Properties

Label 6000.cw
Modulus 60006000
Conductor 7575
Order 2020
Real no
Primitive no
Minimal no
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6000, base_ring=CyclotomicField(20))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,0,10,17]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(257,6000))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 60006000
Conductor: 7575
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 2020
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 75.l
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: Q(ζ75)+\Q(\zeta_{75})^+

Characters in Galois orbit

Character 1-1 11 77 1111 1313 1717 1919 2323 2929 3131 3737 4141
χ6000(257,)\chi_{6000}(257,\cdot) 11 11 ii e(110)e\left(\frac{1}{10}\right) e(320)e\left(\frac{3}{20}\right) e(1120)e\left(\frac{11}{20}\right) e(310)e\left(\frac{3}{10}\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(910)e\left(\frac{9}{10}\right)
χ6000(593,)\chi_{6000}(593,\cdot) 11 11 i-i e(310)e\left(\frac{3}{10}\right) e(920)e\left(\frac{9}{20}\right) e(1320)e\left(\frac{13}{20}\right) e(910)e\left(\frac{9}{10}\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(710)e\left(\frac{7}{10}\right)
χ6000(1457,)\chi_{6000}(1457,\cdot) 11 11 ii e(710)e\left(\frac{7}{10}\right) e(1120)e\left(\frac{11}{20}\right) e(720)e\left(\frac{7}{20}\right) e(110)e\left(\frac{1}{10}\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(310)e\left(\frac{3}{10}\right)
χ6000(1793,)\chi_{6000}(1793,\cdot) 11 11 i-i e(710)e\left(\frac{7}{10}\right) e(120)e\left(\frac{1}{20}\right) e(1720)e\left(\frac{17}{20}\right) e(110)e\left(\frac{1}{10}\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(310)e\left(\frac{3}{10}\right)
χ6000(2657,)\chi_{6000}(2657,\cdot) 11 11 ii e(310)e\left(\frac{3}{10}\right) e(1920)e\left(\frac{19}{20}\right) e(320)e\left(\frac{3}{20}\right) e(910)e\left(\frac{9}{10}\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(710)e\left(\frac{7}{10}\right)
χ6000(2993,)\chi_{6000}(2993,\cdot) 11 11 i-i e(110)e\left(\frac{1}{10}\right) e(1320)e\left(\frac{13}{20}\right) e(120)e\left(\frac{1}{20}\right) e(310)e\left(\frac{3}{10}\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(910)e\left(\frac{9}{10}\right)
χ6000(3857,)\chi_{6000}(3857,\cdot) 11 11 ii e(910)e\left(\frac{9}{10}\right) e(720)e\left(\frac{7}{20}\right) e(1920)e\left(\frac{19}{20}\right) e(710)e\left(\frac{7}{10}\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(110)e\left(\frac{1}{10}\right)
χ6000(5393,)\chi_{6000}(5393,\cdot) 11 11 i-i e(910)e\left(\frac{9}{10}\right) e(1720)e\left(\frac{17}{20}\right) e(920)e\left(\frac{9}{20}\right) e(710)e\left(\frac{7}{10}\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(110)e\left(\frac{1}{10}\right)