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Properties

Label 5850.ee
Modulus 58505850
Conductor 29252925
Order 1515
Real no
Primitive no
Minimal yes
Parity even

Related objects

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5850, base_ring=CyclotomicField(30))
 
M = H._module
 
chi = DirichletCharacter(H, M([10,6,20]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(841,5850))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 58505850
Conductor: 29252925
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 1515
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 2925.ee
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
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
χ5850(841,⋅)\chi_{5850}(841,\cdot) 11 11 e(23)e\left(\frac{2}{3}\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(815)e\left(\frac{8}{15}\right) e(25)e\left(\frac{2}{5}\right) e(415)e\left(\frac{4}{15}\right) e(715)e\left(\frac{7}{15}\right) e(215)e\left(\frac{2}{15}\right) e(23)e\left(\frac{2}{3}\right)
χ5850(1771,⋅)\chi_{5850}(1771,\cdot) 11 11 e(13)e\left(\frac{1}{3}\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(415)e\left(\frac{4}{15}\right) e(15)e\left(\frac{1}{5}\right) e(215)e\left(\frac{2}{15}\right) e(1115)e\left(\frac{11}{15}\right) e(115)e\left(\frac{1}{15}\right) e(13)e\left(\frac{1}{3}\right)
χ5850(2011,⋅)\chi_{5850}(2011,\cdot) 11 11 e(23)e\left(\frac{2}{3}\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(215)e\left(\frac{2}{15}\right) e(35)e\left(\frac{3}{5}\right) e(115)e\left(\frac{1}{15}\right) e(1315)e\left(\frac{13}{15}\right) e(815)e\left(\frac{8}{15}\right) e(23)e\left(\frac{2}{3}\right)
χ5850(2941,⋅)\chi_{5850}(2941,\cdot) 11 11 e(13)e\left(\frac{1}{3}\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(1315)e\left(\frac{13}{15}\right) e(25)e\left(\frac{2}{5}\right) e(1415)e\left(\frac{14}{15}\right) e(215)e\left(\frac{2}{15}\right) e(715)e\left(\frac{7}{15}\right) e(13)e\left(\frac{1}{3}\right)
χ5850(3181,⋅)\chi_{5850}(3181,\cdot) 11 11 e(23)e\left(\frac{2}{3}\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(1115)e\left(\frac{11}{15}\right) e(45)e\left(\frac{4}{5}\right) e(1315)e\left(\frac{13}{15}\right) e(415)e\left(\frac{4}{15}\right) e(1415)e\left(\frac{14}{15}\right) e(23)e\left(\frac{2}{3}\right)
χ5850(4111,⋅)\chi_{5850}(4111,\cdot) 11 11 e(13)e\left(\frac{1}{3}\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(715)e\left(\frac{7}{15}\right) e(35)e\left(\frac{3}{5}\right) e(1115)e\left(\frac{11}{15}\right) e(815)e\left(\frac{8}{15}\right) e(1315)e\left(\frac{13}{15}\right) e(13)e\left(\frac{1}{3}\right)
χ5850(5281,⋅)\chi_{5850}(5281,\cdot) 11 11 e(13)e\left(\frac{1}{3}\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(115)e\left(\frac{1}{15}\right) e(45)e\left(\frac{4}{5}\right) e(815)e\left(\frac{8}{15}\right) e(1415)e\left(\frac{14}{15}\right) e(415)e\left(\frac{4}{15}\right) e(13)e\left(\frac{1}{3}\right)
χ5850(5521,⋅)\chi_{5850}(5521,\cdot) 11 11 e(23)e\left(\frac{2}{3}\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(1415)e\left(\frac{14}{15}\right) e(15)e\left(\frac{1}{5}\right) e(715)e\left(\frac{7}{15}\right) e(115)e\left(\frac{1}{15}\right) e(1115)e\left(\frac{11}{15}\right) e(23)e\left(\frac{2}{3}\right)