Properties

Conductor 4025
Order 110
Real No
Primitive Yes
Parity Even
Orbit Label 4025.ct

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[34]
 
pari: [g,chi] = znchar(Mod(34,4025))
 

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
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = Even
Orbit label = 4025.ct
Orbit index = 72

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 ]
 

\(\chi_{4025}(34,\cdot)\) \(\chi_{4025}(244,\cdot)\) \(\chi_{4025}(314,\cdot)\) \(\chi_{4025}(419,\cdot)\) \(\chi_{4025}(454,\cdot)\) \(\chi_{4025}(559,\cdot)\) \(\chi_{4025}(594,\cdot)\) \(\chi_{4025}(664,\cdot)\) \(\chi_{4025}(734,\cdot)\) \(\chi_{4025}(769,\cdot)\) \(\chi_{4025}(839,\cdot)\) \(\chi_{4025}(1119,\cdot)\) \(\chi_{4025}(1259,\cdot)\) \(\chi_{4025}(1364,\cdot)\) \(\chi_{4025}(1469,\cdot)\) \(\chi_{4025}(1539,\cdot)\) \(\chi_{4025}(1644,\cdot)\) \(\chi_{4025}(1854,\cdot)\) \(\chi_{4025}(2029,\cdot)\) \(\chi_{4025}(2064,\cdot)\) \(\chi_{4025}(2169,\cdot)\) \(\chi_{4025}(2204,\cdot)\) \(\chi_{4025}(2344,\cdot)\) \(\chi_{4025}(2379,\cdot)\) \(\chi_{4025}(2659,\cdot)\) \(\chi_{4025}(2729,\cdot)\) \(\chi_{4025}(2834,\cdot)\) \(\chi_{4025}(2869,\cdot)\) \(\chi_{4025}(3009,\cdot)\) \(\chi_{4025}(3079,\cdot)\) ...

Values on generators

\((2577,1151,3501)\) → \((e\left(\frac{7}{10}\right),-1,e\left(\frac{9}{22}\right))\)

Values

-1123468911121316
\(1\)\(1\)\(e\left(\frac{57}{110}\right)\)\(e\left(\frac{52}{55}\right)\)\(e\left(\frac{2}{55}\right)\)\(e\left(\frac{51}{110}\right)\)\(e\left(\frac{61}{110}\right)\)\(e\left(\frac{49}{55}\right)\)\(e\left(\frac{97}{110}\right)\)\(e\left(\frac{54}{55}\right)\)\(e\left(\frac{29}{55}\right)\)\(e\left(\frac{4}{55}\right)\)
value at  e.g. 2

Related number fields

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