Properties

Conductor 1337
Order 285
Real No
Primitive No
Parity Even
Orbit Label 4011.ce

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[46]
 
pari: [g,chi] = znchar(Mod(46,4011))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 1337
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 285
Real = No
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = No
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = Even
Orbit label = 4011.ce
Orbit index = 57

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 ]
 

\(\chi_{4011}(4,\cdot)\) \(\chi_{4011}(16,\cdot)\) \(\chi_{4011}(46,\cdot)\) \(\chi_{4011}(67,\cdot)\) \(\chi_{4011}(79,\cdot)\) \(\chi_{4011}(100,\cdot)\) \(\chi_{4011}(130,\cdot)\) \(\chi_{4011}(163,\cdot)\) \(\chi_{4011}(172,\cdot)\) \(\chi_{4011}(193,\cdot)\) \(\chi_{4011}(214,\cdot)\) \(\chi_{4011}(256,\cdot)\) \(\chi_{4011}(268,\cdot)\) \(\chi_{4011}(277,\cdot)\) \(\chi_{4011}(289,\cdot)\) \(\chi_{4011}(319,\cdot)\) \(\chi_{4011}(340,\cdot)\) \(\chi_{4011}(361,\cdot)\) \(\chi_{4011}(394,\cdot)\) \(\chi_{4011}(436,\cdot)\) \(\chi_{4011}(457,\cdot)\) \(\chi_{4011}(478,\cdot)\) \(\chi_{4011}(499,\cdot)\) \(\chi_{4011}(520,\cdot)\) \(\chi_{4011}(529,\cdot)\) \(\chi_{4011}(583,\cdot)\) \(\chi_{4011}(613,\cdot)\) \(\chi_{4011}(676,\cdot)\) \(\chi_{4011}(688,\cdot)\) \(\chi_{4011}(772,\cdot)\) ...

Inducing primitive character

\(\chi_{1337}(46,\cdot)\)

Values on generators

\((2675,2866,2311)\) → \((1,e\left(\frac{2}{3}\right),e\left(\frac{89}{95}\right))\)

Values

-112458101113161719
\(1\)\(1\)\(e\left(\frac{158}{285}\right)\)\(e\left(\frac{31}{285}\right)\)\(e\left(\frac{10}{57}\right)\)\(e\left(\frac{63}{95}\right)\)\(e\left(\frac{208}{285}\right)\)\(e\left(\frac{17}{57}\right)\)\(e\left(\frac{88}{95}\right)\)\(e\left(\frac{62}{285}\right)\)\(e\left(\frac{136}{285}\right)\)\(e\left(\frac{77}{285}\right)\)
value at  e.g. 2

Related number fields

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