LMFDB - Group of Dirichlet characters of modulus 12348

Show commands: PariGP / SageMath

sage: H = DirichletGroup(12348)

pari: g = idealstar(,12348,2)

Character group

sage: G.order() pari: g.no
Order	=	3528
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{6}\times C_{294}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{12348}(6175,\cdot)$, $\chi_{12348}(9605,\cdot)$, $\chi_{12348}(11665,\cdot)$

First 32 of 3528 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	$-1$	$1$	$5$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$	$37$
$\chi_{12348}(1,\cdot)$	12348.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{12348}(5,\cdot)$	12348.ek	294	no	$1$	$1$	$e\left(\frac{4}{147}\right)$	$e\left(\frac{103}{294}\right)$	$e\left(\frac{229}{294}\right)$	$e\left(\frac{142}{147}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{101}{294}\right)$	$e\left(\frac{8}{147}\right)$	$e\left(\frac{95}{294}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{44}{147}\right)$
$\chi_{12348}(11,\cdot)$	12348.em	294	yes	$1$	$1$	$e\left(\frac{103}{294}\right)$	$e\left(\frac{121}{147}\right)$	$e\left(\frac{142}{147}\right)$	$e\left(\frac{55}{294}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{53}{147}\right)$	$e\left(\frac{103}{147}\right)$	$e\left(\frac{139}{294}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{52}{147}\right)$
$\chi_{12348}(13,\cdot)$	12348.dq	294	no	$-1$	$1$	$e\left(\frac{229}{294}\right)$	$e\left(\frac{142}{147}\right)$	$e\left(\frac{277}{294}\right)$	$e\left(\frac{23}{98}\right)$	$-1$	$e\left(\frac{95}{147}\right)$	$e\left(\frac{82}{147}\right)$	$e\left(\frac{52}{147}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{36}{49}\right)$
$\chi_{12348}(17,\cdot)$	12348.ei	294	no	$1$	$1$	$e\left(\frac{142}{147}\right)$	$e\left(\frac{55}{294}\right)$	$e\left(\frac{23}{98}\right)$	$e\left(\frac{92}{147}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{131}{294}\right)$	$e\left(\frac{137}{147}\right)$	$e\left(\frac{87}{98}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{43}{147}\right)$
$\chi_{12348}(19,\cdot)$	12348.bf	6	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{12348}(23,\cdot)$	12348.em	294	yes	$1$	$1$	$e\left(\frac{101}{294}\right)$	$e\left(\frac{53}{147}\right)$	$e\left(\frac{95}{147}\right)$	$e\left(\frac{131}{294}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{22}{147}\right)$	$e\left(\frac{101}{147}\right)$	$e\left(\frac{5}{294}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{41}{147}\right)$
$\chi_{12348}(25,\cdot)$	12348.dk	147	no	$1$	$1$	$e\left(\frac{8}{147}\right)$	$e\left(\frac{103}{147}\right)$	$e\left(\frac{82}{147}\right)$	$e\left(\frac{137}{147}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{101}{147}\right)$	$e\left(\frac{16}{147}\right)$	$e\left(\frac{95}{147}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{88}{147}\right)$
$\chi_{12348}(29,\cdot)$	12348.ep	294	no	$-1$	$1$	$e\left(\frac{95}{294}\right)$	$e\left(\frac{139}{294}\right)$	$e\left(\frac{52}{147}\right)$	$e\left(\frac{87}{98}\right)$	$1$	$e\left(\frac{5}{294}\right)$	$e\left(\frac{95}{147}\right)$	$e\left(\frac{289}{294}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{19}{49}\right)$
$\chi_{12348}(31,\cdot)$	12348.da	42	no	$1$	$1$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{10}{21}\right)$
$\chi_{12348}(37,\cdot)$	12348.dl	147	no	$1$	$1$	$e\left(\frac{44}{147}\right)$	$e\left(\frac{52}{147}\right)$	$e\left(\frac{36}{49}\right)$	$e\left(\frac{43}{147}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{41}{147}\right)$	$e\left(\frac{88}{147}\right)$	$e\left(\frac{19}{49}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{92}{147}\right)$
$\chi_{12348}(41,\cdot)$	12348.dr	294	no	$1$	$1$	$e\left(\frac{32}{147}\right)$	$e\left(\frac{89}{294}\right)$	$e\left(\frac{19}{294}\right)$	$e\left(\frac{3}{49}\right)$	$-1$	$e\left(\frac{73}{294}\right)$	$e\left(\frac{64}{147}\right)$	$e\left(\frac{221}{294}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{3}{49}\right)$
$\chi_{12348}(43,\cdot)$	12348.do	294	yes	$-1$	$1$	$e\left(\frac{136}{147}\right)$	$e\left(\frac{121}{294}\right)$	$e\left(\frac{22}{147}\right)$	$e\left(\frac{25}{49}\right)$	$-1$	$e\left(\frac{53}{294}\right)$	$e\left(\frac{125}{147}\right)$	$e\left(\frac{47}{147}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{25}{49}\right)$
$\chi_{12348}(47,\cdot)$	12348.dw	294	yes	$-1$	$1$	$e\left(\frac{2}{49}\right)$	$e\left(\frac{38}{49}\right)$	$e\left(\frac{221}{294}\right)$	$e\left(\frac{115}{147}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{13}{49}\right)$	$e\left(\frac{4}{49}\right)$	$e\left(\frac{265}{294}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{17}{147}\right)$
$\chi_{12348}(53,\cdot)$	12348.dz	294	no	$-1$	$1$	$e\left(\frac{143}{294}\right)$	$e\left(\frac{169}{294}\right)$	$e\left(\frac{34}{49}\right)$	$e\left(\frac{103}{294}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{23}{294}\right)$	$e\left(\frac{143}{147}\right)$	$e\left(\frac{25}{98}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{76}{147}\right)$
$\chi_{12348}(55,\cdot)$	12348.di	98	no	$1$	$1$	$e\left(\frac{37}{98}\right)$	$e\left(\frac{17}{98}\right)$	$e\left(\frac{73}{98}\right)$	$e\left(\frac{15}{98}\right)$	$1$	$e\left(\frac{69}{98}\right)$	$e\left(\frac{37}{49}\right)$	$e\left(\frac{39}{49}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{32}{49}\right)$
$\chi_{12348}(59,\cdot)$	12348.dw	294	yes	$-1$	$1$	$e\left(\frac{22}{49}\right)$	$e\left(\frac{26}{49}\right)$	$e\left(\frac{79}{294}\right)$	$e\left(\frac{89}{147}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{45}{49}\right)$	$e\left(\frac{44}{49}\right)$	$e\left(\frac{269}{294}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{40}{147}\right)$
$\chi_{12348}(61,\cdot)$	12348.ef	294	no	$-1$	$1$	$e\left(\frac{27}{98}\right)$	$e\left(\frac{36}{49}\right)$	$e\left(\frac{83}{294}\right)$	$e\left(\frac{107}{294}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{49}\right)$	$e\left(\frac{27}{49}\right)$	$e\left(\frac{92}{147}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{29}{147}\right)$
$\chi_{12348}(65,\cdot)$	12348.ea	294	no	$-1$	$1$	$e\left(\frac{79}{98}\right)$	$e\left(\frac{31}{98}\right)$	$e\left(\frac{106}{147}\right)$	$e\left(\frac{59}{294}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{97}{98}\right)$	$e\left(\frac{30}{49}\right)$	$e\left(\frac{199}{294}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{5}{147}\right)$
$\chi_{12348}(67,\cdot)$	12348.cc	42	no	$-1$	$1$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{4}{21}\right)$
$\chi_{12348}(71,\cdot)$	12348.dg	98	no	$1$	$1$	$e\left(\frac{1}{98}\right)$	$e\left(\frac{34}{49}\right)$	$e\left(\frac{48}{49}\right)$	$e\left(\frac{11}{98}\right)$	$-1$	$e\left(\frac{40}{49}\right)$	$e\left(\frac{1}{49}\right)$	$e\left(\frac{67}{98}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{30}{49}\right)$
$\chi_{12348}(73,\cdot)$	12348.eh	294	no	$-1$	$1$	$e\left(\frac{233}{294}\right)$	$e\left(\frac{131}{147}\right)$	$e\left(\frac{57}{98}\right)$	$e\left(\frac{211}{294}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{10}{147}\right)$	$e\left(\frac{86}{147}\right)$	$e\left(\frac{13}{49}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{130}{147}\right)$
$\chi_{12348}(79,\cdot)$	12348.cc	42	no	$-1$	$1$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{21}\right)$
$\chi_{12348}(83,\cdot)$	12348.eo	294	yes	$-1$	$1$	$e\left(\frac{85}{147}\right)$	$e\left(\frac{47}{147}\right)$	$e\left(\frac{101}{294}\right)$	$e\left(\frac{34}{49}\right)$	$1$	$e\left(\frac{136}{147}\right)$	$e\left(\frac{23}{147}\right)$	$e\left(\frac{169}{294}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{34}{49}\right)$
$\chi_{12348}(85,\cdot)$	12348.dn	147	no	$1$	$1$	$e\left(\frac{146}{147}\right)$	$e\left(\frac{79}{147}\right)$	$e\left(\frac{2}{147}\right)$	$e\left(\frac{29}{49}\right)$	$1$	$e\left(\frac{116}{147}\right)$	$e\left(\frac{145}{147}\right)$	$e\left(\frac{31}{147}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{29}{49}\right)$
$\chi_{12348}(89,\cdot)$	12348.ei	294	no	$1$	$1$	$e\left(\frac{50}{147}\right)$	$e\left(\frac{185}{294}\right)$	$e\left(\frac{15}{98}\right)$	$e\left(\frac{109}{147}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{13}{294}\right)$	$e\left(\frac{100}{147}\right)$	$e\left(\frac{61}{98}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{11}{147}\right)$
$\chi_{12348}(95,\cdot)$	12348.ee	294	yes	$1$	$1$	$e\left(\frac{19}{98}\right)$	$e\left(\frac{9}{49}\right)$	$e\left(\frac{41}{147}\right)$	$e\left(\frac{235}{294}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{25}{49}\right)$	$e\left(\frac{19}{49}\right)$	$e\left(\frac{95}{294}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{142}{147}\right)$
$\chi_{12348}(97,\cdot)$	12348.cl	42	no	$-1$	$1$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{9}{14}\right)$	$-1$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{7}\right)$
$\chi_{12348}(101,\cdot)$	12348.ek	294	no	$1$	$1$	$e\left(\frac{74}{147}\right)$	$e\left(\frac{215}{294}\right)$	$e\left(\frac{47}{294}\right)$	$e\left(\frac{128}{147}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{31}{294}\right)$	$e\left(\frac{1}{147}\right)$	$e\left(\frac{67}{294}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{79}{147}\right)$
$\chi_{12348}(103,\cdot)$	12348.dt	294	yes	$1$	$1$	$e\left(\frac{197}{294}\right)$	$e\left(\frac{19}{294}\right)$	$e\left(\frac{145}{294}\right)$	$e\left(\frac{11}{294}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{227}{294}\right)$	$e\left(\frac{50}{147}\right)$	$e\left(\frac{58}{147}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{128}{147}\right)$
$\chi_{12348}(107,\cdot)$	12348.ec	294	no	$1$	$1$	$e\left(\frac{163}{294}\right)$	$e\left(\frac{103}{147}\right)$	$e\left(\frac{11}{49}\right)$	$e\left(\frac{29}{294}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{101}{147}\right)$	$e\left(\frac{16}{147}\right)$	$e\left(\frac{47}{98}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{137}{147}\right)$
$\chi_{12348}(109,\cdot)$	12348.dl	147	no	$1$	$1$	$e\left(\frac{139}{147}\right)$	$e\left(\frac{44}{147}\right)$	$e\left(\frac{38}{49}\right)$	$e\left(\frac{59}{147}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{46}{147}\right)$	$e\left(\frac{131}{147}\right)$	$e\left(\frac{1}{49}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{10}{147}\right)$

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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	$12348$
Structure	\(C_{2}\times C_{6}\times C_{294}\)
Order	$3528$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(37\)
\(\chi_{12348}(1,\cdot)\)	12348.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{12348}(5,\cdot)\)	12348.ek	294	no	\(1\)	\(1\)	\(e\left(\frac{4}{147}\right)\)	\(e\left(\frac{103}{294}\right)\)	\(e\left(\frac{229}{294}\right)\)	\(e\left(\frac{142}{147}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{101}{294}\right)\)	\(e\left(\frac{8}{147}\right)\)	\(e\left(\frac{95}{294}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{44}{147}\right)\)
\(\chi_{12348}(11,\cdot)\)	12348.em	294	yes	\(1\)	\(1\)	\(e\left(\frac{103}{294}\right)\)	\(e\left(\frac{121}{147}\right)\)	\(e\left(\frac{142}{147}\right)\)	\(e\left(\frac{55}{294}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{53}{147}\right)\)	\(e\left(\frac{103}{147}\right)\)	\(e\left(\frac{139}{294}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{52}{147}\right)\)
\(\chi_{12348}(13,\cdot)\)	12348.dq	294	no	\(-1\)	\(1\)	\(e\left(\frac{229}{294}\right)\)	\(e\left(\frac{142}{147}\right)\)	\(e\left(\frac{277}{294}\right)\)	\(e\left(\frac{23}{98}\right)\)	\(-1\)	\(e\left(\frac{95}{147}\right)\)	\(e\left(\frac{82}{147}\right)\)	\(e\left(\frac{52}{147}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{36}{49}\right)\)
\(\chi_{12348}(17,\cdot)\)	12348.ei	294	no	\(1\)	\(1\)	\(e\left(\frac{142}{147}\right)\)	\(e\left(\frac{55}{294}\right)\)	\(e\left(\frac{23}{98}\right)\)	\(e\left(\frac{92}{147}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{131}{294}\right)\)	\(e\left(\frac{137}{147}\right)\)	\(e\left(\frac{87}{98}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{43}{147}\right)\)
\(\chi_{12348}(19,\cdot)\)	12348.bf	6	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{12348}(23,\cdot)\)	12348.em	294	yes	\(1\)	\(1\)	\(e\left(\frac{101}{294}\right)\)	\(e\left(\frac{53}{147}\right)\)	\(e\left(\frac{95}{147}\right)\)	\(e\left(\frac{131}{294}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{22}{147}\right)\)	\(e\left(\frac{101}{147}\right)\)	\(e\left(\frac{5}{294}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{41}{147}\right)\)
\(\chi_{12348}(25,\cdot)\)	12348.dk	147	no	\(1\)	\(1\)	\(e\left(\frac{8}{147}\right)\)	\(e\left(\frac{103}{147}\right)\)	\(e\left(\frac{82}{147}\right)\)	\(e\left(\frac{137}{147}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{101}{147}\right)\)	\(e\left(\frac{16}{147}\right)\)	\(e\left(\frac{95}{147}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{88}{147}\right)\)
\(\chi_{12348}(29,\cdot)\)	12348.ep	294	no	\(-1\)	\(1\)	\(e\left(\frac{95}{294}\right)\)	\(e\left(\frac{139}{294}\right)\)	\(e\left(\frac{52}{147}\right)\)	\(e\left(\frac{87}{98}\right)\)	\(1\)	\(e\left(\frac{5}{294}\right)\)	\(e\left(\frac{95}{147}\right)\)	\(e\left(\frac{289}{294}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{19}{49}\right)\)
\(\chi_{12348}(31,\cdot)\)	12348.da	42	no	\(1\)	\(1\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{10}{21}\right)\)
\(\chi_{12348}(37,\cdot)\)	12348.dl	147	no	\(1\)	\(1\)	\(e\left(\frac{44}{147}\right)\)	\(e\left(\frac{52}{147}\right)\)	\(e\left(\frac{36}{49}\right)\)	\(e\left(\frac{43}{147}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{41}{147}\right)\)	\(e\left(\frac{88}{147}\right)\)	\(e\left(\frac{19}{49}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{92}{147}\right)\)
\(\chi_{12348}(41,\cdot)\)	12348.dr	294	no	\(1\)	\(1\)	\(e\left(\frac{32}{147}\right)\)	\(e\left(\frac{89}{294}\right)\)	\(e\left(\frac{19}{294}\right)\)	\(e\left(\frac{3}{49}\right)\)	\(-1\)	\(e\left(\frac{73}{294}\right)\)	\(e\left(\frac{64}{147}\right)\)	\(e\left(\frac{221}{294}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{3}{49}\right)\)
\(\chi_{12348}(43,\cdot)\)	12348.do	294	yes	\(-1\)	\(1\)	\(e\left(\frac{136}{147}\right)\)	\(e\left(\frac{121}{294}\right)\)	\(e\left(\frac{22}{147}\right)\)	\(e\left(\frac{25}{49}\right)\)	\(-1\)	\(e\left(\frac{53}{294}\right)\)	\(e\left(\frac{125}{147}\right)\)	\(e\left(\frac{47}{147}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{25}{49}\right)\)
\(\chi_{12348}(47,\cdot)\)	12348.dw	294	yes	\(-1\)	\(1\)	\(e\left(\frac{2}{49}\right)\)	\(e\left(\frac{38}{49}\right)\)	\(e\left(\frac{221}{294}\right)\)	\(e\left(\frac{115}{147}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{13}{49}\right)\)	\(e\left(\frac{4}{49}\right)\)	\(e\left(\frac{265}{294}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{17}{147}\right)\)
\(\chi_{12348}(53,\cdot)\)	12348.dz	294	no	\(-1\)	\(1\)	\(e\left(\frac{143}{294}\right)\)	\(e\left(\frac{169}{294}\right)\)	\(e\left(\frac{34}{49}\right)\)	\(e\left(\frac{103}{294}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{23}{294}\right)\)	\(e\left(\frac{143}{147}\right)\)	\(e\left(\frac{25}{98}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{76}{147}\right)\)
\(\chi_{12348}(55,\cdot)\)	12348.di	98	no	\(1\)	\(1\)	\(e\left(\frac{37}{98}\right)\)	\(e\left(\frac{17}{98}\right)\)	\(e\left(\frac{73}{98}\right)\)	\(e\left(\frac{15}{98}\right)\)	\(1\)	\(e\left(\frac{69}{98}\right)\)	\(e\left(\frac{37}{49}\right)\)	\(e\left(\frac{39}{49}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{32}{49}\right)\)
\(\chi_{12348}(59,\cdot)\)	12348.dw	294	yes	\(-1\)	\(1\)	\(e\left(\frac{22}{49}\right)\)	\(e\left(\frac{26}{49}\right)\)	\(e\left(\frac{79}{294}\right)\)	\(e\left(\frac{89}{147}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{45}{49}\right)\)	\(e\left(\frac{44}{49}\right)\)	\(e\left(\frac{269}{294}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{40}{147}\right)\)
\(\chi_{12348}(61,\cdot)\)	12348.ef	294	no	\(-1\)	\(1\)	\(e\left(\frac{27}{98}\right)\)	\(e\left(\frac{36}{49}\right)\)	\(e\left(\frac{83}{294}\right)\)	\(e\left(\frac{107}{294}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{49}\right)\)	\(e\left(\frac{27}{49}\right)\)	\(e\left(\frac{92}{147}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{29}{147}\right)\)
\(\chi_{12348}(65,\cdot)\)	12348.ea	294	no	\(-1\)	\(1\)	\(e\left(\frac{79}{98}\right)\)	\(e\left(\frac{31}{98}\right)\)	\(e\left(\frac{106}{147}\right)\)	\(e\left(\frac{59}{294}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{97}{98}\right)\)	\(e\left(\frac{30}{49}\right)\)	\(e\left(\frac{199}{294}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{5}{147}\right)\)
\(\chi_{12348}(67,\cdot)\)	12348.cc	42	no	\(-1\)	\(1\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{4}{21}\right)\)
\(\chi_{12348}(71,\cdot)\)	12348.dg	98	no	\(1\)	\(1\)	\(e\left(\frac{1}{98}\right)\)	\(e\left(\frac{34}{49}\right)\)	\(e\left(\frac{48}{49}\right)\)	\(e\left(\frac{11}{98}\right)\)	\(-1\)	\(e\left(\frac{40}{49}\right)\)	\(e\left(\frac{1}{49}\right)\)	\(e\left(\frac{67}{98}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{30}{49}\right)\)
\(\chi_{12348}(73,\cdot)\)	12348.eh	294	no	\(-1\)	\(1\)	\(e\left(\frac{233}{294}\right)\)	\(e\left(\frac{131}{147}\right)\)	\(e\left(\frac{57}{98}\right)\)	\(e\left(\frac{211}{294}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{10}{147}\right)\)	\(e\left(\frac{86}{147}\right)\)	\(e\left(\frac{13}{49}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{130}{147}\right)\)
\(\chi_{12348}(79,\cdot)\)	12348.cc	42	no	\(-1\)	\(1\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{21}\right)\)
\(\chi_{12348}(83,\cdot)\)	12348.eo	294	yes	\(-1\)	\(1\)	\(e\left(\frac{85}{147}\right)\)	\(e\left(\frac{47}{147}\right)\)	\(e\left(\frac{101}{294}\right)\)	\(e\left(\frac{34}{49}\right)\)	\(1\)	\(e\left(\frac{136}{147}\right)\)	\(e\left(\frac{23}{147}\right)\)	\(e\left(\frac{169}{294}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{34}{49}\right)\)
\(\chi_{12348}(85,\cdot)\)	12348.dn	147	no	\(1\)	\(1\)	\(e\left(\frac{146}{147}\right)\)	\(e\left(\frac{79}{147}\right)\)	\(e\left(\frac{2}{147}\right)\)	\(e\left(\frac{29}{49}\right)\)	\(1\)	\(e\left(\frac{116}{147}\right)\)	\(e\left(\frac{145}{147}\right)\)	\(e\left(\frac{31}{147}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{29}{49}\right)\)
\(\chi_{12348}(89,\cdot)\)	12348.ei	294	no	\(1\)	\(1\)	\(e\left(\frac{50}{147}\right)\)	\(e\left(\frac{185}{294}\right)\)	\(e\left(\frac{15}{98}\right)\)	\(e\left(\frac{109}{147}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{13}{294}\right)\)	\(e\left(\frac{100}{147}\right)\)	\(e\left(\frac{61}{98}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{11}{147}\right)\)
\(\chi_{12348}(95,\cdot)\)	12348.ee	294	yes	\(1\)	\(1\)	\(e\left(\frac{19}{98}\right)\)	\(e\left(\frac{9}{49}\right)\)	\(e\left(\frac{41}{147}\right)\)	\(e\left(\frac{235}{294}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{25}{49}\right)\)	\(e\left(\frac{19}{49}\right)\)	\(e\left(\frac{95}{294}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{142}{147}\right)\)
\(\chi_{12348}(97,\cdot)\)	12348.cl	42	no	\(-1\)	\(1\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(-1\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{7}\right)\)
\(\chi_{12348}(101,\cdot)\)	12348.ek	294	no	\(1\)	\(1\)	\(e\left(\frac{74}{147}\right)\)	\(e\left(\frac{215}{294}\right)\)	\(e\left(\frac{47}{294}\right)\)	\(e\left(\frac{128}{147}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{31}{294}\right)\)	\(e\left(\frac{1}{147}\right)\)	\(e\left(\frac{67}{294}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{79}{147}\right)\)
\(\chi_{12348}(103,\cdot)\)	12348.dt	294	yes	\(1\)	\(1\)	\(e\left(\frac{197}{294}\right)\)	\(e\left(\frac{19}{294}\right)\)	\(e\left(\frac{145}{294}\right)\)	\(e\left(\frac{11}{294}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{227}{294}\right)\)	\(e\left(\frac{50}{147}\right)\)	\(e\left(\frac{58}{147}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{128}{147}\right)\)
\(\chi_{12348}(107,\cdot)\)	12348.ec	294	no	\(1\)	\(1\)	\(e\left(\frac{163}{294}\right)\)	\(e\left(\frac{103}{147}\right)\)	\(e\left(\frac{11}{49}\right)\)	\(e\left(\frac{29}{294}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{101}{147}\right)\)	\(e\left(\frac{16}{147}\right)\)	\(e\left(\frac{47}{98}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{137}{147}\right)\)
\(\chi_{12348}(109,\cdot)\)	12348.dl	147	no	\(1\)	\(1\)	\(e\left(\frac{139}{147}\right)\)	\(e\left(\frac{44}{147}\right)\)	\(e\left(\frac{38}{49}\right)\)	\(e\left(\frac{59}{147}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{46}{147}\right)\)	\(e\left(\frac{131}{147}\right)\)	\(e\left(\frac{1}{49}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{10}{147}\right)\)

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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.