Properties

Conductor 2003
Order 182
Real No
Primitive Yes
Parity Odd
Orbit Label 2003.m

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(2003)
 
sage: chi = H[6]
 
pari: [g,chi] = znchar(Mod(6,2003))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 2003
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 182
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 = Odd
Orbit label = 2003.m
Orbit index = 13

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 ]
 

\(\chi_{2003}(6,\cdot)\) \(\chi_{2003}(17,\cdot)\) \(\chi_{2003}(69,\cdot)\) \(\chi_{2003}(132,\cdot)\) \(\chi_{2003}(216,\cdot)\) \(\chi_{2003}(233,\cdot)\) \(\chi_{2003}(260,\cdot)\) \(\chi_{2003}(295,\cdot)\) \(\chi_{2003}(331,\cdot)\) \(\chi_{2003}(334,\cdot)\) \(\chi_{2003}(374,\cdot)\) \(\chi_{2003}(376,\cdot)\) \(\chi_{2003}(382,\cdot)\) \(\chi_{2003}(387,\cdot)\) \(\chi_{2003}(388,\cdot)\) \(\chi_{2003}(392,\cdot)\) \(\chi_{2003}(456,\cdot)\) \(\chi_{2003}(481,\cdot)\) \(\chi_{2003}(502,\cdot)\) \(\chi_{2003}(524,\cdot)\) \(\chi_{2003}(534,\cdot)\) \(\chi_{2003}(567,\cdot)\) \(\chi_{2003}(584,\cdot)\) \(\chi_{2003}(603,\cdot)\) \(\chi_{2003}(604,\cdot)\) \(\chi_{2003}(605,\cdot)\) \(\chi_{2003}(612,\cdot)\) \(\chi_{2003}(707,\cdot)\) \(\chi_{2003}(802,\cdot)\) \(\chi_{2003}(817,\cdot)\) ...

Values on generators

\(5\) → \(e\left(\frac{153}{182}\right)\)

Values

-11234567891011
\(-1\)\(1\)\(e\left(\frac{25}{26}\right)\)\(e\left(\frac{79}{91}\right)\)\(e\left(\frac{12}{13}\right)\)\(e\left(\frac{153}{182}\right)\)\(e\left(\frac{151}{182}\right)\)\(e\left(\frac{73}{182}\right)\)\(e\left(\frac{23}{26}\right)\)\(e\left(\frac{67}{91}\right)\)\(e\left(\frac{73}{91}\right)\)\(e\left(\frac{5}{26}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{91})\)