Properties

Conductor 225
Order 60
Real No
Primitive No
Parity Odd
Orbit Label 3600.fy

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[97]
pari: [g,chi] = znchar(Mod(97,3600))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 225
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.fy
Orbit index = 155

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 ]

\(\chi_{3600}(97,\cdot)\) \(\chi_{3600}(337,\cdot)\) \(\chi_{3600}(673,\cdot)\) \(\chi_{3600}(817,\cdot)\) \(\chi_{3600}(913,\cdot)\) \(\chi_{3600}(1537,\cdot)\) \(\chi_{3600}(1633,\cdot)\) \(\chi_{3600}(1777,\cdot)\) \(\chi_{3600}(2113,\cdot)\) \(\chi_{3600}(2353,\cdot)\) \(\chi_{3600}(2497,\cdot)\) \(\chi_{3600}(2833,\cdot)\) \(\chi_{3600}(2977,\cdot)\) \(\chi_{3600}(3073,\cdot)\) \(\chi_{3600}(3217,\cdot)\) \(\chi_{3600}(3553,\cdot)\)

Inducing primitive character

\(\chi_{225}(97,\cdot)\)

Values on generators

\((3151,901,2801,577)\) → \((1,1,e\left(\frac{2}{3}\right),e\left(\frac{17}{20}\right))\)

Values

-117111317192329313741
\(-1\)\(1\)\(e\left(\frac{11}{12}\right)\)\(e\left(\frac{4}{15}\right)\)\(e\left(\frac{29}{60}\right)\)\(e\left(\frac{1}{20}\right)\)\(e\left(\frac{3}{10}\right)\)\(e\left(\frac{41}{60}\right)\)\(e\left(\frac{11}{30}\right)\)\(e\left(\frac{2}{15}\right)\)\(e\left(\frac{13}{20}\right)\)\(e\left(\frac{11}{15}\right)\)
value at  e.g. 2

Related number fields

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