Properties

Conductor 575
Order 220
Real No
Primitive No
Parity Odd
Orbit Label 4025.dg

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[8]
 
pari: [g,chi] = znchar(Mod(8,4025))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 575
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 220
Real = No
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = No
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = Odd
Orbit label = 4025.dg
Orbit index = 85

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 ]
 

\(\chi_{4025}(8,\cdot)\) \(\chi_{4025}(78,\cdot)\) \(\chi_{4025}(127,\cdot)\) \(\chi_{4025}(197,\cdot)\) \(\chi_{4025}(288,\cdot)\) \(\chi_{4025}(302,\cdot)\) \(\chi_{4025}(358,\cdot)\) \(\chi_{4025}(372,\cdot)\) \(\chi_{4025}(463,\cdot)\) \(\chi_{4025}(512,\cdot)\) \(\chi_{4025}(533,\cdot)\) \(\chi_{4025}(547,\cdot)\) \(\chi_{4025}(652,\cdot)\) \(\chi_{4025}(673,\cdot)\) \(\chi_{4025}(708,\cdot)\) \(\chi_{4025}(722,\cdot)\) \(\chi_{4025}(813,\cdot)\) \(\chi_{4025}(883,\cdot)\) \(\chi_{4025}(1002,\cdot)\) \(\chi_{4025}(1037,\cdot)\) \(\chi_{4025}(1163,\cdot)\) \(\chi_{4025}(1177,\cdot)\) \(\chi_{4025}(1198,\cdot)\) \(\chi_{4025}(1212,\cdot)\) \(\chi_{4025}(1317,\cdot)\) \(\chi_{4025}(1338,\cdot)\) \(\chi_{4025}(1352,\cdot)\) \(\chi_{4025}(1373,\cdot)\) \(\chi_{4025}(1478,\cdot)\) \(\chi_{4025}(1513,\cdot)\) ...

Inducing primitive character

\(\chi_{575}(8,\cdot)\)

Values on generators

\((2577,1151,3501)\) → \((e\left(\frac{3}{20}\right),1,e\left(\frac{3}{11}\right))\)

Values

-1123468911121316
\(-1\)\(1\)\(e\left(\frac{153}{220}\right)\)\(e\left(\frac{91}{220}\right)\)\(e\left(\frac{43}{110}\right)\)\(e\left(\frac{6}{55}\right)\)\(e\left(\frac{19}{220}\right)\)\(e\left(\frac{91}{110}\right)\)\(e\left(\frac{47}{55}\right)\)\(e\left(\frac{177}{220}\right)\)\(e\left(\frac{147}{220}\right)\)\(e\left(\frac{43}{55}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{220})\)