Properties

Conductor 3600
Order 60
Real No
Primitive Yes
Parity Odd
Orbit Label 3600.gc

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[139]
pari: [g,chi] = znchar(Mod(139,3600))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 3600
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 = Yes
sage: chi.is_odd()
pari: zncharisodd(g,chi)
Parity = Odd
Orbit label = 3600.gc
Orbit index = 159

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 ]

\(\chi_{3600}(139,\cdot)\) \(\chi_{3600}(259,\cdot)\) \(\chi_{3600}(619,\cdot)\) \(\chi_{3600}(859,\cdot)\) \(\chi_{3600}(979,\cdot)\) \(\chi_{3600}(1219,\cdot)\) \(\chi_{3600}(1339,\cdot)\) \(\chi_{3600}(1579,\cdot)\) \(\chi_{3600}(1939,\cdot)\) \(\chi_{3600}(2059,\cdot)\) \(\chi_{3600}(2419,\cdot)\) \(\chi_{3600}(2659,\cdot)\) \(\chi_{3600}(2779,\cdot)\) \(\chi_{3600}(3019,\cdot)\) \(\chi_{3600}(3139,\cdot)\) \(\chi_{3600}(3379,\cdot)\)

Values on generators

\((3151,901,2801,577)\) → \((-1,i,e\left(\frac{1}{3}\right),e\left(\frac{3}{10}\right))\)

Values

-117111317192329313741
\(-1\)\(1\)\(e\left(\frac{5}{6}\right)\)\(e\left(\frac{53}{60}\right)\)\(e\left(\frac{7}{60}\right)\)\(e\left(\frac{9}{10}\right)\)\(e\left(\frac{13}{20}\right)\)\(e\left(\frac{29}{30}\right)\)\(e\left(\frac{41}{60}\right)\)\(e\left(\frac{17}{30}\right)\)\(e\left(\frac{19}{20}\right)\)\(e\left(\frac{11}{30}\right)\)
value at  e.g. 2

Related number fields

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