Properties

Conductor 4003
Order 87
Real No
Primitive Yes
Parity Even
Orbit Label 4003.j

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(4003)
 
sage: chi = H[479]
 
pari: [g,chi] = znchar(Mod(479,4003))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 4003
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 87
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 = 4003.j
Orbit index = 10

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 ]
 

\(\chi_{4003}(10,\cdot)\) \(\chi_{4003}(100,\cdot)\) \(\chi_{4003}(117,\cdot)\) \(\chi_{4003}(127,\cdot)\) \(\chi_{4003}(208,\cdot)\) \(\chi_{4003}(214,\cdot)\) \(\chi_{4003}(285,\cdot)\) \(\chi_{4003}(292,\cdot)\) \(\chi_{4003}(316,\cdot)\) \(\chi_{4003}(318,\cdot)\) \(\chi_{4003}(356,\cdot)\) \(\chi_{4003}(412,\cdot)\) \(\chi_{4003}(479,\cdot)\) \(\chi_{4003}(506,\cdot)\) \(\chi_{4003}(785,\cdot)\) \(\chi_{4003}(787,\cdot)\) \(\chi_{4003}(788,\cdot)\) \(\chi_{4003}(913,\cdot)\) \(\chi_{4003}(945,\cdot)\) \(\chi_{4003}(1020,\cdot)\) \(\chi_{4003}(1049,\cdot)\) \(\chi_{4003}(1057,\cdot)\) \(\chi_{4003}(1165,\cdot)\) \(\chi_{4003}(1201,\cdot)\) \(\chi_{4003}(1270,\cdot)\) \(\chi_{4003}(1321,\cdot)\) \(\chi_{4003}(1385,\cdot)\) \(\chi_{4003}(1444,\cdot)\) \(\chi_{4003}(1618,\cdot)\) \(\chi_{4003}(1622,\cdot)\) ...

Values on generators

\(2\) → \(e\left(\frac{65}{87}\right)\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{65}{87}\right)\)\(e\left(\frac{70}{87}\right)\)\(e\left(\frac{43}{87}\right)\)\(e\left(\frac{2}{87}\right)\)\(e\left(\frac{16}{29}\right)\)\(e\left(\frac{32}{87}\right)\)\(e\left(\frac{7}{29}\right)\)\(e\left(\frac{53}{87}\right)\)\(e\left(\frac{67}{87}\right)\)\(e\left(\frac{19}{29}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{87})\)