LMFDB - Group of Dirichlet characters of modulus 959

Show commands: PariGP / SageMath

sage: H = DirichletGroup(959)

pari: g = idealstar(,959,2)

Character group

sage: G.order() pari: g.no
Order	=	816
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{408}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{959}(549,\cdot)$, $\chi_{959}(414,\cdot)$

First 32 of 816 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$8$	$9$	$10$	$11$	$12$
$\chi_{959}(1,\cdot)$	959.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{959}(2,\cdot)$	959.bc	204	yes	$1$	$1$	$e\left(\frac{41}{102}\right)$	$e\left(\frac{83}{204}\right)$	$e\left(\frac{41}{51}\right)$	$e\left(\frac{37}{204}\right)$	$e\left(\frac{55}{68}\right)$	$e\left(\frac{7}{34}\right)$	$e\left(\frac{83}{102}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{31}{102}\right)$	$e\left(\frac{43}{204}\right)$
$\chi_{959}(3,\cdot)$	959.bf	408	yes	$1$	$1$	$e\left(\frac{83}{204}\right)$	$e\left(\frac{71}{408}\right)$	$e\left(\frac{83}{102}\right)$	$e\left(\frac{157}{408}\right)$	$e\left(\frac{79}{136}\right)$	$e\left(\frac{15}{68}\right)$	$e\left(\frac{71}{204}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{115}{204}\right)$	$e\left(\frac{403}{408}\right)$
$\chi_{959}(4,\cdot)$	959.y	102	yes	$1$	$1$	$e\left(\frac{41}{51}\right)$	$e\left(\frac{83}{102}\right)$	$e\left(\frac{31}{51}\right)$	$e\left(\frac{37}{102}\right)$	$e\left(\frac{21}{34}\right)$	$e\left(\frac{7}{17}\right)$	$e\left(\frac{32}{51}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{31}{51}\right)$	$e\left(\frac{43}{102}\right)$
$\chi_{959}(5,\cdot)$	959.bf	408	yes	$1$	$1$	$e\left(\frac{37}{204}\right)$	$e\left(\frac{157}{408}\right)$	$e\left(\frac{37}{102}\right)$	$e\left(\frac{215}{408}\right)$	$e\left(\frac{77}{136}\right)$	$e\left(\frac{37}{68}\right)$	$e\left(\frac{157}{204}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{125}{204}\right)$	$e\left(\frac{305}{408}\right)$
$\chi_{959}(6,\cdot)$	959.bb	136	yes	$1$	$1$	$e\left(\frac{55}{68}\right)$	$e\left(\frac{79}{136}\right)$	$e\left(\frac{21}{34}\right)$	$e\left(\frac{77}{136}\right)$	$e\left(\frac{53}{136}\right)$	$e\left(\frac{29}{68}\right)$	$e\left(\frac{11}{68}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{59}{68}\right)$	$e\left(\frac{27}{136}\right)$
$\chi_{959}(8,\cdot)$	959.w	68	no	$1$	$1$	$e\left(\frac{7}{34}\right)$	$e\left(\frac{15}{68}\right)$	$e\left(\frac{7}{17}\right)$	$e\left(\frac{37}{68}\right)$	$e\left(\frac{29}{68}\right)$	$e\left(\frac{21}{34}\right)$	$e\left(\frac{15}{34}\right)$	$-i$	$e\left(\frac{31}{34}\right)$	$e\left(\frac{43}{68}\right)$
$\chi_{959}(9,\cdot)$	959.bc	204	yes	$1$	$1$	$e\left(\frac{83}{102}\right)$	$e\left(\frac{71}{204}\right)$	$e\left(\frac{32}{51}\right)$	$e\left(\frac{157}{204}\right)$	$e\left(\frac{11}{68}\right)$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{71}{102}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{13}{102}\right)$	$e\left(\frac{199}{204}\right)$
$\chi_{959}(10,\cdot)$	959.p	24	yes	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{3}{8}\right)$	$-i$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{23}{24}\right)$
$\chi_{959}(11,\cdot)$	959.bc	204	yes	$1$	$1$	$e\left(\frac{31}{102}\right)$	$e\left(\frac{115}{204}\right)$	$e\left(\frac{31}{51}\right)$	$e\left(\frac{125}{204}\right)$	$e\left(\frac{59}{68}\right)$	$e\left(\frac{31}{34}\right)$	$e\left(\frac{13}{102}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{11}{102}\right)$	$e\left(\frac{35}{204}\right)$
$\chi_{959}(12,\cdot)$	959.bf	408	yes	$1$	$1$	$e\left(\frac{43}{204}\right)$	$e\left(\frac{403}{408}\right)$	$e\left(\frac{43}{102}\right)$	$e\left(\frac{305}{408}\right)$	$e\left(\frac{27}{136}\right)$	$e\left(\frac{43}{68}\right)$	$e\left(\frac{199}{204}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{35}{204}\right)$	$e\left(\frac{167}{408}\right)$
$\chi_{959}(13,\cdot)$	959.bb	136	yes	$1$	$1$	$e\left(\frac{57}{68}\right)$	$e\left(\frac{93}{136}\right)$	$e\left(\frac{23}{34}\right)$	$e\left(\frac{39}{136}\right)$	$e\left(\frac{71}{136}\right)$	$e\left(\frac{35}{68}\right)$	$e\left(\frac{25}{68}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{29}{68}\right)$	$e\left(\frac{49}{136}\right)$
$\chi_{959}(15,\cdot)$	959.s	34	no	$1$	$1$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{19}{34}\right)$	$e\left(\frac{3}{17}\right)$	$e\left(\frac{31}{34}\right)$	$e\left(\frac{5}{34}\right)$	$e\left(\frac{13}{17}\right)$	$e\left(\frac{2}{17}\right)$	$-1$	$e\left(\frac{3}{17}\right)$	$e\left(\frac{25}{34}\right)$
$\chi_{959}(16,\cdot)$	959.u	51	yes	$1$	$1$	$e\left(\frac{31}{51}\right)$	$e\left(\frac{32}{51}\right)$	$e\left(\frac{11}{51}\right)$	$e\left(\frac{37}{51}\right)$	$e\left(\frac{4}{17}\right)$	$e\left(\frac{14}{17}\right)$	$e\left(\frac{13}{51}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{51}\right)$	$e\left(\frac{43}{51}\right)$
$\chi_{959}(17,\cdot)$	959.bd	204	yes	$-1$	$1$	$e\left(\frac{13}{102}\right)$	$e\left(\frac{91}{204}\right)$	$e\left(\frac{13}{51}\right)$	$e\left(\frac{161}{204}\right)$	$e\left(\frac{39}{68}\right)$	$e\left(\frac{13}{34}\right)$	$e\left(\frac{91}{102}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{77}{102}\right)$	$e\left(\frac{143}{204}\right)$
$\chi_{959}(18,\cdot)$	959.y	102	yes	$1$	$1$	$e\left(\frac{11}{51}\right)$	$e\left(\frac{77}{102}\right)$	$e\left(\frac{22}{51}\right)$	$e\left(\frac{97}{102}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{11}{17}\right)$	$e\left(\frac{26}{51}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{22}{51}\right)$	$e\left(\frac{19}{102}\right)$
$\chi_{959}(19,\cdot)$	959.bd	204	yes	$-1$	$1$	$e\left(\frac{5}{102}\right)$	$e\left(\frac{35}{204}\right)$	$e\left(\frac{5}{51}\right)$	$e\left(\frac{109}{204}\right)$	$e\left(\frac{15}{68}\right)$	$e\left(\frac{5}{34}\right)$	$e\left(\frac{35}{102}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{61}{102}\right)$	$e\left(\frac{55}{204}\right)$
$\chi_{959}(20,\cdot)$	959.bb	136	yes	$1$	$1$	$e\left(\frac{67}{68}\right)$	$e\left(\frac{27}{136}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{121}{136}\right)$	$e\left(\frac{25}{136}\right)$	$e\left(\frac{65}{68}\right)$	$e\left(\frac{27}{68}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{15}{68}\right)$	$e\left(\frac{23}{136}\right)$
$\chi_{959}(22,\cdot)$	959.s	34	no	$1$	$1$	$e\left(\frac{12}{17}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{7}{17}\right)$	$e\left(\frac{27}{34}\right)$	$e\left(\frac{23}{34}\right)$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{16}{17}\right)$	$-1$	$e\left(\frac{7}{17}\right)$	$e\left(\frac{13}{34}\right)$
$\chi_{959}(23,\cdot)$	959.be	408	yes	$-1$	$1$	$e\left(\frac{175}{204}\right)$	$e\left(\frac{103}{408}\right)$	$e\left(\frac{73}{102}\right)$	$e\left(\frac{245}{408}\right)$	$e\left(\frac{15}{136}\right)$	$e\left(\frac{39}{68}\right)$	$e\left(\frac{103}{204}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{95}{204}\right)$	$e\left(\frac{395}{408}\right)$
$\chi_{959}(24,\cdot)$	959.bf	408	yes	$1$	$1$	$e\left(\frac{125}{204}\right)$	$e\left(\frac{161}{408}\right)$	$e\left(\frac{23}{102}\right)$	$e\left(\frac{379}{408}\right)$	$e\left(\frac{1}{136}\right)$	$e\left(\frac{57}{68}\right)$	$e\left(\frac{161}{204}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{97}{204}\right)$	$e\left(\frac{253}{408}\right)$
$\chi_{959}(25,\cdot)$	959.bc	204	yes	$1$	$1$	$e\left(\frac{37}{102}\right)$	$e\left(\frac{157}{204}\right)$	$e\left(\frac{37}{51}\right)$	$e\left(\frac{11}{204}\right)$	$e\left(\frac{9}{68}\right)$	$e\left(\frac{3}{34}\right)$	$e\left(\frac{55}{102}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{23}{102}\right)$	$e\left(\frac{101}{204}\right)$
$\chi_{959}(26,\cdot)$	959.bf	408	yes	$1$	$1$	$e\left(\frac{49}{204}\right)$	$e\left(\frac{37}{408}\right)$	$e\left(\frac{49}{102}\right)$	$e\left(\frac{191}{408}\right)$	$e\left(\frac{45}{136}\right)$	$e\left(\frac{49}{68}\right)$	$e\left(\frac{37}{204}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{149}{204}\right)$	$e\left(\frac{233}{408}\right)$
$\chi_{959}(27,\cdot)$	959.bb	136	yes	$1$	$1$	$e\left(\frac{15}{68}\right)$	$e\left(\frac{71}{136}\right)$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{21}{136}\right)$	$e\left(\frac{101}{136}\right)$	$e\left(\frac{45}{68}\right)$	$e\left(\frac{3}{68}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{47}{68}\right)$	$e\left(\frac{131}{136}\right)$
$\chi_{959}(29,\cdot)$	959.ba	136	no	$-1$	$1$	$e\left(\frac{47}{68}\right)$	$e\left(\frac{91}{136}\right)$	$e\left(\frac{13}{34}\right)$	$e\left(\frac{25}{136}\right)$	$e\left(\frac{49}{136}\right)$	$e\left(\frac{5}{68}\right)$	$e\left(\frac{23}{68}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{43}{68}\right)$	$e\left(\frac{7}{136}\right)$
$\chi_{959}(30,\cdot)$	959.bc	204	yes	$1$	$1$	$e\left(\frac{101}{102}\right)$	$e\left(\frac{197}{204}\right)$	$e\left(\frac{50}{51}\right)$	$e\left(\frac{19}{204}\right)$	$e\left(\frac{65}{68}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{95}{102}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{49}{102}\right)$	$e\left(\frac{193}{204}\right)$
$\chi_{959}(31,\cdot)$	959.bf	408	yes	$1$	$1$	$e\left(\frac{143}{204}\right)$	$e\left(\frac{287}{408}\right)$	$e\left(\frac{41}{102}\right)$	$e\left(\frac{37}{408}\right)$	$e\left(\frac{55}{136}\right)$	$e\left(\frac{7}{68}\right)$	$e\left(\frac{83}{204}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{31}{204}\right)$	$e\left(\frac{43}{408}\right)$
$\chi_{959}(32,\cdot)$	959.bc	204	yes	$1$	$1$	$e\left(\frac{1}{102}\right)$	$e\left(\frac{7}{204}\right)$	$e\left(\frac{1}{51}\right)$	$e\left(\frac{185}{204}\right)$	$e\left(\frac{3}{68}\right)$	$e\left(\frac{1}{34}\right)$	$e\left(\frac{7}{102}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{53}{102}\right)$	$e\left(\frac{11}{204}\right)$
$\chi_{959}(33,\cdot)$	959.bf	408	yes	$1$	$1$	$e\left(\frac{145}{204}\right)$	$e\left(\frac{301}{408}\right)$	$e\left(\frac{43}{102}\right)$	$e\left(\frac{407}{408}\right)$	$e\left(\frac{61}{136}\right)$	$e\left(\frac{9}{68}\right)$	$e\left(\frac{97}{204}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{137}{204}\right)$	$e\left(\frac{65}{408}\right)$
$\chi_{959}(34,\cdot)$	959.t	34	yes	$-1$	$1$	$e\left(\frac{9}{17}\right)$	$e\left(\frac{29}{34}\right)$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{13}{34}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{12}{17}\right)$	$-1$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{31}{34}\right)$
$\chi_{959}(36,\cdot)$	959.w	68	no	$1$	$1$	$e\left(\frac{21}{34}\right)$	$e\left(\frac{11}{68}\right)$	$e\left(\frac{4}{17}\right)$	$e\left(\frac{9}{68}\right)$	$e\left(\frac{53}{68}\right)$	$e\left(\frac{29}{34}\right)$	$e\left(\frac{11}{34}\right)$	$-i$	$e\left(\frac{25}{34}\right)$	$e\left(\frac{27}{68}\right)$
$\chi_{959}(37,\cdot)$	959.n	12	yes	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$i$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$

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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	$959$
Structure	\(C_{2}\times C_{408}\)
Order	$816$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(8\)	\(9\)	\(10\)	\(11\)	\(12\)
\(\chi_{959}(1,\cdot)\)	959.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{959}(2,\cdot)\)	959.bc	204	yes	\(1\)	\(1\)	\(e\left(\frac{41}{102}\right)\)	\(e\left(\frac{83}{204}\right)\)	\(e\left(\frac{41}{51}\right)\)	\(e\left(\frac{37}{204}\right)\)	\(e\left(\frac{55}{68}\right)\)	\(e\left(\frac{7}{34}\right)\)	\(e\left(\frac{83}{102}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{31}{102}\right)\)	\(e\left(\frac{43}{204}\right)\)
\(\chi_{959}(3,\cdot)\)	959.bf	408	yes	\(1\)	\(1\)	\(e\left(\frac{83}{204}\right)\)	\(e\left(\frac{71}{408}\right)\)	\(e\left(\frac{83}{102}\right)\)	\(e\left(\frac{157}{408}\right)\)	\(e\left(\frac{79}{136}\right)\)	\(e\left(\frac{15}{68}\right)\)	\(e\left(\frac{71}{204}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{115}{204}\right)\)	\(e\left(\frac{403}{408}\right)\)
\(\chi_{959}(4,\cdot)\)	959.y	102	yes	\(1\)	\(1\)	\(e\left(\frac{41}{51}\right)\)	\(e\left(\frac{83}{102}\right)\)	\(e\left(\frac{31}{51}\right)\)	\(e\left(\frac{37}{102}\right)\)	\(e\left(\frac{21}{34}\right)\)	\(e\left(\frac{7}{17}\right)\)	\(e\left(\frac{32}{51}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{31}{51}\right)\)	\(e\left(\frac{43}{102}\right)\)
\(\chi_{959}(5,\cdot)\)	959.bf	408	yes	\(1\)	\(1\)	\(e\left(\frac{37}{204}\right)\)	\(e\left(\frac{157}{408}\right)\)	\(e\left(\frac{37}{102}\right)\)	\(e\left(\frac{215}{408}\right)\)	\(e\left(\frac{77}{136}\right)\)	\(e\left(\frac{37}{68}\right)\)	\(e\left(\frac{157}{204}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{125}{204}\right)\)	\(e\left(\frac{305}{408}\right)\)
\(\chi_{959}(6,\cdot)\)	959.bb	136	yes	\(1\)	\(1\)	\(e\left(\frac{55}{68}\right)\)	\(e\left(\frac{79}{136}\right)\)	\(e\left(\frac{21}{34}\right)\)	\(e\left(\frac{77}{136}\right)\)	\(e\left(\frac{53}{136}\right)\)	\(e\left(\frac{29}{68}\right)\)	\(e\left(\frac{11}{68}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{59}{68}\right)\)	\(e\left(\frac{27}{136}\right)\)
\(\chi_{959}(8,\cdot)\)	959.w	68	no	\(1\)	\(1\)	\(e\left(\frac{7}{34}\right)\)	\(e\left(\frac{15}{68}\right)\)	\(e\left(\frac{7}{17}\right)\)	\(e\left(\frac{37}{68}\right)\)	\(e\left(\frac{29}{68}\right)\)	\(e\left(\frac{21}{34}\right)\)	\(e\left(\frac{15}{34}\right)\)	\(-i\)	\(e\left(\frac{31}{34}\right)\)	\(e\left(\frac{43}{68}\right)\)
\(\chi_{959}(9,\cdot)\)	959.bc	204	yes	\(1\)	\(1\)	\(e\left(\frac{83}{102}\right)\)	\(e\left(\frac{71}{204}\right)\)	\(e\left(\frac{32}{51}\right)\)	\(e\left(\frac{157}{204}\right)\)	\(e\left(\frac{11}{68}\right)\)	\(e\left(\frac{15}{34}\right)\)	\(e\left(\frac{71}{102}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{13}{102}\right)\)	\(e\left(\frac{199}{204}\right)\)
\(\chi_{959}(10,\cdot)\)	959.p	24	yes	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(-i\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{23}{24}\right)\)
\(\chi_{959}(11,\cdot)\)	959.bc	204	yes	\(1\)	\(1\)	\(e\left(\frac{31}{102}\right)\)	\(e\left(\frac{115}{204}\right)\)	\(e\left(\frac{31}{51}\right)\)	\(e\left(\frac{125}{204}\right)\)	\(e\left(\frac{59}{68}\right)\)	\(e\left(\frac{31}{34}\right)\)	\(e\left(\frac{13}{102}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{11}{102}\right)\)	\(e\left(\frac{35}{204}\right)\)
\(\chi_{959}(12,\cdot)\)	959.bf	408	yes	\(1\)	\(1\)	\(e\left(\frac{43}{204}\right)\)	\(e\left(\frac{403}{408}\right)\)	\(e\left(\frac{43}{102}\right)\)	\(e\left(\frac{305}{408}\right)\)	\(e\left(\frac{27}{136}\right)\)	\(e\left(\frac{43}{68}\right)\)	\(e\left(\frac{199}{204}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{35}{204}\right)\)	\(e\left(\frac{167}{408}\right)\)
\(\chi_{959}(13,\cdot)\)	959.bb	136	yes	\(1\)	\(1\)	\(e\left(\frac{57}{68}\right)\)	\(e\left(\frac{93}{136}\right)\)	\(e\left(\frac{23}{34}\right)\)	\(e\left(\frac{39}{136}\right)\)	\(e\left(\frac{71}{136}\right)\)	\(e\left(\frac{35}{68}\right)\)	\(e\left(\frac{25}{68}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{29}{68}\right)\)	\(e\left(\frac{49}{136}\right)\)
\(\chi_{959}(15,\cdot)\)	959.s	34	no	\(1\)	\(1\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{19}{34}\right)\)	\(e\left(\frac{3}{17}\right)\)	\(e\left(\frac{31}{34}\right)\)	\(e\left(\frac{5}{34}\right)\)	\(e\left(\frac{13}{17}\right)\)	\(e\left(\frac{2}{17}\right)\)	\(-1\)	\(e\left(\frac{3}{17}\right)\)	\(e\left(\frac{25}{34}\right)\)
\(\chi_{959}(16,\cdot)\)	959.u	51	yes	\(1\)	\(1\)	\(e\left(\frac{31}{51}\right)\)	\(e\left(\frac{32}{51}\right)\)	\(e\left(\frac{11}{51}\right)\)	\(e\left(\frac{37}{51}\right)\)	\(e\left(\frac{4}{17}\right)\)	\(e\left(\frac{14}{17}\right)\)	\(e\left(\frac{13}{51}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{51}\right)\)	\(e\left(\frac{43}{51}\right)\)
\(\chi_{959}(17,\cdot)\)	959.bd	204	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{102}\right)\)	\(e\left(\frac{91}{204}\right)\)	\(e\left(\frac{13}{51}\right)\)	\(e\left(\frac{161}{204}\right)\)	\(e\left(\frac{39}{68}\right)\)	\(e\left(\frac{13}{34}\right)\)	\(e\left(\frac{91}{102}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{77}{102}\right)\)	\(e\left(\frac{143}{204}\right)\)
\(\chi_{959}(18,\cdot)\)	959.y	102	yes	\(1\)	\(1\)	\(e\left(\frac{11}{51}\right)\)	\(e\left(\frac{77}{102}\right)\)	\(e\left(\frac{22}{51}\right)\)	\(e\left(\frac{97}{102}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{11}{17}\right)\)	\(e\left(\frac{26}{51}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{22}{51}\right)\)	\(e\left(\frac{19}{102}\right)\)
\(\chi_{959}(19,\cdot)\)	959.bd	204	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{102}\right)\)	\(e\left(\frac{35}{204}\right)\)	\(e\left(\frac{5}{51}\right)\)	\(e\left(\frac{109}{204}\right)\)	\(e\left(\frac{15}{68}\right)\)	\(e\left(\frac{5}{34}\right)\)	\(e\left(\frac{35}{102}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{61}{102}\right)\)	\(e\left(\frac{55}{204}\right)\)
\(\chi_{959}(20,\cdot)\)	959.bb	136	yes	\(1\)	\(1\)	\(e\left(\frac{67}{68}\right)\)	\(e\left(\frac{27}{136}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{121}{136}\right)\)	\(e\left(\frac{25}{136}\right)\)	\(e\left(\frac{65}{68}\right)\)	\(e\left(\frac{27}{68}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{15}{68}\right)\)	\(e\left(\frac{23}{136}\right)\)
\(\chi_{959}(22,\cdot)\)	959.s	34	no	\(1\)	\(1\)	\(e\left(\frac{12}{17}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{7}{17}\right)\)	\(e\left(\frac{27}{34}\right)\)	\(e\left(\frac{23}{34}\right)\)	\(e\left(\frac{2}{17}\right)\)	\(e\left(\frac{16}{17}\right)\)	\(-1\)	\(e\left(\frac{7}{17}\right)\)	\(e\left(\frac{13}{34}\right)\)
\(\chi_{959}(23,\cdot)\)	959.be	408	yes	\(-1\)	\(1\)	\(e\left(\frac{175}{204}\right)\)	\(e\left(\frac{103}{408}\right)\)	\(e\left(\frac{73}{102}\right)\)	\(e\left(\frac{245}{408}\right)\)	\(e\left(\frac{15}{136}\right)\)	\(e\left(\frac{39}{68}\right)\)	\(e\left(\frac{103}{204}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{95}{204}\right)\)	\(e\left(\frac{395}{408}\right)\)
\(\chi_{959}(24,\cdot)\)	959.bf	408	yes	\(1\)	\(1\)	\(e\left(\frac{125}{204}\right)\)	\(e\left(\frac{161}{408}\right)\)	\(e\left(\frac{23}{102}\right)\)	\(e\left(\frac{379}{408}\right)\)	\(e\left(\frac{1}{136}\right)\)	\(e\left(\frac{57}{68}\right)\)	\(e\left(\frac{161}{204}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{97}{204}\right)\)	\(e\left(\frac{253}{408}\right)\)
\(\chi_{959}(25,\cdot)\)	959.bc	204	yes	\(1\)	\(1\)	\(e\left(\frac{37}{102}\right)\)	\(e\left(\frac{157}{204}\right)\)	\(e\left(\frac{37}{51}\right)\)	\(e\left(\frac{11}{204}\right)\)	\(e\left(\frac{9}{68}\right)\)	\(e\left(\frac{3}{34}\right)\)	\(e\left(\frac{55}{102}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{23}{102}\right)\)	\(e\left(\frac{101}{204}\right)\)
\(\chi_{959}(26,\cdot)\)	959.bf	408	yes	\(1\)	\(1\)	\(e\left(\frac{49}{204}\right)\)	\(e\left(\frac{37}{408}\right)\)	\(e\left(\frac{49}{102}\right)\)	\(e\left(\frac{191}{408}\right)\)	\(e\left(\frac{45}{136}\right)\)	\(e\left(\frac{49}{68}\right)\)	\(e\left(\frac{37}{204}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{149}{204}\right)\)	\(e\left(\frac{233}{408}\right)\)
\(\chi_{959}(27,\cdot)\)	959.bb	136	yes	\(1\)	\(1\)	\(e\left(\frac{15}{68}\right)\)	\(e\left(\frac{71}{136}\right)\)	\(e\left(\frac{15}{34}\right)\)	\(e\left(\frac{21}{136}\right)\)	\(e\left(\frac{101}{136}\right)\)	\(e\left(\frac{45}{68}\right)\)	\(e\left(\frac{3}{68}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{47}{68}\right)\)	\(e\left(\frac{131}{136}\right)\)
\(\chi_{959}(29,\cdot)\)	959.ba	136	no	\(-1\)	\(1\)	\(e\left(\frac{47}{68}\right)\)	\(e\left(\frac{91}{136}\right)\)	\(e\left(\frac{13}{34}\right)\)	\(e\left(\frac{25}{136}\right)\)	\(e\left(\frac{49}{136}\right)\)	\(e\left(\frac{5}{68}\right)\)	\(e\left(\frac{23}{68}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{43}{68}\right)\)	\(e\left(\frac{7}{136}\right)\)
\(\chi_{959}(30,\cdot)\)	959.bc	204	yes	\(1\)	\(1\)	\(e\left(\frac{101}{102}\right)\)	\(e\left(\frac{197}{204}\right)\)	\(e\left(\frac{50}{51}\right)\)	\(e\left(\frac{19}{204}\right)\)	\(e\left(\frac{65}{68}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{95}{102}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{49}{102}\right)\)	\(e\left(\frac{193}{204}\right)\)
\(\chi_{959}(31,\cdot)\)	959.bf	408	yes	\(1\)	\(1\)	\(e\left(\frac{143}{204}\right)\)	\(e\left(\frac{287}{408}\right)\)	\(e\left(\frac{41}{102}\right)\)	\(e\left(\frac{37}{408}\right)\)	\(e\left(\frac{55}{136}\right)\)	\(e\left(\frac{7}{68}\right)\)	\(e\left(\frac{83}{204}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{31}{204}\right)\)	\(e\left(\frac{43}{408}\right)\)
\(\chi_{959}(32,\cdot)\)	959.bc	204	yes	\(1\)	\(1\)	\(e\left(\frac{1}{102}\right)\)	\(e\left(\frac{7}{204}\right)\)	\(e\left(\frac{1}{51}\right)\)	\(e\left(\frac{185}{204}\right)\)	\(e\left(\frac{3}{68}\right)\)	\(e\left(\frac{1}{34}\right)\)	\(e\left(\frac{7}{102}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{53}{102}\right)\)	\(e\left(\frac{11}{204}\right)\)
\(\chi_{959}(33,\cdot)\)	959.bf	408	yes	\(1\)	\(1\)	\(e\left(\frac{145}{204}\right)\)	\(e\left(\frac{301}{408}\right)\)	\(e\left(\frac{43}{102}\right)\)	\(e\left(\frac{407}{408}\right)\)	\(e\left(\frac{61}{136}\right)\)	\(e\left(\frac{9}{68}\right)\)	\(e\left(\frac{97}{204}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{137}{204}\right)\)	\(e\left(\frac{65}{408}\right)\)
\(\chi_{959}(34,\cdot)\)	959.t	34	yes	\(-1\)	\(1\)	\(e\left(\frac{9}{17}\right)\)	\(e\left(\frac{29}{34}\right)\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{13}{34}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{12}{17}\right)\)	\(-1\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{31}{34}\right)\)
\(\chi_{959}(36,\cdot)\)	959.w	68	no	\(1\)	\(1\)	\(e\left(\frac{21}{34}\right)\)	\(e\left(\frac{11}{68}\right)\)	\(e\left(\frac{4}{17}\right)\)	\(e\left(\frac{9}{68}\right)\)	\(e\left(\frac{53}{68}\right)\)	\(e\left(\frac{29}{34}\right)\)	\(e\left(\frac{11}{34}\right)\)	\(-i\)	\(e\left(\frac{25}{34}\right)\)	\(e\left(\frac{27}{68}\right)\)
\(\chi_{959}(37,\cdot)\)	959.n	12	yes	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)

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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.