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Properties

Label 508288.vt
Modulus $508288$
Conductor $254144$
Order $13680$
Real no
Primitive no
Minimal no
Parity odd

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(508288, base_ring=CyclotomicField(13680)) M = H._module chi = DirichletCharacter(H, M([0,9405,9576,4480])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(73,508288)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(508288\)
Conductor: \(254144\)
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: \(13680\)
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from 254144.sj
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: no
Parity: odd
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Related number fields

Field of values: $\Q(\zeta_{13680})$
Fixed field: Number field defined by a degree 13680 polynomial (not computed)

First 10 of 3456 characters in Galois orbit

Character \(-1\) \(1\) \(3\) \(5\) \(7\) \(9\) \(13\) \(15\) \(17\) \(21\) \(23\) \(25\)
\(\chi_{508288}(73,\cdot)\) \(-1\) \(1\) \(e\left(\frac{2503}{13680}\right)\) \(e\left(\frac{6349}{13680}\right)\) \(e\left(\frac{2047}{2280}\right)\) \(e\left(\frac{2503}{6840}\right)\) \(e\left(\frac{10331}{13680}\right)\) \(e\left(\frac{2213}{3420}\right)\) \(e\left(\frac{1921}{3420}\right)\) \(e\left(\frac{221}{2736}\right)\) \(e\left(\frac{599}{1368}\right)\) \(e\left(\frac{6349}{6840}\right)\)
\(\chi_{508288}(233,\cdot)\) \(-1\) \(1\) \(e\left(\frac{6259}{13680}\right)\) \(e\left(\frac{8017}{13680}\right)\) \(e\left(\frac{331}{2280}\right)\) \(e\left(\frac{6259}{6840}\right)\) \(e\left(\frac{12263}{13680}\right)\) \(e\left(\frac{149}{3420}\right)\) \(e\left(\frac{2653}{3420}\right)\) \(e\left(\frac{1649}{2736}\right)\) \(e\left(\frac{155}{1368}\right)\) \(e\left(\frac{1177}{6840}\right)\)
\(\chi_{508288}(633,\cdot)\) \(-1\) \(1\) \(e\left(\frac{8441}{13680}\right)\) \(e\left(\frac{12803}{13680}\right)\) \(e\left(\frac{689}{2280}\right)\) \(e\left(\frac{1601}{6840}\right)\) \(e\left(\frac{11557}{13680}\right)\) \(e\left(\frac{1891}{3420}\right)\) \(e\left(\frac{2867}{3420}\right)\) \(e\left(\frac{2515}{2736}\right)\) \(e\left(\frac{769}{1368}\right)\) \(e\left(\frac{5963}{6840}\right)\)
\(\chi_{508288}(745,\cdot)\) \(-1\) \(1\) \(e\left(\frac{707}{13680}\right)\) \(e\left(\frac{9281}{13680}\right)\) \(e\left(\frac{1163}{2280}\right)\) \(e\left(\frac{707}{6840}\right)\) \(e\left(\frac{4279}{13680}\right)\) \(e\left(\frac{2497}{3420}\right)\) \(e\left(\frac{1469}{3420}\right)\) \(e\left(\frac{1537}{2736}\right)\) \(e\left(\frac{619}{1368}\right)\) \(e\left(\frac{2441}{6840}\right)\)
\(\chi_{508288}(777,\cdot)\) \(-1\) \(1\) \(e\left(\frac{12463}{13680}\right)\) \(e\left(\frac{7669}{13680}\right)\) \(e\left(\frac{607}{2280}\right)\) \(e\left(\frac{5623}{6840}\right)\) \(e\left(\frac{11171}{13680}\right)\) \(e\left(\frac{1613}{3420}\right)\) \(e\left(\frac{901}{3420}\right)\) \(e\left(\frac{485}{2736}\right)\) \(e\left(\frac{287}{1368}\right)\) \(e\left(\frac{829}{6840}\right)\)
\(\chi_{508288}(921,\cdot)\) \(-1\) \(1\) \(e\left(\frac{6437}{13680}\right)\) \(e\left(\frac{1511}{13680}\right)\) \(e\left(\frac{53}{2280}\right)\) \(e\left(\frac{6437}{6840}\right)\) \(e\left(\frac{7729}{13680}\right)\) \(e\left(\frac{1987}{3420}\right)\) \(e\left(\frac{1799}{3420}\right)\) \(e\left(\frac{1351}{2736}\right)\) \(e\left(\frac{901}{1368}\right)\) \(e\left(\frac{1511}{6840}\right)\)
\(\chi_{508288}(937,\cdot)\) \(-1\) \(1\) \(e\left(\frac{539}{13680}\right)\) \(e\left(\frac{13577}{13680}\right)\) \(e\left(\frac{1451}{2280}\right)\) \(e\left(\frac{539}{6840}\right)\) \(e\left(\frac{5023}{13680}\right)\) \(e\left(\frac{109}{3420}\right)\) \(e\left(\frac{2813}{3420}\right)\) \(e\left(\frac{1849}{2736}\right)\) \(e\left(\frac{499}{1368}\right)\) \(e\left(\frac{6737}{6840}\right)\)
\(\chi_{508288}(985,\cdot)\) \(-1\) \(1\) \(e\left(\frac{9901}{13680}\right)\) \(e\left(\frac{4783}{13680}\right)\) \(e\left(\frac{2149}{2280}\right)\) \(e\left(\frac{3061}{6840}\right)\) \(e\left(\frac{5417}{13680}\right)\) \(e\left(\frac{251}{3420}\right)\) \(e\left(\frac{2587}{3420}\right)\) \(e\left(\frac{1823}{2736}\right)\) \(e\left(\frac{509}{1368}\right)\) \(e\left(\frac{4783}{6840}\right)\)
\(\chi_{508288}(1289,\cdot)\) \(-1\) \(1\) \(e\left(\frac{4159}{13680}\right)\) \(e\left(\frac{6997}{13680}\right)\) \(e\left(\frac{511}{2280}\right)\) \(e\left(\frac{4159}{6840}\right)\) \(e\left(\frac{1043}{13680}\right)\) \(e\left(\frac{2789}{3420}\right)\) \(e\left(\frac{2353}{3420}\right)\) \(e\left(\frac{1445}{2736}\right)\) \(e\left(\frac{23}{1368}\right)\) \(e\left(\frac{157}{6840}\right)\)
\(\chi_{508288}(1449,\cdot)\) \(-1\) \(1\) \(e\left(\frac{6907}{13680}\right)\) \(e\left(\frac{7081}{13680}\right)\) \(e\left(\frac{523}{2280}\right)\) \(e\left(\frac{67}{6840}\right)\) \(e\left(\frac{7439}{13680}\right)\) \(e\left(\frac{77}{3420}\right)\) \(e\left(\frac{889}{3420}\right)\) \(e\left(\frac{2009}{2736}\right)\) \(e\left(\frac{227}{1368}\right)\) \(e\left(\frac{241}{6840}\right)\)