Properties

Conductor 2353
Order 20
Real No
Primitive No
Parity Odd
Orbit Label 4706.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(4706)
sage: chi = H[1945]
pari: [g,chi] = znchar(Mod(1945,4706))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 2353
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Order = 20
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 = 4706.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 ]

\(\chi_{4706}(125,\cdot)\) \(\chi_{4706}(135,\cdot)\) \(\chi_{4706}(421,\cdot)\) \(\chi_{4706}(1945,\cdot)\) \(\chi_{4706}(2033,\cdot)\) \(\chi_{4706}(2231,\cdot)\) \(\chi_{4706}(3021,\cdot)\) \(\chi_{4706}(3843,\cdot)\)

Inducing primitive character

\(\chi_{2353}(1945,\cdot)\)

Values on generators

\((2173,183)\) → \((i,e\left(\frac{4}{5}\right))\)

Values

-113579111517192123
\(-1\)\(1\)\(e\left(\frac{4}{5}\right)\)\(e\left(\frac{1}{20}\right)\)\(-i\)\(e\left(\frac{3}{5}\right)\)\(e\left(\frac{7}{20}\right)\)\(e\left(\frac{17}{20}\right)\)\(-1\)\(i\)\(e\left(\frac{11}{20}\right)\)\(e\left(\frac{9}{10}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{20})\)