Properties

Conductor 1337
Order 190
Real no
Primitive yes
Minimal yes
Parity odd
Orbit label 1337.z

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(1337)
 
sage: chi = H[1084]
 
pari: [g,chi] = znchar(Mod(1084,1337))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 1337
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 190
Real = no
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = yes
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = odd
Orbit label = 1337.z
Orbit index = 26

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 ]
 

\(\chi_{1337}(13,\cdot)\) \(\chi_{1337}(20,\cdot)\) \(\chi_{1337}(27,\cdot)\) \(\chi_{1337}(34,\cdot)\) \(\chi_{1337}(48,\cdot)\) \(\chi_{1337}(90,\cdot)\) \(\chi_{1337}(97,\cdot)\) \(\chi_{1337}(104,\cdot)\) \(\chi_{1337}(118,\cdot)\) \(\chi_{1337}(195,\cdot)\) \(\chi_{1337}(209,\cdot)\) \(\chi_{1337}(237,\cdot)\) \(\chi_{1337}(251,\cdot)\) \(\chi_{1337}(258,\cdot)\) \(\chi_{1337}(272,\cdot)\) \(\chi_{1337}(293,\cdot)\) \(\chi_{1337}(321,\cdot)\) \(\chi_{1337}(335,\cdot)\) \(\chi_{1337}(349,\cdot)\) \(\chi_{1337}(363,\cdot)\) \(\chi_{1337}(384,\cdot)\) \(\chi_{1337}(391,\cdot)\) \(\chi_{1337}(398,\cdot)\) \(\chi_{1337}(405,\cdot)\) \(\chi_{1337}(433,\cdot)\) \(\chi_{1337}(447,\cdot)\) \(\chi_{1337}(454,\cdot)\) \(\chi_{1337}(461,\cdot)\) \(\chi_{1337}(468,\cdot)\) \(\chi_{1337}(482,\cdot)\) ...

Values on generators

\((192,974)\) → \((-1,e\left(\frac{62}{95}\right))\)

Values

-112345689101112
\(-1\)\(1\)\(e\left(\frac{68}{95}\right)\)\(e\left(\frac{39}{190}\right)\)\(e\left(\frac{41}{95}\right)\)\(e\left(\frac{5}{38}\right)\)\(e\left(\frac{35}{38}\right)\)\(e\left(\frac{14}{95}\right)\)\(e\left(\frac{39}{95}\right)\)\(e\left(\frac{161}{190}\right)\)\(e\left(\frac{9}{19}\right)\)\(e\left(\frac{121}{190}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{95})\)