Properties

Conductor 225
Order 60
Real no
Primitive no
Minimal no
Parity even
Orbit label 1350.bd

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(1350)
 
sage: chi = H[17]
 
pari: [g,chi] = znchar(Mod(17,1350))
 

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
Minimal = no
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = even
Orbit label = 1350.bd
Orbit index = 30

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 ]
 

\(\chi_{1350}(17,\cdot)\) \(\chi_{1350}(197,\cdot)\) \(\chi_{1350}(233,\cdot)\) \(\chi_{1350}(287,\cdot)\) \(\chi_{1350}(413,\cdot)\) \(\chi_{1350}(467,\cdot)\) \(\chi_{1350}(503,\cdot)\) \(\chi_{1350}(683,\cdot)\) \(\chi_{1350}(737,\cdot)\) \(\chi_{1350}(773,\cdot)\) \(\chi_{1350}(827,\cdot)\) \(\chi_{1350}(953,\cdot)\) \(\chi_{1350}(1097,\cdot)\) \(\chi_{1350}(1223,\cdot)\) \(\chi_{1350}(1277,\cdot)\) \(\chi_{1350}(1313,\cdot)\)

Values on generators

\((1001,1027)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{13}{20}\right))\)

Values

-117111317192329313741
\(1\)\(1\)\(e\left(\frac{7}{12}\right)\)\(e\left(\frac{7}{30}\right)\)\(e\left(\frac{1}{60}\right)\)\(e\left(\frac{19}{20}\right)\)\(e\left(\frac{7}{10}\right)\)\(e\left(\frac{19}{60}\right)\)\(e\left(\frac{2}{15}\right)\)\(e\left(\frac{13}{15}\right)\)\(e\left(\frac{17}{20}\right)\)\(e\left(\frac{23}{30}\right)\)
value at  e.g. 2

Related number fields

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