Properties

Conductor 8027
Order 957
Real No
Primitive Yes
Parity Even
Orbit Label 8027.bo

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(8027)
 
sage: chi = H[9]
 
pari: [g,chi] = znchar(Mod(9,8027))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 8027
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 957
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 = 8027.bo
Orbit index = 41

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 ]
 

\(\chi_{8027}(9,\cdot)\) \(\chi_{8027}(12,\cdot)\) \(\chi_{8027}(16,\cdot)\) \(\chi_{8027}(25,\cdot)\) \(\chi_{8027}(26,\cdot)\) \(\chi_{8027}(77,\cdot)\) \(\chi_{8027}(81,\cdot)\) \(\chi_{8027}(85,\cdot)\) \(\chi_{8027}(87,\cdot)\) \(\chi_{8027}(94,\cdot)\) \(\chi_{8027}(108,\cdot)\) \(\chi_{8027}(144,\cdot)\) \(\chi_{8027}(147,\cdot)\) \(\chi_{8027}(151,\cdot)\) \(\chi_{8027}(192,\cdot)\) \(\chi_{8027}(196,\cdot)\) \(\chi_{8027}(219,\cdot)\) \(\chi_{8027}(225,\cdot)\) \(\chi_{8027}(256,\cdot)\) \(\chi_{8027}(266,\cdot)\) \(\chi_{8027}(271,\cdot)\) \(\chi_{8027}(279,\cdot)\) \(\chi_{8027}(292,\cdot)\) \(\chi_{8027}(307,\cdot)\) \(\chi_{8027}(358,\cdot)\) \(\chi_{8027}(361,\cdot)\) \(\chi_{8027}(363,\cdot)\) \(\chi_{8027}(372,\cdot)\) \(\chi_{8027}(374,\cdot)\) \(\chi_{8027}(400,\cdot)\) ...

Values on generators

\((350,5935)\) → \((e\left(\frac{5}{11}\right),e\left(\frac{13}{87}\right))\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{56}{957}\right)\)\(e\left(\frac{151}{957}\right)\)\(e\left(\frac{112}{957}\right)\)\(e\left(\frac{358}{957}\right)\)\(e\left(\frac{69}{319}\right)\)\(e\left(\frac{620}{957}\right)\)\(e\left(\frac{56}{319}\right)\)\(e\left(\frac{302}{957}\right)\)\(e\left(\frac{138}{319}\right)\)\(e\left(\frac{73}{319}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{957})\)