Properties

Conductor 175
Order 30
Real no
Primitive no
Minimal yes
Parity even
Orbit label 4025.bu

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(4025)
 
sage: chi = H[254]
 
pari: [g,chi] = znchar(Mod(254,4025))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 175
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 30
Real = no
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = no
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = even
Orbit label = 4025.bu
Orbit index = 47

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 ]
 

\(\chi_{4025}(254,\cdot)\) \(\chi_{4025}(1059,\cdot)\) \(\chi_{4025}(1404,\cdot)\) \(\chi_{4025}(1864,\cdot)\) \(\chi_{4025}(2209,\cdot)\) \(\chi_{4025}(2669,\cdot)\) \(\chi_{4025}(3014,\cdot)\) \(\chi_{4025}(3819,\cdot)\)

Values on generators

\((2577,1151,3501)\) → \((e\left(\frac{1}{10}\right),e\left(\frac{1}{3}\right),1)\)

Values

-1123468911121316
\(1\)\(1\)\(e\left(\frac{23}{30}\right)\)\(e\left(\frac{1}{30}\right)\)\(e\left(\frac{8}{15}\right)\)\(e\left(\frac{4}{5}\right)\)\(e\left(\frac{3}{10}\right)\)\(e\left(\frac{1}{15}\right)\)\(e\left(\frac{14}{15}\right)\)\(e\left(\frac{17}{30}\right)\)\(e\left(\frac{9}{10}\right)\)\(e\left(\frac{1}{15}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{15})\)