LMFDB - Dirichlet character orbit 8112.fh

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8112, base_ring=CyclotomicField(156)) M = H._module chi = DirichletCharacter(H, M([0,39,78,67])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(245,8112)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$8112$
Conductor:	$8112$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$156$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{156})$
Fixed field:	Number field defined by a degree 156 polynomial (not computed)

First 31 of 48 characters in Galois orbit

Character	$-1$	$1$	$5$	$7$	$11$	$17$	$19$	$23$	$25$	$29$	$31$	$35$
$\chi_{8112}(245,\cdot)$	$1$	$1$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{71}{156}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{67}{156}\right)$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{11}{156}\right)$
$\chi_{8112}(293,\cdot)$	$1$	$1$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{43}{156}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{23}{156}\right)$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{55}{156}\right)$
$\chi_{8112}(461,\cdot)$	$1$	$1$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{133}{156}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{53}{156}\right)$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{25}{156}\right)$
$\chi_{8112}(509,\cdot)$	$1$	$1$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{29}{156}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{1}{156}\right)$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{77}{156}\right)$
$\chi_{8112}(869,\cdot)$	$1$	$1$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{95}{156}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{127}{156}\right)$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{107}{156}\right)$
$\chi_{8112}(917,\cdot)$	$1$	$1$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{103}{156}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{95}{156}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{139}{156}\right)$
$\chi_{8112}(1085,\cdot)$	$1$	$1$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{73}{156}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{137}{156}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{97}{156}\right)$
$\chi_{8112}(1133,\cdot)$	$1$	$1$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{5}{156}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{97}{156}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{137}{156}\right)$
$\chi_{8112}(1493,\cdot)$	$1$	$1$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{119}{156}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{31}{156}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{47}{156}\right)$
$\chi_{8112}(1541,\cdot)$	$1$	$1$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{7}{156}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{11}{156}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{67}{156}\right)$
$\chi_{8112}(1757,\cdot)$	$1$	$1$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{137}{156}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{37}{156}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{41}{156}\right)$
$\chi_{8112}(2165,\cdot)$	$1$	$1$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{67}{156}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{83}{156}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{151}{156}\right)$
$\chi_{8112}(2333,\cdot)$	$1$	$1$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{109}{156}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{149}{156}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{85}{156}\right)$
$\chi_{8112}(2381,\cdot)$	$1$	$1$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{113}{156}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{133}{156}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{101}{156}\right)$
$\chi_{8112}(2741,\cdot)$	$1$	$1$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{11}{156}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{151}{156}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{83}{156}\right)$
$\chi_{8112}(2789,\cdot)$	$1$	$1$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{127}{156}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{155}{156}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{79}{156}\right)$
$\chi_{8112}(2957,\cdot)$	$1$	$1$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{49}{156}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{77}{156}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{1}{156}\right)$
$\chi_{8112}(3005,\cdot)$	$1$	$1$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{89}{156}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{73}{156}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{5}{156}\right)$
$\chi_{8112}(3365,\cdot)$	$1$	$1$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{35}{156}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{55}{156}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{23}{156}\right)$
$\chi_{8112}(3413,\cdot)$	$1$	$1$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{31}{156}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{71}{156}\right)$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{7}{156}\right)$
$\chi_{8112}(3581,\cdot)$	$1$	$1$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{145}{156}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{5}{156}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{73}{156}\right)$
$\chi_{8112}(3989,\cdot)$	$1$	$1$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{59}{156}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{115}{156}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{119}{156}\right)$
$\chi_{8112}(4205,\cdot)$	$1$	$1$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{85}{156}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{89}{156}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{145}{156}\right)$
$\chi_{8112}(4253,\cdot)$	$1$	$1$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{41}{156}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{109}{156}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{125}{156}\right)$
$\chi_{8112}(4613,\cdot)$	$1$	$1$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{83}{156}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{19}{156}\right)$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{59}{156}\right)$
$\chi_{8112}(4661,\cdot)$	$1$	$1$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{151}{156}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{59}{156}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{19}{156}\right)$
$\chi_{8112}(4829,\cdot)$	$1$	$1$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{25}{156}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{17}{156}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{61}{156}\right)$
$\chi_{8112}(4877,\cdot)$	$1$	$1$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{17}{156}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{49}{156}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{29}{156}\right)$
$\chi_{8112}(5237,\cdot)$	$1$	$1$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{107}{156}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{79}{156}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{155}{156}\right)$
$\chi_{8112}(5285,\cdot)$	$1$	$1$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{55}{156}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{131}{156}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{103}{156}\right)$
$\chi_{8112}(5453,\cdot)$	$1$	$1$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{121}{156}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{101}{156}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{133}{156}\right)$

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

Character	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(35\)
\(\chi_{8112}(245,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{71}{156}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{67}{156}\right)\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{11}{156}\right)\)
\(\chi_{8112}(293,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{43}{156}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{23}{156}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{55}{156}\right)\)
\(\chi_{8112}(461,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{133}{156}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{53}{156}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{25}{156}\right)\)
\(\chi_{8112}(509,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{29}{156}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{1}{156}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{77}{156}\right)\)
\(\chi_{8112}(869,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{95}{156}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{127}{156}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{107}{156}\right)\)
\(\chi_{8112}(917,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{103}{156}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{95}{156}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{139}{156}\right)\)
\(\chi_{8112}(1085,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{73}{156}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{137}{156}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{97}{156}\right)\)
\(\chi_{8112}(1133,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{5}{156}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{97}{156}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{137}{156}\right)\)
\(\chi_{8112}(1493,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{119}{156}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{31}{156}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{47}{156}\right)\)
\(\chi_{8112}(1541,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{7}{156}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{11}{156}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{67}{156}\right)\)
\(\chi_{8112}(1757,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{137}{156}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{37}{156}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{41}{156}\right)\)
\(\chi_{8112}(2165,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{67}{156}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{83}{156}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{151}{156}\right)\)
\(\chi_{8112}(2333,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{109}{156}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{149}{156}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{85}{156}\right)\)
\(\chi_{8112}(2381,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{113}{156}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{133}{156}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{101}{156}\right)\)
\(\chi_{8112}(2741,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{11}{156}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{151}{156}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{83}{156}\right)\)
\(\chi_{8112}(2789,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{127}{156}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{155}{156}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{79}{156}\right)\)
\(\chi_{8112}(2957,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{49}{156}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{77}{156}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{1}{156}\right)\)
\(\chi_{8112}(3005,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{89}{156}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{73}{156}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{5}{156}\right)\)
\(\chi_{8112}(3365,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{35}{156}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{55}{156}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{23}{156}\right)\)
\(\chi_{8112}(3413,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{31}{156}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{71}{156}\right)\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{7}{156}\right)\)
\(\chi_{8112}(3581,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{145}{156}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{5}{156}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{73}{156}\right)\)
\(\chi_{8112}(3989,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{59}{156}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{115}{156}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{119}{156}\right)\)
\(\chi_{8112}(4205,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{85}{156}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{89}{156}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{145}{156}\right)\)
\(\chi_{8112}(4253,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{41}{156}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{109}{156}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{125}{156}\right)\)
\(\chi_{8112}(4613,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{83}{156}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{19}{156}\right)\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{59}{156}\right)\)
\(\chi_{8112}(4661,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{151}{156}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{59}{156}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{19}{156}\right)\)
\(\chi_{8112}(4829,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{25}{156}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{17}{156}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{61}{156}\right)\)
\(\chi_{8112}(4877,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{17}{156}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{49}{156}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{29}{156}\right)\)
\(\chi_{8112}(5237,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{107}{156}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{79}{156}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{155}{156}\right)\)
\(\chi_{8112}(5285,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{55}{156}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{131}{156}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{103}{156}\right)\)
\(\chi_{8112}(5453,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{121}{156}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{101}{156}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{133}{156}\right)\)

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First 31 of 48 characters in Galois orbit

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	8112.fh
Modulus	$8112$
Conductor	$8112$
Order	$156$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(8112\)
Conductor:	\(8112\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(156\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)