Properties

Conductor 2011
Order 402
Real No
Primitive Yes
Parity Odd
Orbit Label 2011.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(2011)
sage: chi = H[2]
pari: [g,chi] = znchar(Mod(2,2011))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 2011
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Order = 402
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 = 2011.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 ]

\(\chi_{2011}(2,\cdot)\) \(\chi_{2011}(15,\cdot)\) \(\chi_{2011}(32,\cdot)\) \(\chi_{2011}(37,\cdot)\) \(\chi_{2011}(67,\cdot)\) \(\chi_{2011}(91,\cdot)\) \(\chi_{2011}(128,\cdot)\) \(\chi_{2011}(139,\cdot)\) \(\chi_{2011}(143,\cdot)\) \(\chi_{2011}(148,\cdot)\) \(\chi_{2011}(163,\cdot)\) \(\chi_{2011}(171,\cdot)\) \(\chi_{2011}(217,\cdot)\) \(\chi_{2011}(221,\cdot)\) \(\chi_{2011}(230,\cdot)\) \(\chi_{2011}(231,\cdot)\) \(\chi_{2011}(234,\cdot)\) \(\chi_{2011}(240,\cdot)\) \(\chi_{2011}(243,\cdot)\) \(\chi_{2011}(266,\cdot)\) \(\chi_{2011}(275,\cdot)\) \(\chi_{2011}(277,\cdot)\) \(\chi_{2011}(281,\cdot)\) \(\chi_{2011}(341,\cdot)\) \(\chi_{2011}(357,\cdot)\) \(\chi_{2011}(363,\cdot)\) \(\chi_{2011}(364,\cdot)\) \(\chi_{2011}(365,\cdot)\) \(\chi_{2011}(377,\cdot)\) \(\chi_{2011}(388,\cdot)\) ...

Values on generators

\(3\) → \(e\left(\frac{49}{402}\right)\)

Values

-11234567891011
\(-1\)\(1\)\(e\left(\frac{347}{402}\right)\)\(e\left(\frac{49}{402}\right)\)\(e\left(\frac{146}{201}\right)\)\(e\left(\frac{164}{201}\right)\)\(e\left(\frac{66}{67}\right)\)\(e\left(\frac{103}{402}\right)\)\(e\left(\frac{79}{134}\right)\)\(e\left(\frac{49}{201}\right)\)\(e\left(\frac{91}{134}\right)\)\(e\left(\frac{161}{402}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{201})\)