Properties

Conductor 4025
Order 330
Real No
Primitive Yes
Parity Even
Orbit Label 4025.dm

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[9]
 
pari: [g,chi] = znchar(Mod(9,4025))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 4025
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 330
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.dm
Orbit index = 91

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 ]
 

\(\chi_{4025}(4,\cdot)\) \(\chi_{4025}(9,\cdot)\) \(\chi_{4025}(39,\cdot)\) \(\chi_{4025}(144,\cdot)\) \(\chi_{4025}(179,\cdot)\) \(\chi_{4025}(219,\cdot)\) \(\chi_{4025}(284,\cdot)\) \(\chi_{4025}(289,\cdot)\) \(\chi_{4025}(354,\cdot)\) \(\chi_{4025}(394,\cdot)\) \(\chi_{4025}(464,\cdot)\) \(\chi_{4025}(564,\cdot)\) \(\chi_{4025}(604,\cdot)\) \(\chi_{4025}(634,\cdot)\) \(\chi_{4025}(639,\cdot)\) \(\chi_{4025}(669,\cdot)\) \(\chi_{4025}(739,\cdot)\) \(\chi_{4025}(744,\cdot)\) \(\chi_{4025}(809,\cdot)\) \(\chi_{4025}(814,\cdot)\) \(\chi_{4025}(844,\cdot)\) \(\chi_{4025}(984,\cdot)\) \(\chi_{4025}(1089,\cdot)\) \(\chi_{4025}(1094,\cdot)\) \(\chi_{4025}(1129,\cdot)\) \(\chi_{4025}(1159,\cdot)\) \(\chi_{4025}(1269,\cdot)\) \(\chi_{4025}(1304,\cdot)\) \(\chi_{4025}(1369,\cdot)\) \(\chi_{4025}(1409,\cdot)\) ...

Values on generators

\((2577,1151,3501)\) → \((e\left(\frac{7}{10}\right),e\left(\frac{1}{3}\right),e\left(\frac{5}{11}\right))\)

Values

-1123468911121316
\(1\)\(1\)\(e\left(\frac{91}{330}\right)\)\(e\left(\frac{167}{330}\right)\)\(e\left(\frac{91}{165}\right)\)\(e\left(\frac{43}{55}\right)\)\(e\left(\frac{91}{110}\right)\)\(e\left(\frac{2}{165}\right)\)\(e\left(\frac{103}{165}\right)\)\(e\left(\frac{19}{330}\right)\)\(e\left(\frac{73}{110}\right)\)\(e\left(\frac{17}{165}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{165})\)