Properties

Conductor 800
Order 40
Real No
Primitive No
Parity Odd
Orbit Label 4000.ca

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[99]
pari: [g,chi] = znchar(Mod(99,4000))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 800
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Order = 40
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.ca
Orbit index = 53

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 ]

\(\chi_{4000}(99,\cdot)\) \(\chi_{4000}(299,\cdot)\) \(\chi_{4000}(699,\cdot)\) \(\chi_{4000}(899,\cdot)\) \(\chi_{4000}(1099,\cdot)\) \(\chi_{4000}(1299,\cdot)\) \(\chi_{4000}(1699,\cdot)\) \(\chi_{4000}(1899,\cdot)\) \(\chi_{4000}(2099,\cdot)\) \(\chi_{4000}(2299,\cdot)\) \(\chi_{4000}(2699,\cdot)\) \(\chi_{4000}(2899,\cdot)\) \(\chi_{4000}(3099,\cdot)\) \(\chi_{4000}(3299,\cdot)\) \(\chi_{4000}(3699,\cdot)\) \(\chi_{4000}(3899,\cdot)\)

Inducing primitive character

\(\chi_{800}(419,\cdot)\)

Values on generators

\((2751,2501,1377)\) → \((-1,e\left(\frac{3}{8}\right),e\left(\frac{9}{10}\right))\)

Values

-1137911131719212327
\(-1\)\(1\)\(e\left(\frac{37}{40}\right)\)\(-i\)\(e\left(\frac{17}{20}\right)\)\(e\left(\frac{31}{40}\right)\)\(e\left(\frac{29}{40}\right)\)\(e\left(\frac{1}{5}\right)\)\(e\left(\frac{13}{40}\right)\)\(e\left(\frac{27}{40}\right)\)\(e\left(\frac{13}{20}\right)\)\(e\left(\frac{31}{40}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{40})\)