Properties

Conductor 1800
Order 60
Real No
Primitive No
Parity Odd
Orbit Label 3600.fl

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(3600)
sage: chi = H[313]
pari: [g,chi] = znchar(Mod(313,3600))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 1800
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 = Odd
Orbit label = 3600.fl
Orbit index = 142

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 ]

\(\chi_{3600}(313,\cdot)\) \(\chi_{3600}(553,\cdot)\) \(\chi_{3600}(697,\cdot)\) \(\chi_{3600}(1033,\cdot)\) \(\chi_{3600}(1177,\cdot)\) \(\chi_{3600}(1273,\cdot)\) \(\chi_{3600}(1417,\cdot)\) \(\chi_{3600}(1753,\cdot)\) \(\chi_{3600}(1897,\cdot)\) \(\chi_{3600}(2137,\cdot)\) \(\chi_{3600}(2473,\cdot)\) \(\chi_{3600}(2617,\cdot)\) \(\chi_{3600}(2713,\cdot)\) \(\chi_{3600}(3337,\cdot)\) \(\chi_{3600}(3433,\cdot)\) \(\chi_{3600}(3577,\cdot)\)

Inducing primitive character

\(\chi_{1800}(1213,\cdot)\)

Values on generators

\((3151,901,2801,577)\) → \((1,-1,e\left(\frac{2}{3}\right),e\left(\frac{19}{20}\right))\)

Values

-117111317192329313741
\(-1\)\(1\)\(e\left(\frac{5}{12}\right)\)\(e\left(\frac{11}{30}\right)\)\(e\left(\frac{53}{60}\right)\)\(e\left(\frac{7}{20}\right)\)\(e\left(\frac{3}{5}\right)\)\(e\left(\frac{47}{60}\right)\)\(e\left(\frac{1}{15}\right)\)\(e\left(\frac{14}{15}\right)\)\(e\left(\frac{1}{20}\right)\)\(e\left(\frac{2}{15}\right)\)
value at  e.g. 2

Related number fields

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