Properties

Conductor 4025
Order 220
Real No
Primitive Yes
Parity Even
Orbit Label 4025.de

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[27]
 
pari: [g,chi] = znchar(Mod(27,4025))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 4025
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 = Yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = Even
Orbit label = 4025.de
Orbit index = 83

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 ]
 

\(\chi_{4025}(13,\cdot)\) \(\chi_{4025}(27,\cdot)\) \(\chi_{4025}(48,\cdot)\) \(\chi_{4025}(62,\cdot)\) \(\chi_{4025}(167,\cdot)\) \(\chi_{4025}(188,\cdot)\) \(\chi_{4025}(202,\cdot)\) \(\chi_{4025}(223,\cdot)\) \(\chi_{4025}(328,\cdot)\) \(\chi_{4025}(363,\cdot)\) \(\chi_{4025}(377,\cdot)\) \(\chi_{4025}(538,\cdot)\) \(\chi_{4025}(587,\cdot)\) \(\chi_{4025}(692,\cdot)\) \(\chi_{4025}(748,\cdot)\) \(\chi_{4025}(762,\cdot)\) \(\chi_{4025}(853,\cdot)\) \(\chi_{4025}(867,\cdot)\) \(\chi_{4025}(923,\cdot)\) \(\chi_{4025}(972,\cdot)\) \(\chi_{4025}(1028,\cdot)\) \(\chi_{4025}(1112,\cdot)\) \(\chi_{4025}(1133,\cdot)\) \(\chi_{4025}(1273,\cdot)\) \(\chi_{4025}(1392,\cdot)\) \(\chi_{4025}(1462,\cdot)\) \(\chi_{4025}(1497,\cdot)\) \(\chi_{4025}(1553,\cdot)\) \(\chi_{4025}(1567,\cdot)\) \(\chi_{4025}(1623,\cdot)\) ...

Values on generators

\((2577,1151,3501)\) → \((e\left(\frac{1}{20}\right),-1,e\left(\frac{2}{11}\right))\)

Values

-1123468911121316
\(1\)\(1\)\(e\left(\frac{91}{220}\right)\)\(e\left(\frac{167}{220}\right)\)\(e\left(\frac{91}{110}\right)\)\(e\left(\frac{19}{110}\right)\)\(e\left(\frac{53}{220}\right)\)\(e\left(\frac{57}{110}\right)\)\(e\left(\frac{24}{55}\right)\)\(e\left(\frac{129}{220}\right)\)\(e\left(\frac{219}{220}\right)\)\(e\left(\frac{36}{55}\right)\)
value at  e.g. 2

Related number fields

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