Properties

Conductor 1800
Order 60
Real No
Primitive Yes
Parity Odd
Orbit Label 1800.dm

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(1800)
 
sage: chi = H[83]
 
pari: [g,chi] = znchar(Mod(83,1800))
 

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 = Yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = Odd
Orbit label = 1800.dm
Orbit index = 91

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 ]
 

\(\chi_{1800}(83,\cdot)\) \(\chi_{1800}(203,\cdot)\) \(\chi_{1800}(227,\cdot)\) \(\chi_{1800}(347,\cdot)\) \(\chi_{1800}(563,\cdot)\) \(\chi_{1800}(587,\cdot)\) \(\chi_{1800}(803,\cdot)\) \(\chi_{1800}(923,\cdot)\) \(\chi_{1800}(947,\cdot)\) \(\chi_{1800}(1067,\cdot)\) \(\chi_{1800}(1163,\cdot)\) \(\chi_{1800}(1283,\cdot)\) \(\chi_{1800}(1427,\cdot)\) \(\chi_{1800}(1523,\cdot)\) \(\chi_{1800}(1667,\cdot)\) \(\chi_{1800}(1787,\cdot)\)

Values on generators

\((1351,901,1001,577)\) → \((-1,-1,e\left(\frac{1}{6}\right),e\left(\frac{3}{20}\right))\)

Values

-117111317192329313741
\(-1\)\(1\)\(e\left(\frac{11}{12}\right)\)\(e\left(\frac{17}{30}\right)\)\(e\left(\frac{41}{60}\right)\)\(e\left(\frac{9}{20}\right)\)\(e\left(\frac{7}{10}\right)\)\(e\left(\frac{59}{60}\right)\)\(e\left(\frac{29}{30}\right)\)\(e\left(\frac{1}{30}\right)\)\(e\left(\frac{17}{20}\right)\)\(e\left(\frac{13}{30}\right)\)
value at  e.g. 2

Related number fields

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