Properties

Conductor 1000
Order 100
Real No
Primitive No
Parity Odd
Orbit Label 4000.ct

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[1713]
pari: [g,chi] = znchar(Mod(1713,4000))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 1000
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.ct
Orbit index = 72

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 ]

\(\chi_{4000}(17,\cdot)\) \(\chi_{4000}(113,\cdot)\) \(\chi_{4000}(177,\cdot)\) \(\chi_{4000}(273,\cdot)\) \(\chi_{4000}(337,\cdot)\) \(\chi_{4000}(433,\cdot)\) \(\chi_{4000}(497,\cdot)\) \(\chi_{4000}(753,\cdot)\) \(\chi_{4000}(817,\cdot)\) \(\chi_{4000}(913,\cdot)\) \(\chi_{4000}(977,\cdot)\) \(\chi_{4000}(1073,\cdot)\) \(\chi_{4000}(1137,\cdot)\) \(\chi_{4000}(1233,\cdot)\) \(\chi_{4000}(1297,\cdot)\) \(\chi_{4000}(1553,\cdot)\) \(\chi_{4000}(1617,\cdot)\) \(\chi_{4000}(1713,\cdot)\) \(\chi_{4000}(1777,\cdot)\) \(\chi_{4000}(1873,\cdot)\) \(\chi_{4000}(1937,\cdot)\) \(\chi_{4000}(2033,\cdot)\) \(\chi_{4000}(2097,\cdot)\) \(\chi_{4000}(2353,\cdot)\) \(\chi_{4000}(2417,\cdot)\) \(\chi_{4000}(2513,\cdot)\) \(\chi_{4000}(2577,\cdot)\) \(\chi_{4000}(2673,\cdot)\) \(\chi_{4000}(2737,\cdot)\) \(\chi_{4000}(2833,\cdot)\) ...

Inducing primitive character

\(\chi_{1000}(213,\cdot)\)

Values on generators

\((2751,2501,1377)\) → \((1,-1,e\left(\frac{79}{100}\right))\)

Values

-1137911131719212327
\(-1\)\(1\)\(e\left(\frac{3}{100}\right)\)\(e\left(\frac{3}{20}\right)\)\(e\left(\frac{3}{50}\right)\)\(e\left(\frac{27}{50}\right)\)\(e\left(\frac{31}{100}\right)\)\(e\left(\frac{67}{100}\right)\)\(e\left(\frac{18}{25}\right)\)\(e\left(\frac{9}{50}\right)\)\(e\left(\frac{49}{100}\right)\)\(e\left(\frac{9}{100}\right)\)
value at  e.g. 2

Related number fields

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