Properties

Conductor 4025
Order 330
Real no
Primitive yes
Minimal yes
Parity even
Orbit label 4025.dj

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[61]
 
pari: [g,chi] = znchar(Mod(61,4025))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 4025
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 330
Real = no
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = yes
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = even
Orbit label = 4025.dj
Orbit index = 88

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 ]
 

\(\chi_{4025}(61,\cdot)\) \(\chi_{4025}(66,\cdot)\) \(\chi_{4025}(136,\cdot)\) \(\chi_{4025}(166,\cdot)\) \(\chi_{4025}(171,\cdot)\) \(\chi_{4025}(241,\cdot)\) \(\chi_{4025}(306,\cdot)\) \(\chi_{4025}(341,\cdot)\) \(\chi_{4025}(411,\cdot)\) \(\chi_{4025}(481,\cdot)\) \(\chi_{4025}(516,\cdot)\) \(\chi_{4025}(521,\cdot)\) \(\chi_{4025}(586,\cdot)\) \(\chi_{4025}(661,\cdot)\) \(\chi_{4025}(766,\cdot)\) \(\chi_{4025}(796,\cdot)\) \(\chi_{4025}(866,\cdot)\) \(\chi_{4025}(871,\cdot)\) \(\chi_{4025}(941,\cdot)\) \(\chi_{4025}(971,\cdot)\) \(\chi_{4025}(1006,\cdot)\) \(\chi_{4025}(1046,\cdot)\) \(\chi_{4025}(1111,\cdot)\) \(\chi_{4025}(1146,\cdot)\) \(\chi_{4025}(1216,\cdot)\) \(\chi_{4025}(1256,\cdot)\) \(\chi_{4025}(1286,\cdot)\) \(\chi_{4025}(1321,\cdot)\) \(\chi_{4025}(1391,\cdot)\) \(\chi_{4025}(1431,\cdot)\) ...

Values on generators

\((2577,1151,3501)\) → \((e\left(\frac{4}{5}\right),e\left(\frac{5}{6}\right),e\left(\frac{17}{22}\right))\)

Values

-1123468911121316
\(1\)\(1\)\(e\left(\frac{2}{165}\right)\)\(e\left(\frac{263}{330}\right)\)\(e\left(\frac{4}{165}\right)\)\(e\left(\frac{89}{110}\right)\)\(e\left(\frac{2}{55}\right)\)\(e\left(\frac{98}{165}\right)\)\(e\left(\frac{29}{330}\right)\)\(e\left(\frac{271}{330}\right)\)\(e\left(\frac{57}{110}\right)\)\(e\left(\frac{8}{165}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{165})\)