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Properties

Label 2070.u
Modulus 20702070
Conductor 2323
Order 1111
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(2070, base_ring=CyclotomicField(22))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,0,12]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(271,2070))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 20702070
Conductor: 2323
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 1111
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 23.c
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(ζ11)\Q(\zeta_{11})
Fixed field: Q(ζ23)+\Q(\zeta_{23})^+

Characters in Galois orbit

Character −1-1 11 77 1111 1313 1717 1919 2929 3131 3737 4141 4343
χ2070(271,⋅)\chi_{2070}(271,\cdot) 11 11 e(411)e\left(\frac{4}{11}\right) e(1011)e\left(\frac{10}{11}\right) e(711)e\left(\frac{7}{11}\right) e(911)e\left(\frac{9}{11}\right) e(211)e\left(\frac{2}{11}\right) e(911)e\left(\frac{9}{11}\right) e(311)e\left(\frac{3}{11}\right) e(511)e\left(\frac{5}{11}\right) e(611)e\left(\frac{6}{11}\right) e(811)e\left(\frac{8}{11}\right)
χ2070(361,⋅)\chi_{2070}(361,\cdot) 11 11 e(1011)e\left(\frac{10}{11}\right) e(311)e\left(\frac{3}{11}\right) e(111)e\left(\frac{1}{11}\right) e(611)e\left(\frac{6}{11}\right) e(511)e\left(\frac{5}{11}\right) e(611)e\left(\frac{6}{11}\right) e(211)e\left(\frac{2}{11}\right) e(711)e\left(\frac{7}{11}\right) e(411)e\left(\frac{4}{11}\right) e(911)e\left(\frac{9}{11}\right)
χ2070(541,⋅)\chi_{2070}(541,\cdot) 11 11 e(311)e\left(\frac{3}{11}\right) e(211)e\left(\frac{2}{11}\right) e(811)e\left(\frac{8}{11}\right) e(411)e\left(\frac{4}{11}\right) e(711)e\left(\frac{7}{11}\right) e(411)e\left(\frac{4}{11}\right) e(511)e\left(\frac{5}{11}\right) e(111)e\left(\frac{1}{11}\right) e(1011)e\left(\frac{10}{11}\right) e(611)e\left(\frac{6}{11}\right)
χ2070(721,⋅)\chi_{2070}(721,\cdot) 11 11 e(211)e\left(\frac{2}{11}\right) e(511)e\left(\frac{5}{11}\right) e(911)e\left(\frac{9}{11}\right) e(1011)e\left(\frac{10}{11}\right) e(111)e\left(\frac{1}{11}\right) e(1011)e\left(\frac{10}{11}\right) e(711)e\left(\frac{7}{11}\right) e(811)e\left(\frac{8}{11}\right) e(311)e\left(\frac{3}{11}\right) e(411)e\left(\frac{4}{11}\right)
χ2070(811,⋅)\chi_{2070}(811,\cdot) 11 11 e(611)e\left(\frac{6}{11}\right) e(411)e\left(\frac{4}{11}\right) e(511)e\left(\frac{5}{11}\right) e(811)e\left(\frac{8}{11}\right) e(311)e\left(\frac{3}{11}\right) e(811)e\left(\frac{8}{11}\right) e(1011)e\left(\frac{10}{11}\right) e(211)e\left(\frac{2}{11}\right) e(911)e\left(\frac{9}{11}\right) e(111)e\left(\frac{1}{11}\right)
χ2070(901,⋅)\chi_{2070}(901,\cdot) 11 11 e(511)e\left(\frac{5}{11}\right) e(711)e\left(\frac{7}{11}\right) e(611)e\left(\frac{6}{11}\right) e(311)e\left(\frac{3}{11}\right) e(811)e\left(\frac{8}{11}\right) e(311)e\left(\frac{3}{11}\right) e(111)e\left(\frac{1}{11}\right) e(911)e\left(\frac{9}{11}\right) e(211)e\left(\frac{2}{11}\right) e(1011)e\left(\frac{10}{11}\right)
χ2070(991,⋅)\chi_{2070}(991,\cdot) 11 11 e(811)e\left(\frac{8}{11}\right) e(911)e\left(\frac{9}{11}\right) e(311)e\left(\frac{3}{11}\right) e(711)e\left(\frac{7}{11}\right) e(411)e\left(\frac{4}{11}\right) e(711)e\left(\frac{7}{11}\right) e(611)e\left(\frac{6}{11}\right) e(1011)e\left(\frac{10}{11}\right) e(111)e\left(\frac{1}{11}\right) e(511)e\left(\frac{5}{11}\right)
χ2070(1531,⋅)\chi_{2070}(1531,\cdot) 11 11 e(111)e\left(\frac{1}{11}\right) e(811)e\left(\frac{8}{11}\right) e(1011)e\left(\frac{10}{11}\right) e(511)e\left(\frac{5}{11}\right) e(611)e\left(\frac{6}{11}\right) e(511)e\left(\frac{5}{11}\right) e(911)e\left(\frac{9}{11}\right) e(411)e\left(\frac{4}{11}\right) e(711)e\left(\frac{7}{11}\right) e(211)e\left(\frac{2}{11}\right)
χ2070(1711,⋅)\chi_{2070}(1711,\cdot) 11 11 e(711)e\left(\frac{7}{11}\right) e(111)e\left(\frac{1}{11}\right) e(411)e\left(\frac{4}{11}\right) e(211)e\left(\frac{2}{11}\right) e(911)e\left(\frac{9}{11}\right) e(211)e\left(\frac{2}{11}\right) e(811)e\left(\frac{8}{11}\right) e(611)e\left(\frac{6}{11}\right) e(511)e\left(\frac{5}{11}\right) e(311)e\left(\frac{3}{11}\right)
χ2070(1981,⋅)\chi_{2070}(1981,\cdot) 11 11 e(911)e\left(\frac{9}{11}\right) e(611)e\left(\frac{6}{11}\right) e(211)e\left(\frac{2}{11}\right) e(111)e\left(\frac{1}{11}\right) e(1011)e\left(\frac{10}{11}\right) e(111)e\left(\frac{1}{11}\right) e(411)e\left(\frac{4}{11}\right) e(311)e\left(\frac{3}{11}\right) e(811)e\left(\frac{8}{11}\right) e(711)e\left(\frac{7}{11}\right)