Properties

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

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[311]
pari: [g,chi] = znchar(Mod(311,9450))

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.go
Orbit index = 171

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 ]

\(\chi_{9450}(311,\cdot)\) \(\chi_{9450}(941,\cdot)\) \(\chi_{9450}(1181,\cdot)\) \(\chi_{9450}(1571,\cdot)\) \(\chi_{9450}(1811,\cdot)\) \(\chi_{9450}(2441,\cdot)\) \(\chi_{9450}(2831,\cdot)\) \(\chi_{9450}(3071,\cdot)\) \(\chi_{9450}(3461,\cdot)\) \(\chi_{9450}(4091,\cdot)\) \(\chi_{9450}(4331,\cdot)\) \(\chi_{9450}(4721,\cdot)\) \(\chi_{9450}(4961,\cdot)\) \(\chi_{9450}(5591,\cdot)\) \(\chi_{9450}(5981,\cdot)\) \(\chi_{9450}(6221,\cdot)\) \(\chi_{9450}(6611,\cdot)\) \(\chi_{9450}(7241,\cdot)\) \(\chi_{9450}(7481,\cdot)\) \(\chi_{9450}(7871,\cdot)\) \(\chi_{9450}(8111,\cdot)\) \(\chi_{9450}(8741,\cdot)\) \(\chi_{9450}(9131,\cdot)\) \(\chi_{9450}(9371,\cdot)\)

Inducing primitive character

\(\chi_{4725}(311,\cdot)\)

Values on generators

\((9101,6427,6751)\) → \((e\left(\frac{17}{18}\right),e\left(\frac{4}{5}\right),e\left(\frac{1}{6}\right))\)

Values

-1111131719232931374143
\(1\)\(1\)\(e\left(\frac{67}{90}\right)\)\(e\left(\frac{23}{90}\right)\)\(e\left(\frac{11}{15}\right)\)\(e\left(\frac{17}{30}\right)\)\(e\left(\frac{47}{90}\right)\)\(e\left(\frac{49}{90}\right)\)\(e\left(\frac{41}{90}\right)\)\(e\left(\frac{1}{5}\right)\)\(e\left(\frac{34}{45}\right)\)\(e\left(\frac{7}{9}\right)\)
value at  e.g. 2

Related number fields

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