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Properties

Label 2200.fm
Modulus 22002200
Conductor 200200
Order 2020
Real no
Primitive no
Minimal yes
Parity odd

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2200, base_ring=CyclotomicField(20)) M = H._module chi = DirichletCharacter(H, M([0,10,3,0])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(133,2200)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 22002200
Conductor: 200200
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: 2020
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from 200.x
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: odd
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Related number fields

Field of values: Q(ζ20)\Q(\zeta_{20})
Fixed field: 20.0.3125000000000000000000000000000000.1

Characters in Galois orbit

Character −1-1 11 33 77 99 1313 1717 1919 2121 2323 2727 2929
χ2200(133,⋅)\chi_{2200}(133,\cdot) −1-1 11 e(1120)e\left(\frac{11}{20}\right) −i-i e(110)e\left(\frac{1}{10}\right) e(720)e\left(\frac{7}{20}\right) e(1920)e\left(\frac{19}{20}\right) e(15)e\left(\frac{1}{5}\right) e(310)e\left(\frac{3}{10}\right) e(1320)e\left(\frac{13}{20}\right) e(1320)e\left(\frac{13}{20}\right) e(45)e\left(\frac{4}{5}\right)
χ2200(397,⋅)\chi_{2200}(397,\cdot) −1-1 11 e(920)e\left(\frac{9}{20}\right) ii e(910)e\left(\frac{9}{10}\right) e(1320)e\left(\frac{13}{20}\right) e(120)e\left(\frac{1}{20}\right) e(45)e\left(\frac{4}{5}\right) e(710)e\left(\frac{7}{10}\right) e(720)e\left(\frac{7}{20}\right) e(720)e\left(\frac{7}{20}\right) e(15)e\left(\frac{1}{5}\right)
χ2200(573,⋅)\chi_{2200}(573,\cdot) −1-1 11 e(720)e\left(\frac{7}{20}\right) −i-i e(710)e\left(\frac{7}{10}\right) e(1920)e\left(\frac{19}{20}\right) e(320)e\left(\frac{3}{20}\right) e(25)e\left(\frac{2}{5}\right) e(110)e\left(\frac{1}{10}\right) e(120)e\left(\frac{1}{20}\right) e(120)e\left(\frac{1}{20}\right) e(35)e\left(\frac{3}{5}\right)
χ2200(837,⋅)\chi_{2200}(837,\cdot) −1-1 11 e(1320)e\left(\frac{13}{20}\right) ii e(310)e\left(\frac{3}{10}\right) e(120)e\left(\frac{1}{20}\right) e(1720)e\left(\frac{17}{20}\right) e(35)e\left(\frac{3}{5}\right) e(910)e\left(\frac{9}{10}\right) e(1920)e\left(\frac{19}{20}\right) e(1920)e\left(\frac{19}{20}\right) e(25)e\left(\frac{2}{5}\right)
χ2200(1013,⋅)\chi_{2200}(1013,\cdot) −1-1 11 e(320)e\left(\frac{3}{20}\right) −i-i e(310)e\left(\frac{3}{10}\right) e(1120)e\left(\frac{11}{20}\right) e(720)e\left(\frac{7}{20}\right) e(35)e\left(\frac{3}{5}\right) e(910)e\left(\frac{9}{10}\right) e(920)e\left(\frac{9}{20}\right) e(920)e\left(\frac{9}{20}\right) e(25)e\left(\frac{2}{5}\right)
χ2200(1277,⋅)\chi_{2200}(1277,\cdot) −1-1 11 e(1720)e\left(\frac{17}{20}\right) ii e(710)e\left(\frac{7}{10}\right) e(920)e\left(\frac{9}{20}\right) e(1320)e\left(\frac{13}{20}\right) e(25)e\left(\frac{2}{5}\right) e(110)e\left(\frac{1}{10}\right) e(1120)e\left(\frac{11}{20}\right) e(1120)e\left(\frac{11}{20}\right) e(35)e\left(\frac{3}{5}\right)
χ2200(1453,⋅)\chi_{2200}(1453,\cdot) −1-1 11 e(1920)e\left(\frac{19}{20}\right) −i-i e(910)e\left(\frac{9}{10}\right) e(320)e\left(\frac{3}{20}\right) e(1120)e\left(\frac{11}{20}\right) e(45)e\left(\frac{4}{5}\right) e(710)e\left(\frac{7}{10}\right) e(1720)e\left(\frac{17}{20}\right) e(1720)e\left(\frac{17}{20}\right) e(15)e\left(\frac{1}{5}\right)
χ2200(1717,⋅)\chi_{2200}(1717,\cdot) −1-1 11 e(120)e\left(\frac{1}{20}\right) ii e(110)e\left(\frac{1}{10}\right) e(1720)e\left(\frac{17}{20}\right) e(920)e\left(\frac{9}{20}\right) e(15)e\left(\frac{1}{5}\right) e(310)e\left(\frac{3}{10}\right) e(320)e\left(\frac{3}{20}\right) e(320)e\left(\frac{3}{20}\right) e(45)e\left(\frac{4}{5}\right)