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Properties

Label 8325.gl
Modulus 83258325
Conductor 925925
Order 3030
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(30))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,9,5]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(64,8325))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 83258325
Conductor: 925925
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 3030
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 925.bl
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(ζ15)\Q(\zeta_{15})
Fixed field: 30.30.712054643298888889330514089285546802246873454578235396184027194976806640625.1

Characters in Galois orbit

Character −1-1 11 22 44 77 88 1111 1313 1414 1616 1717 1919
χ8325(64,⋅)\chi_{8325}(64,\cdot) 11 11 e(715)e\left(\frac{7}{15}\right) e(1415)e\left(\frac{14}{15}\right) e(56)e\left(\frac{5}{6}\right) e(25)e\left(\frac{2}{5}\right) e(45)e\left(\frac{4}{5}\right) e(815)e\left(\frac{8}{15}\right) e(310)e\left(\frac{3}{10}\right) e(1315)e\left(\frac{13}{15}\right) e(115)e\left(\frac{1}{15}\right) e(730)e\left(\frac{7}{30}\right)
χ8325(1639,⋅)\chi_{8325}(1639,\cdot) 11 11 e(215)e\left(\frac{2}{15}\right) e(415)e\left(\frac{4}{15}\right) e(16)e\left(\frac{1}{6}\right) e(25)e\left(\frac{2}{5}\right) e(45)e\left(\frac{4}{5}\right) e(1315)e\left(\frac{13}{15}\right) e(310)e\left(\frac{3}{10}\right) e(815)e\left(\frac{8}{15}\right) e(1115)e\left(\frac{11}{15}\right) e(1730)e\left(\frac{17}{30}\right)
χ8325(1729,⋅)\chi_{8325}(1729,\cdot) 11 11 e(415)e\left(\frac{4}{15}\right) e(815)e\left(\frac{8}{15}\right) e(56)e\left(\frac{5}{6}\right) e(45)e\left(\frac{4}{5}\right) e(35)e\left(\frac{3}{5}\right) e(1115)e\left(\frac{11}{15}\right) e(110)e\left(\frac{1}{10}\right) e(115)e\left(\frac{1}{15}\right) e(715)e\left(\frac{7}{15}\right) e(1930)e\left(\frac{19}{30}\right)
χ8325(3304,⋅)\chi_{8325}(3304,\cdot) 11 11 e(1415)e\left(\frac{14}{15}\right) e(1315)e\left(\frac{13}{15}\right) e(16)e\left(\frac{1}{6}\right) e(45)e\left(\frac{4}{5}\right) e(35)e\left(\frac{3}{5}\right) e(115)e\left(\frac{1}{15}\right) e(110)e\left(\frac{1}{10}\right) e(1115)e\left(\frac{11}{15}\right) e(215)e\left(\frac{2}{15}\right) e(2930)e\left(\frac{29}{30}\right)
χ8325(3394,⋅)\chi_{8325}(3394,\cdot) 11 11 e(115)e\left(\frac{1}{15}\right) e(215)e\left(\frac{2}{15}\right) e(56)e\left(\frac{5}{6}\right) e(15)e\left(\frac{1}{5}\right) e(25)e\left(\frac{2}{5}\right) e(1415)e\left(\frac{14}{15}\right) e(910)e\left(\frac{9}{10}\right) e(415)e\left(\frac{4}{15}\right) e(1315)e\left(\frac{13}{15}\right) e(130)e\left(\frac{1}{30}\right)
χ8325(4969,⋅)\chi_{8325}(4969,\cdot) 11 11 e(1115)e\left(\frac{11}{15}\right) e(715)e\left(\frac{7}{15}\right) e(16)e\left(\frac{1}{6}\right) e(15)e\left(\frac{1}{5}\right) e(25)e\left(\frac{2}{5}\right) e(415)e\left(\frac{4}{15}\right) e(910)e\left(\frac{9}{10}\right) e(1415)e\left(\frac{14}{15}\right) e(815)e\left(\frac{8}{15}\right) e(1130)e\left(\frac{11}{30}\right)
χ8325(5059,⋅)\chi_{8325}(5059,\cdot) 11 11 e(1315)e\left(\frac{13}{15}\right) e(1115)e\left(\frac{11}{15}\right) e(56)e\left(\frac{5}{6}\right) e(35)e\left(\frac{3}{5}\right) e(15)e\left(\frac{1}{5}\right) e(215)e\left(\frac{2}{15}\right) e(710)e\left(\frac{7}{10}\right) e(715)e\left(\frac{7}{15}\right) e(415)e\left(\frac{4}{15}\right) e(1330)e\left(\frac{13}{30}\right)
χ8325(6634,⋅)\chi_{8325}(6634,\cdot) 11 11 e(815)e\left(\frac{8}{15}\right) e(115)e\left(\frac{1}{15}\right) e(16)e\left(\frac{1}{6}\right) e(35)e\left(\frac{3}{5}\right) e(15)e\left(\frac{1}{5}\right) e(715)e\left(\frac{7}{15}\right) e(710)e\left(\frac{7}{10}\right) e(215)e\left(\frac{2}{15}\right) e(1415)e\left(\frac{14}{15}\right) e(2330)e\left(\frac{23}{30}\right)