Properties

Conductor 4011
Order 570
Real No
Primitive Yes
Parity Even
Orbit Label 4011.ck

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[17]
 
pari: [g,chi] = znchar(Mod(17,4011))
 

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 = Even
Orbit label = 4011.ck
Orbit index = 63

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 ]
 

\(\chi_{4011}(17,\cdot)\) \(\chi_{4011}(26,\cdot)\) \(\chi_{4011}(59,\cdot)\) \(\chi_{4011}(68,\cdot)\) \(\chi_{4011}(80,\cdot)\) \(\chi_{4011}(194,\cdot)\) \(\chi_{4011}(206,\cdot)\) \(\chi_{4011}(215,\cdot)\) \(\chi_{4011}(236,\cdot)\) \(\chi_{4011}(269,\cdot)\) \(\chi_{4011}(299,\cdot)\) \(\chi_{4011}(311,\cdot)\) \(\chi_{4011}(320,\cdot)\) \(\chi_{4011}(353,\cdot)\) \(\chi_{4011}(395,\cdot)\) \(\chi_{4011}(416,\cdot)\) \(\chi_{4011}(425,\cdot)\) \(\chi_{4011}(446,\cdot)\) \(\chi_{4011}(467,\cdot)\) \(\chi_{4011}(479,\cdot)\) \(\chi_{4011}(500,\cdot)\) \(\chi_{4011}(551,\cdot)\) \(\chi_{4011}(593,\cdot)\) \(\chi_{4011}(677,\cdot)\) \(\chi_{4011}(731,\cdot)\) \(\chi_{4011}(773,\cdot)\) \(\chi_{4011}(782,\cdot)\) \(\chi_{4011}(815,\cdot)\) \(\chi_{4011}(824,\cdot)\) \(\chi_{4011}(836,\cdot)\) ...

Values on generators

\((2675,2866,2311)\) → \((-1,e\left(\frac{1}{6}\right),e\left(\frac{49}{95}\right))\)

Values

-112458101113161719
\(1\)\(1\)\(e\left(\frac{301}{570}\right)\)\(e\left(\frac{16}{285}\right)\)\(e\left(\frac{7}{57}\right)\)\(e\left(\frac{111}{190}\right)\)\(e\left(\frac{371}{570}\right)\)\(e\left(\frac{1}{114}\right)\)\(e\left(\frac{51}{190}\right)\)\(e\left(\frac{32}{285}\right)\)\(e\left(\frac{61}{285}\right)\)\(e\left(\frac{199}{570}\right)\)
value at  e.g. 2

Related number fields

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