Properties

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

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[79]
pari: [g,chi] = znchar(Mod(79,9450))

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.gn
Orbit index = 170

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 ]

\(\chi_{9450}(79,\cdot)\) \(\chi_{9450}(319,\cdot)\) \(\chi_{9450}(709,\cdot)\) \(\chi_{9450}(1339,\cdot)\) \(\chi_{9450}(1579,\cdot)\) \(\chi_{9450}(1969,\cdot)\) \(\chi_{9450}(2209,\cdot)\) \(\chi_{9450}(2839,\cdot)\) \(\chi_{9450}(3229,\cdot)\) \(\chi_{9450}(3469,\cdot)\) \(\chi_{9450}(3859,\cdot)\) \(\chi_{9450}(4489,\cdot)\) \(\chi_{9450}(4729,\cdot)\) \(\chi_{9450}(5119,\cdot)\) \(\chi_{9450}(5359,\cdot)\) \(\chi_{9450}(5989,\cdot)\) \(\chi_{9450}(6379,\cdot)\) \(\chi_{9450}(6619,\cdot)\) \(\chi_{9450}(7009,\cdot)\) \(\chi_{9450}(7639,\cdot)\) \(\chi_{9450}(7879,\cdot)\) \(\chi_{9450}(8269,\cdot)\) \(\chi_{9450}(8509,\cdot)\) \(\chi_{9450}(9139,\cdot)\)

Inducing primitive character

\(\chi_{4725}(79,\cdot)\)

Values on generators

\((9101,6427,6751)\) → \((e\left(\frac{5}{9}\right),e\left(\frac{1}{10}\right),e\left(\frac{1}{3}\right))\)

Values

-1111131719232931374143
\(1\)\(1\)\(e\left(\frac{7}{45}\right)\)\(e\left(\frac{31}{90}\right)\)\(e\left(\frac{29}{30}\right)\)\(e\left(\frac{2}{15}\right)\)\(e\left(\frac{79}{90}\right)\)\(e\left(\frac{34}{45}\right)\)\(e\left(\frac{11}{45}\right)\)\(e\left(\frac{9}{10}\right)\)\(e\left(\frac{38}{45}\right)\)\(e\left(\frac{13}{18}\right)\)
value at  e.g. 2

Related number fields

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