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Properties

Label 1950.bw
Modulus 19501950
Conductor 325325
Order 1515
Real no
Primitive no
Minimal yes
Parity even

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1950, base_ring=CyclotomicField(30)) M = H._module chi = DirichletCharacter(H, M([0,24,20])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(61,1950)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 19501950
Conductor: 325325
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 325.y
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: yes
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: Number field defined by a degree 15 polynomial

Characters in Galois orbit

Character −1-1 11 77 1111 1717 1919 2323 2929 3131 3737 4141 4343
χ1950(61,⋅)\chi_{1950}(61,\cdot) 11 11 e(13)e\left(\frac{1}{3}\right) e(715)e\left(\frac{7}{15}\right) e(1115)e\left(\frac{11}{15}\right) 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(25)e\left(\frac{2}{5}\right) e(1315)e\left(\frac{13}{15}\right) e(1315)e\left(\frac{13}{15}\right) e(13)e\left(\frac{1}{3}\right)
χ1950(211,⋅)\chi_{1950}(211,\cdot) 11 11 e(23)e\left(\frac{2}{3}\right) e(215)e\left(\frac{2}{15}\right) e(115)e\left(\frac{1}{15}\right) 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(25)e\left(\frac{2}{5}\right) e(815)e\left(\frac{8}{15}\right) e(815)e\left(\frac{8}{15}\right) e(23)e\left(\frac{2}{3}\right)
χ1950(841,⋅)\chi_{1950}(841,\cdot) 11 11 e(13)e\left(\frac{1}{3}\right) e(1315)e\left(\frac{13}{15}\right) e(1415)e\left(\frac{14}{15}\right) 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(35)e\left(\frac{3}{5}\right) e(715)e\left(\frac{7}{15}\right) e(715)e\left(\frac{7}{15}\right) e(13)e\left(\frac{1}{3}\right)
χ1950(991,⋅)\chi_{1950}(991,\cdot) 11 11 e(23)e\left(\frac{2}{3}\right) e(815)e\left(\frac{8}{15}\right) e(415)e\left(\frac{4}{15}\right) 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(35)e\left(\frac{3}{5}\right) e(215)e\left(\frac{2}{15}\right) e(215)e\left(\frac{2}{15}\right) e(23)e\left(\frac{2}{3}\right)
χ1950(1231,⋅)\chi_{1950}(1231,\cdot) 11 11 e(13)e\left(\frac{1}{3}\right) e(115)e\left(\frac{1}{15}\right) e(815)e\left(\frac{8}{15}\right) 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(15)e\left(\frac{1}{5}\right) e(415)e\left(\frac{4}{15}\right) e(415)e\left(\frac{4}{15}\right) e(13)e\left(\frac{1}{3}\right)
χ1950(1381,⋅)\chi_{1950}(1381,\cdot) 11 11 e(23)e\left(\frac{2}{3}\right) e(1115)e\left(\frac{11}{15}\right) e(1315)e\left(\frac{13}{15}\right) 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(15)e\left(\frac{1}{5}\right) e(1415)e\left(\frac{14}{15}\right) e(1415)e\left(\frac{14}{15}\right) e(23)e\left(\frac{2}{3}\right)
χ1950(1621,⋅)\chi_{1950}(1621,\cdot) 11 11 e(13)e\left(\frac{1}{3}\right) e(415)e\left(\frac{4}{15}\right) e(215)e\left(\frac{2}{15}\right) 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(45)e\left(\frac{4}{5}\right) e(115)e\left(\frac{1}{15}\right) e(115)e\left(\frac{1}{15}\right) e(13)e\left(\frac{1}{3}\right)
χ1950(1771,⋅)\chi_{1950}(1771,\cdot) 11 11 e(23)e\left(\frac{2}{3}\right) e(1415)e\left(\frac{14}{15}\right) e(715)e\left(\frac{7}{15}\right) 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(45)e\left(\frac{4}{5}\right) e(1115)e\left(\frac{11}{15}\right) e(1115)e\left(\frac{11}{15}\right) e(23)e\left(\frac{2}{3}\right)