Properties

Conductor 1343
Order 312
Real no
Primitive no
Minimal yes
Parity even
Orbit label 4029.cx

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(4029)
 
sage: chi = H[19]
 
pari: [g,chi] = znchar(Mod(19,4029))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 1343
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 312
Real = no
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = no
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = even
Orbit label = 4029.cx
Orbit index = 76

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 ]
 

\(\chi_{4029}(19,\cdot)\) \(\chi_{4029}(25,\cdot)\) \(\chi_{4029}(49,\cdot)\) \(\chi_{4029}(76,\cdot)\) \(\chi_{4029}(121,\cdot)\) \(\chi_{4029}(151,\cdot)\) \(\chi_{4029}(178,\cdot)\) \(\chi_{4029}(202,\cdot)\) \(\chi_{4029}(253,\cdot)\) \(\chi_{4029}(325,\cdot)\) \(\chi_{4029}(400,\cdot)\) \(\chi_{4029}(406,\cdot)\) \(\chi_{4029}(427,\cdot)\) \(\chi_{4029}(478,\cdot)\) \(\chi_{4029}(604,\cdot)\) \(\chi_{4029}(637,\cdot)\) \(\chi_{4029}(682,\cdot)\) \(\chi_{4029}(784,\cdot)\) \(\chi_{4029}(835,\cdot)\) \(\chi_{4029}(841,\cdot)\) \(\chi_{4029}(961,\cdot)\) \(\chi_{4029}(967,\cdot)\) \(\chi_{4029}(988,\cdot)\) \(\chi_{4029}(1063,\cdot)\) \(\chi_{4029}(1069,\cdot)\) \(\chi_{4029}(1198,\cdot)\) \(\chi_{4029}(1216,\cdot)\) \(\chi_{4029}(1273,\cdot)\) \(\chi_{4029}(1300,\cdot)\) \(\chi_{4029}(1345,\cdot)\) ...

Values on generators

\((2687,3556,3163)\) → \((1,e\left(\frac{7}{8}\right),e\left(\frac{16}{39}\right))\)

Values

-11245781011131416
\(1\)\(1\)\(e\left(\frac{139}{156}\right)\)\(e\left(\frac{61}{78}\right)\)\(e\left(\frac{253}{312}\right)\)\(e\left(\frac{115}{312}\right)\)\(e\left(\frac{35}{52}\right)\)\(e\left(\frac{73}{104}\right)\)\(e\left(\frac{7}{312}\right)\)\(e\left(\frac{35}{78}\right)\)\(e\left(\frac{27}{104}\right)\)\(e\left(\frac{22}{39}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{312})\)