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Properties

Label 1881.cb
Modulus 18811881
Conductor 209209
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(1881, base_ring=CyclotomicField(30))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,18,10]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(64,1881))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 18811881
Conductor: 209209
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 1515
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 209.n
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 22 44 55 77 88 1010 1313 1414 1616 1717
χ1881(64,⋅)\chi_{1881}(64,\cdot) 11 11 e(1415)e\left(\frac{14}{15}\right) e(1315)e\left(\frac{13}{15}\right) e(1115)e\left(\frac{11}{15}\right) e(15)e\left(\frac{1}{5}\right) e(45)e\left(\frac{4}{5}\right) e(23)e\left(\frac{2}{3}\right) e(415)e\left(\frac{4}{15}\right) e(215)e\left(\frac{2}{15}\right) e(1115)e\left(\frac{11}{15}\right) e(1115)e\left(\frac{11}{15}\right)
χ1881(163,⋅)\chi_{1881}(163,\cdot) 11 11 e(415)e\left(\frac{4}{15}\right) e(815)e\left(\frac{8}{15}\right) e(115)e\left(\frac{1}{15}\right) e(15)e\left(\frac{1}{5}\right) e(45)e\left(\frac{4}{5}\right) e(13)e\left(\frac{1}{3}\right) e(1415)e\left(\frac{14}{15}\right) e(715)e\left(\frac{7}{15}\right) e(115)e\left(\frac{1}{15}\right) e(115)e\left(\frac{1}{15}\right)
χ1881(235,⋅)\chi_{1881}(235,\cdot) 11 11 e(815)e\left(\frac{8}{15}\right) e(115)e\left(\frac{1}{15}\right) e(215)e\left(\frac{2}{15}\right) e(25)e\left(\frac{2}{5}\right) e(35)e\left(\frac{3}{5}\right) e(23)e\left(\frac{2}{3}\right) e(1315)e\left(\frac{13}{15}\right) e(1415)e\left(\frac{14}{15}\right) e(215)e\left(\frac{2}{15}\right) e(215)e\left(\frac{2}{15}\right)
χ1881(334,⋅)\chi_{1881}(334,\cdot) 11 11 e(1315)e\left(\frac{13}{15}\right) e(1115)e\left(\frac{11}{15}\right) e(715)e\left(\frac{7}{15}\right) e(25)e\left(\frac{2}{5}\right) e(35)e\left(\frac{3}{5}\right) e(13)e\left(\frac{1}{3}\right) e(815)e\left(\frac{8}{15}\right) e(415)e\left(\frac{4}{15}\right) e(715)e\left(\frac{7}{15}\right) e(715)e\left(\frac{7}{15}\right)
χ1881(577,⋅)\chi_{1881}(577,\cdot) 11 11 e(1115)e\left(\frac{11}{15}\right) e(715)e\left(\frac{7}{15}\right) e(1415)e\left(\frac{14}{15}\right) e(45)e\left(\frac{4}{5}\right) e(15)e\left(\frac{1}{5}\right) e(23)e\left(\frac{2}{3}\right) e(115)e\left(\frac{1}{15}\right) e(815)e\left(\frac{8}{15}\right) e(1415)e\left(\frac{14}{15}\right) e(1415)e\left(\frac{14}{15}\right)
χ1881(676,⋅)\chi_{1881}(676,\cdot) 11 11 e(115)e\left(\frac{1}{15}\right) e(215)e\left(\frac{2}{15}\right) e(415)e\left(\frac{4}{15}\right) e(45)e\left(\frac{4}{5}\right) e(15)e\left(\frac{1}{5}\right) e(13)e\left(\frac{1}{3}\right) e(1115)e\left(\frac{11}{15}\right) e(1315)e\left(\frac{13}{15}\right) e(415)e\left(\frac{4}{15}\right) e(415)e\left(\frac{4}{15}\right)
χ1881(1774,⋅)\chi_{1881}(1774,\cdot) 11 11 e(215)e\left(\frac{2}{15}\right) e(415)e\left(\frac{4}{15}\right) e(815)e\left(\frac{8}{15}\right) e(35)e\left(\frac{3}{5}\right) e(25)e\left(\frac{2}{5}\right) e(23)e\left(\frac{2}{3}\right) e(715)e\left(\frac{7}{15}\right) e(1115)e\left(\frac{11}{15}\right) e(815)e\left(\frac{8}{15}\right) e(815)e\left(\frac{8}{15}\right)
χ1881(1873,⋅)\chi_{1881}(1873,\cdot) 11 11 e(715)e\left(\frac{7}{15}\right) e(1415)e\left(\frac{14}{15}\right) e(1315)e\left(\frac{13}{15}\right) e(35)e\left(\frac{3}{5}\right) e(25)e\left(\frac{2}{5}\right) e(13)e\left(\frac{1}{3}\right) e(215)e\left(\frac{2}{15}\right) e(115)e\left(\frac{1}{15}\right) e(1315)e\left(\frac{13}{15}\right) e(1315)e\left(\frac{13}{15}\right)