LMFDB - Group of Dirichlet characters of modulus 24648

sage:H = DirichletGroup(24648)

pari:g = idealstar(,24648,2)

Character group

sage:G.order() pari:g.no
Order	=	7488
sage:H.invariants() pari:g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{6}\times C_{156}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{24648}(18487,\cdot)$, $\chi_{24648}(12325,\cdot)$, $\chi_{24648}(16433,\cdot)$, $\chi_{24648}(11377,\cdot)$, $\chi_{24648}(12169,\cdot)$

First 32 of 7488 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	$-1$	$1$	$5$	$7$	$11$	$17$	$19$	$23$	$25$	$29$	$31$	$35$
$\chi_{24648}(1,\cdot)$	24648.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{24648}(5,\cdot)$	24648.qd	156	yes	$1$	$1$	$e\left(\frac{5}{156}\right)$	$e\left(\frac{59}{156}\right)$	$e\left(\frac{47}{156}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{107}{156}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{41}{156}\right)$	$e\left(\frac{16}{39}\right)$
$\chi_{24648}(7,\cdot)$	24648.rl	156	no	$-1$	$1$	$e\left(\frac{59}{156}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{19}{156}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{125}{156}\right)$	$e\left(\frac{38}{39}\right)$
$\chi_{24648}(11,\cdot)$	24648.rh	156	yes	$-1$	$1$	$e\left(\frac{47}{156}\right)$	$e\left(\frac{19}{156}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{127}{156}\right)$	$-1$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{89}{156}\right)$	$e\left(\frac{11}{26}\right)$
$\chi_{24648}(17,\cdot)$	24648.lu	78	no	$1$	$1$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{31}{39}\right)$
$\chi_{24648}(19,\cdot)$	24648.qn	156	no	$1$	$1$	$e\left(\frac{107}{156}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{127}{156}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{35}{156}\right)$	$e\left(\frac{20}{39}\right)$
$\chi_{24648}(23,\cdot)$	24648.da	6	no	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$1$
$\chi_{24648}(25,\cdot)$	24648.mh	78	no	$1$	$1$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{32}{39}\right)$
$\chi_{24648}(29,\cdot)$	24648.oa	78	yes	$1$	$1$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{53}{78}\right)$	$-1$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{23}{26}\right)$
$\chi_{24648}(31,\cdot)$	24648.sg	156	no	$1$	$1$	$e\left(\frac{41}{156}\right)$	$e\left(\frac{125}{156}\right)$	$e\left(\frac{89}{156}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{35}{156}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{71}{156}\right)$	$e\left(\frac{5}{78}\right)$
$\chi_{24648}(35,\cdot)$	24648.pb	78	yes	$-1$	$1$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{20}{39}\right)$	$1$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{5}{13}\right)$
$\chi_{24648}(37,\cdot)$	24648.rv	156	no	$1$	$1$	$e\left(\frac{133}{156}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{23}{156}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{139}{156}\right)$	$e\left(\frac{7}{39}\right)$
$\chi_{24648}(41,\cdot)$	24648.qt	156	no	$-1$	$1$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{137}{156}\right)$	$e\left(\frac{73}{156}\right)$	$e\left(\frac{67}{78}\right)$	$e\left(\frac{29}{156}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{29}{39}\right)$
$\chi_{24648}(43,\cdot)$	24648.ok	78	no	$1$	$1$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{73}{78}\right)$	$-1$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{15}{26}\right)$
$\chi_{24648}(47,\cdot)$	24648.sk	156	no	$1$	$1$	$e\left(\frac{101}{156}\right)$	$e\left(\frac{53}{156}\right)$	$e\left(\frac{29}{156}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{149}{156}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{17}{156}\right)$	$e\left(\frac{77}{78}\right)$
$\chi_{24648}(49,\cdot)$	24648.nm	78	no	$1$	$1$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{37}{39}\right)$
$\chi_{24648}(53,\cdot)$	24648.og	78	no	$1$	$1$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{67}{78}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{41}{78}\right)$
$\chi_{24648}(55,\cdot)$	24648.cu	6	no	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{24648}(59,\cdot)$	24648.qk	156	yes	$1$	$1$	$e\left(\frac{139}{156}\right)$	$e\left(\frac{101}{156}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{47}{156}\right)$	$-1$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{1}{156}\right)$	$e\left(\frac{7}{13}\right)$
$\chi_{24648}(61,\cdot)$	24648.pk	78	no	$-1$	$1$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{7}{39}\right)$
$\chi_{24648}(67,\cdot)$	24648.qr	156	no	$1$	$1$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{5}{156}\right)$	$e\left(\frac{67}{156}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{17}{156}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{17}{39}\right)$
$\chi_{24648}(71,\cdot)$	24648.ra	156	no	$1$	$1$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{115}{156}\right)$	$e\left(\frac{59}{156}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{79}{156}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{41}{78}\right)$
$\chi_{24648}(73,\cdot)$	24648.sl	156	no	$-1$	$1$	$e\left(\frac{35}{156}\right)$	$e\left(\frac{101}{156}\right)$	$e\left(\frac{17}{156}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{47}{156}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{131}{156}\right)$	$e\left(\frac{34}{39}\right)$
$\chi_{24648}(77,\cdot)$	24648.my	78	yes	$1$	$1$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{31}{78}\right)$
$\chi_{24648}(83,\cdot)$	24648.qg	156	yes	$-1$	$1$	$e\left(\frac{17}{156}\right)$	$e\left(\frac{29}{156}\right)$	$e\left(\frac{113}{156}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{5}{156}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{155}{156}\right)$	$e\left(\frac{23}{78}\right)$
$\chi_{24648}(85,\cdot)$	24648.rv	156	no	$1$	$1$	$e\left(\frac{113}{156}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{43}{156}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{131}{156}\right)$	$e\left(\frac{8}{39}\right)$
$\chi_{24648}(89,\cdot)$	24648.ro	156	no	$1$	$1$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{41}{156}\right)$	$e\left(\frac{19}{156}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{155}{156}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{37}{78}\right)$
$\chi_{24648}(95,\cdot)$	24648.oz	78	no	$1$	$1$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{35}{39}\right)$	$1$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{12}{13}\right)$
$\chi_{24648}(97,\cdot)$	24648.rb	156	no	$-1$	$1$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{103}{156}\right)$	$e\left(\frac{23}{156}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{85}{156}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{7}{39}\right)$
$\chi_{24648}(101,\cdot)$	24648.pl	78	yes	$-1$	$1$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{32}{39}\right)$
$\chi_{24648}(103,\cdot)$	24648.fl	6	no	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{24648}(107,\cdot)$	24648.nt	78	yes	$-1$	$1$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{4}{39}\right)$

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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	$24648$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{6}\times C_{156}\)
Order	$7488$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(35\)
\(\chi_{24648}(1,\cdot)\)	24648.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{24648}(5,\cdot)\)	24648.qd	156	yes	\(1\)	\(1\)	\(e\left(\frac{5}{156}\right)\)	\(e\left(\frac{59}{156}\right)\)	\(e\left(\frac{47}{156}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{107}{156}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{41}{156}\right)\)	\(e\left(\frac{16}{39}\right)\)
\(\chi_{24648}(7,\cdot)\)	24648.rl	156	no	\(-1\)	\(1\)	\(e\left(\frac{59}{156}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{19}{156}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{125}{156}\right)\)	\(e\left(\frac{38}{39}\right)\)
\(\chi_{24648}(11,\cdot)\)	24648.rh	156	yes	\(-1\)	\(1\)	\(e\left(\frac{47}{156}\right)\)	\(e\left(\frac{19}{156}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{127}{156}\right)\)	\(-1\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{89}{156}\right)\)	\(e\left(\frac{11}{26}\right)\)
\(\chi_{24648}(17,\cdot)\)	24648.lu	78	no	\(1\)	\(1\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{31}{39}\right)\)
\(\chi_{24648}(19,\cdot)\)	24648.qn	156	no	\(1\)	\(1\)	\(e\left(\frac{107}{156}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{127}{156}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{35}{156}\right)\)	\(e\left(\frac{20}{39}\right)\)
\(\chi_{24648}(23,\cdot)\)	24648.da	6	no	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(1\)
\(\chi_{24648}(25,\cdot)\)	24648.mh	78	no	\(1\)	\(1\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{32}{39}\right)\)
\(\chi_{24648}(29,\cdot)\)	24648.oa	78	yes	\(1\)	\(1\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(-1\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{23}{26}\right)\)
\(\chi_{24648}(31,\cdot)\)	24648.sg	156	no	\(1\)	\(1\)	\(e\left(\frac{41}{156}\right)\)	\(e\left(\frac{125}{156}\right)\)	\(e\left(\frac{89}{156}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{35}{156}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{71}{156}\right)\)	\(e\left(\frac{5}{78}\right)\)
\(\chi_{24648}(35,\cdot)\)	24648.pb	78	yes	\(-1\)	\(1\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(1\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{5}{13}\right)\)
\(\chi_{24648}(37,\cdot)\)	24648.rv	156	no	\(1\)	\(1\)	\(e\left(\frac{133}{156}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{23}{156}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{139}{156}\right)\)	\(e\left(\frac{7}{39}\right)\)
\(\chi_{24648}(41,\cdot)\)	24648.qt	156	no	\(-1\)	\(1\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{137}{156}\right)\)	\(e\left(\frac{73}{156}\right)\)	\(e\left(\frac{67}{78}\right)\)	\(e\left(\frac{29}{156}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{29}{39}\right)\)
\(\chi_{24648}(43,\cdot)\)	24648.ok	78	no	\(1\)	\(1\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(-1\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{15}{26}\right)\)
\(\chi_{24648}(47,\cdot)\)	24648.sk	156	no	\(1\)	\(1\)	\(e\left(\frac{101}{156}\right)\)	\(e\left(\frac{53}{156}\right)\)	\(e\left(\frac{29}{156}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{149}{156}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{17}{156}\right)\)	\(e\left(\frac{77}{78}\right)\)
\(\chi_{24648}(49,\cdot)\)	24648.nm	78	no	\(1\)	\(1\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{37}{39}\right)\)
\(\chi_{24648}(53,\cdot)\)	24648.og	78	no	\(1\)	\(1\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{67}{78}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{41}{78}\right)\)
\(\chi_{24648}(55,\cdot)\)	24648.cu	6	no	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{24648}(59,\cdot)\)	24648.qk	156	yes	\(1\)	\(1\)	\(e\left(\frac{139}{156}\right)\)	\(e\left(\frac{101}{156}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{47}{156}\right)\)	\(-1\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{1}{156}\right)\)	\(e\left(\frac{7}{13}\right)\)
\(\chi_{24648}(61,\cdot)\)	24648.pk	78	no	\(-1\)	\(1\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{7}{39}\right)\)
\(\chi_{24648}(67,\cdot)\)	24648.qr	156	no	\(1\)	\(1\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{5}{156}\right)\)	\(e\left(\frac{67}{156}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{17}{156}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{17}{39}\right)\)
\(\chi_{24648}(71,\cdot)\)	24648.ra	156	no	\(1\)	\(1\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{115}{156}\right)\)	\(e\left(\frac{59}{156}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{79}{156}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{41}{78}\right)\)
\(\chi_{24648}(73,\cdot)\)	24648.sl	156	no	\(-1\)	\(1\)	\(e\left(\frac{35}{156}\right)\)	\(e\left(\frac{101}{156}\right)\)	\(e\left(\frac{17}{156}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{47}{156}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{131}{156}\right)\)	\(e\left(\frac{34}{39}\right)\)
\(\chi_{24648}(77,\cdot)\)	24648.my	78	yes	\(1\)	\(1\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{31}{78}\right)\)
\(\chi_{24648}(83,\cdot)\)	24648.qg	156	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{156}\right)\)	\(e\left(\frac{29}{156}\right)\)	\(e\left(\frac{113}{156}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{5}{156}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{155}{156}\right)\)	\(e\left(\frac{23}{78}\right)\)
\(\chi_{24648}(85,\cdot)\)	24648.rv	156	no	\(1\)	\(1\)	\(e\left(\frac{113}{156}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{43}{156}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{131}{156}\right)\)	\(e\left(\frac{8}{39}\right)\)
\(\chi_{24648}(89,\cdot)\)	24648.ro	156	no	\(1\)	\(1\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{41}{156}\right)\)	\(e\left(\frac{19}{156}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{155}{156}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{37}{78}\right)\)
\(\chi_{24648}(95,\cdot)\)	24648.oz	78	no	\(1\)	\(1\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(1\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{12}{13}\right)\)
\(\chi_{24648}(97,\cdot)\)	24648.rb	156	no	\(-1\)	\(1\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{103}{156}\right)\)	\(e\left(\frac{23}{156}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{85}{156}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{7}{39}\right)\)
\(\chi_{24648}(101,\cdot)\)	24648.pl	78	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{32}{39}\right)\)
\(\chi_{24648}(103,\cdot)\)	24648.fl	6	no	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{24648}(107,\cdot)\)	24648.nt	78	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{4}{39}\right)\)

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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.