Properties

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

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[137]
pari: [g,chi] = znchar(Mod(137,4000))

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.cu
Orbit index = 73

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 ]

\(\chi_{4000}(137,\cdot)\) \(\chi_{4000}(153,\cdot)\) \(\chi_{4000}(297,\cdot)\) \(\chi_{4000}(313,\cdot)\) \(\chi_{4000}(473,\cdot)\) \(\chi_{4000}(617,\cdot)\) \(\chi_{4000}(633,\cdot)\) \(\chi_{4000}(777,\cdot)\) \(\chi_{4000}(937,\cdot)\) \(\chi_{4000}(953,\cdot)\) \(\chi_{4000}(1097,\cdot)\) \(\chi_{4000}(1113,\cdot)\) \(\chi_{4000}(1273,\cdot)\) \(\chi_{4000}(1417,\cdot)\) \(\chi_{4000}(1433,\cdot)\) \(\chi_{4000}(1577,\cdot)\) \(\chi_{4000}(1737,\cdot)\) \(\chi_{4000}(1753,\cdot)\) \(\chi_{4000}(1897,\cdot)\) \(\chi_{4000}(1913,\cdot)\) \(\chi_{4000}(2073,\cdot)\) \(\chi_{4000}(2217,\cdot)\) \(\chi_{4000}(2233,\cdot)\) \(\chi_{4000}(2377,\cdot)\) \(\chi_{4000}(2537,\cdot)\) \(\chi_{4000}(2553,\cdot)\) \(\chi_{4000}(2697,\cdot)\) \(\chi_{4000}(2713,\cdot)\) \(\chi_{4000}(2873,\cdot)\) \(\chi_{4000}(3017,\cdot)\) ...

Inducing primitive character

\(\chi_{2000}(637,\cdot)\)

Values on generators

\((2751,2501,1377)\) → \((1,-i,e\left(\frac{9}{100}\right))\)

Values

-1137911131719212327
\(-1\)\(1\)\(e\left(\frac{22}{25}\right)\)\(e\left(\frac{3}{20}\right)\)\(e\left(\frac{19}{25}\right)\)\(e\left(\frac{59}{100}\right)\)\(e\left(\frac{19}{25}\right)\)\(e\left(\frac{57}{100}\right)\)\(e\left(\frac{87}{100}\right)\)\(e\left(\frac{3}{100}\right)\)\(e\left(\frac{29}{100}\right)\)\(e\left(\frac{16}{25}\right)\)
value at  e.g. 2

Related number fields

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