Properties

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

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[221]
 
pari: [g,chi] = znchar(Mod(221,3600))
 

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.gd
Orbit index = 160

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 ]
 

\(\chi_{3600}(221,\cdot)\) \(\chi_{3600}(461,\cdot)\) \(\chi_{3600}(581,\cdot)\) \(\chi_{3600}(821,\cdot)\) \(\chi_{3600}(941,\cdot)\) \(\chi_{3600}(1181,\cdot)\) \(\chi_{3600}(1541,\cdot)\) \(\chi_{3600}(1661,\cdot)\) \(\chi_{3600}(2021,\cdot)\) \(\chi_{3600}(2261,\cdot)\) \(\chi_{3600}(2381,\cdot)\) \(\chi_{3600}(2621,\cdot)\) \(\chi_{3600}(2741,\cdot)\) \(\chi_{3600}(2981,\cdot)\) \(\chi_{3600}(3341,\cdot)\) \(\chi_{3600}(3461,\cdot)\)

Values on generators

\((3151,901,2801,577)\) → \((1,-i,e\left(\frac{5}{6}\right),e\left(\frac{3}{5}\right))\)

Values

-117111317192329313741
\(-1\)\(1\)\(e\left(\frac{5}{6}\right)\)\(e\left(\frac{11}{60}\right)\)\(e\left(\frac{19}{60}\right)\)\(e\left(\frac{3}{10}\right)\)\(e\left(\frac{1}{20}\right)\)\(e\left(\frac{4}{15}\right)\)\(e\left(\frac{17}{60}\right)\)\(e\left(\frac{7}{15}\right)\)\(e\left(\frac{3}{20}\right)\)\(e\left(\frac{1}{15}\right)\)
value at  e.g. 2

Related number fields

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