Properties

Conductor 575
Order 55
Real No
Primitive No
Parity Even
Orbit Label 4025.cf

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[36]
 
pari: [g,chi] = znchar(Mod(36,4025))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 575
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 55
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 = Even
Orbit label = 4025.cf
Orbit index = 58

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 ]
 

\(\chi_{4025}(36,\cdot)\) \(\chi_{4025}(71,\cdot)\) \(\chi_{4025}(141,\cdot)\) \(\chi_{4025}(211,\cdot)\) \(\chi_{4025}(246,\cdot)\) \(\chi_{4025}(386,\cdot)\) \(\chi_{4025}(491,\cdot)\) \(\chi_{4025}(561,\cdot)\) \(\chi_{4025}(771,\cdot)\) \(\chi_{4025}(841,\cdot)\) \(\chi_{4025}(946,\cdot)\) \(\chi_{4025}(1016,\cdot)\) \(\chi_{4025}(1156,\cdot)\) \(\chi_{4025}(1191,\cdot)\) \(\chi_{4025}(1296,\cdot)\) \(\chi_{4025}(1366,\cdot)\) \(\chi_{4025}(1646,\cdot)\) \(\chi_{4025}(1681,\cdot)\) \(\chi_{4025}(1821,\cdot)\) \(\chi_{4025}(1856,\cdot)\) \(\chi_{4025}(1961,\cdot)\) \(\chi_{4025}(1996,\cdot)\) \(\chi_{4025}(2171,\cdot)\) \(\chi_{4025}(2381,\cdot)\) \(\chi_{4025}(2486,\cdot)\) \(\chi_{4025}(2556,\cdot)\) \(\chi_{4025}(2661,\cdot)\) \(\chi_{4025}(2766,\cdot)\) \(\chi_{4025}(2906,\cdot)\) \(\chi_{4025}(3186,\cdot)\) ...

Inducing primitive character

\(\chi_{575}(36,\cdot)\)

Values on generators

\((2577,1151,3501)\) → \((e\left(\frac{4}{5}\right),1,e\left(\frac{7}{11}\right))\)

Values

-1123468911121316
\(1\)\(1\)\(e\left(\frac{4}{55}\right)\)\(e\left(\frac{43}{55}\right)\)\(e\left(\frac{8}{55}\right)\)\(e\left(\frac{47}{55}\right)\)\(e\left(\frac{12}{55}\right)\)\(e\left(\frac{31}{55}\right)\)\(e\left(\frac{29}{55}\right)\)\(e\left(\frac{51}{55}\right)\)\(e\left(\frac{6}{55}\right)\)\(e\left(\frac{16}{55}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{55})\)