Properties

Conductor 4001
Order 100
Real No
Primitive No
Parity Even
Orbit Label 8002.n

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[25]
pari: [g,chi] = znchar(Mod(25,8002))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 4001
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
sage: chi.is_odd()
pari: zncharisodd(g,chi)
Parity = Even
Orbit label = 8002.n
Orbit index = 14

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 ]

\(\chi_{8002}(25,\cdot)\) \(\chi_{8002}(379,\cdot)\) \(\chi_{8002}(579,\cdot)\) \(\chi_{8002}(583,\cdot)\) \(\chi_{8002}(1735,\cdot)\) \(\chi_{8002}(1761,\cdot)\) \(\chi_{8002}(1773,\cdot)\) \(\chi_{8002}(1785,\cdot)\) \(\chi_{8002}(1873,\cdot)\) \(\chi_{8002}(2333,\cdot)\) \(\chi_{8002}(2545,\cdot)\) \(\chi_{8002}(2847,\cdot)\) \(\chi_{8002}(2977,\cdot)\) \(\chi_{8002}(3017,\cdot)\) \(\chi_{8002}(3347,\cdot)\) \(\chi_{8002}(3353,\cdot)\) \(\chi_{8002}(3651,\cdot)\) \(\chi_{8002}(3717,\cdot)\) \(\chi_{8002}(3841,\cdot)\) \(\chi_{8002}(3897,\cdot)\) \(\chi_{8002}(4105,\cdot)\) \(\chi_{8002}(4161,\cdot)\) \(\chi_{8002}(4285,\cdot)\) \(\chi_{8002}(4351,\cdot)\) \(\chi_{8002}(4649,\cdot)\) \(\chi_{8002}(4655,\cdot)\) \(\chi_{8002}(4985,\cdot)\) \(\chi_{8002}(5025,\cdot)\) \(\chi_{8002}(5155,\cdot)\) \(\chi_{8002}(5457,\cdot)\) ...

Inducing primitive character

\(\chi_{4001}(25,\cdot)\)

Values on generators

\(3\) → \(e\left(\frac{59}{100}\right)\)

Values

-113579111315171921
\(1\)\(1\)\(e\left(\frac{59}{100}\right)\)\(e\left(\frac{1}{5}\right)\)\(e\left(\frac{13}{25}\right)\)\(e\left(\frac{9}{50}\right)\)\(-i\)\(e\left(\frac{19}{25}\right)\)\(e\left(\frac{79}{100}\right)\)\(e\left(\frac{29}{100}\right)\)\(e\left(\frac{4}{25}\right)\)\(e\left(\frac{11}{100}\right)\)
value at  e.g. 2

Related number fields

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