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Properties

Label 8325.gy
Modulus 83258325
Conductor 185185
Order 3636
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(8325, base_ring=CyclotomicField(36))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,9,7]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(757,8325))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 83258325
Conductor: 185185
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 3636
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 185.z
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(ζ36)\Q(\zeta_{36})
Fixed field: 36.36.57444765302724909954814307473256133361395843470561362005770206451416015625.2

Characters in Galois orbit

Character −1-1 11 22 44 77 88 1111 1313 1414 1616 1717 1919
χ8325(757,⋅)\chi_{8325}(757,\cdot) 11 11 e(49)e\left(\frac{4}{9}\right) e(89)e\left(\frac{8}{9}\right) e(1736)e\left(\frac{17}{36}\right) e(13)e\left(\frac{1}{3}\right) e(56)e\left(\frac{5}{6}\right) e(89)e\left(\frac{8}{9}\right) e(1112)e\left(\frac{11}{12}\right) e(79)e\left(\frac{7}{9}\right) e(1118)e\left(\frac{11}{18}\right) e(1136)e\left(\frac{11}{36}\right)
χ8325(2107,⋅)\chi_{8325}(2107,\cdot) 11 11 e(79)e\left(\frac{7}{9}\right) e(59)e\left(\frac{5}{9}\right) e(536)e\left(\frac{5}{36}\right) e(13)e\left(\frac{1}{3}\right) e(56)e\left(\frac{5}{6}\right) e(59)e\left(\frac{5}{9}\right) e(1112)e\left(\frac{11}{12}\right) e(19)e\left(\frac{1}{9}\right) e(1718)e\left(\frac{17}{18}\right) e(3536)e\left(\frac{35}{36}\right)
χ8325(3232,⋅)\chi_{8325}(3232,\cdot) 11 11 e(59)e\left(\frac{5}{9}\right) e(19)e\left(\frac{1}{9}\right) e(136)e\left(\frac{1}{36}\right) e(23)e\left(\frac{2}{3}\right) e(16)e\left(\frac{1}{6}\right) e(19)e\left(\frac{1}{9}\right) e(712)e\left(\frac{7}{12}\right) e(29)e\left(\frac{2}{9}\right) e(718)e\left(\frac{7}{18}\right) e(736)e\left(\frac{7}{36}\right)
χ8325(3493,⋅)\chi_{8325}(3493,\cdot) 11 11 e(19)e\left(\frac{1}{9}\right) e(29)e\left(\frac{2}{9}\right) e(1136)e\left(\frac{11}{36}\right) e(13)e\left(\frac{1}{3}\right) e(56)e\left(\frac{5}{6}\right) e(29)e\left(\frac{2}{9}\right) e(512)e\left(\frac{5}{12}\right) e(49)e\left(\frac{4}{9}\right) e(518)e\left(\frac{5}{18}\right) e(536)e\left(\frac{5}{36}\right)
χ8325(3682,⋅)\chi_{8325}(3682,\cdot) 11 11 e(29)e\left(\frac{2}{9}\right) e(49)e\left(\frac{4}{9}\right) e(1336)e\left(\frac{13}{36}\right) e(23)e\left(\frac{2}{3}\right) e(16)e\left(\frac{1}{6}\right) e(49)e\left(\frac{4}{9}\right) e(712)e\left(\frac{7}{12}\right) e(89)e\left(\frac{8}{9}\right) e(118)e\left(\frac{1}{18}\right) e(1936)e\left(\frac{19}{36}\right)
χ8325(3718,⋅)\chi_{8325}(3718,\cdot) 11 11 e(29)e\left(\frac{2}{9}\right) e(49)e\left(\frac{4}{9}\right) e(3136)e\left(\frac{31}{36}\right) e(23)e\left(\frac{2}{3}\right) e(16)e\left(\frac{1}{6}\right) e(49)e\left(\frac{4}{9}\right) e(112)e\left(\frac{1}{12}\right) e(89)e\left(\frac{8}{9}\right) e(118)e\left(\frac{1}{18}\right) e(136)e\left(\frac{1}{36}\right)
χ8325(3907,⋅)\chi_{8325}(3907,\cdot) 11 11 e(19)e\left(\frac{1}{9}\right) e(29)e\left(\frac{2}{9}\right) e(2936)e\left(\frac{29}{36}\right) e(13)e\left(\frac{1}{3}\right) e(56)e\left(\frac{5}{6}\right) e(29)e\left(\frac{2}{9}\right) e(1112)e\left(\frac{11}{12}\right) e(49)e\left(\frac{4}{9}\right) e(518)e\left(\frac{5}{18}\right) e(2336)e\left(\frac{23}{36}\right)
χ8325(4168,⋅)\chi_{8325}(4168,\cdot) 11 11 e(59)e\left(\frac{5}{9}\right) e(19)e\left(\frac{1}{9}\right) e(1936)e\left(\frac{19}{36}\right) e(23)e\left(\frac{2}{3}\right) e(16)e\left(\frac{1}{6}\right) e(19)e\left(\frac{1}{9}\right) e(112)e\left(\frac{1}{12}\right) e(29)e\left(\frac{2}{9}\right) e(718)e\left(\frac{7}{18}\right) e(2536)e\left(\frac{25}{36}\right)
χ8325(5293,⋅)\chi_{8325}(5293,\cdot) 11 11 e(79)e\left(\frac{7}{9}\right) e(59)e\left(\frac{5}{9}\right) e(2336)e\left(\frac{23}{36}\right) e(13)e\left(\frac{1}{3}\right) e(56)e\left(\frac{5}{6}\right) e(59)e\left(\frac{5}{9}\right) e(512)e\left(\frac{5}{12}\right) e(19)e\left(\frac{1}{9}\right) e(1718)e\left(\frac{17}{18}\right) e(1736)e\left(\frac{17}{36}\right)
χ8325(6643,⋅)\chi_{8325}(6643,\cdot) 11 11 e(49)e\left(\frac{4}{9}\right) e(89)e\left(\frac{8}{9}\right) e(3536)e\left(\frac{35}{36}\right) e(13)e\left(\frac{1}{3}\right) e(56)e\left(\frac{5}{6}\right) e(89)e\left(\frac{8}{9}\right) e(512)e\left(\frac{5}{12}\right) e(79)e\left(\frac{7}{9}\right) e(1118)e\left(\frac{11}{18}\right) e(2936)e\left(\frac{29}{36}\right)
χ8325(7543,⋅)\chi_{8325}(7543,\cdot) 11 11 e(89)e\left(\frac{8}{9}\right) e(79)e\left(\frac{7}{9}\right) e(736)e\left(\frac{7}{36}\right) e(23)e\left(\frac{2}{3}\right) e(16)e\left(\frac{1}{6}\right) e(79)e\left(\frac{7}{9}\right) e(112)e\left(\frac{1}{12}\right) e(59)e\left(\frac{5}{9}\right) e(1318)e\left(\frac{13}{18}\right) e(1336)e\left(\frac{13}{36}\right)
χ8325(8182,⋅)\chi_{8325}(8182,\cdot) 11 11 e(89)e\left(\frac{8}{9}\right) e(79)e\left(\frac{7}{9}\right) e(2536)e\left(\frac{25}{36}\right) e(23)e\left(\frac{2}{3}\right) e(16)e\left(\frac{1}{6}\right) e(79)e\left(\frac{7}{9}\right) e(712)e\left(\frac{7}{12}\right) e(59)e\left(\frac{5}{9}\right) e(1318)e\left(\frac{13}{18}\right) e(3136)e\left(\frac{31}{36}\right)