LMFDB - Dirichlet character orbit 8112.fp

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8112, base_ring=CyclotomicField(156)) M = H._module chi = DirichletCharacter(H, M([78,0,0,125])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(175,8112)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$8112$
Conductor:	$676$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$156$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 676.w	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	$-1$	$1$	$5$	$7$	$11$	$17$	$19$	$23$	$25$	$29$	$31$	$35$
$\chi_{8112}(175,\cdot)$	$1$	$1$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{37}{156}\right)$	$e\left(\frac{5}{156}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{35}{78}\right)$
$\chi_{8112}(223,\cdot)$	$1$	$1$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{53}{156}\right)$	$e\left(\frac{121}{156}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{67}{78}\right)$
$\chi_{8112}(271,\cdot)$	$1$	$1$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{59}{156}\right)$	$e\left(\frac{67}{156}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{1}{78}\right)$
$\chi_{8112}(799,\cdot)$	$1$	$1$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{133}{156}\right)$	$e\left(\frac{77}{156}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{71}{78}\right)$
$\chi_{8112}(847,\cdot)$	$1$	$1$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{29}{156}\right)$	$e\left(\frac{25}{156}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{19}{78}\right)$
$\chi_{8112}(895,\cdot)$	$1$	$1$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{83}{156}\right)$	$e\left(\frac{7}{156}\right)$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{49}{78}\right)$
$\chi_{8112}(943,\cdot)$	$1$	$1$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{151}{156}\right)$	$e\left(\frac{71}{156}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{29}{78}\right)$
$\chi_{8112}(1423,\cdot)$	$1$	$1$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{73}{156}\right)$	$e\left(\frac{149}{156}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{29}{78}\right)$
$\chi_{8112}(1471,\cdot)$	$1$	$1$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{5}{156}\right)$	$e\left(\frac{85}{156}\right)$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{49}{78}\right)$
$\chi_{8112}(1519,\cdot)$	$1$	$1$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{107}{156}\right)$	$e\left(\frac{103}{156}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{19}{78}\right)$
$\chi_{8112}(1567,\cdot)$	$1$	$1$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{55}{156}\right)$	$e\left(\frac{155}{156}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{71}{78}\right)$
$\chi_{8112}(2095,\cdot)$	$1$	$1$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{137}{156}\right)$	$e\left(\frac{145}{156}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{1}{78}\right)$
$\chi_{8112}(2143,\cdot)$	$1$	$1$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{131}{156}\right)$	$e\left(\frac{43}{156}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{67}{78}\right)$
$\chi_{8112}(2191,\cdot)$	$1$	$1$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{115}{156}\right)$	$e\left(\frac{83}{156}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{35}{78}\right)$
$\chi_{8112}(2671,\cdot)$	$1$	$1$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{109}{156}\right)$	$e\left(\frac{137}{156}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{23}{78}\right)$
$\chi_{8112}(2719,\cdot)$	$1$	$1$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{113}{156}\right)$	$e\left(\frac{49}{156}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{31}{78}\right)$
$\chi_{8112}(2767,\cdot)$	$1$	$1$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{155}{156}\right)$	$e\left(\frac{139}{156}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{37}{78}\right)$
$\chi_{8112}(2815,\cdot)$	$1$	$1$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{19}{156}\right)$	$e\left(\frac{11}{156}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{77}{78}\right)$
$\chi_{8112}(3295,\cdot)$	$1$	$1$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{49}{156}\right)$	$e\left(\frac{53}{156}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{59}{78}\right)$
$\chi_{8112}(3343,\cdot)$	$1$	$1$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{89}{156}\right)$	$e\left(\frac{109}{156}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{61}{78}\right)$
$\chi_{8112}(3391,\cdot)$	$1$	$1$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{23}{156}\right)$	$e\left(\frac{79}{156}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{7}{78}\right)$
$\chi_{8112}(3439,\cdot)$	$1$	$1$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{79}{156}\right)$	$e\left(\frac{95}{156}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{41}{78}\right)$
$\chi_{8112}(3919,\cdot)$	$1$	$1$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{145}{156}\right)$	$e\left(\frac{125}{156}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{17}{78}\right)$
$\chi_{8112}(4015,\cdot)$	$1$	$1$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{47}{156}\right)$	$e\left(\frac{19}{156}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{55}{78}\right)$
$\chi_{8112}(4063,\cdot)$	$1$	$1$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{139}{156}\right)$	$e\left(\frac{23}{156}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{5}{78}\right)$
$\chi_{8112}(4543,\cdot)$	$1$	$1$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{85}{156}\right)$	$e\left(\frac{41}{156}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{53}{78}\right)$
$\chi_{8112}(4591,\cdot)$	$1$	$1$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{41}{156}\right)$	$e\left(\frac{73}{156}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{43}{78}\right)$
$\chi_{8112}(4639,\cdot)$	$1$	$1$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{71}{156}\right)$	$e\left(\frac{115}{156}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{25}{78}\right)$
$\chi_{8112}(4687,\cdot)$	$1$	$1$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{43}{156}\right)$	$e\left(\frac{107}{156}\right)$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{47}{78}\right)$
$\chi_{8112}(5167,\cdot)$	$1$	$1$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{25}{156}\right)$	$e\left(\frac{113}{156}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{11}{78}\right)$
$\chi_{8112}(5215,\cdot)$	$1$	$1$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{17}{156}\right)$	$e\left(\frac{133}{156}\right)$	$e\left(\frac{67}{78}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{73}{78}\right)$

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	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(35\)
\(\chi_{8112}(175,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{37}{156}\right)\)	\(e\left(\frac{5}{156}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{35}{78}\right)\)
\(\chi_{8112}(223,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{53}{156}\right)\)	\(e\left(\frac{121}{156}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{67}{78}\right)\)
\(\chi_{8112}(271,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{59}{156}\right)\)	\(e\left(\frac{67}{156}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{1}{78}\right)\)
\(\chi_{8112}(799,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{133}{156}\right)\)	\(e\left(\frac{77}{156}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{71}{78}\right)\)
\(\chi_{8112}(847,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{29}{156}\right)\)	\(e\left(\frac{25}{156}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{19}{78}\right)\)
\(\chi_{8112}(895,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{83}{156}\right)\)	\(e\left(\frac{7}{156}\right)\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{49}{78}\right)\)
\(\chi_{8112}(943,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{151}{156}\right)\)	\(e\left(\frac{71}{156}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{29}{78}\right)\)
\(\chi_{8112}(1423,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{73}{156}\right)\)	\(e\left(\frac{149}{156}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{29}{78}\right)\)
\(\chi_{8112}(1471,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{5}{156}\right)\)	\(e\left(\frac{85}{156}\right)\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{49}{78}\right)\)
\(\chi_{8112}(1519,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{107}{156}\right)\)	\(e\left(\frac{103}{156}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{19}{78}\right)\)
\(\chi_{8112}(1567,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{55}{156}\right)\)	\(e\left(\frac{155}{156}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{71}{78}\right)\)
\(\chi_{8112}(2095,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{137}{156}\right)\)	\(e\left(\frac{145}{156}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{1}{78}\right)\)
\(\chi_{8112}(2143,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{131}{156}\right)\)	\(e\left(\frac{43}{156}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{67}{78}\right)\)
\(\chi_{8112}(2191,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{115}{156}\right)\)	\(e\left(\frac{83}{156}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{35}{78}\right)\)
\(\chi_{8112}(2671,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{109}{156}\right)\)	\(e\left(\frac{137}{156}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{23}{78}\right)\)
\(\chi_{8112}(2719,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{113}{156}\right)\)	\(e\left(\frac{49}{156}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{31}{78}\right)\)
\(\chi_{8112}(2767,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{155}{156}\right)\)	\(e\left(\frac{139}{156}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{37}{78}\right)\)
\(\chi_{8112}(2815,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{19}{156}\right)\)	\(e\left(\frac{11}{156}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{77}{78}\right)\)
\(\chi_{8112}(3295,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{49}{156}\right)\)	\(e\left(\frac{53}{156}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{59}{78}\right)\)
\(\chi_{8112}(3343,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{89}{156}\right)\)	\(e\left(\frac{109}{156}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{61}{78}\right)\)
\(\chi_{8112}(3391,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{23}{156}\right)\)	\(e\left(\frac{79}{156}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{7}{78}\right)\)
\(\chi_{8112}(3439,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{79}{156}\right)\)	\(e\left(\frac{95}{156}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{41}{78}\right)\)
\(\chi_{8112}(3919,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{145}{156}\right)\)	\(e\left(\frac{125}{156}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{17}{78}\right)\)
\(\chi_{8112}(4015,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{47}{156}\right)\)	\(e\left(\frac{19}{156}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{55}{78}\right)\)
\(\chi_{8112}(4063,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{139}{156}\right)\)	\(e\left(\frac{23}{156}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{5}{78}\right)\)
\(\chi_{8112}(4543,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{85}{156}\right)\)	\(e\left(\frac{41}{156}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{53}{78}\right)\)
\(\chi_{8112}(4591,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{41}{156}\right)\)	\(e\left(\frac{73}{156}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{43}{78}\right)\)
\(\chi_{8112}(4639,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{71}{156}\right)\)	\(e\left(\frac{115}{156}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{25}{78}\right)\)
\(\chi_{8112}(4687,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{43}{156}\right)\)	\(e\left(\frac{107}{156}\right)\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{47}{78}\right)\)
\(\chi_{8112}(5167,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{25}{156}\right)\)	\(e\left(\frac{113}{156}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{11}{78}\right)\)
\(\chi_{8112}(5215,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{17}{156}\right)\)	\(e\left(\frac{133}{156}\right)\)	\(e\left(\frac{67}{78}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{73}{78}\right)\)

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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.fp
Modulus	$8112$
Conductor	$676$
Order	$156$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(8112\)
Conductor:	\(676\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(156\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 676.w	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)