Properties

Conductor 2000
Order 100
Real No
Primitive No
Parity Odd
Orbit Label 4000.cx

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[39]
pari: [g,chi] = znchar(Mod(39,4000))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 2000
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 = Odd
Orbit label = 4000.cx
Orbit index = 76

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 ]

\(\chi_{4000}(39,\cdot)\) \(\chi_{4000}(119,\cdot)\) \(\chi_{4000}(279,\cdot)\) \(\chi_{4000}(359,\cdot)\) \(\chi_{4000}(439,\cdot)\) \(\chi_{4000}(519,\cdot)\) \(\chi_{4000}(679,\cdot)\) \(\chi_{4000}(759,\cdot)\) \(\chi_{4000}(839,\cdot)\) \(\chi_{4000}(919,\cdot)\) \(\chi_{4000}(1079,\cdot)\) \(\chi_{4000}(1159,\cdot)\) \(\chi_{4000}(1239,\cdot)\) \(\chi_{4000}(1319,\cdot)\) \(\chi_{4000}(1479,\cdot)\) \(\chi_{4000}(1559,\cdot)\) \(\chi_{4000}(1639,\cdot)\) \(\chi_{4000}(1719,\cdot)\) \(\chi_{4000}(1879,\cdot)\) \(\chi_{4000}(1959,\cdot)\) \(\chi_{4000}(2039,\cdot)\) \(\chi_{4000}(2119,\cdot)\) \(\chi_{4000}(2279,\cdot)\) \(\chi_{4000}(2359,\cdot)\) \(\chi_{4000}(2439,\cdot)\) \(\chi_{4000}(2519,\cdot)\) \(\chi_{4000}(2679,\cdot)\) \(\chi_{4000}(2759,\cdot)\) \(\chi_{4000}(2839,\cdot)\) \(\chi_{4000}(2919,\cdot)\) ...

Inducing primitive character

\(\chi_{2000}(539,\cdot)\)

Values on generators

\((2751,2501,1377)\) → \((-1,i,e\left(\frac{23}{50}\right))\)

Values

-1137911131719212327
\(-1\)\(1\)\(e\left(\frac{47}{100}\right)\)\(e\left(\frac{1}{10}\right)\)\(e\left(\frac{47}{50}\right)\)\(e\left(\frac{71}{100}\right)\)\(e\left(\frac{69}{100}\right)\)\(e\left(\frac{29}{50}\right)\)\(e\left(\frac{53}{100}\right)\)\(e\left(\frac{57}{100}\right)\)\(e\left(\frac{13}{50}\right)\)\(e\left(\frac{41}{100}\right)\)
value at  e.g. 2

Related number fields

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