Properties

Conductor 4011
Order 570
Real No
Primitive Yes
Parity Odd
Orbit Label 4011.cl

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(4011)
 
sage: chi = H[47]
 
pari: [g,chi] = znchar(Mod(47,4011))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 4011
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 570
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 = 4011.cl
Orbit index = 64

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 ]
 

\(\chi_{4011}(47,\cdot)\) \(\chi_{4011}(89,\cdot)\) \(\chi_{4011}(101,\cdot)\) \(\chi_{4011}(110,\cdot)\) \(\chi_{4011}(131,\cdot)\) \(\chi_{4011}(143,\cdot)\) \(\chi_{4011}(164,\cdot)\) \(\chi_{4011}(173,\cdot)\) \(\chi_{4011}(248,\cdot)\) \(\chi_{4011}(278,\cdot)\) \(\chi_{4011}(290,\cdot)\) \(\chi_{4011}(332,\cdot)\) \(\chi_{4011}(362,\cdot)\) \(\chi_{4011}(374,\cdot)\) \(\chi_{4011}(404,\cdot)\) \(\chi_{4011}(458,\cdot)\) \(\chi_{4011}(488,\cdot)\) \(\chi_{4011}(509,\cdot)\) \(\chi_{4011}(530,\cdot)\) \(\chi_{4011}(563,\cdot)\) \(\chi_{4011}(626,\cdot)\) \(\chi_{4011}(635,\cdot)\) \(\chi_{4011}(647,\cdot)\) \(\chi_{4011}(656,\cdot)\) \(\chi_{4011}(668,\cdot)\) \(\chi_{4011}(689,\cdot)\) \(\chi_{4011}(710,\cdot)\) \(\chi_{4011}(719,\cdot)\) \(\chi_{4011}(740,\cdot)\) \(\chi_{4011}(752,\cdot)\) ...

Values on generators

\((2675,2866,2311)\) → \((-1,e\left(\frac{5}{6}\right),e\left(\frac{123}{190}\right))\)

Values

-112458101113161719
\(-1\)\(1\)\(e\left(\frac{371}{570}\right)\)\(e\left(\frac{86}{285}\right)\)\(e\left(\frac{2}{57}\right)\)\(e\left(\frac{181}{190}\right)\)\(e\left(\frac{391}{570}\right)\)\(e\left(\frac{49}{57}\right)\)\(e\left(\frac{1}{190}\right)\)\(e\left(\frac{172}{285}\right)\)\(e\left(\frac{221}{285}\right)\)\(e\left(\frac{232}{285}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{285})\)