Properties

Conductor 4001
Order 50
Real No
Primitive No
Parity Even
Orbit Label 8002.l

Related objects

Learn more about

Show commands for: SageMath / Pari/GP
sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
sage: H = DirichletGroup_conrey(8002)
sage: chi = H[625]
pari: [g,chi] = znchar(Mod(625,8002))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 4001
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Order = 50
Real = No
sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
Primitive = No
sage: chi.is_odd()
pari: zncharisodd(g,chi)
Parity = Even
Orbit label = 8002.l
Orbit index = 12

Galois orbit

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

\(\chi_{8002}(625,\cdot)\) \(\chi_{8002}(1429,\cdot)\) \(\chi_{8002}(1473,\cdot)\) \(\chi_{8002}(1529,\cdot)\) \(\chi_{8002}(3253,\cdot)\) \(\chi_{8002}(3407,\cdot)\) \(\chi_{8002}(3805,\cdot)\) \(\chi_{8002}(4015,\cdot)\) \(\chi_{8002}(4315,\cdot)\) \(\chi_{8002}(4347,\cdot)\) \(\chi_{8002}(4637,\cdot)\) \(\chi_{8002}(5595,\cdot)\) \(\chi_{8002}(6471,\cdot)\) \(\chi_{8002}(6745,\cdot)\) \(\chi_{8002}(6815,\cdot)\) \(\chi_{8002}(7159,\cdot)\) \(\chi_{8002}(7385,\cdot)\) \(\chi_{8002}(7607,\cdot)\) \(\chi_{8002}(7611,\cdot)\) \(\chi_{8002}(7801,\cdot)\)

Inducing primitive character

\(\chi_{4001}(625,\cdot)\)

Values on generators

\(3\) → \(e\left(\frac{9}{50}\right)\)

Values

-113579111315171921
\(1\)\(1\)\(e\left(\frac{9}{50}\right)\)\(e\left(\frac{2}{5}\right)\)\(e\left(\frac{1}{25}\right)\)\(e\left(\frac{9}{25}\right)\)\(-1\)\(e\left(\frac{13}{25}\right)\)\(e\left(\frac{29}{50}\right)\)\(e\left(\frac{29}{50}\right)\)\(e\left(\frac{8}{25}\right)\)\(e\left(\frac{11}{50}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{25})\)