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Properties

Label 28900.bv
Modulus 2890028900
Conductor 17001700
Order 2020
Real no
Primitive no
Minimal no
Parity even

Related objects

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(28900, base_ring=CyclotomicField(20))
 
M = H._module
 
chi = DirichletCharacter(H, M([10,13,10]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(3467,28900))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 2890028900
Conductor: 17001700
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 2020
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 1700.bu
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

Field of values: Q(ζ20)\Q(\zeta_{20})
Fixed field: 20.20.6152325135647583007812500000000000000000000.1

Characters in Galois orbit

Character −1-1 11 33 77 99 1111 1313 1919 2121 2323 2727 2929
χ28900(3467,⋅)\chi_{28900}(3467,\cdot) 11 11 e(1120)e\left(\frac{11}{20}\right) ii e(110)e\left(\frac{1}{10}\right) e(25)e\left(\frac{2}{5}\right) e(720)e\left(\frac{7}{20}\right) e(15)e\left(\frac{1}{5}\right) e(45)e\left(\frac{4}{5}\right) e(320)e\left(\frac{3}{20}\right) e(1320)e\left(\frac{13}{20}\right) e(45)e\left(\frac{4}{5}\right)
χ28900(4623,⋅)\chi_{28900}(4623,\cdot) 11 11 e(1720)e\left(\frac{17}{20}\right) −i-i e(710)e\left(\frac{7}{10}\right) e(45)e\left(\frac{4}{5}\right) e(920)e\left(\frac{9}{20}\right) e(25)e\left(\frac{2}{5}\right) e(35)e\left(\frac{3}{5}\right) e(120)e\left(\frac{1}{20}\right) e(1120)e\left(\frac{11}{20}\right) e(35)e\left(\frac{3}{5}\right)
χ28900(9247,⋅)\chi_{28900}(9247,\cdot) 11 11 e(1920)e\left(\frac{19}{20}\right) ii e(910)e\left(\frac{9}{10}\right) e(35)e\left(\frac{3}{5}\right) e(320)e\left(\frac{3}{20}\right) e(45)e\left(\frac{4}{5}\right) e(15)e\left(\frac{1}{5}\right) e(720)e\left(\frac{7}{20}\right) e(1720)e\left(\frac{17}{20}\right) e(15)e\left(\frac{1}{5}\right)
χ28900(10403,⋅)\chi_{28900}(10403,\cdot) 11 11 e(920)e\left(\frac{9}{20}\right) −i-i e(910)e\left(\frac{9}{10}\right) e(35)e\left(\frac{3}{5}\right) e(1320)e\left(\frac{13}{20}\right) e(45)e\left(\frac{4}{5}\right) e(15)e\left(\frac{1}{5}\right) e(1720)e\left(\frac{17}{20}\right) e(720)e\left(\frac{7}{20}\right) e(15)e\left(\frac{1}{5}\right)
χ28900(15027,⋅)\chi_{28900}(15027,\cdot) 11 11 e(720)e\left(\frac{7}{20}\right) ii e(710)e\left(\frac{7}{10}\right) e(45)e\left(\frac{4}{5}\right) e(1920)e\left(\frac{19}{20}\right) e(25)e\left(\frac{2}{5}\right) e(35)e\left(\frac{3}{5}\right) e(1120)e\left(\frac{11}{20}\right) e(120)e\left(\frac{1}{20}\right) e(35)e\left(\frac{3}{5}\right)
χ28900(16183,⋅)\chi_{28900}(16183,\cdot) 11 11 e(120)e\left(\frac{1}{20}\right) −i-i e(110)e\left(\frac{1}{10}\right) e(25)e\left(\frac{2}{5}\right) e(1720)e\left(\frac{17}{20}\right) e(15)e\left(\frac{1}{5}\right) e(45)e\left(\frac{4}{5}\right) e(1320)e\left(\frac{13}{20}\right) e(320)e\left(\frac{3}{20}\right) e(45)e\left(\frac{4}{5}\right)
χ28900(21963,⋅)\chi_{28900}(21963,\cdot) 11 11 e(1320)e\left(\frac{13}{20}\right) −i-i e(310)e\left(\frac{3}{10}\right) e(15)e\left(\frac{1}{5}\right) e(120)e\left(\frac{1}{20}\right) e(35)e\left(\frac{3}{5}\right) e(25)e\left(\frac{2}{5}\right) e(920)e\left(\frac{9}{20}\right) e(1920)e\left(\frac{19}{20}\right) e(25)e\left(\frac{2}{5}\right)
χ28900(26587,⋅)\chi_{28900}(26587,\cdot) 11 11 e(320)e\left(\frac{3}{20}\right) ii e(310)e\left(\frac{3}{10}\right) e(15)e\left(\frac{1}{5}\right) e(1120)e\left(\frac{11}{20}\right) e(35)e\left(\frac{3}{5}\right) e(25)e\left(\frac{2}{5}\right) e(1920)e\left(\frac{19}{20}\right) e(920)e\left(\frac{9}{20}\right) e(25)e\left(\frac{2}{5}\right)