Properties

Modulus 4000
Conductor 125
Order 100
Real no
Primitive no
Minimal yes
Parity odd
Orbit label 4000.cq

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(4000)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,0,83]))
 
pari: [g,chi] = znchar(Mod(33,4000))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Modulus = 4000
Conductor = 125
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 100
Real = no
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = no
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = odd
Orbit label = 4000.cq
Orbit index = 69

Galois orbit

sage: chi.galois_orbit()
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

\(\chi_{4000}(33,\cdot)\) \(\chi_{4000}(97,\cdot)\) \(\chi_{4000}(353,\cdot)\) \(\chi_{4000}(417,\cdot)\) \(\chi_{4000}(513,\cdot)\) \(\chi_{4000}(577,\cdot)\) \(\chi_{4000}(673,\cdot)\) \(\chi_{4000}(737,\cdot)\) \(\chi_{4000}(833,\cdot)\) \(\chi_{4000}(897,\cdot)\) \(\chi_{4000}(1153,\cdot)\) \(\chi_{4000}(1217,\cdot)\) \(\chi_{4000}(1313,\cdot)\) \(\chi_{4000}(1377,\cdot)\) \(\chi_{4000}(1473,\cdot)\) \(\chi_{4000}(1537,\cdot)\) \(\chi_{4000}(1633,\cdot)\) \(\chi_{4000}(1697,\cdot)\) \(\chi_{4000}(1953,\cdot)\) \(\chi_{4000}(2017,\cdot)\) \(\chi_{4000}(2113,\cdot)\) \(\chi_{4000}(2177,\cdot)\) \(\chi_{4000}(2273,\cdot)\) \(\chi_{4000}(2337,\cdot)\) \(\chi_{4000}(2433,\cdot)\) \(\chi_{4000}(2497,\cdot)\) \(\chi_{4000}(2753,\cdot)\) \(\chi_{4000}(2817,\cdot)\) \(\chi_{4000}(2913,\cdot)\) \(\chi_{4000}(2977,\cdot)\) ...

Values on generators

\((2751,2501,1377)\) → \((1,1,e\left(\frac{83}{100}\right))\)

Values

-1137911131719212327
\(-1\)\(1\)\(e\left(\frac{81}{100}\right)\)\(e\left(\frac{11}{20}\right)\)\(e\left(\frac{31}{50}\right)\)\(e\left(\frac{2}{25}\right)\)\(e\left(\frac{37}{100}\right)\)\(e\left(\frac{59}{100}\right)\)\(e\left(\frac{47}{50}\right)\)\(e\left(\frac{9}{25}\right)\)\(e\left(\frac{73}{100}\right)\)\(e\left(\frac{43}{100}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{100})\)