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Properties

Label 3267.o
Modulus 32673267
Conductor 9999
Order 1515
Real no
Primitive no
Minimal no
Parity even

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3267, base_ring=CyclotomicField(30)) M = H._module chi = DirichletCharacter(H, M([20,18])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(856,3267)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 32673267
Conductor: 9999
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: 1515
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from 99.m
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Related number fields

Field of values: Q(ζ15)\Q(\zeta_{15})
Fixed field: 15.15.10943023107606534329121.1

Characters in Galois orbit

Character −1-1 11 22 44 55 77 88 1010 1313 1414 1616 1717
χ3267(856,⋅)\chi_{3267}(856,\cdot) 11 11 e(415)e\left(\frac{4}{15}\right) e(815)e\left(\frac{8}{15}\right) e(1115)e\left(\frac{11}{15}\right) e(1315)e\left(\frac{13}{15}\right) e(45)e\left(\frac{4}{5}\right) 11 e(1415)e\left(\frac{14}{15}\right) e(215)e\left(\frac{2}{15}\right) e(115)e\left(\frac{1}{15}\right) e(25)e\left(\frac{2}{5}\right)
χ3267(874,⋅)\chi_{3267}(874,\cdot) 11 11 e(1115)e\left(\frac{11}{15}\right) e(715)e\left(\frac{7}{15}\right) e(415)e\left(\frac{4}{15}\right) e(215)e\left(\frac{2}{15}\right) e(15)e\left(\frac{1}{5}\right) 11 e(115)e\left(\frac{1}{15}\right) e(1315)e\left(\frac{13}{15}\right) e(1415)e\left(\frac{14}{15}\right) e(35)e\left(\frac{3}{5}\right)
χ3267(928,⋅)\chi_{3267}(928,\cdot) 11 11 e(815)e\left(\frac{8}{15}\right) e(115)e\left(\frac{1}{15}\right) e(715)e\left(\frac{7}{15}\right) e(1115)e\left(\frac{11}{15}\right) e(35)e\left(\frac{3}{5}\right) 11 e(1315)e\left(\frac{13}{15}\right) e(415)e\left(\frac{4}{15}\right) e(215)e\left(\frac{2}{15}\right) e(45)e\left(\frac{4}{5}\right)
χ3267(1576,⋅)\chi_{3267}(1576,\cdot) 11 11 e(215)e\left(\frac{2}{15}\right) e(415)e\left(\frac{4}{15}\right) e(1315)e\left(\frac{13}{15}\right) e(1415)e\left(\frac{14}{15}\right) e(25)e\left(\frac{2}{5}\right) 11 e(715)e\left(\frac{7}{15}\right) e(115)e\left(\frac{1}{15}\right) e(815)e\left(\frac{8}{15}\right) e(15)e\left(\frac{1}{5}\right)
χ3267(1963,⋅)\chi_{3267}(1963,\cdot) 11 11 e(115)e\left(\frac{1}{15}\right) e(215)e\left(\frac{2}{15}\right) e(1415)e\left(\frac{14}{15}\right) e(715)e\left(\frac{7}{15}\right) e(15)e\left(\frac{1}{5}\right) 11 e(1115)e\left(\frac{11}{15}\right) e(815)e\left(\frac{8}{15}\right) e(415)e\left(\frac{4}{15}\right) e(35)e\left(\frac{3}{5}\right)
χ3267(2017,⋅)\chi_{3267}(2017,\cdot) 11 11 e(1315)e\left(\frac{13}{15}\right) e(1115)e\left(\frac{11}{15}\right) e(215)e\left(\frac{2}{15}\right) e(115)e\left(\frac{1}{15}\right) e(35)e\left(\frac{3}{5}\right) 11 e(815)e\left(\frac{8}{15}\right) e(1415)e\left(\frac{14}{15}\right) e(715)e\left(\frac{7}{15}\right) e(45)e\left(\frac{4}{5}\right)
χ3267(2665,⋅)\chi_{3267}(2665,\cdot) 11 11 e(715)e\left(\frac{7}{15}\right) e(1415)e\left(\frac{14}{15}\right) e(815)e\left(\frac{8}{15}\right) e(415)e\left(\frac{4}{15}\right) e(25)e\left(\frac{2}{5}\right) 11 e(215)e\left(\frac{2}{15}\right) e(1115)e\left(\frac{11}{15}\right) e(1315)e\left(\frac{13}{15}\right) e(15)e\left(\frac{1}{5}\right)
χ3267(3034,⋅)\chi_{3267}(3034,\cdot) 11 11 e(1415)e\left(\frac{14}{15}\right) e(1315)e\left(\frac{13}{15}\right) e(115)e\left(\frac{1}{15}\right) e(815)e\left(\frac{8}{15}\right) e(45)e\left(\frac{4}{5}\right) 11 e(415)e\left(\frac{4}{15}\right) e(715)e\left(\frac{7}{15}\right) e(1115)e\left(\frac{11}{15}\right) e(25)e\left(\frac{2}{5}\right)