LMFDB - Dirichlet character orbit 83200.bdo

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(960)) M = H._module chi = DirichletCharacter(H, M([480,315,768,560])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(11, 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("83200.11"); 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:	$83200$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$960$	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:	yes	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);

Related number fields

Field of values:	$\Q(\zeta_{960})$	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 960 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 31 of 256 characters in Galois orbit

Character	$-1$	$1$	$3$	$7$	$9$	$11$	$17$	$19$	$21$	$23$	$27$	$29$
$\chi_{83200}(11,\cdot)$	$1$	$1$	$e\left(\frac{881}{960}\right)$	$e\left(\frac{19}{96}\right)$	$e\left(\frac{401}{480}\right)$	$e\left(\frac{263}{960}\right)$	$e\left(\frac{181}{240}\right)$	$e\left(\frac{349}{960}\right)$	$e\left(\frac{37}{320}\right)$	$e\left(\frac{349}{480}\right)$	$e\left(\frac{241}{320}\right)$	$e\left(\frac{281}{960}\right)$
$\chi_{83200}(691,\cdot)$	$1$	$1$	$e\left(\frac{179}{960}\right)$	$e\left(\frac{25}{96}\right)$	$e\left(\frac{179}{480}\right)$	$e\left(\frac{437}{960}\right)$	$e\left(\frac{79}{240}\right)$	$e\left(\frac{631}{960}\right)$	$e\left(\frac{143}{320}\right)$	$e\left(\frac{151}{480}\right)$	$e\left(\frac{179}{320}\right)$	$e\left(\frac{299}{960}\right)$
$\chi_{83200}(891,\cdot)$	$1$	$1$	$e\left(\frac{589}{960}\right)$	$e\left(\frac{71}{96}\right)$	$e\left(\frac{109}{480}\right)$	$e\left(\frac{907}{960}\right)$	$e\left(\frac{209}{240}\right)$	$e\left(\frac{521}{960}\right)$	$e\left(\frac{113}{320}\right)$	$e\left(\frac{41}{480}\right)$	$e\left(\frac{269}{320}\right)$	$e\left(\frac{469}{960}\right)$
$\chi_{83200}(1731,\cdot)$	$1$	$1$	$e\left(\frac{23}{960}\right)$	$e\left(\frac{37}{96}\right)$	$e\left(\frac{23}{480}\right)$	$e\left(\frac{689}{960}\right)$	$e\left(\frac{163}{240}\right)$	$e\left(\frac{907}{960}\right)$	$e\left(\frac{131}{320}\right)$	$e\left(\frac{427}{480}\right)$	$e\left(\frac{23}{320}\right)$	$e\left(\frac{623}{960}\right)$
$\chi_{83200}(1891,\cdot)$	$1$	$1$	$e\left(\frac{319}{960}\right)$	$e\left(\frac{29}{96}\right)$	$e\left(\frac{319}{480}\right)$	$e\left(\frac{457}{960}\right)$	$e\left(\frac{59}{240}\right)$	$e\left(\frac{851}{960}\right)$	$e\left(\frac{203}{320}\right)$	$e\left(\frac{371}{480}\right)$	$e\left(\frac{319}{320}\right)$	$e\left(\frac{919}{960}\right)$
$\chi_{83200}(1931,\cdot)$	$1$	$1$	$e\left(\frac{913}{960}\right)$	$e\left(\frac{83}{96}\right)$	$e\left(\frac{433}{480}\right)$	$e\left(\frac{679}{960}\right)$	$e\left(\frac{53}{240}\right)$	$e\left(\frac{317}{960}\right)$	$e\left(\frac{261}{320}\right)$	$e\left(\frac{317}{480}\right)$	$e\left(\frac{273}{320}\right)$	$e\left(\frac{313}{960}\right)$
$\chi_{83200}(2091,\cdot)$	$1$	$1$	$e\left(\frac{569}{960}\right)$	$e\left(\frac{43}{96}\right)$	$e\left(\frac{89}{480}\right)$	$e\left(\frac{767}{960}\right)$	$e\left(\frac{109}{240}\right)$	$e\left(\frac{901}{960}\right)$	$e\left(\frac{13}{320}\right)$	$e\left(\frac{421}{480}\right)$	$e\left(\frac{249}{320}\right)$	$e\left(\frac{929}{960}\right)$
$\chi_{83200}(2771,\cdot)$	$1$	$1$	$e\left(\frac{827}{960}\right)$	$e\left(\frac{49}{96}\right)$	$e\left(\frac{347}{480}\right)$	$e\left(\frac{941}{960}\right)$	$e\left(\frac{7}{240}\right)$	$e\left(\frac{223}{960}\right)$	$e\left(\frac{119}{320}\right)$	$e\left(\frac{223}{480}\right)$	$e\left(\frac{187}{320}\right)$	$e\left(\frac{947}{960}\right)$
$\chi_{83200}(2931,\cdot)$	$1$	$1$	$e\left(\frac{163}{960}\right)$	$e\left(\frac{41}{96}\right)$	$e\left(\frac{163}{480}\right)$	$e\left(\frac{709}{960}\right)$	$e\left(\frac{143}{240}\right)$	$e\left(\frac{167}{960}\right)$	$e\left(\frac{191}{320}\right)$	$e\left(\frac{167}{480}\right)$	$e\left(\frac{163}{320}\right)$	$e\left(\frac{283}{960}\right)$
$\chi_{83200}(2971,\cdot)$	$1$	$1$	$e\left(\frac{277}{960}\right)$	$e\left(\frac{95}{96}\right)$	$e\left(\frac{277}{480}\right)$	$e\left(\frac{451}{960}\right)$	$e\left(\frac{137}{240}\right)$	$e\left(\frac{113}{960}\right)$	$e\left(\frac{89}{320}\right)$	$e\left(\frac{113}{480}\right)$	$e\left(\frac{277}{320}\right)$	$e\left(\frac{157}{960}\right)$
$\chi_{83200}(3131,\cdot)$	$1$	$1$	$e\left(\frac{893}{960}\right)$	$e\left(\frac{55}{96}\right)$	$e\left(\frac{413}{480}\right)$	$e\left(\frac{539}{960}\right)$	$e\left(\frac{193}{240}\right)$	$e\left(\frac{697}{960}\right)$	$e\left(\frac{161}{320}\right)$	$e\left(\frac{217}{480}\right)$	$e\left(\frac{253}{320}\right)$	$e\left(\frac{773}{960}\right)$
$\chi_{83200}(3811,\cdot)$	$1$	$1$	$e\left(\frac{671}{960}\right)$	$e\left(\frac{61}{96}\right)$	$e\left(\frac{191}{480}\right)$	$e\left(\frac{233}{960}\right)$	$e\left(\frac{91}{240}\right)$	$e\left(\frac{499}{960}\right)$	$e\left(\frac{107}{320}\right)$	$e\left(\frac{19}{480}\right)$	$e\left(\frac{31}{320}\right)$	$e\left(\frac{311}{960}\right)$
$\chi_{83200}(3971,\cdot)$	$1$	$1$	$e\left(\frac{7}{960}\right)$	$e\left(\frac{53}{96}\right)$	$e\left(\frac{7}{480}\right)$	$e\left(\frac{1}{960}\right)$	$e\left(\frac{227}{240}\right)$	$e\left(\frac{443}{960}\right)$	$e\left(\frac{179}{320}\right)$	$e\left(\frac{443}{480}\right)$	$e\left(\frac{7}{320}\right)$	$e\left(\frac{607}{960}\right)$
$\chi_{83200}(4011,\cdot)$	$1$	$1$	$e\left(\frac{601}{960}\right)$	$e\left(\frac{11}{96}\right)$	$e\left(\frac{121}{480}\right)$	$e\left(\frac{223}{960}\right)$	$e\left(\frac{221}{240}\right)$	$e\left(\frac{869}{960}\right)$	$e\left(\frac{237}{320}\right)$	$e\left(\frac{389}{480}\right)$	$e\left(\frac{281}{320}\right)$	$e\left(\frac{1}{960}\right)$
$\chi_{83200}(4171,\cdot)$	$1$	$1$	$e\left(\frac{257}{960}\right)$	$e\left(\frac{67}{96}\right)$	$e\left(\frac{257}{480}\right)$	$e\left(\frac{311}{960}\right)$	$e\left(\frac{37}{240}\right)$	$e\left(\frac{493}{960}\right)$	$e\left(\frac{309}{320}\right)$	$e\left(\frac{13}{480}\right)$	$e\left(\frac{257}{320}\right)$	$e\left(\frac{617}{960}\right)$
$\chi_{83200}(5011,\cdot)$	$1$	$1$	$e\left(\frac{811}{960}\right)$	$e\left(\frac{65}{96}\right)$	$e\left(\frac{331}{480}\right)$	$e\left(\frac{253}{960}\right)$	$e\left(\frac{71}{240}\right)$	$e\left(\frac{719}{960}\right)$	$e\left(\frac{167}{320}\right)$	$e\left(\frac{239}{480}\right)$	$e\left(\frac{171}{320}\right)$	$e\left(\frac{931}{960}\right)$
$\chi_{83200}(5211,\cdot)$	$1$	$1$	$e\left(\frac{581}{960}\right)$	$e\left(\frac{79}{96}\right)$	$e\left(\frac{101}{480}\right)$	$e\left(\frac{83}{960}\right)$	$e\left(\frac{121}{240}\right)$	$e\left(\frac{289}{960}\right)$	$e\left(\frac{137}{320}\right)$	$e\left(\frac{289}{480}\right)$	$e\left(\frac{261}{320}\right)$	$e\left(\frac{461}{960}\right)$
$\chi_{83200}(5891,\cdot)$	$1$	$1$	$e\left(\frac{359}{960}\right)$	$e\left(\frac{85}{96}\right)$	$e\left(\frac{359}{480}\right)$	$e\left(\frac{737}{960}\right)$	$e\left(\frac{19}{240}\right)$	$e\left(\frac{91}{960}\right)$	$e\left(\frac{83}{320}\right)$	$e\left(\frac{91}{480}\right)$	$e\left(\frac{39}{320}\right)$	$e\left(\frac{959}{960}\right)$
$\chi_{83200}(6091,\cdot)$	$1$	$1$	$e\left(\frac{289}{960}\right)$	$e\left(\frac{35}{96}\right)$	$e\left(\frac{289}{480}\right)$	$e\left(\frac{727}{960}\right)$	$e\left(\frac{149}{240}\right)$	$e\left(\frac{461}{960}\right)$	$e\left(\frac{213}{320}\right)$	$e\left(\frac{461}{480}\right)$	$e\left(\frac{289}{320}\right)$	$e\left(\frac{649}{960}\right)$
$\chi_{83200}(6931,\cdot)$	$1$	$1$	$e\left(\frac{203}{960}\right)$	$e\left(\frac{1}{96}\right)$	$e\left(\frac{203}{480}\right)$	$e\left(\frac{29}{960}\right)$	$e\left(\frac{103}{240}\right)$	$e\left(\frac{367}{960}\right)$	$e\left(\frac{71}{320}\right)$	$e\left(\frac{367}{480}\right)$	$e\left(\frac{203}{320}\right)$	$e\left(\frac{323}{960}\right)$
$\chi_{83200}(7091,\cdot)$	$1$	$1$	$e\left(\frac{499}{960}\right)$	$e\left(\frac{89}{96}\right)$	$e\left(\frac{19}{480}\right)$	$e\left(\frac{757}{960}\right)$	$e\left(\frac{239}{240}\right)$	$e\left(\frac{311}{960}\right)$	$e\left(\frac{143}{320}\right)$	$e\left(\frac{311}{480}\right)$	$e\left(\frac{179}{320}\right)$	$e\left(\frac{619}{960}\right)$
$\chi_{83200}(7131,\cdot)$	$1$	$1$	$e\left(\frac{613}{960}\right)$	$e\left(\frac{47}{96}\right)$	$e\left(\frac{133}{480}\right)$	$e\left(\frac{499}{960}\right)$	$e\left(\frac{233}{240}\right)$	$e\left(\frac{257}{960}\right)$	$e\left(\frac{41}{320}\right)$	$e\left(\frac{257}{480}\right)$	$e\left(\frac{293}{320}\right)$	$e\left(\frac{493}{960}\right)$
$\chi_{83200}(7291,\cdot)$	$1$	$1$	$e\left(\frac{269}{960}\right)$	$e\left(\frac{7}{96}\right)$	$e\left(\frac{269}{480}\right)$	$e\left(\frac{587}{960}\right)$	$e\left(\frac{49}{240}\right)$	$e\left(\frac{841}{960}\right)$	$e\left(\frac{113}{320}\right)$	$e\left(\frac{361}{480}\right)$	$e\left(\frac{269}{320}\right)$	$e\left(\frac{149}{960}\right)$
$\chi_{83200}(7971,\cdot)$	$1$	$1$	$e\left(\frac{47}{960}\right)$	$e\left(\frac{13}{96}\right)$	$e\left(\frac{47}{480}\right)$	$e\left(\frac{281}{960}\right)$	$e\left(\frac{187}{240}\right)$	$e\left(\frac{643}{960}\right)$	$e\left(\frac{59}{320}\right)$	$e\left(\frac{163}{480}\right)$	$e\left(\frac{47}{320}\right)$	$e\left(\frac{647}{960}\right)$
$\chi_{83200}(8131,\cdot)$	$1$	$1$	$e\left(\frac{343}{960}\right)$	$e\left(\frac{5}{96}\right)$	$e\left(\frac{343}{480}\right)$	$e\left(\frac{49}{960}\right)$	$e\left(\frac{83}{240}\right)$	$e\left(\frac{587}{960}\right)$	$e\left(\frac{131}{320}\right)$	$e\left(\frac{107}{480}\right)$	$e\left(\frac{23}{320}\right)$	$e\left(\frac{943}{960}\right)$
$\chi_{83200}(8171,\cdot)$	$1$	$1$	$e\left(\frac{937}{960}\right)$	$e\left(\frac{59}{96}\right)$	$e\left(\frac{457}{480}\right)$	$e\left(\frac{271}{960}\right)$	$e\left(\frac{77}{240}\right)$	$e\left(\frac{53}{960}\right)$	$e\left(\frac{189}{320}\right)$	$e\left(\frac{53}{480}\right)$	$e\left(\frac{297}{320}\right)$	$e\left(\frac{337}{960}\right)$
$\chi_{83200}(8331,\cdot)$	$1$	$1$	$e\left(\frac{593}{960}\right)$	$e\left(\frac{19}{96}\right)$	$e\left(\frac{113}{480}\right)$	$e\left(\frac{359}{960}\right)$	$e\left(\frac{133}{240}\right)$	$e\left(\frac{637}{960}\right)$	$e\left(\frac{261}{320}\right)$	$e\left(\frac{157}{480}\right)$	$e\left(\frac{273}{320}\right)$	$e\left(\frac{953}{960}\right)$
$\chi_{83200}(9011,\cdot)$	$1$	$1$	$e\left(\frac{851}{960}\right)$	$e\left(\frac{25}{96}\right)$	$e\left(\frac{371}{480}\right)$	$e\left(\frac{533}{960}\right)$	$e\left(\frac{31}{240}\right)$	$e\left(\frac{919}{960}\right)$	$e\left(\frac{47}{320}\right)$	$e\left(\frac{439}{480}\right)$	$e\left(\frac{211}{320}\right)$	$e\left(\frac{11}{960}\right)$
$\chi_{83200}(9171,\cdot)$	$1$	$1$	$e\left(\frac{187}{960}\right)$	$e\left(\frac{17}{96}\right)$	$e\left(\frac{187}{480}\right)$	$e\left(\frac{301}{960}\right)$	$e\left(\frac{167}{240}\right)$	$e\left(\frac{863}{960}\right)$	$e\left(\frac{119}{320}\right)$	$e\left(\frac{383}{480}\right)$	$e\left(\frac{187}{320}\right)$	$e\left(\frac{307}{960}\right)$
$\chi_{83200}(9211,\cdot)$	$1$	$1$	$e\left(\frac{301}{960}\right)$	$e\left(\frac{71}{96}\right)$	$e\left(\frac{301}{480}\right)$	$e\left(\frac{43}{960}\right)$	$e\left(\frac{161}{240}\right)$	$e\left(\frac{809}{960}\right)$	$e\left(\frac{17}{320}\right)$	$e\left(\frac{329}{480}\right)$	$e\left(\frac{301}{320}\right)$	$e\left(\frac{181}{960}\right)$
$\chi_{83200}(9371,\cdot)$	$1$	$1$	$e\left(\frac{917}{960}\right)$	$e\left(\frac{31}{96}\right)$	$e\left(\frac{437}{480}\right)$	$e\left(\frac{131}{960}\right)$	$e\left(\frac{217}{240}\right)$	$e\left(\frac{433}{960}\right)$	$e\left(\frac{89}{320}\right)$	$e\left(\frac{433}{480}\right)$	$e\left(\frac{277}{320}\right)$	$e\left(\frac{797}{960}\right)$

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	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)	\(29\)
\(\chi_{83200}(11,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{881}{960}\right)\)	\(e\left(\frac{19}{96}\right)\)	\(e\left(\frac{401}{480}\right)\)	\(e\left(\frac{263}{960}\right)\)	\(e\left(\frac{181}{240}\right)\)	\(e\left(\frac{349}{960}\right)\)	\(e\left(\frac{37}{320}\right)\)	\(e\left(\frac{349}{480}\right)\)	\(e\left(\frac{241}{320}\right)\)	\(e\left(\frac{281}{960}\right)\)
\(\chi_{83200}(691,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{179}{960}\right)\)	\(e\left(\frac{25}{96}\right)\)	\(e\left(\frac{179}{480}\right)\)	\(e\left(\frac{437}{960}\right)\)	\(e\left(\frac{79}{240}\right)\)	\(e\left(\frac{631}{960}\right)\)	\(e\left(\frac{143}{320}\right)\)	\(e\left(\frac{151}{480}\right)\)	\(e\left(\frac{179}{320}\right)\)	\(e\left(\frac{299}{960}\right)\)
\(\chi_{83200}(891,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{589}{960}\right)\)	\(e\left(\frac{71}{96}\right)\)	\(e\left(\frac{109}{480}\right)\)	\(e\left(\frac{907}{960}\right)\)	\(e\left(\frac{209}{240}\right)\)	\(e\left(\frac{521}{960}\right)\)	\(e\left(\frac{113}{320}\right)\)	\(e\left(\frac{41}{480}\right)\)	\(e\left(\frac{269}{320}\right)\)	\(e\left(\frac{469}{960}\right)\)
\(\chi_{83200}(1731,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{960}\right)\)	\(e\left(\frac{37}{96}\right)\)	\(e\left(\frac{23}{480}\right)\)	\(e\left(\frac{689}{960}\right)\)	\(e\left(\frac{163}{240}\right)\)	\(e\left(\frac{907}{960}\right)\)	\(e\left(\frac{131}{320}\right)\)	\(e\left(\frac{427}{480}\right)\)	\(e\left(\frac{23}{320}\right)\)	\(e\left(\frac{623}{960}\right)\)
\(\chi_{83200}(1891,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{319}{960}\right)\)	\(e\left(\frac{29}{96}\right)\)	\(e\left(\frac{319}{480}\right)\)	\(e\left(\frac{457}{960}\right)\)	\(e\left(\frac{59}{240}\right)\)	\(e\left(\frac{851}{960}\right)\)	\(e\left(\frac{203}{320}\right)\)	\(e\left(\frac{371}{480}\right)\)	\(e\left(\frac{319}{320}\right)\)	\(e\left(\frac{919}{960}\right)\)
\(\chi_{83200}(1931,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{913}{960}\right)\)	\(e\left(\frac{83}{96}\right)\)	\(e\left(\frac{433}{480}\right)\)	\(e\left(\frac{679}{960}\right)\)	\(e\left(\frac{53}{240}\right)\)	\(e\left(\frac{317}{960}\right)\)	\(e\left(\frac{261}{320}\right)\)	\(e\left(\frac{317}{480}\right)\)	\(e\left(\frac{273}{320}\right)\)	\(e\left(\frac{313}{960}\right)\)
\(\chi_{83200}(2091,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{569}{960}\right)\)	\(e\left(\frac{43}{96}\right)\)	\(e\left(\frac{89}{480}\right)\)	\(e\left(\frac{767}{960}\right)\)	\(e\left(\frac{109}{240}\right)\)	\(e\left(\frac{901}{960}\right)\)	\(e\left(\frac{13}{320}\right)\)	\(e\left(\frac{421}{480}\right)\)	\(e\left(\frac{249}{320}\right)\)	\(e\left(\frac{929}{960}\right)\)
\(\chi_{83200}(2771,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{827}{960}\right)\)	\(e\left(\frac{49}{96}\right)\)	\(e\left(\frac{347}{480}\right)\)	\(e\left(\frac{941}{960}\right)\)	\(e\left(\frac{7}{240}\right)\)	\(e\left(\frac{223}{960}\right)\)	\(e\left(\frac{119}{320}\right)\)	\(e\left(\frac{223}{480}\right)\)	\(e\left(\frac{187}{320}\right)\)	\(e\left(\frac{947}{960}\right)\)
\(\chi_{83200}(2931,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{163}{960}\right)\)	\(e\left(\frac{41}{96}\right)\)	\(e\left(\frac{163}{480}\right)\)	\(e\left(\frac{709}{960}\right)\)	\(e\left(\frac{143}{240}\right)\)	\(e\left(\frac{167}{960}\right)\)	\(e\left(\frac{191}{320}\right)\)	\(e\left(\frac{167}{480}\right)\)	\(e\left(\frac{163}{320}\right)\)	\(e\left(\frac{283}{960}\right)\)
\(\chi_{83200}(2971,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{277}{960}\right)\)	\(e\left(\frac{95}{96}\right)\)	\(e\left(\frac{277}{480}\right)\)	\(e\left(\frac{451}{960}\right)\)	\(e\left(\frac{137}{240}\right)\)	\(e\left(\frac{113}{960}\right)\)	\(e\left(\frac{89}{320}\right)\)	\(e\left(\frac{113}{480}\right)\)	\(e\left(\frac{277}{320}\right)\)	\(e\left(\frac{157}{960}\right)\)
\(\chi_{83200}(3131,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{893}{960}\right)\)	\(e\left(\frac{55}{96}\right)\)	\(e\left(\frac{413}{480}\right)\)	\(e\left(\frac{539}{960}\right)\)	\(e\left(\frac{193}{240}\right)\)	\(e\left(\frac{697}{960}\right)\)	\(e\left(\frac{161}{320}\right)\)	\(e\left(\frac{217}{480}\right)\)	\(e\left(\frac{253}{320}\right)\)	\(e\left(\frac{773}{960}\right)\)
\(\chi_{83200}(3811,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{671}{960}\right)\)	\(e\left(\frac{61}{96}\right)\)	\(e\left(\frac{191}{480}\right)\)	\(e\left(\frac{233}{960}\right)\)	\(e\left(\frac{91}{240}\right)\)	\(e\left(\frac{499}{960}\right)\)	\(e\left(\frac{107}{320}\right)\)	\(e\left(\frac{19}{480}\right)\)	\(e\left(\frac{31}{320}\right)\)	\(e\left(\frac{311}{960}\right)\)
\(\chi_{83200}(3971,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{960}\right)\)	\(e\left(\frac{53}{96}\right)\)	\(e\left(\frac{7}{480}\right)\)	\(e\left(\frac{1}{960}\right)\)	\(e\left(\frac{227}{240}\right)\)	\(e\left(\frac{443}{960}\right)\)	\(e\left(\frac{179}{320}\right)\)	\(e\left(\frac{443}{480}\right)\)	\(e\left(\frac{7}{320}\right)\)	\(e\left(\frac{607}{960}\right)\)
\(\chi_{83200}(4011,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{601}{960}\right)\)	\(e\left(\frac{11}{96}\right)\)	\(e\left(\frac{121}{480}\right)\)	\(e\left(\frac{223}{960}\right)\)	\(e\left(\frac{221}{240}\right)\)	\(e\left(\frac{869}{960}\right)\)	\(e\left(\frac{237}{320}\right)\)	\(e\left(\frac{389}{480}\right)\)	\(e\left(\frac{281}{320}\right)\)	\(e\left(\frac{1}{960}\right)\)
\(\chi_{83200}(4171,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{257}{960}\right)\)	\(e\left(\frac{67}{96}\right)\)	\(e\left(\frac{257}{480}\right)\)	\(e\left(\frac{311}{960}\right)\)	\(e\left(\frac{37}{240}\right)\)	\(e\left(\frac{493}{960}\right)\)	\(e\left(\frac{309}{320}\right)\)	\(e\left(\frac{13}{480}\right)\)	\(e\left(\frac{257}{320}\right)\)	\(e\left(\frac{617}{960}\right)\)
\(\chi_{83200}(5011,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{811}{960}\right)\)	\(e\left(\frac{65}{96}\right)\)	\(e\left(\frac{331}{480}\right)\)	\(e\left(\frac{253}{960}\right)\)	\(e\left(\frac{71}{240}\right)\)	\(e\left(\frac{719}{960}\right)\)	\(e\left(\frac{167}{320}\right)\)	\(e\left(\frac{239}{480}\right)\)	\(e\left(\frac{171}{320}\right)\)	\(e\left(\frac{931}{960}\right)\)
\(\chi_{83200}(5211,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{581}{960}\right)\)	\(e\left(\frac{79}{96}\right)\)	\(e\left(\frac{101}{480}\right)\)	\(e\left(\frac{83}{960}\right)\)	\(e\left(\frac{121}{240}\right)\)	\(e\left(\frac{289}{960}\right)\)	\(e\left(\frac{137}{320}\right)\)	\(e\left(\frac{289}{480}\right)\)	\(e\left(\frac{261}{320}\right)\)	\(e\left(\frac{461}{960}\right)\)
\(\chi_{83200}(5891,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{359}{960}\right)\)	\(e\left(\frac{85}{96}\right)\)	\(e\left(\frac{359}{480}\right)\)	\(e\left(\frac{737}{960}\right)\)	\(e\left(\frac{19}{240}\right)\)	\(e\left(\frac{91}{960}\right)\)	\(e\left(\frac{83}{320}\right)\)	\(e\left(\frac{91}{480}\right)\)	\(e\left(\frac{39}{320}\right)\)	\(e\left(\frac{959}{960}\right)\)
\(\chi_{83200}(6091,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{289}{960}\right)\)	\(e\left(\frac{35}{96}\right)\)	\(e\left(\frac{289}{480}\right)\)	\(e\left(\frac{727}{960}\right)\)	\(e\left(\frac{149}{240}\right)\)	\(e\left(\frac{461}{960}\right)\)	\(e\left(\frac{213}{320}\right)\)	\(e\left(\frac{461}{480}\right)\)	\(e\left(\frac{289}{320}\right)\)	\(e\left(\frac{649}{960}\right)\)
\(\chi_{83200}(6931,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{203}{960}\right)\)	\(e\left(\frac{1}{96}\right)\)	\(e\left(\frac{203}{480}\right)\)	\(e\left(\frac{29}{960}\right)\)	\(e\left(\frac{103}{240}\right)\)	\(e\left(\frac{367}{960}\right)\)	\(e\left(\frac{71}{320}\right)\)	\(e\left(\frac{367}{480}\right)\)	\(e\left(\frac{203}{320}\right)\)	\(e\left(\frac{323}{960}\right)\)
\(\chi_{83200}(7091,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{499}{960}\right)\)	\(e\left(\frac{89}{96}\right)\)	\(e\left(\frac{19}{480}\right)\)	\(e\left(\frac{757}{960}\right)\)	\(e\left(\frac{239}{240}\right)\)	\(e\left(\frac{311}{960}\right)\)	\(e\left(\frac{143}{320}\right)\)	\(e\left(\frac{311}{480}\right)\)	\(e\left(\frac{179}{320}\right)\)	\(e\left(\frac{619}{960}\right)\)
\(\chi_{83200}(7131,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{613}{960}\right)\)	\(e\left(\frac{47}{96}\right)\)	\(e\left(\frac{133}{480}\right)\)	\(e\left(\frac{499}{960}\right)\)	\(e\left(\frac{233}{240}\right)\)	\(e\left(\frac{257}{960}\right)\)	\(e\left(\frac{41}{320}\right)\)	\(e\left(\frac{257}{480}\right)\)	\(e\left(\frac{293}{320}\right)\)	\(e\left(\frac{493}{960}\right)\)
\(\chi_{83200}(7291,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{269}{960}\right)\)	\(e\left(\frac{7}{96}\right)\)	\(e\left(\frac{269}{480}\right)\)	\(e\left(\frac{587}{960}\right)\)	\(e\left(\frac{49}{240}\right)\)	\(e\left(\frac{841}{960}\right)\)	\(e\left(\frac{113}{320}\right)\)	\(e\left(\frac{361}{480}\right)\)	\(e\left(\frac{269}{320}\right)\)	\(e\left(\frac{149}{960}\right)\)
\(\chi_{83200}(7971,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{960}\right)\)	\(e\left(\frac{13}{96}\right)\)	\(e\left(\frac{47}{480}\right)\)	\(e\left(\frac{281}{960}\right)\)	\(e\left(\frac{187}{240}\right)\)	\(e\left(\frac{643}{960}\right)\)	\(e\left(\frac{59}{320}\right)\)	\(e\left(\frac{163}{480}\right)\)	\(e\left(\frac{47}{320}\right)\)	\(e\left(\frac{647}{960}\right)\)
\(\chi_{83200}(8131,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{343}{960}\right)\)	\(e\left(\frac{5}{96}\right)\)	\(e\left(\frac{343}{480}\right)\)	\(e\left(\frac{49}{960}\right)\)	\(e\left(\frac{83}{240}\right)\)	\(e\left(\frac{587}{960}\right)\)	\(e\left(\frac{131}{320}\right)\)	\(e\left(\frac{107}{480}\right)\)	\(e\left(\frac{23}{320}\right)\)	\(e\left(\frac{943}{960}\right)\)
\(\chi_{83200}(8171,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{937}{960}\right)\)	\(e\left(\frac{59}{96}\right)\)	\(e\left(\frac{457}{480}\right)\)	\(e\left(\frac{271}{960}\right)\)	\(e\left(\frac{77}{240}\right)\)	\(e\left(\frac{53}{960}\right)\)	\(e\left(\frac{189}{320}\right)\)	\(e\left(\frac{53}{480}\right)\)	\(e\left(\frac{297}{320}\right)\)	\(e\left(\frac{337}{960}\right)\)
\(\chi_{83200}(8331,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{593}{960}\right)\)	\(e\left(\frac{19}{96}\right)\)	\(e\left(\frac{113}{480}\right)\)	\(e\left(\frac{359}{960}\right)\)	\(e\left(\frac{133}{240}\right)\)	\(e\left(\frac{637}{960}\right)\)	\(e\left(\frac{261}{320}\right)\)	\(e\left(\frac{157}{480}\right)\)	\(e\left(\frac{273}{320}\right)\)	\(e\left(\frac{953}{960}\right)\)
\(\chi_{83200}(9011,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{851}{960}\right)\)	\(e\left(\frac{25}{96}\right)\)	\(e\left(\frac{371}{480}\right)\)	\(e\left(\frac{533}{960}\right)\)	\(e\left(\frac{31}{240}\right)\)	\(e\left(\frac{919}{960}\right)\)	\(e\left(\frac{47}{320}\right)\)	\(e\left(\frac{439}{480}\right)\)	\(e\left(\frac{211}{320}\right)\)	\(e\left(\frac{11}{960}\right)\)
\(\chi_{83200}(9171,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{187}{960}\right)\)	\(e\left(\frac{17}{96}\right)\)	\(e\left(\frac{187}{480}\right)\)	\(e\left(\frac{301}{960}\right)\)	\(e\left(\frac{167}{240}\right)\)	\(e\left(\frac{863}{960}\right)\)	\(e\left(\frac{119}{320}\right)\)	\(e\left(\frac{383}{480}\right)\)	\(e\left(\frac{187}{320}\right)\)	\(e\left(\frac{307}{960}\right)\)
\(\chi_{83200}(9211,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{301}{960}\right)\)	\(e\left(\frac{71}{96}\right)\)	\(e\left(\frac{301}{480}\right)\)	\(e\left(\frac{43}{960}\right)\)	\(e\left(\frac{161}{240}\right)\)	\(e\left(\frac{809}{960}\right)\)	\(e\left(\frac{17}{320}\right)\)	\(e\left(\frac{329}{480}\right)\)	\(e\left(\frac{301}{320}\right)\)	\(e\left(\frac{181}{960}\right)\)
\(\chi_{83200}(9371,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{917}{960}\right)\)	\(e\left(\frac{31}{96}\right)\)	\(e\left(\frac{437}{480}\right)\)	\(e\left(\frac{131}{960}\right)\)	\(e\left(\frac{217}{240}\right)\)	\(e\left(\frac{433}{960}\right)\)	\(e\left(\frac{89}{320}\right)\)	\(e\left(\frac{433}{480}\right)\)	\(e\left(\frac{277}{320}\right)\)	\(e\left(\frac{797}{960}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Basic properties

Related number fields

First 31 of 256 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.bdo
Modulus	$83200$
Conductor	$83200$
Order	$960$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(83200\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(83200\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(960\)	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:	yes	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);