Properties

Conductor 4000
Order 200
Real No
Primitive Yes
Parity Odd
Orbit Label 4000.db

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(4000)
sage: chi = H[11]
pari: [g,chi] = znchar(Mod(11,4000))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 4000
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Order = 200
Real = No
sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
Primitive = Yes
sage: chi.is_odd()
pari: zncharisodd(g,chi)
Parity = Odd
Orbit label = 4000.db
Orbit index = 80

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 ]

\(\chi_{4000}(11,\cdot)\) \(\chi_{4000}(91,\cdot)\) \(\chi_{4000}(131,\cdot)\) \(\chi_{4000}(171,\cdot)\) \(\chi_{4000}(211,\cdot)\) \(\chi_{4000}(291,\cdot)\) \(\chi_{4000}(331,\cdot)\) \(\chi_{4000}(371,\cdot)\) \(\chi_{4000}(411,\cdot)\) \(\chi_{4000}(491,\cdot)\) \(\chi_{4000}(531,\cdot)\) \(\chi_{4000}(571,\cdot)\) \(\chi_{4000}(611,\cdot)\) \(\chi_{4000}(691,\cdot)\) \(\chi_{4000}(731,\cdot)\) \(\chi_{4000}(771,\cdot)\) \(\chi_{4000}(811,\cdot)\) \(\chi_{4000}(891,\cdot)\) \(\chi_{4000}(931,\cdot)\) \(\chi_{4000}(971,\cdot)\) \(\chi_{4000}(1011,\cdot)\) \(\chi_{4000}(1091,\cdot)\) \(\chi_{4000}(1131,\cdot)\) \(\chi_{4000}(1171,\cdot)\) \(\chi_{4000}(1211,\cdot)\) \(\chi_{4000}(1291,\cdot)\) \(\chi_{4000}(1331,\cdot)\) \(\chi_{4000}(1371,\cdot)\) \(\chi_{4000}(1411,\cdot)\) \(\chi_{4000}(1491,\cdot)\) ...

Values on generators

\((2751,2501,1377)\) → \((-1,e\left(\frac{5}{8}\right),e\left(\frac{19}{25}\right))\)

Values

-1137911131719212327
\(-1\)\(1\)\(e\left(\frac{139}{200}\right)\)\(e\left(\frac{7}{20}\right)\)\(e\left(\frac{39}{100}\right)\)\(e\left(\frac{77}{200}\right)\)\(e\left(\frac{3}{200}\right)\)\(e\left(\frac{49}{50}\right)\)\(e\left(\frac{111}{200}\right)\)\(e\left(\frac{9}{200}\right)\)\(e\left(\frac{81}{100}\right)\)\(e\left(\frac{17}{200}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{200})\)