Properties

Conductor 945
Order 36
Real No
Primitive No
Parity Even
Orbit Label 9450.fb

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[157]
pari: [g,chi] = znchar(Mod(157,9450))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 945
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Order = 36
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.fb
Orbit index = 132

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 ]

\(\chi_{9450}(157,\cdot)\) \(\chi_{9450}(943,\cdot)\) \(\chi_{9450}(1543,\cdot)\) \(\chi_{9450}(2707,\cdot)\) \(\chi_{9450}(3307,\cdot)\) \(\chi_{9450}(4093,\cdot)\) \(\chi_{9450}(4693,\cdot)\) \(\chi_{9450}(5857,\cdot)\) \(\chi_{9450}(6457,\cdot)\) \(\chi_{9450}(7243,\cdot)\) \(\chi_{9450}(7843,\cdot)\) \(\chi_{9450}(9007,\cdot)\)

Inducing primitive character

\(\chi_{945}(157,\cdot)\)

Values on generators

\((9101,6427,6751)\) → \((e\left(\frac{7}{9}\right),i,e\left(\frac{1}{6}\right))\)

Values

-1111131719232931374143
\(1\)\(1\)\(e\left(\frac{7}{9}\right)\)\(e\left(\frac{17}{36}\right)\)\(e\left(\frac{1}{12}\right)\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{23}{36}\right)\)\(e\left(\frac{5}{18}\right)\)\(e\left(\frac{13}{18}\right)\)\(i\)\(e\left(\frac{13}{18}\right)\)\(e\left(\frac{31}{36}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{36})\)