LMFDB - Dirichlet character orbit 228672.bjf

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(228672, base_ring=CyclotomicField(264)) M = H._module chi = DirichletCharacter(H, M([132,165,132,106])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(71, 228672)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("228672.71"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$228672$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$38112$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$264$	comment:Order sage:chi.multiplicative_order() gp:charorder(g,chi) magma:Order(chi);
Real:	no	comment:Whether the character is real sage:chi.multiplicative_order() <= 2 gp:charorder(g,chi) <= 2 magma:Order(chi) le 2;
Primitive:	no, induced from 38112.lj	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	no
Parity:	odd	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);

Related number fields

Field of values:	$\Q(\zeta_{264})$	comment:Field of values of chi sage:CyclotomicField(chi.multiplicative_order()) gp:nfinit(polcyclo(charorder(g,chi))) magma:CyclotomicField(Order(chi));
Fixed field:	Number field defined by a degree 264 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 31 of 80 characters in Galois orbit

Character	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$
$\chi_{228672}(71,\cdot)$	$-1$	$1$	$e\left(\frac{139}{264}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{89}{264}\right)$	$e\left(\frac{245}{264}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{71}{264}\right)$	$e\left(\frac{61}{132}\right)$	$e\left(\frac{7}{132}\right)$	$e\left(\frac{227}{264}\right)$	$e\left(\frac{13}{22}\right)$
$\chi_{228672}(6695,\cdot)$	$-1$	$1$	$e\left(\frac{31}{264}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{149}{264}\right)$	$e\left(\frac{161}{264}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{107}{264}\right)$	$e\left(\frac{25}{132}\right)$	$e\left(\frac{31}{132}\right)$	$e\left(\frac{119}{264}\right)$	$e\left(\frac{1}{22}\right)$
$\chi_{228672}(7271,\cdot)$	$-1$	$1$	$e\left(\frac{167}{264}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{181}{264}\right)$	$e\left(\frac{169}{264}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{91}{264}\right)$	$e\left(\frac{41}{132}\right)$	$e\left(\frac{35}{132}\right)$	$e\left(\frac{79}{264}\right)$	$e\left(\frac{21}{22}\right)$
$\chi_{228672}(13031,\cdot)$	$-1$	$1$	$e\left(\frac{151}{264}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{53}{264}\right)$	$e\left(\frac{137}{264}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{155}{264}\right)$	$e\left(\frac{109}{132}\right)$	$e\left(\frac{19}{132}\right)$	$e\left(\frac{239}{264}\right)$	$e\left(\frac{7}{22}\right)$
$\chi_{228672}(15767,\cdot)$	$-1$	$1$	$e\left(\frac{1}{264}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{107}{264}\right)$	$e\left(\frac{167}{264}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{29}{264}\right)$	$e\left(\frac{103}{132}\right)$	$e\left(\frac{1}{132}\right)$	$e\left(\frac{89}{264}\right)$	$e\left(\frac{5}{22}\right)$
$\chi_{228672}(17351,\cdot)$	$-1$	$1$	$e\left(\frac{211}{264}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{137}{264}\right)$	$e\left(\frac{125}{264}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{47}{264}\right)$	$e\left(\frac{85}{132}\right)$	$e\left(\frac{79}{132}\right)$	$e\left(\frac{35}{264}\right)$	$e\left(\frac{21}{22}\right)$
$\chi_{228672}(19367,\cdot)$	$-1$	$1$	$e\left(\frac{247}{264}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{29}{264}\right)$	$e\left(\frac{65}{264}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{35}{264}\right)$	$e\left(\frac{97}{132}\right)$	$e\left(\frac{115}{132}\right)$	$e\left(\frac{71}{264}\right)$	$e\left(\frac{3}{22}\right)$
$\chi_{228672}(21383,\cdot)$	$-1$	$1$	$e\left(\frac{259}{264}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{257}{264}\right)$	$e\left(\frac{221}{264}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{119}{264}\right)$	$e\left(\frac{13}{132}\right)$	$e\left(\frac{127}{132}\right)$	$e\left(\frac{83}{264}\right)$	$e\left(\frac{19}{22}\right)$
$\chi_{228672}(22247,\cdot)$	$-1$	$1$	$e\left(\frac{23}{264}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{85}{264}\right)$	$e\left(\frac{145}{264}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{139}{264}\right)$	$e\left(\frac{125}{132}\right)$	$e\left(\frac{23}{132}\right)$	$e\left(\frac{199}{264}\right)$	$e\left(\frac{5}{22}\right)$
$\chi_{228672}(33911,\cdot)$	$-1$	$1$	$e\left(\frac{5}{264}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{7}{264}\right)$	$e\left(\frac{43}{264}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{145}{264}\right)$	$e\left(\frac{119}{132}\right)$	$e\left(\frac{5}{132}\right)$	$e\left(\frac{181}{264}\right)$	$e\left(\frac{3}{22}\right)$
$\chi_{228672}(34919,\cdot)$	$-1$	$1$	$e\left(\frac{47}{264}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{13}{264}\right)$	$e\left(\frac{193}{264}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{43}{264}\right)$	$e\left(\frac{89}{132}\right)$	$e\left(\frac{47}{132}\right)$	$e\left(\frac{223}{264}\right)$	$e\left(\frac{15}{22}\right)$
$\chi_{228672}(36647,\cdot)$	$-1$	$1$	$e\left(\frac{191}{264}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{109}{264}\right)$	$e\left(\frac{217}{264}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{259}{264}\right)$	$e\left(\frac{5}{132}\right)$	$e\left(\frac{59}{132}\right)$	$e\left(\frac{103}{264}\right)$	$e\left(\frac{9}{22}\right)$
$\chi_{228672}(37223,\cdot)$	$-1$	$1$	$e\left(\frac{119}{264}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{61}{264}\right)$	$e\left(\frac{73}{264}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{19}{264}\right)$	$e\left(\frac{113}{132}\right)$	$e\left(\frac{119}{132}\right)$	$e\left(\frac{31}{264}\right)$	$e\left(\frac{1}{22}\right)$
$\chi_{228672}(40391,\cdot)$	$-1$	$1$	$e\left(\frac{227}{264}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{1}{264}\right)$	$e\left(\frac{157}{264}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{247}{264}\right)$	$e\left(\frac{17}{132}\right)$	$e\left(\frac{95}{132}\right)$	$e\left(\frac{139}{264}\right)$	$e\left(\frac{13}{22}\right)$
$\chi_{228672}(40823,\cdot)$	$-1$	$1$	$e\left(\frac{173}{264}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{31}{264}\right)$	$e\left(\frac{115}{264}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{1}{264}\right)$	$e\left(\frac{131}{132}\right)$	$e\left(\frac{41}{132}\right)$	$e\left(\frac{85}{264}\right)$	$e\left(\frac{7}{22}\right)$
$\chi_{228672}(42263,\cdot)$	$-1$	$1$	$e\left(\frac{25}{264}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{35}{264}\right)$	$e\left(\frac{215}{264}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{197}{264}\right)$	$e\left(\frac{67}{132}\right)$	$e\left(\frac{25}{132}\right)$	$e\left(\frac{113}{264}\right)$	$e\left(\frac{15}{22}\right)$
$\chi_{228672}(42695,\cdot)$	$-1$	$1$	$e\left(\frac{91}{264}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{233}{264}\right)$	$e\left(\frac{149}{264}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{263}{264}\right)$	$e\left(\frac{1}{132}\right)$	$e\left(\frac{91}{132}\right)$	$e\left(\frac{179}{264}\right)$	$e\left(\frac{15}{22}\right)$
$\chi_{228672}(44135,\cdot)$	$-1$	$1$	$e\left(\frac{239}{264}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{229}{264}\right)$	$e\left(\frac{49}{264}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{67}{264}\right)$	$e\left(\frac{65}{132}\right)$	$e\left(\frac{107}{132}\right)$	$e\left(\frac{151}{264}\right)$	$e\left(\frac{7}{22}\right)$
$\chi_{228672}(44567,\cdot)$	$-1$	$1$	$e\left(\frac{161}{264}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{67}{264}\right)$	$e\left(\frac{223}{264}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{181}{264}\right)$	$e\left(\frac{83}{132}\right)$	$e\left(\frac{29}{132}\right)$	$e\left(\frac{73}{264}\right)$	$e\left(\frac{13}{22}\right)$
$\chi_{228672}(47735,\cdot)$	$-1$	$1$	$e\left(\frac{53}{264}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{127}{264}\right)$	$e\left(\frac{139}{264}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{217}{264}\right)$	$e\left(\frac{47}{132}\right)$	$e\left(\frac{53}{132}\right)$	$e\left(\frac{229}{264}\right)$	$e\left(\frac{1}{22}\right)$
$\chi_{228672}(48311,\cdot)$	$-1$	$1$	$e\left(\frac{125}{264}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{175}{264}\right)$	$e\left(\frac{19}{264}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{193}{264}\right)$	$e\left(\frac{71}{132}\right)$	$e\left(\frac{125}{132}\right)$	$e\left(\frac{37}{264}\right)$	$e\left(\frac{9}{22}\right)$
$\chi_{228672}(50039,\cdot)$	$-1$	$1$	$e\left(\frac{245}{264}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{79}{264}\right)$	$e\left(\frac{259}{264}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{241}{264}\right)$	$e\left(\frac{23}{132}\right)$	$e\left(\frac{113}{132}\right)$	$e\left(\frac{157}{264}\right)$	$e\left(\frac{15}{22}\right)$
$\chi_{228672}(51047,\cdot)$	$-1$	$1$	$e\left(\frac{71}{264}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{205}{264}\right)$	$e\left(\frac{241}{264}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{211}{264}\right)$	$e\left(\frac{53}{132}\right)$	$e\left(\frac{71}{132}\right)$	$e\left(\frac{247}{264}\right)$	$e\left(\frac{3}{22}\right)$
$\chi_{228672}(62711,\cdot)$	$-1$	$1$	$e\left(\frac{221}{264}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{151}{264}\right)$	$e\left(\frac{211}{264}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{73}{264}\right)$	$e\left(\frac{59}{132}\right)$	$e\left(\frac{89}{132}\right)$	$e\left(\frac{133}{264}\right)$	$e\left(\frac{5}{22}\right)$
$\chi_{228672}(63575,\cdot)$	$-1$	$1$	$e\left(\frac{193}{264}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{59}{264}\right)$	$e\left(\frac{23}{264}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{53}{264}\right)$	$e\left(\frac{79}{132}\right)$	$e\left(\frac{61}{132}\right)$	$e\left(\frac{17}{264}\right)$	$e\left(\frac{19}{22}\right)$
$\chi_{228672}(65591,\cdot)$	$-1$	$1$	$e\left(\frac{181}{264}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{95}{264}\right)$	$e\left(\frac{131}{264}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{233}{264}\right)$	$e\left(\frac{31}{132}\right)$	$e\left(\frac{49}{132}\right)$	$e\left(\frac{5}{264}\right)$	$e\left(\frac{3}{22}\right)$
$\chi_{228672}(67607,\cdot)$	$-1$	$1$	$e\left(\frac{145}{264}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{203}{264}\right)$	$e\left(\frac{191}{264}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{245}{264}\right)$	$e\left(\frac{19}{132}\right)$	$e\left(\frac{13}{132}\right)$	$e\left(\frac{233}{264}\right)$	$e\left(\frac{21}{22}\right)$
$\chi_{228672}(69191,\cdot)$	$-1$	$1$	$e\left(\frac{67}{264}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{41}{264}\right)$	$e\left(\frac{101}{264}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{95}{264}\right)$	$e\left(\frac{37}{132}\right)$	$e\left(\frac{67}{132}\right)$	$e\left(\frac{155}{264}\right)$	$e\left(\frac{5}{22}\right)$
$\chi_{228672}(71927,\cdot)$	$-1$	$1$	$e\left(\frac{85}{264}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{119}{264}\right)$	$e\left(\frac{203}{264}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{89}{264}\right)$	$e\left(\frac{43}{132}\right)$	$e\left(\frac{85}{132}\right)$	$e\left(\frac{173}{264}\right)$	$e\left(\frac{7}{22}\right)$
$\chi_{228672}(77687,\cdot)$	$-1$	$1$	$e\left(\frac{101}{264}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{247}{264}\right)$	$e\left(\frac{235}{264}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{25}{264}\right)$	$e\left(\frac{107}{132}\right)$	$e\left(\frac{101}{132}\right)$	$e\left(\frac{13}{264}\right)$	$e\left(\frac{21}{22}\right)$
$\chi_{228672}(78263,\cdot)$	$-1$	$1$	$e\left(\frac{229}{264}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{215}{264}\right)$	$e\left(\frac{227}{264}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{41}{264}\right)$	$e\left(\frac{91}{132}\right)$	$e\left(\frac{97}{132}\right)$	$e\left(\frac{53}{264}\right)$	$e\left(\frac{1}{22}\right)$

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	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)
\(\chi_{228672}(71,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{139}{264}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{89}{264}\right)\)	\(e\left(\frac{245}{264}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{71}{264}\right)\)	\(e\left(\frac{61}{132}\right)\)	\(e\left(\frac{7}{132}\right)\)	\(e\left(\frac{227}{264}\right)\)	\(e\left(\frac{13}{22}\right)\)
\(\chi_{228672}(6695,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{264}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{149}{264}\right)\)	\(e\left(\frac{161}{264}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{107}{264}\right)\)	\(e\left(\frac{25}{132}\right)\)	\(e\left(\frac{31}{132}\right)\)	\(e\left(\frac{119}{264}\right)\)	\(e\left(\frac{1}{22}\right)\)
\(\chi_{228672}(7271,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{167}{264}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{181}{264}\right)\)	\(e\left(\frac{169}{264}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{91}{264}\right)\)	\(e\left(\frac{41}{132}\right)\)	\(e\left(\frac{35}{132}\right)\)	\(e\left(\frac{79}{264}\right)\)	\(e\left(\frac{21}{22}\right)\)
\(\chi_{228672}(13031,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{151}{264}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{53}{264}\right)\)	\(e\left(\frac{137}{264}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{155}{264}\right)\)	\(e\left(\frac{109}{132}\right)\)	\(e\left(\frac{19}{132}\right)\)	\(e\left(\frac{239}{264}\right)\)	\(e\left(\frac{7}{22}\right)\)
\(\chi_{228672}(15767,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{264}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{107}{264}\right)\)	\(e\left(\frac{167}{264}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{29}{264}\right)\)	\(e\left(\frac{103}{132}\right)\)	\(e\left(\frac{1}{132}\right)\)	\(e\left(\frac{89}{264}\right)\)	\(e\left(\frac{5}{22}\right)\)
\(\chi_{228672}(17351,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{211}{264}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{137}{264}\right)\)	\(e\left(\frac{125}{264}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{47}{264}\right)\)	\(e\left(\frac{85}{132}\right)\)	\(e\left(\frac{79}{132}\right)\)	\(e\left(\frac{35}{264}\right)\)	\(e\left(\frac{21}{22}\right)\)
\(\chi_{228672}(19367,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{247}{264}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{29}{264}\right)\)	\(e\left(\frac{65}{264}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{35}{264}\right)\)	\(e\left(\frac{97}{132}\right)\)	\(e\left(\frac{115}{132}\right)\)	\(e\left(\frac{71}{264}\right)\)	\(e\left(\frac{3}{22}\right)\)
\(\chi_{228672}(21383,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{259}{264}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{257}{264}\right)\)	\(e\left(\frac{221}{264}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{119}{264}\right)\)	\(e\left(\frac{13}{132}\right)\)	\(e\left(\frac{127}{132}\right)\)	\(e\left(\frac{83}{264}\right)\)	\(e\left(\frac{19}{22}\right)\)
\(\chi_{228672}(22247,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{264}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{85}{264}\right)\)	\(e\left(\frac{145}{264}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{139}{264}\right)\)	\(e\left(\frac{125}{132}\right)\)	\(e\left(\frac{23}{132}\right)\)	\(e\left(\frac{199}{264}\right)\)	\(e\left(\frac{5}{22}\right)\)
\(\chi_{228672}(33911,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{264}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{7}{264}\right)\)	\(e\left(\frac{43}{264}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{145}{264}\right)\)	\(e\left(\frac{119}{132}\right)\)	\(e\left(\frac{5}{132}\right)\)	\(e\left(\frac{181}{264}\right)\)	\(e\left(\frac{3}{22}\right)\)
\(\chi_{228672}(34919,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{47}{264}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{13}{264}\right)\)	\(e\left(\frac{193}{264}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{43}{264}\right)\)	\(e\left(\frac{89}{132}\right)\)	\(e\left(\frac{47}{132}\right)\)	\(e\left(\frac{223}{264}\right)\)	\(e\left(\frac{15}{22}\right)\)
\(\chi_{228672}(36647,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{191}{264}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{109}{264}\right)\)	\(e\left(\frac{217}{264}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{259}{264}\right)\)	\(e\left(\frac{5}{132}\right)\)	\(e\left(\frac{59}{132}\right)\)	\(e\left(\frac{103}{264}\right)\)	\(e\left(\frac{9}{22}\right)\)
\(\chi_{228672}(37223,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{119}{264}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{61}{264}\right)\)	\(e\left(\frac{73}{264}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{19}{264}\right)\)	\(e\left(\frac{113}{132}\right)\)	\(e\left(\frac{119}{132}\right)\)	\(e\left(\frac{31}{264}\right)\)	\(e\left(\frac{1}{22}\right)\)
\(\chi_{228672}(40391,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{227}{264}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{1}{264}\right)\)	\(e\left(\frac{157}{264}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{247}{264}\right)\)	\(e\left(\frac{17}{132}\right)\)	\(e\left(\frac{95}{132}\right)\)	\(e\left(\frac{139}{264}\right)\)	\(e\left(\frac{13}{22}\right)\)
\(\chi_{228672}(40823,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{173}{264}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{31}{264}\right)\)	\(e\left(\frac{115}{264}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{1}{264}\right)\)	\(e\left(\frac{131}{132}\right)\)	\(e\left(\frac{41}{132}\right)\)	\(e\left(\frac{85}{264}\right)\)	\(e\left(\frac{7}{22}\right)\)
\(\chi_{228672}(42263,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{25}{264}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{35}{264}\right)\)	\(e\left(\frac{215}{264}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{197}{264}\right)\)	\(e\left(\frac{67}{132}\right)\)	\(e\left(\frac{25}{132}\right)\)	\(e\left(\frac{113}{264}\right)\)	\(e\left(\frac{15}{22}\right)\)
\(\chi_{228672}(42695,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{91}{264}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{233}{264}\right)\)	\(e\left(\frac{149}{264}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{263}{264}\right)\)	\(e\left(\frac{1}{132}\right)\)	\(e\left(\frac{91}{132}\right)\)	\(e\left(\frac{179}{264}\right)\)	\(e\left(\frac{15}{22}\right)\)
\(\chi_{228672}(44135,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{239}{264}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{229}{264}\right)\)	\(e\left(\frac{49}{264}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{67}{264}\right)\)	\(e\left(\frac{65}{132}\right)\)	\(e\left(\frac{107}{132}\right)\)	\(e\left(\frac{151}{264}\right)\)	\(e\left(\frac{7}{22}\right)\)
\(\chi_{228672}(44567,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{161}{264}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{67}{264}\right)\)	\(e\left(\frac{223}{264}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{181}{264}\right)\)	\(e\left(\frac{83}{132}\right)\)	\(e\left(\frac{29}{132}\right)\)	\(e\left(\frac{73}{264}\right)\)	\(e\left(\frac{13}{22}\right)\)
\(\chi_{228672}(47735,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{53}{264}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{127}{264}\right)\)	\(e\left(\frac{139}{264}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{217}{264}\right)\)	\(e\left(\frac{47}{132}\right)\)	\(e\left(\frac{53}{132}\right)\)	\(e\left(\frac{229}{264}\right)\)	\(e\left(\frac{1}{22}\right)\)
\(\chi_{228672}(48311,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{125}{264}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{175}{264}\right)\)	\(e\left(\frac{19}{264}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{193}{264}\right)\)	\(e\left(\frac{71}{132}\right)\)	\(e\left(\frac{125}{132}\right)\)	\(e\left(\frac{37}{264}\right)\)	\(e\left(\frac{9}{22}\right)\)
\(\chi_{228672}(50039,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{245}{264}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{79}{264}\right)\)	\(e\left(\frac{259}{264}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{241}{264}\right)\)	\(e\left(\frac{23}{132}\right)\)	\(e\left(\frac{113}{132}\right)\)	\(e\left(\frac{157}{264}\right)\)	\(e\left(\frac{15}{22}\right)\)
\(\chi_{228672}(51047,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{71}{264}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{205}{264}\right)\)	\(e\left(\frac{241}{264}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{211}{264}\right)\)	\(e\left(\frac{53}{132}\right)\)	\(e\left(\frac{71}{132}\right)\)	\(e\left(\frac{247}{264}\right)\)	\(e\left(\frac{3}{22}\right)\)
\(\chi_{228672}(62711,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{221}{264}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{151}{264}\right)\)	\(e\left(\frac{211}{264}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{73}{264}\right)\)	\(e\left(\frac{59}{132}\right)\)	\(e\left(\frac{89}{132}\right)\)	\(e\left(\frac{133}{264}\right)\)	\(e\left(\frac{5}{22}\right)\)
\(\chi_{228672}(63575,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{193}{264}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{59}{264}\right)\)	\(e\left(\frac{23}{264}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{53}{264}\right)\)	\(e\left(\frac{79}{132}\right)\)	\(e\left(\frac{61}{132}\right)\)	\(e\left(\frac{17}{264}\right)\)	\(e\left(\frac{19}{22}\right)\)
\(\chi_{228672}(65591,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{181}{264}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{95}{264}\right)\)	\(e\left(\frac{131}{264}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{233}{264}\right)\)	\(e\left(\frac{31}{132}\right)\)	\(e\left(\frac{49}{132}\right)\)	\(e\left(\frac{5}{264}\right)\)	\(e\left(\frac{3}{22}\right)\)
\(\chi_{228672}(67607,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{145}{264}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{203}{264}\right)\)	\(e\left(\frac{191}{264}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{245}{264}\right)\)	\(e\left(\frac{19}{132}\right)\)	\(e\left(\frac{13}{132}\right)\)	\(e\left(\frac{233}{264}\right)\)	\(e\left(\frac{21}{22}\right)\)
\(\chi_{228672}(69191,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{67}{264}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{41}{264}\right)\)	\(e\left(\frac{101}{264}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{95}{264}\right)\)	\(e\left(\frac{37}{132}\right)\)	\(e\left(\frac{67}{132}\right)\)	\(e\left(\frac{155}{264}\right)\)	\(e\left(\frac{5}{22}\right)\)
\(\chi_{228672}(71927,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{85}{264}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{119}{264}\right)\)	\(e\left(\frac{203}{264}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{89}{264}\right)\)	\(e\left(\frac{43}{132}\right)\)	\(e\left(\frac{85}{132}\right)\)	\(e\left(\frac{173}{264}\right)\)	\(e\left(\frac{7}{22}\right)\)
\(\chi_{228672}(77687,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{101}{264}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{247}{264}\right)\)	\(e\left(\frac{235}{264}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{25}{264}\right)\)	\(e\left(\frac{107}{132}\right)\)	\(e\left(\frac{101}{132}\right)\)	\(e\left(\frac{13}{264}\right)\)	\(e\left(\frac{21}{22}\right)\)
\(\chi_{228672}(78263,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{229}{264}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{215}{264}\right)\)	\(e\left(\frac{227}{264}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{41}{264}\right)\)	\(e\left(\frac{91}{132}\right)\)	\(e\left(\frac{97}{132}\right)\)	\(e\left(\frac{53}{264}\right)\)	\(e\left(\frac{1}{22}\right)\)

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First 31 of 80 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	228672.bjf
Modulus	$228672$
Conductor	$38112$
Order	$264$
Real	no
Primitive	no
Minimal	no
Parity	odd

Modulus:	\(228672\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(38112\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(264\)	comment:Order sage:chi.multiplicative_order() gp:charorder(g,chi) magma:Order(chi);
Real:	no	comment:Whether the character is real sage:chi.multiplicative_order() <= 2 gp:charorder(g,chi) <= 2 magma:Order(chi) le 2;
Primitive:	no, induced from 38112.lj	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	no
Parity:	odd	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);