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Properties

Label 4140.bz
Modulus 41404140
Conductor 345345
Order 2222
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(4140, base_ring=CyclotomicField(22))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,11,11,5]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(89,4140))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 41404140
Conductor: 345345
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 2222
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 345.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(ζ11)\Q(\zeta_{11})
Fixed field: Number field defined by a degree 22 polynomial

Characters in Galois orbit

Character −1-1 11 77 1111 1313 1717 1919 2929 3131 3737 4141 4343
χ4140(89,⋅)\chi_{4140}(89,\cdot) 11 11 e(911)e\left(\frac{9}{11}\right) e(611)e\left(\frac{6}{11}\right) e(1522)e\left(\frac{15}{22}\right) e(1322)e\left(\frac{13}{22}\right) e(922)e\left(\frac{9}{22}\right) e(1322)e\left(\frac{13}{22}\right) e(411)e\left(\frac{4}{11}\right) e(311)e\left(\frac{3}{11}\right) e(522)e\left(\frac{5}{22}\right) e(711)e\left(\frac{7}{11}\right)
χ4140(1169,⋅)\chi_{4140}(1169,\cdot) 11 11 e(511)e\left(\frac{5}{11}\right) e(711)e\left(\frac{7}{11}\right) e(122)e\left(\frac{1}{22}\right) e(1722)e\left(\frac{17}{22}\right) e(522)e\left(\frac{5}{22}\right) e(1722)e\left(\frac{17}{22}\right) e(111)e\left(\frac{1}{11}\right) e(911)e\left(\frac{9}{11}\right) e(1522)e\left(\frac{15}{22}\right) e(1011)e\left(\frac{10}{11}\right)
χ4140(1349,⋅)\chi_{4140}(1349,\cdot) 11 11 e(211)e\left(\frac{2}{11}\right) e(511)e\left(\frac{5}{11}\right) e(722)e\left(\frac{7}{22}\right) e(922)e\left(\frac{9}{22}\right) e(1322)e\left(\frac{13}{22}\right) e(922)e\left(\frac{9}{22}\right) e(711)e\left(\frac{7}{11}\right) e(811)e\left(\frac{8}{11}\right) e(1722)e\left(\frac{17}{22}\right) e(411)e\left(\frac{4}{11}\right)
χ4140(1529,⋅)\chi_{4140}(1529,\cdot) 11 11 e(311)e\left(\frac{3}{11}\right) e(211)e\left(\frac{2}{11}\right) e(522)e\left(\frac{5}{22}\right) e(1922)e\left(\frac{19}{22}\right) e(322)e\left(\frac{3}{22}\right) e(1922)e\left(\frac{19}{22}\right) e(511)e\left(\frac{5}{11}\right) e(111)e\left(\frac{1}{11}\right) e(922)e\left(\frac{9}{22}\right) e(611)e\left(\frac{6}{11}\right)
χ4140(1709,⋅)\chi_{4140}(1709,\cdot) 11 11 e(1011)e\left(\frac{10}{11}\right) e(311)e\left(\frac{3}{11}\right) e(1322)e\left(\frac{13}{22}\right) e(122)e\left(\frac{1}{22}\right) e(2122)e\left(\frac{21}{22}\right) e(122)e\left(\frac{1}{22}\right) e(211)e\left(\frac{2}{11}\right) e(711)e\left(\frac{7}{11}\right) e(1922)e\left(\frac{19}{22}\right) e(911)e\left(\frac{9}{11}\right)
χ4140(2429,⋅)\chi_{4140}(2429,\cdot) 11 11 e(711)e\left(\frac{7}{11}\right) e(111)e\left(\frac{1}{11}\right) e(1922)e\left(\frac{19}{22}\right) e(1522)e\left(\frac{15}{22}\right) e(722)e\left(\frac{7}{22}\right) e(1522)e\left(\frac{15}{22}\right) e(811)e\left(\frac{8}{11}\right) e(611)e\left(\frac{6}{11}\right) e(2122)e\left(\frac{21}{22}\right) e(311)e\left(\frac{3}{11}\right)
χ4140(2609,⋅)\chi_{4140}(2609,\cdot) 11 11 e(111)e\left(\frac{1}{11}\right) e(811)e\left(\frac{8}{11}\right) e(922)e\left(\frac{9}{22}\right) e(2122)e\left(\frac{21}{22}\right) e(122)e\left(\frac{1}{22}\right) e(2122)e\left(\frac{21}{22}\right) e(911)e\left(\frac{9}{11}\right) e(411)e\left(\frac{4}{11}\right) e(322)e\left(\frac{3}{22}\right) e(211)e\left(\frac{2}{11}\right)
χ4140(3149,⋅)\chi_{4140}(3149,\cdot) 11 11 e(811)e\left(\frac{8}{11}\right) e(911)e\left(\frac{9}{11}\right) e(1722)e\left(\frac{17}{22}\right) e(322)e\left(\frac{3}{22}\right) e(1922)e\left(\frac{19}{22}\right) e(322)e\left(\frac{3}{22}\right) e(611)e\left(\frac{6}{11}\right) e(1011)e\left(\frac{10}{11}\right) e(1322)e\left(\frac{13}{22}\right) e(511)e\left(\frac{5}{11}\right)
χ4140(3329,⋅)\chi_{4140}(3329,\cdot) 11 11 e(611)e\left(\frac{6}{11}\right) e(411)e\left(\frac{4}{11}\right) e(2122)e\left(\frac{21}{22}\right) e(522)e\left(\frac{5}{22}\right) e(1722)e\left(\frac{17}{22}\right) e(522)e\left(\frac{5}{22}\right) e(1011)e\left(\frac{10}{11}\right) e(211)e\left(\frac{2}{11}\right) e(722)e\left(\frac{7}{22}\right) e(111)e\left(\frac{1}{11}\right)
χ4140(3869,⋅)\chi_{4140}(3869,\cdot) 11 11 e(411)e\left(\frac{4}{11}\right) e(1011)e\left(\frac{10}{11}\right) e(322)e\left(\frac{3}{22}\right) e(722)e\left(\frac{7}{22}\right) e(1522)e\left(\frac{15}{22}\right) e(722)e\left(\frac{7}{22}\right) e(311)e\left(\frac{3}{11}\right) e(511)e\left(\frac{5}{11}\right) e(122)e\left(\frac{1}{22}\right) e(811)e\left(\frac{8}{11}\right)