LMFDB - Group of Dirichlet characters of modulus 119952

Show commands: PariGP / SageMath

sage: H = DirichletGroup(119952)

pari: g = idealstar(,119952,2)

Character group

sage: G.order() pari: g.no
Order	=	32256
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{12}\times C_{336}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{119952}(104959,\cdot)$, $\chi_{119952}(29989,\cdot)$, $\chi_{119952}(106625,\cdot)$, $\chi_{119952}(117505,\cdot)$, $\chi_{119952}(14113,\cdot)$

First 32 of 32256 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	$-1$	$1$	$5$	$11$	$13$	$19$	$23$	$25$	$29$	$31$	$37$	$41$
$\chi_{119952}(1,\cdot)$	119952.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{119952}(5,\cdot)$	119952.bzi	336	yes	$-1$	$1$	$e\left(\frac{1}{336}\right)$	$e\left(\frac{299}{336}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{199}{336}\right)$	$e\left(\frac{1}{168}\right)$	$e\left(\frac{25}{336}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{221}{336}\right)$	$e\left(\frac{155}{336}\right)$
$\chi_{119952}(11,\cdot)$	119952.bzm	336	yes	$-1$	$1$	$e\left(\frac{299}{336}\right)$	$e\left(\frac{25}{336}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{197}{336}\right)$	$e\left(\frac{131}{168}\right)$	$e\left(\frac{251}{336}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{55}{336}\right)$	$e\left(\frac{145}{336}\right)$
$\chi_{119952}(13,\cdot)$	119952.bli	84	yes	$-1$	$1$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{71}{84}\right)$	$i$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{59}{84}\right)$
$\chi_{119952}(19,\cdot)$	119952.wp	24	no	$1$	$1$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{17}{24}\right)$	$i$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{119952}(23,\cdot)$	119952.bzt	336	no	$-1$	$1$	$e\left(\frac{199}{336}\right)$	$e\left(\frac{197}{336}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{37}{336}\right)$	$e\left(\frac{31}{168}\right)$	$e\left(\frac{271}{336}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{131}{336}\right)$	$e\left(\frac{17}{336}\right)$
$\chi_{119952}(25,\cdot)$	119952.byc	168	no	$1$	$1$	$e\left(\frac{1}{168}\right)$	$e\left(\frac{131}{168}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{31}{168}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{25}{168}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{53}{168}\right)$	$e\left(\frac{155}{168}\right)$
$\chi_{119952}(29,\cdot)$	119952.bzb	336	yes	$1$	$1$	$e\left(\frac{25}{336}\right)$	$e\left(\frac{251}{336}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{271}{336}\right)$	$e\left(\frac{25}{168}\right)$	$e\left(\frac{233}{336}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{31}{112}\right)$	$e\left(\frac{235}{336}\right)$
$\chi_{119952}(31,\cdot)$	119952.bhe	48	no	$-1$	$1$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{17}{48}\right)$
$\chi_{119952}(37,\cdot)$	119952.byo	336	no	$-1$	$1$	$e\left(\frac{221}{336}\right)$	$e\left(\frac{55}{336}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{131}{336}\right)$	$e\left(\frac{53}{168}\right)$	$e\left(\frac{31}{112}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{233}{336}\right)$	$e\left(\frac{69}{112}\right)$
$\chi_{119952}(41,\cdot)$	119952.cam	336	no	$-1$	$1$	$e\left(\frac{155}{336}\right)$	$e\left(\frac{145}{336}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{17}{336}\right)$	$e\left(\frac{155}{168}\right)$	$e\left(\frac{235}{336}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{69}{112}\right)$	$e\left(\frac{29}{336}\right)$
$\chi_{119952}(43,\cdot)$	119952.bxf	168	yes	$-1$	$1$	$e\left(\frac{59}{168}\right)$	$e\left(\frac{1}{168}\right)$	$e\left(\frac{25}{84}\right)$	$1$	$e\left(\frac{107}{168}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{103}{168}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{53}{56}\right)$	$e\left(\frac{59}{168}\right)$
$\chi_{119952}(47,\cdot)$	119952.bne	84	no	$-1$	$1$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{31}{84}\right)$
$\chi_{119952}(53,\cdot)$	119952.bve	168	no	$-1$	$1$	$e\left(\frac{5}{168}\right)$	$e\left(\frac{67}{168}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{29}{168}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{51}{56}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{125}{168}\right)$	$e\left(\frac{11}{56}\right)$
$\chi_{119952}(55,\cdot)$	119952.ys	28	no	$1$	$1$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{5}{7}\right)$	$1$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{23}{28}\right)$	$-i$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{25}{28}\right)$
$\chi_{119952}(59,\cdot)$	119952.bwq	168	yes	$-1$	$1$	$e\left(\frac{29}{56}\right)$	$e\left(\frac{19}{56}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{17}{56}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{47}{168}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{131}{168}\right)$	$e\left(\frac{31}{168}\right)$
$\chi_{119952}(61,\cdot)$	119952.byx	336	yes	$1$	$1$	$e\left(\frac{69}{112}\right)$	$e\left(\frac{23}{112}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{67}{112}\right)$	$e\left(\frac{13}{56}\right)$	$e\left(\frac{23}{336}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{107}{336}\right)$	$e\left(\frac{277}{336}\right)$
$\chi_{119952}(65,\cdot)$	119952.caz	336	no	$1$	$1$	$e\left(\frac{51}{112}\right)$	$e\left(\frac{17}{112}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{41}{112}\right)$	$e\left(\frac{51}{56}\right)$	$e\left(\frac{17}{336}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{269}{336}\right)$	$e\left(\frac{55}{336}\right)$
$\chi_{119952}(67,\cdot)$	119952.lu	12	no	$-1$	$1$	$i$	$-i$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{12}\right)$	$-1$	$-1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{119952}(71,\cdot)$	119952.bsx	112	no	$-1$	$1$	$e\left(\frac{99}{112}\right)$	$e\left(\frac{89}{112}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{73}{112}\right)$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{11}{112}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{95}{112}\right)$	$e\left(\frac{85}{112}\right)$
$\chi_{119952}(73,\cdot)$	119952.cag	336	no	$1$	$1$	$e\left(\frac{205}{336}\right)$	$e\left(\frac{311}{336}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{55}{336}\right)$	$e\left(\frac{37}{168}\right)$	$e\left(\frac{47}{112}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{1}{336}\right)$	$e\left(\frac{73}{112}\right)$
$\chi_{119952}(79,\cdot)$	119952.bgi	48	no	$1$	$1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{7}{48}\right)$
$\chi_{119952}(83,\cdot)$	119952.bva	168	yes	$-1$	$1$	$e\left(\frac{113}{168}\right)$	$e\left(\frac{103}{168}\right)$	$e\left(\frac{13}{84}\right)$	$-1$	$e\left(\frac{101}{168}\right)$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{25}{168}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{55}{56}\right)$	$e\left(\frac{113}{168}\right)$
$\chi_{119952}(89,\cdot)$	119952.bmj	84	no	$1$	$1$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{27}{28}\right)$
$\chi_{119952}(95,\cdot)$	119952.cad	336	no	$-1$	$1$	$e\left(\frac{33}{112}\right)$	$e\left(\frac{67}{112}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{43}{112}\right)$	$e\left(\frac{33}{56}\right)$	$e\left(\frac{235}{336}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{319}{336}\right)$	$e\left(\frac{29}{336}\right)$
$\chi_{119952}(97,\cdot)$	119952.bhq	48	no	$1$	$1$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{37}{48}\right)$
$\chi_{119952}(101,\cdot)$	119952.boo	84	yes	$1$	$1$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{71}{84}\right)$	$1$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{4}{21}\right)$
$\chi_{119952}(103,\cdot)$	119952.bdy	42	no	$1$	$1$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{11}{42}\right)$	$1$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{1}{42}\right)$
$\chi_{119952}(107,\cdot)$	119952.byr	336	no	$-1$	$1$	$e\left(\frac{233}{336}\right)$	$e\left(\frac{115}{336}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{335}{336}\right)$	$e\left(\frac{65}{168}\right)$	$e\left(\frac{19}{112}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{29}{336}\right)$	$e\left(\frac{17}{112}\right)$
$\chi_{119952}(109,\cdot)$	119952.byo	336	no	$-1$	$1$	$e\left(\frac{271}{336}\right)$	$e\left(\frac{221}{336}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{1}{336}\right)$	$e\left(\frac{103}{168}\right)$	$e\left(\frac{37}{112}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{307}{336}\right)$	$e\left(\frac{39}{112}\right)$
$\chi_{119952}(113,\cdot)$	119952.cbp	336	no	$1$	$1$	$e\left(\frac{23}{336}\right)$	$e\left(\frac{157}{336}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{293}{336}\right)$	$e\left(\frac{23}{168}\right)$	$e\left(\frac{127}{336}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{33}{112}\right)$	$e\left(\frac{233}{336}\right)$
$\chi_{119952}(115,\cdot)$	119952.blw	84	yes	$1$	$1$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{37}{42}\right)$	$i$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{43}{84}\right)$

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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	$119952$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{12}\times C_{336}\)
Order	$32256$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(11\)	\(13\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{119952}(1,\cdot)\)	119952.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{119952}(5,\cdot)\)	119952.bzi	336	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{336}\right)\)	\(e\left(\frac{299}{336}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{199}{336}\right)\)	\(e\left(\frac{1}{168}\right)\)	\(e\left(\frac{25}{336}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{221}{336}\right)\)	\(e\left(\frac{155}{336}\right)\)
\(\chi_{119952}(11,\cdot)\)	119952.bzm	336	yes	\(-1\)	\(1\)	\(e\left(\frac{299}{336}\right)\)	\(e\left(\frac{25}{336}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{197}{336}\right)\)	\(e\left(\frac{131}{168}\right)\)	\(e\left(\frac{251}{336}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{55}{336}\right)\)	\(e\left(\frac{145}{336}\right)\)
\(\chi_{119952}(13,\cdot)\)	119952.bli	84	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{71}{84}\right)\)	\(i\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{59}{84}\right)\)
\(\chi_{119952}(19,\cdot)\)	119952.wp	24	no	\(1\)	\(1\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(i\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{119952}(23,\cdot)\)	119952.bzt	336	no	\(-1\)	\(1\)	\(e\left(\frac{199}{336}\right)\)	\(e\left(\frac{197}{336}\right)\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{37}{336}\right)\)	\(e\left(\frac{31}{168}\right)\)	\(e\left(\frac{271}{336}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{131}{336}\right)\)	\(e\left(\frac{17}{336}\right)\)
\(\chi_{119952}(25,\cdot)\)	119952.byc	168	no	\(1\)	\(1\)	\(e\left(\frac{1}{168}\right)\)	\(e\left(\frac{131}{168}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{31}{168}\right)\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{25}{168}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{53}{168}\right)\)	\(e\left(\frac{155}{168}\right)\)
\(\chi_{119952}(29,\cdot)\)	119952.bzb	336	yes	\(1\)	\(1\)	\(e\left(\frac{25}{336}\right)\)	\(e\left(\frac{251}{336}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{271}{336}\right)\)	\(e\left(\frac{25}{168}\right)\)	\(e\left(\frac{233}{336}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{31}{112}\right)\)	\(e\left(\frac{235}{336}\right)\)
\(\chi_{119952}(31,\cdot)\)	119952.bhe	48	no	\(-1\)	\(1\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{17}{48}\right)\)
\(\chi_{119952}(37,\cdot)\)	119952.byo	336	no	\(-1\)	\(1\)	\(e\left(\frac{221}{336}\right)\)	\(e\left(\frac{55}{336}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{131}{336}\right)\)	\(e\left(\frac{53}{168}\right)\)	\(e\left(\frac{31}{112}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{233}{336}\right)\)	\(e\left(\frac{69}{112}\right)\)
\(\chi_{119952}(41,\cdot)\)	119952.cam	336	no	\(-1\)	\(1\)	\(e\left(\frac{155}{336}\right)\)	\(e\left(\frac{145}{336}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{17}{336}\right)\)	\(e\left(\frac{155}{168}\right)\)	\(e\left(\frac{235}{336}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{69}{112}\right)\)	\(e\left(\frac{29}{336}\right)\)
\(\chi_{119952}(43,\cdot)\)	119952.bxf	168	yes	\(-1\)	\(1\)	\(e\left(\frac{59}{168}\right)\)	\(e\left(\frac{1}{168}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(1\)	\(e\left(\frac{107}{168}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{103}{168}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{53}{56}\right)\)	\(e\left(\frac{59}{168}\right)\)
\(\chi_{119952}(47,\cdot)\)	119952.bne	84	no	\(-1\)	\(1\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{31}{84}\right)\)
\(\chi_{119952}(53,\cdot)\)	119952.bve	168	no	\(-1\)	\(1\)	\(e\left(\frac{5}{168}\right)\)	\(e\left(\frac{67}{168}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{29}{168}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{51}{56}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{125}{168}\right)\)	\(e\left(\frac{11}{56}\right)\)
\(\chi_{119952}(55,\cdot)\)	119952.ys	28	no	\(1\)	\(1\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(1\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(-i\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{25}{28}\right)\)
\(\chi_{119952}(59,\cdot)\)	119952.bwq	168	yes	\(-1\)	\(1\)	\(e\left(\frac{29}{56}\right)\)	\(e\left(\frac{19}{56}\right)\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{17}{56}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{47}{168}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{131}{168}\right)\)	\(e\left(\frac{31}{168}\right)\)
\(\chi_{119952}(61,\cdot)\)	119952.byx	336	yes	\(1\)	\(1\)	\(e\left(\frac{69}{112}\right)\)	\(e\left(\frac{23}{112}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{67}{112}\right)\)	\(e\left(\frac{13}{56}\right)\)	\(e\left(\frac{23}{336}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{107}{336}\right)\)	\(e\left(\frac{277}{336}\right)\)
\(\chi_{119952}(65,\cdot)\)	119952.caz	336	no	\(1\)	\(1\)	\(e\left(\frac{51}{112}\right)\)	\(e\left(\frac{17}{112}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{41}{112}\right)\)	\(e\left(\frac{51}{56}\right)\)	\(e\left(\frac{17}{336}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{269}{336}\right)\)	\(e\left(\frac{55}{336}\right)\)
\(\chi_{119952}(67,\cdot)\)	119952.lu	12	no	\(-1\)	\(1\)	\(i\)	\(-i\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{119952}(71,\cdot)\)	119952.bsx	112	no	\(-1\)	\(1\)	\(e\left(\frac{99}{112}\right)\)	\(e\left(\frac{89}{112}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{73}{112}\right)\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{11}{112}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{95}{112}\right)\)	\(e\left(\frac{85}{112}\right)\)
\(\chi_{119952}(73,\cdot)\)	119952.cag	336	no	\(1\)	\(1\)	\(e\left(\frac{205}{336}\right)\)	\(e\left(\frac{311}{336}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{55}{336}\right)\)	\(e\left(\frac{37}{168}\right)\)	\(e\left(\frac{47}{112}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{1}{336}\right)\)	\(e\left(\frac{73}{112}\right)\)
\(\chi_{119952}(79,\cdot)\)	119952.bgi	48	no	\(1\)	\(1\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{7}{48}\right)\)
\(\chi_{119952}(83,\cdot)\)	119952.bva	168	yes	\(-1\)	\(1\)	\(e\left(\frac{113}{168}\right)\)	\(e\left(\frac{103}{168}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(-1\)	\(e\left(\frac{101}{168}\right)\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{25}{168}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{55}{56}\right)\)	\(e\left(\frac{113}{168}\right)\)
\(\chi_{119952}(89,\cdot)\)	119952.bmj	84	no	\(1\)	\(1\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{27}{28}\right)\)
\(\chi_{119952}(95,\cdot)\)	119952.cad	336	no	\(-1\)	\(1\)	\(e\left(\frac{33}{112}\right)\)	\(e\left(\frac{67}{112}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{43}{112}\right)\)	\(e\left(\frac{33}{56}\right)\)	\(e\left(\frac{235}{336}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{319}{336}\right)\)	\(e\left(\frac{29}{336}\right)\)
\(\chi_{119952}(97,\cdot)\)	119952.bhq	48	no	\(1\)	\(1\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{37}{48}\right)\)
\(\chi_{119952}(101,\cdot)\)	119952.boo	84	yes	\(1\)	\(1\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{71}{84}\right)\)	\(1\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{4}{21}\right)\)
\(\chi_{119952}(103,\cdot)\)	119952.bdy	42	no	\(1\)	\(1\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(1\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{1}{42}\right)\)
\(\chi_{119952}(107,\cdot)\)	119952.byr	336	no	\(-1\)	\(1\)	\(e\left(\frac{233}{336}\right)\)	\(e\left(\frac{115}{336}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{335}{336}\right)\)	\(e\left(\frac{65}{168}\right)\)	\(e\left(\frac{19}{112}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{29}{336}\right)\)	\(e\left(\frac{17}{112}\right)\)
\(\chi_{119952}(109,\cdot)\)	119952.byo	336	no	\(-1\)	\(1\)	\(e\left(\frac{271}{336}\right)\)	\(e\left(\frac{221}{336}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{1}{336}\right)\)	\(e\left(\frac{103}{168}\right)\)	\(e\left(\frac{37}{112}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{307}{336}\right)\)	\(e\left(\frac{39}{112}\right)\)
\(\chi_{119952}(113,\cdot)\)	119952.cbp	336	no	\(1\)	\(1\)	\(e\left(\frac{23}{336}\right)\)	\(e\left(\frac{157}{336}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{293}{336}\right)\)	\(e\left(\frac{23}{168}\right)\)	\(e\left(\frac{127}{336}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{33}{112}\right)\)	\(e\left(\frac{233}{336}\right)\)
\(\chi_{119952}(115,\cdot)\)	119952.blw	84	yes	\(1\)	\(1\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(i\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{43}{84}\right)\)

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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.