LMFDB - Dirichlet character orbit 56644.en

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(56644, base_ring=CyclotomicField(336)) M = H._module chi = DirichletCharacter(H, M([0,160,189])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(65,56644)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$56644$
Conductor:	$833$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$336$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 833.bm	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{336})$
Fixed field:	Number field defined by a degree 336 polynomial (not computed)

First 31 of 96 characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$9$	$11$	$13$	$15$	$19$	$23$	$25$	$27$
$\chi_{56644}(65,\cdot)$	$-1$	$1$	$e\left(\frac{13}{336}\right)$	$e\left(\frac{209}{336}\right)$	$e\left(\frac{13}{168}\right)$	$e\left(\frac{331}{336}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{37}{56}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{179}{336}\right)$	$e\left(\frac{41}{168}\right)$	$e\left(\frac{13}{112}\right)$
$\chi_{56644}(249,\cdot)$	$-1$	$1$	$e\left(\frac{227}{336}\right)$	$e\left(\frac{31}{336}\right)$	$e\left(\frac{59}{168}\right)$	$e\left(\frac{197}{336}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{205}{336}\right)$	$e\left(\frac{31}{168}\right)$	$e\left(\frac{3}{112}\right)$
$\chi_{56644}(513,\cdot)$	$-1$	$1$	$e\left(\frac{325}{336}\right)$	$e\left(\frac{185}{336}\right)$	$e\left(\frac{157}{168}\right)$	$e\left(\frac{211}{336}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{29}{56}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{107}{336}\right)$	$e\left(\frac{17}{168}\right)$	$e\left(\frac{101}{112}\right)$
$\chi_{56644}(653,\cdot)$	$-1$	$1$	$e\left(\frac{55}{336}\right)$	$e\left(\frac{83}{336}\right)$	$e\left(\frac{55}{168}\right)$	$e\left(\frac{289}{336}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{23}{56}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{137}{336}\right)$	$e\left(\frac{83}{168}\right)$	$e\left(\frac{55}{112}\right)$
$\chi_{56644}(709,\cdot)$	$-1$	$1$	$e\left(\frac{241}{336}\right)$	$e\left(\frac{101}{336}\right)$	$e\left(\frac{73}{168}\right)$	$e\left(\frac{295}{336}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{1}{56}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{191}{336}\right)$	$e\left(\frac{101}{168}\right)$	$e\left(\frac{17}{112}\right)$
$\chi_{56644}(2181,\cdot)$	$-1$	$1$	$e\left(\frac{233}{336}\right)$	$e\left(\frac{205}{336}\right)$	$e\left(\frac{65}{168}\right)$	$e\left(\frac{143}{336}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{17}{56}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{55}{336}\right)$	$e\left(\frac{37}{168}\right)$	$e\left(\frac{9}{112}\right)$
$\chi_{56644}(2237,\cdot)$	$-1$	$1$	$e\left(\frac{95}{336}\right)$	$e\left(\frac{235}{336}\right)$	$e\left(\frac{95}{168}\right)$	$e\left(\frac{41}{336}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{55}{56}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{145}{336}\right)$	$e\left(\frac{67}{168}\right)$	$e\left(\frac{95}{112}\right)$
$\chi_{56644}(2377,\cdot)$	$-1$	$1$	$e\left(\frac{317}{336}\right)$	$e\left(\frac{289}{336}\right)$	$e\left(\frac{149}{168}\right)$	$e\left(\frac{59}{336}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{45}{56}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{307}{336}\right)$	$e\left(\frac{121}{168}\right)$	$e\left(\frac{93}{112}\right)$
$\chi_{56644}(2641,\cdot)$	$-1$	$1$	$e\left(\frac{43}{336}\right)$	$e\left(\frac{71}{336}\right)$	$e\left(\frac{43}{168}\right)$	$e\left(\frac{61}{336}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{19}{56}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{101}{336}\right)$	$e\left(\frac{71}{168}\right)$	$e\left(\frac{43}{112}\right)$
$\chi_{56644}(2825,\cdot)$	$-1$	$1$	$e\left(\frac{53}{336}\right)$	$e\left(\frac{25}{336}\right)$	$e\left(\frac{53}{168}\right)$	$e\left(\frac{83}{336}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{13}{56}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{187}{336}\right)$	$e\left(\frac{25}{168}\right)$	$e\left(\frac{53}{112}\right)$
$\chi_{56644}(2965,\cdot)$	$-1$	$1$	$e\left(\frac{23}{336}\right)$	$e\left(\frac{163}{336}\right)$	$e\left(\frac{23}{168}\right)$	$e\left(\frac{17}{336}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{31}{56}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{265}{336}\right)$	$e\left(\frac{163}{168}\right)$	$e\left(\frac{23}{112}\right)$
$\chi_{56644}(3021,\cdot)$	$-1$	$1$	$e\left(\frac{305}{336}\right)$	$e\left(\frac{277}{336}\right)$	$e\left(\frac{137}{168}\right)$	$e\left(\frac{167}{336}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{41}{56}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{271}{336}\right)$	$e\left(\frac{109}{168}\right)$	$e\left(\frac{81}{112}\right)$
$\chi_{56644}(4953,\cdot)$	$-1$	$1$	$e\left(\frac{59}{336}\right)$	$e\left(\frac{199}{336}\right)$	$e\left(\frac{59}{168}\right)$	$e\left(\frac{29}{336}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{37}{336}\right)$	$e\left(\frac{31}{168}\right)$	$e\left(\frac{59}{112}\right)$
$\chi_{56644}(6029,\cdot)$	$-1$	$1$	$e\left(\frac{19}{336}\right)$	$e\left(\frac{47}{336}\right)$	$e\left(\frac{19}{168}\right)$	$e\left(\frac{277}{336}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{11}{56}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{29}{336}\right)$	$e\left(\frac{47}{168}\right)$	$e\left(\frac{19}{112}\right)$
$\chi_{56644}(7961,\cdot)$	$-1$	$1$	$e\left(\frac{73}{336}\right)$	$e\left(\frac{269}{336}\right)$	$e\left(\frac{73}{168}\right)$	$e\left(\frac{127}{336}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{1}{56}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{23}{336}\right)$	$e\left(\frac{101}{168}\right)$	$e\left(\frac{73}{112}\right)$
$\chi_{56644}(8157,\cdot)$	$-1$	$1$	$e\left(\frac{157}{336}\right)$	$e\left(\frac{17}{336}\right)$	$e\left(\frac{157}{168}\right)$	$e\left(\frac{43}{336}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{29}{56}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{275}{336}\right)$	$e\left(\frac{17}{168}\right)$	$e\left(\frac{45}{112}\right)$
$\chi_{56644}(8341,\cdot)$	$-1$	$1$	$e\left(\frac{131}{336}\right)$	$e\left(\frac{271}{336}\right)$	$e\left(\frac{131}{168}\right)$	$e\left(\frac{53}{336}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{11}{56}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{253}{336}\right)$	$e\left(\frac{103}{168}\right)$	$e\left(\frac{19}{112}\right)$
$\chi_{56644}(8745,\cdot)$	$-1$	$1$	$e\left(\frac{199}{336}\right)$	$e\left(\frac{227}{336}\right)$	$e\left(\frac{31}{168}\right)$	$e\left(\frac{1}{336}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{15}{56}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{233}{336}\right)$	$e\left(\frac{59}{168}\right)$	$e\left(\frac{87}{112}\right)$
$\chi_{56644}(10273,\cdot)$	$-1$	$1$	$e\left(\frac{137}{336}\right)$	$e\left(\frac{109}{336}\right)$	$e\left(\frac{137}{168}\right)$	$e\left(\frac{335}{336}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{41}{56}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{103}{336}\right)$	$e\left(\frac{109}{168}\right)$	$e\left(\frac{25}{112}\right)$
$\chi_{56644}(10329,\cdot)$	$-1$	$1$	$e\left(\frac{335}{336}\right)$	$e\left(\frac{139}{336}\right)$	$e\left(\frac{167}{168}\right)$	$e\left(\frac{233}{336}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{23}{56}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{193}{336}\right)$	$e\left(\frac{139}{168}\right)$	$e\left(\frac{111}{112}\right)$
$\chi_{56644}(10469,\cdot)$	$-1$	$1$	$e\left(\frac{221}{336}\right)$	$e\left(\frac{193}{336}\right)$	$e\left(\frac{53}{168}\right)$	$e\left(\frac{251}{336}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{13}{56}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{19}{336}\right)$	$e\left(\frac{25}{168}\right)$	$e\left(\frac{109}{112}\right)$
$\chi_{56644}(10733,\cdot)$	$-1$	$1$	$e\left(\frac{187}{336}\right)$	$e\left(\frac{215}{336}\right)$	$e\left(\frac{19}{168}\right)$	$e\left(\frac{109}{336}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{11}{56}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{197}{336}\right)$	$e\left(\frac{47}{168}\right)$	$e\left(\frac{75}{112}\right)$
$\chi_{56644}(10917,\cdot)$	$-1$	$1$	$e\left(\frac{293}{336}\right)$	$e\left(\frac{265}{336}\right)$	$e\left(\frac{125}{168}\right)$	$e\left(\frac{275}{336}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{37}{56}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{235}{336}\right)$	$e\left(\frac{97}{168}\right)$	$e\left(\frac{69}{112}\right)$
$\chi_{56644}(11057,\cdot)$	$-1$	$1$	$e\left(\frac{263}{336}\right)$	$e\left(\frac{67}{336}\right)$	$e\left(\frac{95}{168}\right)$	$e\left(\frac{209}{336}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{55}{56}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{313}{336}\right)$	$e\left(\frac{67}{168}\right)$	$e\left(\frac{39}{112}\right)$
$\chi_{56644}(11113,\cdot)$	$-1$	$1$	$e\left(\frac{209}{336}\right)$	$e\left(\frac{181}{336}\right)$	$e\left(\frac{41}{168}\right)$	$e\left(\frac{23}{336}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{9}{56}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{319}{336}\right)$	$e\left(\frac{13}{168}\right)$	$e\left(\frac{97}{112}\right)$
$\chi_{56644}(13045,\cdot)$	$-1$	$1$	$e\left(\frac{299}{336}\right)$	$e\left(\frac{103}{336}\right)$	$e\left(\frac{131}{168}\right)$	$e\left(\frac{221}{336}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{11}{56}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{85}{336}\right)$	$e\left(\frac{103}{168}\right)$	$e\left(\frac{75}{112}\right)$
$\chi_{56644}(14121,\cdot)$	$-1$	$1$	$e\left(\frac{163}{336}\right)$	$e\left(\frac{191}{336}\right)$	$e\left(\frac{163}{168}\right)$	$e\left(\frac{325}{336}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{3}{56}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{125}{336}\right)$	$e\left(\frac{23}{168}\right)$	$e\left(\frac{51}{112}\right)$
$\chi_{56644}(16109,\cdot)$	$-1$	$1$	$e\left(\frac{319}{336}\right)$	$e\left(\frac{11}{336}\right)$	$e\left(\frac{151}{168}\right)$	$e\left(\frac{265}{336}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{55}{56}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{257}{336}\right)$	$e\left(\frac{11}{168}\right)$	$e\left(\frac{95}{112}\right)$
$\chi_{56644}(16697,\cdot)$	$-1$	$1$	$e\left(\frac{277}{336}\right)$	$e\left(\frac{137}{336}\right)$	$e\left(\frac{109}{168}\right)$	$e\left(\frac{307}{336}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{13}{56}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{299}{336}\right)$	$e\left(\frac{137}{168}\right)$	$e\left(\frac{53}{112}\right)$
$\chi_{56644}(16893,\cdot)$	$-1$	$1$	$e\left(\frac{193}{336}\right)$	$e\left(\frac{53}{336}\right)$	$e\left(\frac{25}{168}\right)$	$e\left(\frac{55}{336}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{41}{56}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{47}{336}\right)$	$e\left(\frac{53}{168}\right)$	$e\left(\frac{81}{112}\right)$
$\chi_{56644}(18365,\cdot)$	$-1$	$1$	$e\left(\frac{41}{336}\right)$	$e\left(\frac{13}{336}\right)$	$e\left(\frac{41}{168}\right)$	$e\left(\frac{191}{336}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{9}{56}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{151}{336}\right)$	$e\left(\frac{13}{168}\right)$	$e\left(\frac{41}{112}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(9\)	\(11\)	\(13\)	\(15\)	\(19\)	\(23\)	\(25\)	\(27\)
\(\chi_{56644}(65,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{336}\right)\)	\(e\left(\frac{209}{336}\right)\)	\(e\left(\frac{13}{168}\right)\)	\(e\left(\frac{331}{336}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{37}{56}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{179}{336}\right)\)	\(e\left(\frac{41}{168}\right)\)	\(e\left(\frac{13}{112}\right)\)
\(\chi_{56644}(249,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{227}{336}\right)\)	\(e\left(\frac{31}{336}\right)\)	\(e\left(\frac{59}{168}\right)\)	\(e\left(\frac{197}{336}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{205}{336}\right)\)	\(e\left(\frac{31}{168}\right)\)	\(e\left(\frac{3}{112}\right)\)
\(\chi_{56644}(513,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{325}{336}\right)\)	\(e\left(\frac{185}{336}\right)\)	\(e\left(\frac{157}{168}\right)\)	\(e\left(\frac{211}{336}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{29}{56}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{107}{336}\right)\)	\(e\left(\frac{17}{168}\right)\)	\(e\left(\frac{101}{112}\right)\)
\(\chi_{56644}(653,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{55}{336}\right)\)	\(e\left(\frac{83}{336}\right)\)	\(e\left(\frac{55}{168}\right)\)	\(e\left(\frac{289}{336}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{23}{56}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{137}{336}\right)\)	\(e\left(\frac{83}{168}\right)\)	\(e\left(\frac{55}{112}\right)\)
\(\chi_{56644}(709,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{241}{336}\right)\)	\(e\left(\frac{101}{336}\right)\)	\(e\left(\frac{73}{168}\right)\)	\(e\left(\frac{295}{336}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{1}{56}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{191}{336}\right)\)	\(e\left(\frac{101}{168}\right)\)	\(e\left(\frac{17}{112}\right)\)
\(\chi_{56644}(2181,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{233}{336}\right)\)	\(e\left(\frac{205}{336}\right)\)	\(e\left(\frac{65}{168}\right)\)	\(e\left(\frac{143}{336}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{17}{56}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{55}{336}\right)\)	\(e\left(\frac{37}{168}\right)\)	\(e\left(\frac{9}{112}\right)\)
\(\chi_{56644}(2237,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{95}{336}\right)\)	\(e\left(\frac{235}{336}\right)\)	\(e\left(\frac{95}{168}\right)\)	\(e\left(\frac{41}{336}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{55}{56}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{145}{336}\right)\)	\(e\left(\frac{67}{168}\right)\)	\(e\left(\frac{95}{112}\right)\)
\(\chi_{56644}(2377,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{317}{336}\right)\)	\(e\left(\frac{289}{336}\right)\)	\(e\left(\frac{149}{168}\right)\)	\(e\left(\frac{59}{336}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{45}{56}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{307}{336}\right)\)	\(e\left(\frac{121}{168}\right)\)	\(e\left(\frac{93}{112}\right)\)
\(\chi_{56644}(2641,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{43}{336}\right)\)	\(e\left(\frac{71}{336}\right)\)	\(e\left(\frac{43}{168}\right)\)	\(e\left(\frac{61}{336}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{19}{56}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{101}{336}\right)\)	\(e\left(\frac{71}{168}\right)\)	\(e\left(\frac{43}{112}\right)\)
\(\chi_{56644}(2825,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{53}{336}\right)\)	\(e\left(\frac{25}{336}\right)\)	\(e\left(\frac{53}{168}\right)\)	\(e\left(\frac{83}{336}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{13}{56}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{187}{336}\right)\)	\(e\left(\frac{25}{168}\right)\)	\(e\left(\frac{53}{112}\right)\)
\(\chi_{56644}(2965,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{336}\right)\)	\(e\left(\frac{163}{336}\right)\)	\(e\left(\frac{23}{168}\right)\)	\(e\left(\frac{17}{336}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{31}{56}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{265}{336}\right)\)	\(e\left(\frac{163}{168}\right)\)	\(e\left(\frac{23}{112}\right)\)
\(\chi_{56644}(3021,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{305}{336}\right)\)	\(e\left(\frac{277}{336}\right)\)	\(e\left(\frac{137}{168}\right)\)	\(e\left(\frac{167}{336}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{41}{56}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{271}{336}\right)\)	\(e\left(\frac{109}{168}\right)\)	\(e\left(\frac{81}{112}\right)\)
\(\chi_{56644}(4953,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{59}{336}\right)\)	\(e\left(\frac{199}{336}\right)\)	\(e\left(\frac{59}{168}\right)\)	\(e\left(\frac{29}{336}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{37}{336}\right)\)	\(e\left(\frac{31}{168}\right)\)	\(e\left(\frac{59}{112}\right)\)
\(\chi_{56644}(6029,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{336}\right)\)	\(e\left(\frac{47}{336}\right)\)	\(e\left(\frac{19}{168}\right)\)	\(e\left(\frac{277}{336}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{11}{56}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{29}{336}\right)\)	\(e\left(\frac{47}{168}\right)\)	\(e\left(\frac{19}{112}\right)\)
\(\chi_{56644}(7961,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{73}{336}\right)\)	\(e\left(\frac{269}{336}\right)\)	\(e\left(\frac{73}{168}\right)\)	\(e\left(\frac{127}{336}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{1}{56}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{23}{336}\right)\)	\(e\left(\frac{101}{168}\right)\)	\(e\left(\frac{73}{112}\right)\)
\(\chi_{56644}(8157,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{157}{336}\right)\)	\(e\left(\frac{17}{336}\right)\)	\(e\left(\frac{157}{168}\right)\)	\(e\left(\frac{43}{336}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{29}{56}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{275}{336}\right)\)	\(e\left(\frac{17}{168}\right)\)	\(e\left(\frac{45}{112}\right)\)
\(\chi_{56644}(8341,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{131}{336}\right)\)	\(e\left(\frac{271}{336}\right)\)	\(e\left(\frac{131}{168}\right)\)	\(e\left(\frac{53}{336}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{11}{56}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{253}{336}\right)\)	\(e\left(\frac{103}{168}\right)\)	\(e\left(\frac{19}{112}\right)\)
\(\chi_{56644}(8745,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{199}{336}\right)\)	\(e\left(\frac{227}{336}\right)\)	\(e\left(\frac{31}{168}\right)\)	\(e\left(\frac{1}{336}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{15}{56}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{233}{336}\right)\)	\(e\left(\frac{59}{168}\right)\)	\(e\left(\frac{87}{112}\right)\)
\(\chi_{56644}(10273,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{137}{336}\right)\)	\(e\left(\frac{109}{336}\right)\)	\(e\left(\frac{137}{168}\right)\)	\(e\left(\frac{335}{336}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{41}{56}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{103}{336}\right)\)	\(e\left(\frac{109}{168}\right)\)	\(e\left(\frac{25}{112}\right)\)
\(\chi_{56644}(10329,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{335}{336}\right)\)	\(e\left(\frac{139}{336}\right)\)	\(e\left(\frac{167}{168}\right)\)	\(e\left(\frac{233}{336}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{23}{56}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{193}{336}\right)\)	\(e\left(\frac{139}{168}\right)\)	\(e\left(\frac{111}{112}\right)\)
\(\chi_{56644}(10469,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{221}{336}\right)\)	\(e\left(\frac{193}{336}\right)\)	\(e\left(\frac{53}{168}\right)\)	\(e\left(\frac{251}{336}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{13}{56}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{19}{336}\right)\)	\(e\left(\frac{25}{168}\right)\)	\(e\left(\frac{109}{112}\right)\)
\(\chi_{56644}(10733,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{187}{336}\right)\)	\(e\left(\frac{215}{336}\right)\)	\(e\left(\frac{19}{168}\right)\)	\(e\left(\frac{109}{336}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{11}{56}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{197}{336}\right)\)	\(e\left(\frac{47}{168}\right)\)	\(e\left(\frac{75}{112}\right)\)
\(\chi_{56644}(10917,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{293}{336}\right)\)	\(e\left(\frac{265}{336}\right)\)	\(e\left(\frac{125}{168}\right)\)	\(e\left(\frac{275}{336}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{37}{56}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{235}{336}\right)\)	\(e\left(\frac{97}{168}\right)\)	\(e\left(\frac{69}{112}\right)\)
\(\chi_{56644}(11057,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{263}{336}\right)\)	\(e\left(\frac{67}{336}\right)\)	\(e\left(\frac{95}{168}\right)\)	\(e\left(\frac{209}{336}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{55}{56}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{313}{336}\right)\)	\(e\left(\frac{67}{168}\right)\)	\(e\left(\frac{39}{112}\right)\)
\(\chi_{56644}(11113,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{209}{336}\right)\)	\(e\left(\frac{181}{336}\right)\)	\(e\left(\frac{41}{168}\right)\)	\(e\left(\frac{23}{336}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{9}{56}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{319}{336}\right)\)	\(e\left(\frac{13}{168}\right)\)	\(e\left(\frac{97}{112}\right)\)
\(\chi_{56644}(13045,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{299}{336}\right)\)	\(e\left(\frac{103}{336}\right)\)	\(e\left(\frac{131}{168}\right)\)	\(e\left(\frac{221}{336}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{11}{56}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{85}{336}\right)\)	\(e\left(\frac{103}{168}\right)\)	\(e\left(\frac{75}{112}\right)\)
\(\chi_{56644}(14121,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{163}{336}\right)\)	\(e\left(\frac{191}{336}\right)\)	\(e\left(\frac{163}{168}\right)\)	\(e\left(\frac{325}{336}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{3}{56}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{125}{336}\right)\)	\(e\left(\frac{23}{168}\right)\)	\(e\left(\frac{51}{112}\right)\)
\(\chi_{56644}(16109,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{319}{336}\right)\)	\(e\left(\frac{11}{336}\right)\)	\(e\left(\frac{151}{168}\right)\)	\(e\left(\frac{265}{336}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{55}{56}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{257}{336}\right)\)	\(e\left(\frac{11}{168}\right)\)	\(e\left(\frac{95}{112}\right)\)
\(\chi_{56644}(16697,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{277}{336}\right)\)	\(e\left(\frac{137}{336}\right)\)	\(e\left(\frac{109}{168}\right)\)	\(e\left(\frac{307}{336}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{13}{56}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{299}{336}\right)\)	\(e\left(\frac{137}{168}\right)\)	\(e\left(\frac{53}{112}\right)\)
\(\chi_{56644}(16893,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{193}{336}\right)\)	\(e\left(\frac{53}{336}\right)\)	\(e\left(\frac{25}{168}\right)\)	\(e\left(\frac{55}{336}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{41}{56}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{47}{336}\right)\)	\(e\left(\frac{53}{168}\right)\)	\(e\left(\frac{81}{112}\right)\)
\(\chi_{56644}(18365,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{41}{336}\right)\)	\(e\left(\frac{13}{336}\right)\)	\(e\left(\frac{41}{168}\right)\)	\(e\left(\frac{191}{336}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{9}{56}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{151}{336}\right)\)	\(e\left(\frac{13}{168}\right)\)	\(e\left(\frac{41}{112}\right)\)

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First 31 of 96 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	56644.en
Modulus	$56644$
Conductor	$833$
Order	$336$
Real	no
Primitive	no
Minimal	yes
Parity	odd

Modulus:	\(56644\)
Conductor:	\(833\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(336\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 833.bm	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)