Properties

Conductor 4725
Order 90
Real No
Primitive No
Parity Even
Orbit Label 9450.gq

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(9450)
sage: chi = H[6971]
pari: [g,chi] = znchar(Mod(6971,9450))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 4725
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Order = 90
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 = 9450.gq
Orbit index = 173

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 ]

\(\chi_{9450}(41,\cdot)\) \(\chi_{9450}(461,\cdot)\) \(\chi_{9450}(671,\cdot)\) \(\chi_{9450}(1091,\cdot)\) \(\chi_{9450}(1721,\cdot)\) \(\chi_{9450}(1931,\cdot)\) \(\chi_{9450}(2561,\cdot)\) \(\chi_{9450}(2981,\cdot)\) \(\chi_{9450}(3191,\cdot)\) \(\chi_{9450}(3611,\cdot)\) \(\chi_{9450}(3821,\cdot)\) \(\chi_{9450}(4241,\cdot)\) \(\chi_{9450}(4871,\cdot)\) \(\chi_{9450}(5081,\cdot)\) \(\chi_{9450}(5711,\cdot)\) \(\chi_{9450}(6131,\cdot)\) \(\chi_{9450}(6341,\cdot)\) \(\chi_{9450}(6761,\cdot)\) \(\chi_{9450}(6971,\cdot)\) \(\chi_{9450}(7391,\cdot)\) \(\chi_{9450}(8021,\cdot)\) \(\chi_{9450}(8231,\cdot)\) \(\chi_{9450}(8861,\cdot)\) \(\chi_{9450}(9281,\cdot)\)

Inducing primitive character

\(\chi_{4725}(2246,\cdot)\)

Values on generators

\((9101,6427,6751)\) → \((e\left(\frac{5}{18}\right),e\left(\frac{3}{5}\right),-1)\)

Values

-1111131719232931374143
\(1\)\(1\)\(e\left(\frac{19}{90}\right)\)\(e\left(\frac{11}{90}\right)\)\(e\left(\frac{7}{15}\right)\)\(e\left(\frac{19}{30}\right)\)\(e\left(\frac{59}{90}\right)\)\(e\left(\frac{43}{90}\right)\)\(e\left(\frac{77}{90}\right)\)\(e\left(\frac{1}{15}\right)\)\(e\left(\frac{28}{45}\right)\)\(e\left(\frac{1}{9}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{45})\)