 1372

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1372)

pari: g = idealstar(,1372,2)

Character group

sage: G.order() pari: g.no
Order	=	588
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{294}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{1372}(687,\cdot)$, $\chi_{1372}(689,\cdot)$

First 32 of 588 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	$-1$	$1$	$3$	$5$	$9$	$11$	$13$	$15$	$17$	$19$	$23$	$25$
$\chi_{1372}(1,\cdot)$	1372.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1372}(3,\cdot)$	1372.v	294	yes	$1$	$1$	$e\left(\frac{74}{147}\right)$	$e\left(\frac{29}{294}\right)$	$e\left(\frac{1}{147}\right)$	$e\left(\frac{61}{294}\right)$	$e\left(\frac{95}{98}\right)$	$e\left(\frac{59}{98}\right)$	$e\left(\frac{25}{294}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{17}{294}\right)$	$e\left(\frac{29}{147}\right)$
$\chi_{1372}(5,\cdot)$	1372.x	294	no	$-1$	$1$	$e\left(\frac{29}{294}\right)$	$e\left(\frac{253}{294}\right)$	$e\left(\frac{29}{147}\right)$	$e\left(\frac{76}{147}\right)$	$e\left(\frac{11}{98}\right)$	$e\left(\frac{47}{49}\right)$	$e\left(\frac{137}{294}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{26}{147}\right)$	$e\left(\frac{106}{147}\right)$
$\chi_{1372}(9,\cdot)$	1372.u	147	no	$1$	$1$	$e\left(\frac{1}{147}\right)$	$e\left(\frac{29}{147}\right)$	$e\left(\frac{2}{147}\right)$	$e\left(\frac{61}{147}\right)$	$e\left(\frac{46}{49}\right)$	$e\left(\frac{10}{49}\right)$	$e\left(\frac{25}{147}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{17}{147}\right)$	$e\left(\frac{58}{147}\right)$
$\chi_{1372}(11,\cdot)$	1372.w	294	yes	$-1$	$1$	$e\left(\frac{61}{294}\right)$	$e\left(\frac{76}{147}\right)$	$e\left(\frac{61}{147}\right)$	$e\left(\frac{193}{294}\right)$	$e\left(\frac{31}{49}\right)$	$e\left(\frac{71}{98}\right)$	$e\left(\frac{101}{147}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{155}{294}\right)$	$e\left(\frac{5}{147}\right)$
$\chi_{1372}(13,\cdot)$	1372.r	98	no	$-1$	$1$	$e\left(\frac{95}{98}\right)$	$e\left(\frac{11}{98}\right)$	$e\left(\frac{46}{49}\right)$	$e\left(\frac{31}{49}\right)$	$e\left(\frac{27}{98}\right)$	$e\left(\frac{4}{49}\right)$	$e\left(\frac{23}{98}\right)$	$-1$	$e\left(\frac{48}{49}\right)$	$e\left(\frac{11}{49}\right)$
$\chi_{1372}(15,\cdot)$	1372.s	98	yes	$-1$	$1$	$e\left(\frac{59}{98}\right)$	$e\left(\frac{47}{49}\right)$	$e\left(\frac{10}{49}\right)$	$e\left(\frac{71}{98}\right)$	$e\left(\frac{4}{49}\right)$	$e\left(\frac{55}{98}\right)$	$e\left(\frac{27}{49}\right)$	$-1$	$e\left(\frac{23}{98}\right)$	$e\left(\frac{45}{49}\right)$
$\chi_{1372}(17,\cdot)$	1372.x	294	no	$-1$	$1$	$e\left(\frac{25}{294}\right)$	$e\left(\frac{137}{294}\right)$	$e\left(\frac{25}{147}\right)$	$e\left(\frac{101}{147}\right)$	$e\left(\frac{23}{98}\right)$	$e\left(\frac{27}{49}\right)$	$e\left(\frac{37}{294}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{139}{147}\right)$	$e\left(\frac{137}{147}\right)$
$\chi_{1372}(19,\cdot)$	1372.f	6	no	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{1372}(23,\cdot)$	1372.w	294	yes	$-1$	$1$	$e\left(\frac{17}{294}\right)$	$e\left(\frac{26}{147}\right)$	$e\left(\frac{17}{147}\right)$	$e\left(\frac{155}{294}\right)$	$e\left(\frac{48}{49}\right)$	$e\left(\frac{23}{98}\right)$	$e\left(\frac{139}{147}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{289}{294}\right)$	$e\left(\frac{52}{147}\right)$
$\chi_{1372}(25,\cdot)$	1372.u	147	no	$1$	$1$	$e\left(\frac{29}{147}\right)$	$e\left(\frac{106}{147}\right)$	$e\left(\frac{58}{147}\right)$	$e\left(\frac{5}{147}\right)$	$e\left(\frac{11}{49}\right)$	$e\left(\frac{45}{49}\right)$	$e\left(\frac{137}{147}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{52}{147}\right)$	$e\left(\frac{65}{147}\right)$
$\chi_{1372}(27,\cdot)$	1372.t	98	yes	$1$	$1$	$e\left(\frac{25}{49}\right)$	$e\left(\frac{29}{98}\right)$	$e\left(\frac{1}{49}\right)$	$e\left(\frac{61}{98}\right)$	$e\left(\frac{89}{98}\right)$	$e\left(\frac{79}{98}\right)$	$e\left(\frac{25}{98}\right)$	$1$	$e\left(\frac{17}{98}\right)$	$e\left(\frac{29}{49}\right)$
$\chi_{1372}(29,\cdot)$	1372.q	49	no	$1$	$1$	$e\left(\frac{38}{49}\right)$	$e\left(\frac{24}{49}\right)$	$e\left(\frac{27}{49}\right)$	$e\left(\frac{15}{49}\right)$	$e\left(\frac{1}{49}\right)$	$e\left(\frac{13}{49}\right)$	$e\left(\frac{19}{49}\right)$	$1$	$e\left(\frac{9}{49}\right)$	$e\left(\frac{48}{49}\right)$
$\chi_{1372}(31,\cdot)$	1372.p	42	no	$1$	$1$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{5}{21}\right)$
$\chi_{1372}(33,\cdot)$	1372.x	294	no	$-1$	$1$	$e\left(\frac{209}{294}\right)$	$e\left(\frac{181}{294}\right)$	$e\left(\frac{62}{147}\right)$	$e\left(\frac{127}{147}\right)$	$e\left(\frac{59}{98}\right)$	$e\left(\frac{16}{49}\right)$	$e\left(\frac{227}{294}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{86}{147}\right)$	$e\left(\frac{34}{147}\right)$
$\chi_{1372}(37,\cdot)$	1372.u	147	no	$1$	$1$	$e\left(\frac{37}{147}\right)$	$e\left(\frac{44}{147}\right)$	$e\left(\frac{74}{147}\right)$	$e\left(\frac{52}{147}\right)$	$e\left(\frac{36}{49}\right)$	$e\left(\frac{27}{49}\right)$	$e\left(\frac{43}{147}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{41}{147}\right)$	$e\left(\frac{88}{147}\right)$
$\chi_{1372}(39,\cdot)$	1372.w	294	yes	$-1$	$1$	$e\left(\frac{139}{294}\right)$	$e\left(\frac{31}{147}\right)$	$e\left(\frac{139}{147}\right)$	$e\left(\frac{247}{294}\right)$	$e\left(\frac{12}{49}\right)$	$e\left(\frac{67}{98}\right)$	$e\left(\frac{47}{147}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{294}\right)$	$e\left(\frac{62}{147}\right)$
$\chi_{1372}(41,\cdot)$	1372.r	98	no	$-1$	$1$	$e\left(\frac{61}{98}\right)$	$e\left(\frac{5}{98}\right)$	$e\left(\frac{12}{49}\right)$	$e\left(\frac{23}{49}\right)$	$e\left(\frac{39}{98}\right)$	$e\left(\frac{33}{49}\right)$	$e\left(\frac{55}{98}\right)$	$-1$	$e\left(\frac{4}{49}\right)$	$e\left(\frac{5}{49}\right)$
$\chi_{1372}(43,\cdot)$	1372.s	98	yes	$-1$	$1$	$e\left(\frac{51}{98}\right)$	$e\left(\frac{29}{49}\right)$	$e\left(\frac{2}{49}\right)$	$e\left(\frac{73}{98}\right)$	$e\left(\frac{40}{49}\right)$	$e\left(\frac{11}{98}\right)$	$e\left(\frac{25}{49}\right)$	$-1$	$e\left(\frac{83}{98}\right)$	$e\left(\frac{9}{49}\right)$
$\chi_{1372}(45,\cdot)$	1372.x	294	no	$-1$	$1$	$e\left(\frac{31}{294}\right)$	$e\left(\frac{17}{294}\right)$	$e\left(\frac{31}{147}\right)$	$e\left(\frac{137}{147}\right)$	$e\left(\frac{5}{98}\right)$	$e\left(\frac{8}{49}\right)$	$e\left(\frac{187}{294}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{43}{147}\right)$	$e\left(\frac{17}{147}\right)$
$\chi_{1372}(47,\cdot)$	1372.v	294	yes	$1$	$1$	$e\left(\frac{34}{147}\right)$	$e\left(\frac{61}{294}\right)$	$e\left(\frac{68}{147}\right)$	$e\left(\frac{179}{294}\right)$	$e\left(\frac{41}{98}\right)$	$e\left(\frac{43}{98}\right)$	$e\left(\frac{83}{294}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{127}{294}\right)$	$e\left(\frac{61}{147}\right)$
$\chi_{1372}(51,\cdot)$	1372.w	294	yes	$-1$	$1$	$e\left(\frac{173}{294}\right)$	$e\left(\frac{83}{147}\right)$	$e\left(\frac{26}{147}\right)$	$e\left(\frac{263}{294}\right)$	$e\left(\frac{10}{49}\right)$	$e\left(\frac{15}{98}\right)$	$e\left(\frac{31}{147}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{294}\right)$	$e\left(\frac{19}{147}\right)$
$\chi_{1372}(53,\cdot)$	1372.u	147	no	$1$	$1$	$e\left(\frac{5}{147}\right)$	$e\left(\frac{145}{147}\right)$	$e\left(\frac{10}{147}\right)$	$e\left(\frac{11}{147}\right)$	$e\left(\frac{34}{49}\right)$	$e\left(\frac{1}{49}\right)$	$e\left(\frac{125}{147}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{85}{147}\right)$	$e\left(\frac{143}{147}\right)$
$\chi_{1372}(55,\cdot)$	1372.t	98	yes	$1$	$1$	$e\left(\frac{15}{49}\right)$	$e\left(\frac{37}{98}\right)$	$e\left(\frac{30}{49}\right)$	$e\left(\frac{17}{98}\right)$	$e\left(\frac{73}{98}\right)$	$e\left(\frac{67}{98}\right)$	$e\left(\frac{15}{98}\right)$	$1$	$e\left(\frac{69}{98}\right)$	$e\left(\frac{37}{49}\right)$
$\chi_{1372}(57,\cdot)$	1372.q	49	no	$1$	$1$	$e\left(\frac{41}{49}\right)$	$e\left(\frac{13}{49}\right)$	$e\left(\frac{33}{49}\right)$	$e\left(\frac{2}{49}\right)$	$e\left(\frac{23}{49}\right)$	$e\left(\frac{5}{49}\right)$	$e\left(\frac{45}{49}\right)$	$1$	$e\left(\frac{11}{49}\right)$	$e\left(\frac{26}{49}\right)$
$\chi_{1372}(59,\cdot)$	1372.v	294	yes	$1$	$1$	$e\left(\frac{80}{147}\right)$	$e\left(\frac{83}{294}\right)$	$e\left(\frac{13}{147}\right)$	$e\left(\frac{205}{294}\right)$	$e\left(\frac{59}{98}\right)$	$e\left(\frac{81}{98}\right)$	$e\left(\frac{31}{294}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{221}{294}\right)$	$e\left(\frac{83}{147}\right)$
$\chi_{1372}(61,\cdot)$	1372.x	294	no	$-1$	$1$	$e\left(\frac{263}{294}\right)$	$e\left(\frac{277}{294}\right)$	$e\left(\frac{116}{147}\right)$	$e\left(\frac{10}{147}\right)$	$e\left(\frac{93}{98}\right)$	$e\left(\frac{41}{49}\right)$	$e\left(\frac{107}{294}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{104}{147}\right)$	$e\left(\frac{130}{147}\right)$
$\chi_{1372}(65,\cdot)$	1372.u	147	no	$1$	$1$	$e\left(\frac{10}{147}\right)$	$e\left(\frac{143}{147}\right)$	$e\left(\frac{20}{147}\right)$	$e\left(\frac{22}{147}\right)$	$e\left(\frac{19}{49}\right)$	$e\left(\frac{2}{49}\right)$	$e\left(\frac{103}{147}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{23}{147}\right)$	$e\left(\frac{139}{147}\right)$
$\chi_{1372}(67,\cdot)$	1372.o	42	no	$-1$	$1$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{2}{21}\right)$
$\chi_{1372}(69,\cdot)$	1372.r	98	no	$-1$	$1$	$e\left(\frac{55}{98}\right)$	$e\left(\frac{27}{98}\right)$	$e\left(\frac{6}{49}\right)$	$e\left(\frac{36}{49}\right)$	$e\left(\frac{93}{98}\right)$	$e\left(\frac{41}{49}\right)$	$e\left(\frac{3}{98}\right)$	$-1$	$e\left(\frac{2}{49}\right)$	$e\left(\frac{27}{49}\right)$
$\chi_{1372}(71,\cdot)$	1372.s	98	yes	$-1$	$1$	$e\left(\frac{71}{98}\right)$	$e\left(\frac{25}{49}\right)$	$e\left(\frac{22}{49}\right)$	$e\left(\frac{19}{98}\right)$	$e\left(\frac{48}{49}\right)$	$e\left(\frac{23}{98}\right)$	$e\left(\frac{30}{49}\right)$	$-1$	$e\left(\frac{31}{98}\right)$	$e\left(\frac{1}{49}\right)$
$\chi_{1372}(73,\cdot)$	1372.x	294	no	$-1$	$1$	$e\left(\frac{79}{294}\right)$	$e\left(\frac{233}{294}\right)$	$e\left(\frac{79}{147}\right)$	$e\left(\frac{131}{147}\right)$	$e\left(\frac{57}{98}\right)$	$e\left(\frac{3}{49}\right)$	$e\left(\frac{211}{294}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{10}{147}\right)$	$e\left(\frac{86}{147}\right)$

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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	$1372$
Structure	\(C_{2}\times C_{294}\)
Order	$588$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(23\)	\(25\)
\(\chi_{1372}(1,\cdot)\)	1372.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1372}(3,\cdot)\)	1372.v	294	yes	\(1\)	\(1\)	\(e\left(\frac{74}{147}\right)\)	\(e\left(\frac{29}{294}\right)\)	\(e\left(\frac{1}{147}\right)\)	\(e\left(\frac{61}{294}\right)\)	\(e\left(\frac{95}{98}\right)\)	\(e\left(\frac{59}{98}\right)\)	\(e\left(\frac{25}{294}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{17}{294}\right)\)	\(e\left(\frac{29}{147}\right)\)
\(\chi_{1372}(5,\cdot)\)	1372.x	294	no	\(-1\)	\(1\)	\(e\left(\frac{29}{294}\right)\)	\(e\left(\frac{253}{294}\right)\)	\(e\left(\frac{29}{147}\right)\)	\(e\left(\frac{76}{147}\right)\)	\(e\left(\frac{11}{98}\right)\)	\(e\left(\frac{47}{49}\right)\)	\(e\left(\frac{137}{294}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{26}{147}\right)\)	\(e\left(\frac{106}{147}\right)\)
\(\chi_{1372}(9,\cdot)\)	1372.u	147	no	\(1\)	\(1\)	\(e\left(\frac{1}{147}\right)\)	\(e\left(\frac{29}{147}\right)\)	\(e\left(\frac{2}{147}\right)\)	\(e\left(\frac{61}{147}\right)\)	\(e\left(\frac{46}{49}\right)\)	\(e\left(\frac{10}{49}\right)\)	\(e\left(\frac{25}{147}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{17}{147}\right)\)	\(e\left(\frac{58}{147}\right)\)
\(\chi_{1372}(11,\cdot)\)	1372.w	294	yes	\(-1\)	\(1\)	\(e\left(\frac{61}{294}\right)\)	\(e\left(\frac{76}{147}\right)\)	\(e\left(\frac{61}{147}\right)\)	\(e\left(\frac{193}{294}\right)\)	\(e\left(\frac{31}{49}\right)\)	\(e\left(\frac{71}{98}\right)\)	\(e\left(\frac{101}{147}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{155}{294}\right)\)	\(e\left(\frac{5}{147}\right)\)
\(\chi_{1372}(13,\cdot)\)	1372.r	98	no	\(-1\)	\(1\)	\(e\left(\frac{95}{98}\right)\)	\(e\left(\frac{11}{98}\right)\)	\(e\left(\frac{46}{49}\right)\)	\(e\left(\frac{31}{49}\right)\)	\(e\left(\frac{27}{98}\right)\)	\(e\left(\frac{4}{49}\right)\)	\(e\left(\frac{23}{98}\right)\)	\(-1\)	\(e\left(\frac{48}{49}\right)\)	\(e\left(\frac{11}{49}\right)\)
\(\chi_{1372}(15,\cdot)\)	1372.s	98	yes	\(-1\)	\(1\)	\(e\left(\frac{59}{98}\right)\)	\(e\left(\frac{47}{49}\right)\)	\(e\left(\frac{10}{49}\right)\)	\(e\left(\frac{71}{98}\right)\)	\(e\left(\frac{4}{49}\right)\)	\(e\left(\frac{55}{98}\right)\)	\(e\left(\frac{27}{49}\right)\)	\(-1\)	\(e\left(\frac{23}{98}\right)\)	\(e\left(\frac{45}{49}\right)\)
\(\chi_{1372}(17,\cdot)\)	1372.x	294	no	\(-1\)	\(1\)	\(e\left(\frac{25}{294}\right)\)	\(e\left(\frac{137}{294}\right)\)	\(e\left(\frac{25}{147}\right)\)	\(e\left(\frac{101}{147}\right)\)	\(e\left(\frac{23}{98}\right)\)	\(e\left(\frac{27}{49}\right)\)	\(e\left(\frac{37}{294}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{139}{147}\right)\)	\(e\left(\frac{137}{147}\right)\)
\(\chi_{1372}(19,\cdot)\)	1372.f	6	no	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{1372}(23,\cdot)\)	1372.w	294	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{294}\right)\)	\(e\left(\frac{26}{147}\right)\)	\(e\left(\frac{17}{147}\right)\)	\(e\left(\frac{155}{294}\right)\)	\(e\left(\frac{48}{49}\right)\)	\(e\left(\frac{23}{98}\right)\)	\(e\left(\frac{139}{147}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{289}{294}\right)\)	\(e\left(\frac{52}{147}\right)\)
\(\chi_{1372}(25,\cdot)\)	1372.u	147	no	\(1\)	\(1\)	\(e\left(\frac{29}{147}\right)\)	\(e\left(\frac{106}{147}\right)\)	\(e\left(\frac{58}{147}\right)\)	\(e\left(\frac{5}{147}\right)\)	\(e\left(\frac{11}{49}\right)\)	\(e\left(\frac{45}{49}\right)\)	\(e\left(\frac{137}{147}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{52}{147}\right)\)	\(e\left(\frac{65}{147}\right)\)
\(\chi_{1372}(27,\cdot)\)	1372.t	98	yes	\(1\)	\(1\)	\(e\left(\frac{25}{49}\right)\)	\(e\left(\frac{29}{98}\right)\)	\(e\left(\frac{1}{49}\right)\)	\(e\left(\frac{61}{98}\right)\)	\(e\left(\frac{89}{98}\right)\)	\(e\left(\frac{79}{98}\right)\)	\(e\left(\frac{25}{98}\right)\)	\(1\)	\(e\left(\frac{17}{98}\right)\)	\(e\left(\frac{29}{49}\right)\)
\(\chi_{1372}(29,\cdot)\)	1372.q	49	no	\(1\)	\(1\)	\(e\left(\frac{38}{49}\right)\)	\(e\left(\frac{24}{49}\right)\)	\(e\left(\frac{27}{49}\right)\)	\(e\left(\frac{15}{49}\right)\)	\(e\left(\frac{1}{49}\right)\)	\(e\left(\frac{13}{49}\right)\)	\(e\left(\frac{19}{49}\right)\)	\(1\)	\(e\left(\frac{9}{49}\right)\)	\(e\left(\frac{48}{49}\right)\)
\(\chi_{1372}(31,\cdot)\)	1372.p	42	no	\(1\)	\(1\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{5}{21}\right)\)
\(\chi_{1372}(33,\cdot)\)	1372.x	294	no	\(-1\)	\(1\)	\(e\left(\frac{209}{294}\right)\)	\(e\left(\frac{181}{294}\right)\)	\(e\left(\frac{62}{147}\right)\)	\(e\left(\frac{127}{147}\right)\)	\(e\left(\frac{59}{98}\right)\)	\(e\left(\frac{16}{49}\right)\)	\(e\left(\frac{227}{294}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{86}{147}\right)\)	\(e\left(\frac{34}{147}\right)\)
\(\chi_{1372}(37,\cdot)\)	1372.u	147	no	\(1\)	\(1\)	\(e\left(\frac{37}{147}\right)\)	\(e\left(\frac{44}{147}\right)\)	\(e\left(\frac{74}{147}\right)\)	\(e\left(\frac{52}{147}\right)\)	\(e\left(\frac{36}{49}\right)\)	\(e\left(\frac{27}{49}\right)\)	\(e\left(\frac{43}{147}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{41}{147}\right)\)	\(e\left(\frac{88}{147}\right)\)
\(\chi_{1372}(39,\cdot)\)	1372.w	294	yes	\(-1\)	\(1\)	\(e\left(\frac{139}{294}\right)\)	\(e\left(\frac{31}{147}\right)\)	\(e\left(\frac{139}{147}\right)\)	\(e\left(\frac{247}{294}\right)\)	\(e\left(\frac{12}{49}\right)\)	\(e\left(\frac{67}{98}\right)\)	\(e\left(\frac{47}{147}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{294}\right)\)	\(e\left(\frac{62}{147}\right)\)
\(\chi_{1372}(41,\cdot)\)	1372.r	98	no	\(-1\)	\(1\)	\(e\left(\frac{61}{98}\right)\)	\(e\left(\frac{5}{98}\right)\)	\(e\left(\frac{12}{49}\right)\)	\(e\left(\frac{23}{49}\right)\)	\(e\left(\frac{39}{98}\right)\)	\(e\left(\frac{33}{49}\right)\)	\(e\left(\frac{55}{98}\right)\)	\(-1\)	\(e\left(\frac{4}{49}\right)\)	\(e\left(\frac{5}{49}\right)\)
\(\chi_{1372}(43,\cdot)\)	1372.s	98	yes	\(-1\)	\(1\)	\(e\left(\frac{51}{98}\right)\)	\(e\left(\frac{29}{49}\right)\)	\(e\left(\frac{2}{49}\right)\)	\(e\left(\frac{73}{98}\right)\)	\(e\left(\frac{40}{49}\right)\)	\(e\left(\frac{11}{98}\right)\)	\(e\left(\frac{25}{49}\right)\)	\(-1\)	\(e\left(\frac{83}{98}\right)\)	\(e\left(\frac{9}{49}\right)\)
\(\chi_{1372}(45,\cdot)\)	1372.x	294	no	\(-1\)	\(1\)	\(e\left(\frac{31}{294}\right)\)	\(e\left(\frac{17}{294}\right)\)	\(e\left(\frac{31}{147}\right)\)	\(e\left(\frac{137}{147}\right)\)	\(e\left(\frac{5}{98}\right)\)	\(e\left(\frac{8}{49}\right)\)	\(e\left(\frac{187}{294}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{43}{147}\right)\)	\(e\left(\frac{17}{147}\right)\)
\(\chi_{1372}(47,\cdot)\)	1372.v	294	yes	\(1\)	\(1\)	\(e\left(\frac{34}{147}\right)\)	\(e\left(\frac{61}{294}\right)\)	\(e\left(\frac{68}{147}\right)\)	\(e\left(\frac{179}{294}\right)\)	\(e\left(\frac{41}{98}\right)\)	\(e\left(\frac{43}{98}\right)\)	\(e\left(\frac{83}{294}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{127}{294}\right)\)	\(e\left(\frac{61}{147}\right)\)
\(\chi_{1372}(51,\cdot)\)	1372.w	294	yes	\(-1\)	\(1\)	\(e\left(\frac{173}{294}\right)\)	\(e\left(\frac{83}{147}\right)\)	\(e\left(\frac{26}{147}\right)\)	\(e\left(\frac{263}{294}\right)\)	\(e\left(\frac{10}{49}\right)\)	\(e\left(\frac{15}{98}\right)\)	\(e\left(\frac{31}{147}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{294}\right)\)	\(e\left(\frac{19}{147}\right)\)
\(\chi_{1372}(53,\cdot)\)	1372.u	147	no	\(1\)	\(1\)	\(e\left(\frac{5}{147}\right)\)	\(e\left(\frac{145}{147}\right)\)	\(e\left(\frac{10}{147}\right)\)	\(e\left(\frac{11}{147}\right)\)	\(e\left(\frac{34}{49}\right)\)	\(e\left(\frac{1}{49}\right)\)	\(e\left(\frac{125}{147}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{85}{147}\right)\)	\(e\left(\frac{143}{147}\right)\)
\(\chi_{1372}(55,\cdot)\)	1372.t	98	yes	\(1\)	\(1\)	\(e\left(\frac{15}{49}\right)\)	\(e\left(\frac{37}{98}\right)\)	\(e\left(\frac{30}{49}\right)\)	\(e\left(\frac{17}{98}\right)\)	\(e\left(\frac{73}{98}\right)\)	\(e\left(\frac{67}{98}\right)\)	\(e\left(\frac{15}{98}\right)\)	\(1\)	\(e\left(\frac{69}{98}\right)\)	\(e\left(\frac{37}{49}\right)\)
\(\chi_{1372}(57,\cdot)\)	1372.q	49	no	\(1\)	\(1\)	\(e\left(\frac{41}{49}\right)\)	\(e\left(\frac{13}{49}\right)\)	\(e\left(\frac{33}{49}\right)\)	\(e\left(\frac{2}{49}\right)\)	\(e\left(\frac{23}{49}\right)\)	\(e\left(\frac{5}{49}\right)\)	\(e\left(\frac{45}{49}\right)\)	\(1\)	\(e\left(\frac{11}{49}\right)\)	\(e\left(\frac{26}{49}\right)\)
\(\chi_{1372}(59,\cdot)\)	1372.v	294	yes	\(1\)	\(1\)	\(e\left(\frac{80}{147}\right)\)	\(e\left(\frac{83}{294}\right)\)	\(e\left(\frac{13}{147}\right)\)	\(e\left(\frac{205}{294}\right)\)	\(e\left(\frac{59}{98}\right)\)	\(e\left(\frac{81}{98}\right)\)	\(e\left(\frac{31}{294}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{221}{294}\right)\)	\(e\left(\frac{83}{147}\right)\)
\(\chi_{1372}(61,\cdot)\)	1372.x	294	no	\(-1\)	\(1\)	\(e\left(\frac{263}{294}\right)\)	\(e\left(\frac{277}{294}\right)\)	\(e\left(\frac{116}{147}\right)\)	\(e\left(\frac{10}{147}\right)\)	\(e\left(\frac{93}{98}\right)\)	\(e\left(\frac{41}{49}\right)\)	\(e\left(\frac{107}{294}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{104}{147}\right)\)	\(e\left(\frac{130}{147}\right)\)
\(\chi_{1372}(65,\cdot)\)	1372.u	147	no	\(1\)	\(1\)	\(e\left(\frac{10}{147}\right)\)	\(e\left(\frac{143}{147}\right)\)	\(e\left(\frac{20}{147}\right)\)	\(e\left(\frac{22}{147}\right)\)	\(e\left(\frac{19}{49}\right)\)	\(e\left(\frac{2}{49}\right)\)	\(e\left(\frac{103}{147}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{23}{147}\right)\)	\(e\left(\frac{139}{147}\right)\)
\(\chi_{1372}(67,\cdot)\)	1372.o	42	no	\(-1\)	\(1\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{2}{21}\right)\)
\(\chi_{1372}(69,\cdot)\)	1372.r	98	no	\(-1\)	\(1\)	\(e\left(\frac{55}{98}\right)\)	\(e\left(\frac{27}{98}\right)\)	\(e\left(\frac{6}{49}\right)\)	\(e\left(\frac{36}{49}\right)\)	\(e\left(\frac{93}{98}\right)\)	\(e\left(\frac{41}{49}\right)\)	\(e\left(\frac{3}{98}\right)\)	\(-1\)	\(e\left(\frac{2}{49}\right)\)	\(e\left(\frac{27}{49}\right)\)
\(\chi_{1372}(71,\cdot)\)	1372.s	98	yes	\(-1\)	\(1\)	\(e\left(\frac{71}{98}\right)\)	\(e\left(\frac{25}{49}\right)\)	\(e\left(\frac{22}{49}\right)\)	\(e\left(\frac{19}{98}\right)\)	\(e\left(\frac{48}{49}\right)\)	\(e\left(\frac{23}{98}\right)\)	\(e\left(\frac{30}{49}\right)\)	\(-1\)	\(e\left(\frac{31}{98}\right)\)	\(e\left(\frac{1}{49}\right)\)
\(\chi_{1372}(73,\cdot)\)	1372.x	294	no	\(-1\)	\(1\)	\(e\left(\frac{79}{294}\right)\)	\(e\left(\frac{233}{294}\right)\)	\(e\left(\frac{79}{147}\right)\)	\(e\left(\frac{131}{147}\right)\)	\(e\left(\frac{57}{98}\right)\)	\(e\left(\frac{3}{49}\right)\)	\(e\left(\frac{211}{294}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{10}{147}\right)\)	\(e\left(\frac{86}{147}\right)\)

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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.