Properties

Conductor 4001
Order 40
Real No
Primitive No
Parity Even
Orbit Label 8002.k

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[673]
pari: [g,chi] = znchar(Mod(673,8002))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 4001
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 = Even
Orbit label = 8002.k
Orbit index = 11

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 ]

\(\chi_{8002}(673,\cdot)\) \(\chi_{8002}(1031,\cdot)\) \(\chi_{8002}(1119,\cdot)\) \(\chi_{8002}(1363,\cdot)\) \(\chi_{8002}(1955,\cdot)\) \(\chi_{8002}(2271,\cdot)\) \(\chi_{8002}(2895,\cdot)\) \(\chi_{8002}(3125,\cdot)\) \(\chi_{8002}(4877,\cdot)\) \(\chi_{8002}(5107,\cdot)\) \(\chi_{8002}(5731,\cdot)\) \(\chi_{8002}(6047,\cdot)\) \(\chi_{8002}(6639,\cdot)\) \(\chi_{8002}(6883,\cdot)\) \(\chi_{8002}(6971,\cdot)\) \(\chi_{8002}(7329,\cdot)\)

Inducing primitive character

\(\chi_{4001}(673,\cdot)\)

Values on generators

\(3\) → \(e\left(\frac{9}{40}\right)\)

Values

-113579111315171921
\(1\)\(1\)\(e\left(\frac{9}{40}\right)\)\(-1\)\(e\left(\frac{3}{10}\right)\)\(e\left(\frac{9}{20}\right)\)\(e\left(\frac{5}{8}\right)\)\(e\left(\frac{9}{10}\right)\)\(e\left(\frac{29}{40}\right)\)\(e\left(\frac{39}{40}\right)\)\(e\left(\frac{9}{10}\right)\)\(e\left(\frac{21}{40}\right)\)
value at  e.g. 2

Related number fields

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