LMFDB - Dirichlet character orbit 83200.bdg

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(83200, base_ring=CyclotomicField(480)) M = H._module chi = DirichletCharacter(H, M([0,465,96,40])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(41, 83200)) 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("83200.41"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$83200$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$41600$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$480$	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 41600.zo	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:	$\Q(\zeta_{480})$	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 480 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 31 of 128 characters in Galois orbit

Character	$-1$	$1$	$3$	$7$	$9$	$11$	$17$	$19$	$21$	$23$	$27$	$29$
$\chi_{83200}(41,\cdot)$	$-1$	$1$	$e\left(\frac{307}{480}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{67}{240}\right)$	$e\left(\frac{61}{480}\right)$	$e\left(\frac{107}{120}\right)$	$e\left(\frac{143}{480}\right)$	$e\left(\frac{39}{160}\right)$	$e\left(\frac{143}{240}\right)$	$e\left(\frac{147}{160}\right)$	$e\left(\frac{427}{480}\right)$
$\chi_{83200}(761,\cdot)$	$-1$	$1$	$e\left(\frac{353}{480}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{113}{240}\right)$	$e\left(\frac{239}{480}\right)$	$e\left(\frac{73}{120}\right)$	$e\left(\frac{277}{480}\right)$	$e\left(\frac{61}{160}\right)$	$e\left(\frac{37}{240}\right)$	$e\left(\frac{33}{160}\right)$	$e\left(\frac{233}{480}\right)$
$\chi_{83200}(921,\cdot)$	$-1$	$1$	$e\left(\frac{61}{480}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{61}{240}\right)$	$e\left(\frac{403}{480}\right)$	$e\left(\frac{101}{120}\right)$	$e\left(\frac{449}{480}\right)$	$e\left(\frac{137}{160}\right)$	$e\left(\frac{209}{240}\right)$	$e\left(\frac{61}{160}\right)$	$e\left(\frac{421}{480}\right)$
$\chi_{83200}(2121,\cdot)$	$-1$	$1$	$e\left(\frac{31}{480}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{31}{240}\right)$	$e\left(\frac{433}{480}\right)$	$e\left(\frac{71}{120}\right)$	$e\left(\frac{299}{480}\right)$	$e\left(\frac{67}{160}\right)$	$e\left(\frac{59}{240}\right)$	$e\left(\frac{31}{160}\right)$	$e\left(\frac{151}{480}\right)$
$\chi_{83200}(2281,\cdot)$	$-1$	$1$	$e\left(\frac{59}{480}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{59}{240}\right)$	$e\left(\frac{437}{480}\right)$	$e\left(\frac{19}{120}\right)$	$e\left(\frac{151}{480}\right)$	$e\left(\frac{143}{160}\right)$	$e\left(\frac{151}{240}\right)$	$e\left(\frac{59}{160}\right)$	$e\left(\frac{179}{480}\right)$
$\chi_{83200}(2841,\cdot)$	$-1$	$1$	$e\left(\frac{77}{480}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{77}{240}\right)$	$e\left(\frac{131}{480}\right)$	$e\left(\frac{37}{120}\right)$	$e\left(\frac{433}{480}\right)$	$e\left(\frac{89}{160}\right)$	$e\left(\frac{193}{240}\right)$	$e\left(\frac{77}{160}\right)$	$e\left(\frac{437}{480}\right)$
$\chi_{83200}(4361,\cdot)$	$-1$	$1$	$e\left(\frac{263}{480}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{23}{240}\right)$	$e\left(\frac{329}{480}\right)$	$e\left(\frac{103}{120}\right)$	$e\left(\frac{307}{480}\right)$	$e\left(\frac{11}{160}\right)$	$e\left(\frac{67}{240}\right)$	$e\left(\frac{103}{160}\right)$	$e\left(\frac{383}{480}\right)$
$\chi_{83200}(4921,\cdot)$	$-1$	$1$	$e\left(\frac{281}{480}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{41}{240}\right)$	$e\left(\frac{23}{480}\right)$	$e\left(\frac{1}{120}\right)$	$e\left(\frac{109}{480}\right)$	$e\left(\frac{117}{160}\right)$	$e\left(\frac{109}{240}\right)$	$e\left(\frac{121}{160}\right)$	$e\left(\frac{161}{480}\right)$
$\chi_{83200}(5081,\cdot)$	$-1$	$1$	$e\left(\frac{469}{480}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{229}{240}\right)$	$e\left(\frac{187}{480}\right)$	$e\left(\frac{29}{120}\right)$	$e\left(\frac{281}{480}\right)$	$e\left(\frac{33}{160}\right)$	$e\left(\frac{41}{240}\right)$	$e\left(\frac{149}{160}\right)$	$e\left(\frac{349}{480}\right)$
$\chi_{83200}(6281,\cdot)$	$-1$	$1$	$e\left(\frac{439}{480}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{199}{240}\right)$	$e\left(\frac{217}{480}\right)$	$e\left(\frac{119}{120}\right)$	$e\left(\frac{131}{480}\right)$	$e\left(\frac{123}{160}\right)$	$e\left(\frac{131}{240}\right)$	$e\left(\frac{119}{160}\right)$	$e\left(\frac{79}{480}\right)$
$\chi_{83200}(6441,\cdot)$	$-1$	$1$	$e\left(\frac{467}{480}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{227}{240}\right)$	$e\left(\frac{221}{480}\right)$	$e\left(\frac{67}{120}\right)$	$e\left(\frac{463}{480}\right)$	$e\left(\frac{39}{160}\right)$	$e\left(\frac{223}{240}\right)$	$e\left(\frac{147}{160}\right)$	$e\left(\frac{107}{480}\right)$
$\chi_{83200}(7161,\cdot)$	$-1$	$1$	$e\left(\frac{193}{480}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{193}{240}\right)$	$e\left(\frac{79}{480}\right)$	$e\left(\frac{113}{120}\right)$	$e\left(\frac{437}{480}\right)$	$e\left(\frac{61}{160}\right)$	$e\left(\frac{197}{240}\right)$	$e\left(\frac{33}{160}\right)$	$e\left(\frac{73}{480}\right)$
$\chi_{83200}(8361,\cdot)$	$-1$	$1$	$e\left(\frac{163}{480}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{163}{240}\right)$	$e\left(\frac{109}{480}\right)$	$e\left(\frac{83}{120}\right)$	$e\left(\frac{287}{480}\right)$	$e\left(\frac{151}{160}\right)$	$e\left(\frac{47}{240}\right)$	$e\left(\frac{3}{160}\right)$	$e\left(\frac{283}{480}\right)$
$\chi_{83200}(8521,\cdot)$	$-1$	$1$	$e\left(\frac{191}{480}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{191}{240}\right)$	$e\left(\frac{113}{480}\right)$	$e\left(\frac{31}{120}\right)$	$e\left(\frac{139}{480}\right)$	$e\left(\frac{67}{160}\right)$	$e\left(\frac{139}{240}\right)$	$e\left(\frac{31}{160}\right)$	$e\left(\frac{311}{480}\right)$
$\chi_{83200}(9081,\cdot)$	$-1$	$1$	$e\left(\frac{209}{480}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{209}{240}\right)$	$e\left(\frac{287}{480}\right)$	$e\left(\frac{49}{120}\right)$	$e\left(\frac{421}{480}\right)$	$e\left(\frac{13}{160}\right)$	$e\left(\frac{181}{240}\right)$	$e\left(\frac{49}{160}\right)$	$e\left(\frac{89}{480}\right)$
$\chi_{83200}(9241,\cdot)$	$-1$	$1$	$e\left(\frac{397}{480}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{157}{240}\right)$	$e\left(\frac{451}{480}\right)$	$e\left(\frac{77}{120}\right)$	$e\left(\frac{113}{480}\right)$	$e\left(\frac{89}{160}\right)$	$e\left(\frac{113}{240}\right)$	$e\left(\frac{77}{160}\right)$	$e\left(\frac{277}{480}\right)$
$\chi_{83200}(10441,\cdot)$	$-1$	$1$	$e\left(\frac{367}{480}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{127}{240}\right)$	$e\left(\frac{1}{480}\right)$	$e\left(\frac{47}{120}\right)$	$e\left(\frac{443}{480}\right)$	$e\left(\frac{19}{160}\right)$	$e\left(\frac{203}{240}\right)$	$e\left(\frac{47}{160}\right)$	$e\left(\frac{7}{480}\right)$
$\chi_{83200}(11161,\cdot)$	$-1$	$1$	$e\left(\frac{413}{480}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{173}{240}\right)$	$e\left(\frac{179}{480}\right)$	$e\left(\frac{13}{120}\right)$	$e\left(\frac{97}{480}\right)$	$e\left(\frac{41}{160}\right)$	$e\left(\frac{97}{240}\right)$	$e\left(\frac{93}{160}\right)$	$e\left(\frac{293}{480}\right)$
$\chi_{83200}(11321,\cdot)$	$-1$	$1$	$e\left(\frac{121}{480}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{121}{240}\right)$	$e\left(\frac{343}{480}\right)$	$e\left(\frac{41}{120}\right)$	$e\left(\frac{269}{480}\right)$	$e\left(\frac{117}{160}\right)$	$e\left(\frac{29}{240}\right)$	$e\left(\frac{121}{160}\right)$	$e\left(\frac{1}{480}\right)$
$\chi_{83200}(12521,\cdot)$	$-1$	$1$	$e\left(\frac{91}{480}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{91}{240}\right)$	$e\left(\frac{373}{480}\right)$	$e\left(\frac{11}{120}\right)$	$e\left(\frac{119}{480}\right)$	$e\left(\frac{47}{160}\right)$	$e\left(\frac{119}{240}\right)$	$e\left(\frac{91}{160}\right)$	$e\left(\frac{211}{480}\right)$
$\chi_{83200}(12681,\cdot)$	$-1$	$1$	$e\left(\frac{119}{480}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{119}{240}\right)$	$e\left(\frac{377}{480}\right)$	$e\left(\frac{79}{120}\right)$	$e\left(\frac{451}{480}\right)$	$e\left(\frac{123}{160}\right)$	$e\left(\frac{211}{240}\right)$	$e\left(\frac{119}{160}\right)$	$e\left(\frac{239}{480}\right)$
$\chi_{83200}(13241,\cdot)$	$-1$	$1$	$e\left(\frac{137}{480}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{137}{240}\right)$	$e\left(\frac{71}{480}\right)$	$e\left(\frac{97}{120}\right)$	$e\left(\frac{253}{480}\right)$	$e\left(\frac{69}{160}\right)$	$e\left(\frac{13}{240}\right)$	$e\left(\frac{137}{160}\right)$	$e\left(\frac{17}{480}\right)$
$\chi_{83200}(14761,\cdot)$	$-1$	$1$	$e\left(\frac{323}{480}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{83}{240}\right)$	$e\left(\frac{269}{480}\right)$	$e\left(\frac{43}{120}\right)$	$e\left(\frac{127}{480}\right)$	$e\left(\frac{151}{160}\right)$	$e\left(\frac{127}{240}\right)$	$e\left(\frac{3}{160}\right)$	$e\left(\frac{443}{480}\right)$
$\chi_{83200}(15321,\cdot)$	$-1$	$1$	$e\left(\frac{341}{480}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{101}{240}\right)$	$e\left(\frac{443}{480}\right)$	$e\left(\frac{61}{120}\right)$	$e\left(\frac{409}{480}\right)$	$e\left(\frac{97}{160}\right)$	$e\left(\frac{169}{240}\right)$	$e\left(\frac{21}{160}\right)$	$e\left(\frac{221}{480}\right)$
$\chi_{83200}(15481,\cdot)$	$-1$	$1$	$e\left(\frac{49}{480}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{49}{240}\right)$	$e\left(\frac{127}{480}\right)$	$e\left(\frac{89}{120}\right)$	$e\left(\frac{101}{480}\right)$	$e\left(\frac{13}{160}\right)$	$e\left(\frac{101}{240}\right)$	$e\left(\frac{49}{160}\right)$	$e\left(\frac{409}{480}\right)$
$\chi_{83200}(16681,\cdot)$	$-1$	$1$	$e\left(\frac{19}{480}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{19}{240}\right)$	$e\left(\frac{157}{480}\right)$	$e\left(\frac{59}{120}\right)$	$e\left(\frac{431}{480}\right)$	$e\left(\frac{103}{160}\right)$	$e\left(\frac{191}{240}\right)$	$e\left(\frac{19}{160}\right)$	$e\left(\frac{139}{480}\right)$
$\chi_{83200}(16841,\cdot)$	$-1$	$1$	$e\left(\frac{47}{480}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{47}{240}\right)$	$e\left(\frac{161}{480}\right)$	$e\left(\frac{7}{120}\right)$	$e\left(\frac{283}{480}\right)$	$e\left(\frac{19}{160}\right)$	$e\left(\frac{43}{240}\right)$	$e\left(\frac{47}{160}\right)$	$e\left(\frac{167}{480}\right)$
$\chi_{83200}(17561,\cdot)$	$-1$	$1$	$e\left(\frac{253}{480}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{13}{240}\right)$	$e\left(\frac{19}{480}\right)$	$e\left(\frac{53}{120}\right)$	$e\left(\frac{257}{480}\right)$	$e\left(\frac{41}{160}\right)$	$e\left(\frac{17}{240}\right)$	$e\left(\frac{93}{160}\right)$	$e\left(\frac{133}{480}\right)$
$\chi_{83200}(18761,\cdot)$	$-1$	$1$	$e\left(\frac{223}{480}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{223}{240}\right)$	$e\left(\frac{49}{480}\right)$	$e\left(\frac{23}{120}\right)$	$e\left(\frac{107}{480}\right)$	$e\left(\frac{131}{160}\right)$	$e\left(\frac{107}{240}\right)$	$e\left(\frac{63}{160}\right)$	$e\left(\frac{343}{480}\right)$
$\chi_{83200}(18921,\cdot)$	$-1$	$1$	$e\left(\frac{251}{480}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{11}{240}\right)$	$e\left(\frac{53}{480}\right)$	$e\left(\frac{91}{120}\right)$	$e\left(\frac{439}{480}\right)$	$e\left(\frac{47}{160}\right)$	$e\left(\frac{199}{240}\right)$	$e\left(\frac{91}{160}\right)$	$e\left(\frac{371}{480}\right)$
$\chi_{83200}(19481,\cdot)$	$-1$	$1$	$e\left(\frac{269}{480}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{29}{240}\right)$	$e\left(\frac{227}{480}\right)$	$e\left(\frac{109}{120}\right)$	$e\left(\frac{241}{480}\right)$	$e\left(\frac{153}{160}\right)$	$e\left(\frac{1}{240}\right)$	$e\left(\frac{109}{160}\right)$	$e\left(\frac{149}{480}\right)$

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	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)	\(29\)
\(\chi_{83200}(41,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{307}{480}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{67}{240}\right)\)	\(e\left(\frac{61}{480}\right)\)	\(e\left(\frac{107}{120}\right)\)	\(e\left(\frac{143}{480}\right)\)	\(e\left(\frac{39}{160}\right)\)	\(e\left(\frac{143}{240}\right)\)	\(e\left(\frac{147}{160}\right)\)	\(e\left(\frac{427}{480}\right)\)
\(\chi_{83200}(761,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{353}{480}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{113}{240}\right)\)	\(e\left(\frac{239}{480}\right)\)	\(e\left(\frac{73}{120}\right)\)	\(e\left(\frac{277}{480}\right)\)	\(e\left(\frac{61}{160}\right)\)	\(e\left(\frac{37}{240}\right)\)	\(e\left(\frac{33}{160}\right)\)	\(e\left(\frac{233}{480}\right)\)
\(\chi_{83200}(921,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{61}{480}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{61}{240}\right)\)	\(e\left(\frac{403}{480}\right)\)	\(e\left(\frac{101}{120}\right)\)	\(e\left(\frac{449}{480}\right)\)	\(e\left(\frac{137}{160}\right)\)	\(e\left(\frac{209}{240}\right)\)	\(e\left(\frac{61}{160}\right)\)	\(e\left(\frac{421}{480}\right)\)
\(\chi_{83200}(2121,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{480}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{31}{240}\right)\)	\(e\left(\frac{433}{480}\right)\)	\(e\left(\frac{71}{120}\right)\)	\(e\left(\frac{299}{480}\right)\)	\(e\left(\frac{67}{160}\right)\)	\(e\left(\frac{59}{240}\right)\)	\(e\left(\frac{31}{160}\right)\)	\(e\left(\frac{151}{480}\right)\)
\(\chi_{83200}(2281,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{59}{480}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{59}{240}\right)\)	\(e\left(\frac{437}{480}\right)\)	\(e\left(\frac{19}{120}\right)\)	\(e\left(\frac{151}{480}\right)\)	\(e\left(\frac{143}{160}\right)\)	\(e\left(\frac{151}{240}\right)\)	\(e\left(\frac{59}{160}\right)\)	\(e\left(\frac{179}{480}\right)\)
\(\chi_{83200}(2841,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{77}{480}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{77}{240}\right)\)	\(e\left(\frac{131}{480}\right)\)	\(e\left(\frac{37}{120}\right)\)	\(e\left(\frac{433}{480}\right)\)	\(e\left(\frac{89}{160}\right)\)	\(e\left(\frac{193}{240}\right)\)	\(e\left(\frac{77}{160}\right)\)	\(e\left(\frac{437}{480}\right)\)
\(\chi_{83200}(4361,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{263}{480}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{23}{240}\right)\)	\(e\left(\frac{329}{480}\right)\)	\(e\left(\frac{103}{120}\right)\)	\(e\left(\frac{307}{480}\right)\)	\(e\left(\frac{11}{160}\right)\)	\(e\left(\frac{67}{240}\right)\)	\(e\left(\frac{103}{160}\right)\)	\(e\left(\frac{383}{480}\right)\)
\(\chi_{83200}(4921,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{281}{480}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{41}{240}\right)\)	\(e\left(\frac{23}{480}\right)\)	\(e\left(\frac{1}{120}\right)\)	\(e\left(\frac{109}{480}\right)\)	\(e\left(\frac{117}{160}\right)\)	\(e\left(\frac{109}{240}\right)\)	\(e\left(\frac{121}{160}\right)\)	\(e\left(\frac{161}{480}\right)\)
\(\chi_{83200}(5081,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{469}{480}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{229}{240}\right)\)	\(e\left(\frac{187}{480}\right)\)	\(e\left(\frac{29}{120}\right)\)	\(e\left(\frac{281}{480}\right)\)	\(e\left(\frac{33}{160}\right)\)	\(e\left(\frac{41}{240}\right)\)	\(e\left(\frac{149}{160}\right)\)	\(e\left(\frac{349}{480}\right)\)
\(\chi_{83200}(6281,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{439}{480}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{199}{240}\right)\)	\(e\left(\frac{217}{480}\right)\)	\(e\left(\frac{119}{120}\right)\)	\(e\left(\frac{131}{480}\right)\)	\(e\left(\frac{123}{160}\right)\)	\(e\left(\frac{131}{240}\right)\)	\(e\left(\frac{119}{160}\right)\)	\(e\left(\frac{79}{480}\right)\)
\(\chi_{83200}(6441,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{467}{480}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{227}{240}\right)\)	\(e\left(\frac{221}{480}\right)\)	\(e\left(\frac{67}{120}\right)\)	\(e\left(\frac{463}{480}\right)\)	\(e\left(\frac{39}{160}\right)\)	\(e\left(\frac{223}{240}\right)\)	\(e\left(\frac{147}{160}\right)\)	\(e\left(\frac{107}{480}\right)\)
\(\chi_{83200}(7161,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{193}{480}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{193}{240}\right)\)	\(e\left(\frac{79}{480}\right)\)	\(e\left(\frac{113}{120}\right)\)	\(e\left(\frac{437}{480}\right)\)	\(e\left(\frac{61}{160}\right)\)	\(e\left(\frac{197}{240}\right)\)	\(e\left(\frac{33}{160}\right)\)	\(e\left(\frac{73}{480}\right)\)
\(\chi_{83200}(8361,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{163}{480}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{163}{240}\right)\)	\(e\left(\frac{109}{480}\right)\)	\(e\left(\frac{83}{120}\right)\)	\(e\left(\frac{287}{480}\right)\)	\(e\left(\frac{151}{160}\right)\)	\(e\left(\frac{47}{240}\right)\)	\(e\left(\frac{3}{160}\right)\)	\(e\left(\frac{283}{480}\right)\)
\(\chi_{83200}(8521,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{191}{480}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{191}{240}\right)\)	\(e\left(\frac{113}{480}\right)\)	\(e\left(\frac{31}{120}\right)\)	\(e\left(\frac{139}{480}\right)\)	\(e\left(\frac{67}{160}\right)\)	\(e\left(\frac{139}{240}\right)\)	\(e\left(\frac{31}{160}\right)\)	\(e\left(\frac{311}{480}\right)\)
\(\chi_{83200}(9081,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{209}{480}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{209}{240}\right)\)	\(e\left(\frac{287}{480}\right)\)	\(e\left(\frac{49}{120}\right)\)	\(e\left(\frac{421}{480}\right)\)	\(e\left(\frac{13}{160}\right)\)	\(e\left(\frac{181}{240}\right)\)	\(e\left(\frac{49}{160}\right)\)	\(e\left(\frac{89}{480}\right)\)
\(\chi_{83200}(9241,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{397}{480}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{157}{240}\right)\)	\(e\left(\frac{451}{480}\right)\)	\(e\left(\frac{77}{120}\right)\)	\(e\left(\frac{113}{480}\right)\)	\(e\left(\frac{89}{160}\right)\)	\(e\left(\frac{113}{240}\right)\)	\(e\left(\frac{77}{160}\right)\)	\(e\left(\frac{277}{480}\right)\)
\(\chi_{83200}(10441,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{367}{480}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{127}{240}\right)\)	\(e\left(\frac{1}{480}\right)\)	\(e\left(\frac{47}{120}\right)\)	\(e\left(\frac{443}{480}\right)\)	\(e\left(\frac{19}{160}\right)\)	\(e\left(\frac{203}{240}\right)\)	\(e\left(\frac{47}{160}\right)\)	\(e\left(\frac{7}{480}\right)\)
\(\chi_{83200}(11161,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{413}{480}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{173}{240}\right)\)	\(e\left(\frac{179}{480}\right)\)	\(e\left(\frac{13}{120}\right)\)	\(e\left(\frac{97}{480}\right)\)	\(e\left(\frac{41}{160}\right)\)	\(e\left(\frac{97}{240}\right)\)	\(e\left(\frac{93}{160}\right)\)	\(e\left(\frac{293}{480}\right)\)
\(\chi_{83200}(11321,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{121}{480}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{121}{240}\right)\)	\(e\left(\frac{343}{480}\right)\)	\(e\left(\frac{41}{120}\right)\)	\(e\left(\frac{269}{480}\right)\)	\(e\left(\frac{117}{160}\right)\)	\(e\left(\frac{29}{240}\right)\)	\(e\left(\frac{121}{160}\right)\)	\(e\left(\frac{1}{480}\right)\)
\(\chi_{83200}(12521,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{91}{480}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{91}{240}\right)\)	\(e\left(\frac{373}{480}\right)\)	\(e\left(\frac{11}{120}\right)\)	\(e\left(\frac{119}{480}\right)\)	\(e\left(\frac{47}{160}\right)\)	\(e\left(\frac{119}{240}\right)\)	\(e\left(\frac{91}{160}\right)\)	\(e\left(\frac{211}{480}\right)\)
\(\chi_{83200}(12681,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{119}{480}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{119}{240}\right)\)	\(e\left(\frac{377}{480}\right)\)	\(e\left(\frac{79}{120}\right)\)	\(e\left(\frac{451}{480}\right)\)	\(e\left(\frac{123}{160}\right)\)	\(e\left(\frac{211}{240}\right)\)	\(e\left(\frac{119}{160}\right)\)	\(e\left(\frac{239}{480}\right)\)
\(\chi_{83200}(13241,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{137}{480}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{137}{240}\right)\)	\(e\left(\frac{71}{480}\right)\)	\(e\left(\frac{97}{120}\right)\)	\(e\left(\frac{253}{480}\right)\)	\(e\left(\frac{69}{160}\right)\)	\(e\left(\frac{13}{240}\right)\)	\(e\left(\frac{137}{160}\right)\)	\(e\left(\frac{17}{480}\right)\)
\(\chi_{83200}(14761,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{323}{480}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{83}{240}\right)\)	\(e\left(\frac{269}{480}\right)\)	\(e\left(\frac{43}{120}\right)\)	\(e\left(\frac{127}{480}\right)\)	\(e\left(\frac{151}{160}\right)\)	\(e\left(\frac{127}{240}\right)\)	\(e\left(\frac{3}{160}\right)\)	\(e\left(\frac{443}{480}\right)\)
\(\chi_{83200}(15321,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{341}{480}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{101}{240}\right)\)	\(e\left(\frac{443}{480}\right)\)	\(e\left(\frac{61}{120}\right)\)	\(e\left(\frac{409}{480}\right)\)	\(e\left(\frac{97}{160}\right)\)	\(e\left(\frac{169}{240}\right)\)	\(e\left(\frac{21}{160}\right)\)	\(e\left(\frac{221}{480}\right)\)
\(\chi_{83200}(15481,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{49}{480}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{49}{240}\right)\)	\(e\left(\frac{127}{480}\right)\)	\(e\left(\frac{89}{120}\right)\)	\(e\left(\frac{101}{480}\right)\)	\(e\left(\frac{13}{160}\right)\)	\(e\left(\frac{101}{240}\right)\)	\(e\left(\frac{49}{160}\right)\)	\(e\left(\frac{409}{480}\right)\)
\(\chi_{83200}(16681,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{480}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{19}{240}\right)\)	\(e\left(\frac{157}{480}\right)\)	\(e\left(\frac{59}{120}\right)\)	\(e\left(\frac{431}{480}\right)\)	\(e\left(\frac{103}{160}\right)\)	\(e\left(\frac{191}{240}\right)\)	\(e\left(\frac{19}{160}\right)\)	\(e\left(\frac{139}{480}\right)\)
\(\chi_{83200}(16841,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{47}{480}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{47}{240}\right)\)	\(e\left(\frac{161}{480}\right)\)	\(e\left(\frac{7}{120}\right)\)	\(e\left(\frac{283}{480}\right)\)	\(e\left(\frac{19}{160}\right)\)	\(e\left(\frac{43}{240}\right)\)	\(e\left(\frac{47}{160}\right)\)	\(e\left(\frac{167}{480}\right)\)
\(\chi_{83200}(17561,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{253}{480}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{13}{240}\right)\)	\(e\left(\frac{19}{480}\right)\)	\(e\left(\frac{53}{120}\right)\)	\(e\left(\frac{257}{480}\right)\)	\(e\left(\frac{41}{160}\right)\)	\(e\left(\frac{17}{240}\right)\)	\(e\left(\frac{93}{160}\right)\)	\(e\left(\frac{133}{480}\right)\)
\(\chi_{83200}(18761,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{223}{480}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{223}{240}\right)\)	\(e\left(\frac{49}{480}\right)\)	\(e\left(\frac{23}{120}\right)\)	\(e\left(\frac{107}{480}\right)\)	\(e\left(\frac{131}{160}\right)\)	\(e\left(\frac{107}{240}\right)\)	\(e\left(\frac{63}{160}\right)\)	\(e\left(\frac{343}{480}\right)\)
\(\chi_{83200}(18921,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{251}{480}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{11}{240}\right)\)	\(e\left(\frac{53}{480}\right)\)	\(e\left(\frac{91}{120}\right)\)	\(e\left(\frac{439}{480}\right)\)	\(e\left(\frac{47}{160}\right)\)	\(e\left(\frac{199}{240}\right)\)	\(e\left(\frac{91}{160}\right)\)	\(e\left(\frac{371}{480}\right)\)
\(\chi_{83200}(19481,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{269}{480}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{29}{240}\right)\)	\(e\left(\frac{227}{480}\right)\)	\(e\left(\frac{109}{120}\right)\)	\(e\left(\frac{241}{480}\right)\)	\(e\left(\frac{153}{160}\right)\)	\(e\left(\frac{1}{240}\right)\)	\(e\left(\frac{109}{160}\right)\)	\(e\left(\frac{149}{480}\right)\)

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First 31 of 128 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	83200.bdg
Modulus	$83200$
Conductor	$41600$
Order	$480$
Real	no
Primitive	no
Minimal	no
Parity	odd

Modulus:	\(83200\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(41600\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(480\)	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 41600.zo	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);