Properties

Conductor 4025
Order 110
Real no
Primitive yes
Minimal yes
Parity even
Orbit label 4025.cv

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[111]
 
pari: [g,chi] = znchar(Mod(111,4025))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 4025
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 110
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.cv
Orbit index = 74

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 ]
 

\(\chi_{4025}(111,\cdot)\) \(\chi_{4025}(181,\cdot)\) \(\chi_{4025}(286,\cdot)\) \(\chi_{4025}(356,\cdot)\) \(\chi_{4025}(566,\cdot)\) \(\chi_{4025}(636,\cdot)\) \(\chi_{4025}(741,\cdot)\) \(\chi_{4025}(881,\cdot)\) \(\chi_{4025}(916,\cdot)\) \(\chi_{4025}(986,\cdot)\) \(\chi_{4025}(1056,\cdot)\) \(\chi_{4025}(1091,\cdot)\) \(\chi_{4025}(1161,\cdot)\) \(\chi_{4025}(1371,\cdot)\) \(\chi_{4025}(1441,\cdot)\) \(\chi_{4025}(1546,\cdot)\) \(\chi_{4025}(1581,\cdot)\) \(\chi_{4025}(1686,\cdot)\) \(\chi_{4025}(1721,\cdot)\) \(\chi_{4025}(1791,\cdot)\) \(\chi_{4025}(1861,\cdot)\) \(\chi_{4025}(1896,\cdot)\) \(\chi_{4025}(1966,\cdot)\) \(\chi_{4025}(2246,\cdot)\) \(\chi_{4025}(2386,\cdot)\) \(\chi_{4025}(2491,\cdot)\) \(\chi_{4025}(2596,\cdot)\) \(\chi_{4025}(2666,\cdot)\) \(\chi_{4025}(2771,\cdot)\) \(\chi_{4025}(2981,\cdot)\) ...

Values on generators

\((2577,1151,3501)\) → \((e\left(\frac{4}{5}\right),-1,e\left(\frac{15}{22}\right))\)

Values

-1123468911121316
\(1\)\(1\)\(e\left(\frac{9}{55}\right)\)\(e\left(\frac{1}{110}\right)\)\(e\left(\frac{18}{55}\right)\)\(e\left(\frac{19}{110}\right)\)\(e\left(\frac{27}{55}\right)\)\(e\left(\frac{1}{55}\right)\)\(e\left(\frac{103}{110}\right)\)\(e\left(\frac{37}{110}\right)\)\(e\left(\frac{27}{110}\right)\)\(e\left(\frac{36}{55}\right)\)
value at  e.g. 2

Related number fields

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