Properties

Conductor 2015
Order 60
Real No
Primitive No
Parity Even
Orbit Label 4030.gj

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(4030)
sage: chi = H[317]
pari: [g,chi] = znchar(Mod(317,4030))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 2015
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Order = 60
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 = 4030.gj
Orbit index = 166

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 ]

\(\chi_{4030}(317,\cdot)\) \(\chi_{4030}(577,\cdot)\) \(\chi_{4030}(723,\cdot)\) \(\chi_{4030}(1113,\cdot)\) \(\chi_{4030}(1227,\cdot)\) \(\chi_{4030}(1373,\cdot)\) \(\chi_{4030}(2153,\cdot)\) \(\chi_{4030}(2283,\cdot)\) \(\chi_{4030}(2397,\cdot)\) \(\chi_{4030}(2673,\cdot)\) \(\chi_{4030}(2787,\cdot)\) \(\chi_{4030}(2933,\cdot)\) \(\chi_{4030}(3047,\cdot)\) \(\chi_{4030}(3583,\cdot)\) \(\chi_{4030}(3827,\cdot)\) \(\chi_{4030}(3957,\cdot)\)

Inducing primitive character

\(\chi_{2015}(317,\cdot)\)

Values on generators

\((807,1861,2731)\) → \((i,-i,e\left(\frac{14}{15}\right))\)

Values

-1137911171921232729
\(1\)\(1\)\(e\left(\frac{41}{60}\right)\)\(e\left(\frac{19}{30}\right)\)\(e\left(\frac{11}{30}\right)\)\(e\left(\frac{43}{60}\right)\)\(e\left(\frac{17}{60}\right)\)\(e\left(\frac{59}{60}\right)\)\(e\left(\frac{19}{60}\right)\)\(e\left(\frac{9}{20}\right)\)\(e\left(\frac{1}{20}\right)\)\(e\left(\frac{9}{10}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{60})\)