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Properties

Label 2128.gt
Modulus 21282128
Conductor 21282128
Order 3636
Real no
Primitive yes
Minimal yes
Parity even

Related objects

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2128, base_ring=CyclotomicField(36))
 
M = H._module
 
chi = DirichletCharacter(H, M([18,27,24,34]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(67,2128))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 21282128
Conductor: 21282128
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 3636
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
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: Number field defined by a degree 36 polynomial

Characters in Galois orbit

Character −1-1 11 33 55 99 1111 1313 1515 1717 2323 2525 2727
χ2128(67,⋅)\chi_{2128}(67,\cdot) 11 11 e(2536)e\left(\frac{25}{36}\right) e(736)e\left(\frac{7}{36}\right) e(718)e\left(\frac{7}{18}\right) ii e(3536)e\left(\frac{35}{36}\right) e(89)e\left(\frac{8}{9}\right) e(19)e\left(\frac{1}{9}\right) e(29)e\left(\frac{2}{9}\right) e(718)e\left(\frac{7}{18}\right) e(112)e\left(\frac{1}{12}\right)
χ2128(611,⋅)\chi_{2128}(611,\cdot) 11 11 e(1736)e\left(\frac{17}{36}\right) e(3536)e\left(\frac{35}{36}\right) e(1718)e\left(\frac{17}{18}\right) ii e(3136)e\left(\frac{31}{36}\right) e(49)e\left(\frac{4}{9}\right) e(59)e\left(\frac{5}{9}\right) e(19)e\left(\frac{1}{9}\right) e(1718)e\left(\frac{17}{18}\right) e(512)e\left(\frac{5}{12}\right)
χ2128(667,⋅)\chi_{2128}(667,\cdot) 11 11 e(1136)e\left(\frac{11}{36}\right) e(2936)e\left(\frac{29}{36}\right) e(1118)e\left(\frac{11}{18}\right) −i-i e(136)e\left(\frac{1}{36}\right) e(19)e\left(\frac{1}{9}\right) e(89)e\left(\frac{8}{9}\right) e(79)e\left(\frac{7}{9}\right) e(1118)e\left(\frac{11}{18}\right) e(1112)e\left(\frac{11}{12}\right)
χ2128(851,⋅)\chi_{2128}(851,\cdot) 11 11 e(1336)e\left(\frac{13}{36}\right) e(3136)e\left(\frac{31}{36}\right) e(1318)e\left(\frac{13}{18}\right) ii e(1136)e\left(\frac{11}{36}\right) e(29)e\left(\frac{2}{9}\right) e(79)e\left(\frac{7}{9}\right) e(59)e\left(\frac{5}{9}\right) e(1318)e\left(\frac{13}{18}\right) e(112)e\left(\frac{1}{12}\right)
χ2128(963,⋅)\chi_{2128}(963,\cdot) 11 11 e(136)e\left(\frac{1}{36}\right) e(1936)e\left(\frac{19}{36}\right) e(118)e\left(\frac{1}{18}\right) ii e(2336)e\left(\frac{23}{36}\right) e(59)e\left(\frac{5}{9}\right) e(49)e\left(\frac{4}{9}\right) e(89)e\left(\frac{8}{9}\right) e(118)e\left(\frac{1}{18}\right) e(112)e\left(\frac{1}{12}\right)
χ2128(1059,⋅)\chi_{2128}(1059,\cdot) 11 11 e(536)e\left(\frac{5}{36}\right) e(2336)e\left(\frac{23}{36}\right) e(518)e\left(\frac{5}{18}\right) ii e(736)e\left(\frac{7}{36}\right) e(79)e\left(\frac{7}{9}\right) e(29)e\left(\frac{2}{9}\right) e(49)e\left(\frac{4}{9}\right) e(518)e\left(\frac{5}{18}\right) e(512)e\left(\frac{5}{12}\right)
χ2128(1131,⋅)\chi_{2128}(1131,\cdot) 11 11 e(736)e\left(\frac{7}{36}\right) e(2536)e\left(\frac{25}{36}\right) e(718)e\left(\frac{7}{18}\right) −i-i e(1736)e\left(\frac{17}{36}\right) e(89)e\left(\frac{8}{9}\right) e(19)e\left(\frac{1}{9}\right) e(29)e\left(\frac{2}{9}\right) e(718)e\left(\frac{7}{18}\right) e(712)e\left(\frac{7}{12}\right)
χ2128(1675,⋅)\chi_{2128}(1675,\cdot) 11 11 e(3536)e\left(\frac{35}{36}\right) e(1736)e\left(\frac{17}{36}\right) e(1718)e\left(\frac{17}{18}\right) −i-i e(1336)e\left(\frac{13}{36}\right) e(49)e\left(\frac{4}{9}\right) e(59)e\left(\frac{5}{9}\right) e(19)e\left(\frac{1}{9}\right) e(1718)e\left(\frac{17}{18}\right) e(1112)e\left(\frac{11}{12}\right)
χ2128(1731,⋅)\chi_{2128}(1731,\cdot) 11 11 e(2936)e\left(\frac{29}{36}\right) e(1136)e\left(\frac{11}{36}\right) e(1118)e\left(\frac{11}{18}\right) ii e(1936)e\left(\frac{19}{36}\right) e(19)e\left(\frac{1}{9}\right) e(89)e\left(\frac{8}{9}\right) e(79)e\left(\frac{7}{9}\right) e(1118)e\left(\frac{11}{18}\right) e(512)e\left(\frac{5}{12}\right)
χ2128(1915,⋅)\chi_{2128}(1915,\cdot) 11 11 e(3136)e\left(\frac{31}{36}\right) e(1336)e\left(\frac{13}{36}\right) e(1318)e\left(\frac{13}{18}\right) −i-i e(2936)e\left(\frac{29}{36}\right) e(29)e\left(\frac{2}{9}\right) e(79)e\left(\frac{7}{9}\right) e(59)e\left(\frac{5}{9}\right) e(1318)e\left(\frac{13}{18}\right) e(712)e\left(\frac{7}{12}\right)
χ2128(2027,⋅)\chi_{2128}(2027,\cdot) 11 11 e(1936)e\left(\frac{19}{36}\right) e(136)e\left(\frac{1}{36}\right) e(118)e\left(\frac{1}{18}\right) −i-i e(536)e\left(\frac{5}{36}\right) e(59)e\left(\frac{5}{9}\right) e(49)e\left(\frac{4}{9}\right) e(89)e\left(\frac{8}{9}\right) e(118)e\left(\frac{1}{18}\right) e(712)e\left(\frac{7}{12}\right)
χ2128(2123,⋅)\chi_{2128}(2123,\cdot) 11 11 e(2336)e\left(\frac{23}{36}\right) e(536)e\left(\frac{5}{36}\right) e(518)e\left(\frac{5}{18}\right) −i-i e(2536)e\left(\frac{25}{36}\right) e(79)e\left(\frac{7}{9}\right) e(29)e\left(\frac{2}{9}\right) e(49)e\left(\frac{4}{9}\right) e(518)e\left(\frac{5}{18}\right) e(1112)e\left(\frac{11}{12}\right)