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Properties

Label 1936.be
Modulus 19361936
Conductor 968968
Order 2222
Real no
Primitive no
Minimal no
Parity even

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1936, base_ring=CyclotomicField(22)) M = H._module chi = DirichletCharacter(H, M([11,11,21])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(87,1936)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 19361936
Conductor: 968968
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: 2222
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from 968.w
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Related number fields

Field of values: Q(ζ11)\Q(\zeta_{11})
Fixed field: 22.22.42765144951456754503592723360164151789017189226381312.1

Characters in Galois orbit

Character −1-1 11 33 55 77 99 1313 1515 1717 1919 2121 2323
χ1936(87,⋅)\chi_{1936}(87,\cdot) 11 11 11 e(322)e\left(\frac{3}{22}\right) e(211)e\left(\frac{2}{11}\right) 11 e(1011)e\left(\frac{10}{11}\right) e(322)e\left(\frac{3}{22}\right) e(1722)e\left(\frac{17}{22}\right) e(522)e\left(\frac{5}{22}\right) e(211)e\left(\frac{2}{11}\right) e(722)e\left(\frac{7}{22}\right)
χ1936(263,⋅)\chi_{1936}(263,\cdot) 11 11 11 e(922)e\left(\frac{9}{22}\right) e(611)e\left(\frac{6}{11}\right) 11 e(811)e\left(\frac{8}{11}\right) e(922)e\left(\frac{9}{22}\right) e(722)e\left(\frac{7}{22}\right) e(1522)e\left(\frac{15}{22}\right) e(611)e\left(\frac{6}{11}\right) e(2122)e\left(\frac{21}{22}\right)
χ1936(439,⋅)\chi_{1936}(439,\cdot) 11 11 11 e(1522)e\left(\frac{15}{22}\right) e(1011)e\left(\frac{10}{11}\right) 11 e(611)e\left(\frac{6}{11}\right) e(1522)e\left(\frac{15}{22}\right) e(1922)e\left(\frac{19}{22}\right) e(322)e\left(\frac{3}{22}\right) e(1011)e\left(\frac{10}{11}\right) e(1322)e\left(\frac{13}{22}\right)
χ1936(615,⋅)\chi_{1936}(615,\cdot) 11 11 11 e(2122)e\left(\frac{21}{22}\right) e(311)e\left(\frac{3}{11}\right) 11 e(411)e\left(\frac{4}{11}\right) e(2122)e\left(\frac{21}{22}\right) e(922)e\left(\frac{9}{22}\right) e(1322)e\left(\frac{13}{22}\right) e(311)e\left(\frac{3}{11}\right) e(522)e\left(\frac{5}{22}\right)
χ1936(791,⋅)\chi_{1936}(791,\cdot) 11 11 11 e(522)e\left(\frac{5}{22}\right) e(711)e\left(\frac{7}{11}\right) 11 e(211)e\left(\frac{2}{11}\right) e(522)e\left(\frac{5}{22}\right) e(2122)e\left(\frac{21}{22}\right) e(122)e\left(\frac{1}{22}\right) e(711)e\left(\frac{7}{11}\right) e(1922)e\left(\frac{19}{22}\right)
χ1936(1143,⋅)\chi_{1936}(1143,\cdot) 11 11 11 e(1722)e\left(\frac{17}{22}\right) e(411)e\left(\frac{4}{11}\right) 11 e(911)e\left(\frac{9}{11}\right) e(1722)e\left(\frac{17}{22}\right) e(122)e\left(\frac{1}{22}\right) e(2122)e\left(\frac{21}{22}\right) e(411)e\left(\frac{4}{11}\right) e(322)e\left(\frac{3}{22}\right)
χ1936(1319,⋅)\chi_{1936}(1319,\cdot) 11 11 11 e(122)e\left(\frac{1}{22}\right) e(811)e\left(\frac{8}{11}\right) 11 e(711)e\left(\frac{7}{11}\right) e(122)e\left(\frac{1}{22}\right) e(1322)e\left(\frac{13}{22}\right) e(922)e\left(\frac{9}{22}\right) e(811)e\left(\frac{8}{11}\right) e(1722)e\left(\frac{17}{22}\right)
χ1936(1495,⋅)\chi_{1936}(1495,\cdot) 11 11 11 e(722)e\left(\frac{7}{22}\right) e(111)e\left(\frac{1}{11}\right) 11 e(511)e\left(\frac{5}{11}\right) e(722)e\left(\frac{7}{22}\right) e(322)e\left(\frac{3}{22}\right) e(1922)e\left(\frac{19}{22}\right) e(111)e\left(\frac{1}{11}\right) e(922)e\left(\frac{9}{22}\right)
χ1936(1671,⋅)\chi_{1936}(1671,\cdot) 11 11 11 e(1322)e\left(\frac{13}{22}\right) e(511)e\left(\frac{5}{11}\right) 11 e(311)e\left(\frac{3}{11}\right) e(1322)e\left(\frac{13}{22}\right) e(1522)e\left(\frac{15}{22}\right) e(722)e\left(\frac{7}{22}\right) e(511)e\left(\frac{5}{11}\right) e(122)e\left(\frac{1}{22}\right)
χ1936(1847,⋅)\chi_{1936}(1847,\cdot) 11 11 11 e(1922)e\left(\frac{19}{22}\right) e(911)e\left(\frac{9}{11}\right) 11 e(111)e\left(\frac{1}{11}\right) e(1922)e\left(\frac{19}{22}\right) e(522)e\left(\frac{5}{22}\right) e(1722)e\left(\frac{17}{22}\right) e(911)e\left(\frac{9}{11}\right) e(1522)e\left(\frac{15}{22}\right)