Properties

Conductor 1337
Order 570
Real No
Primitive No
Parity Even
Orbit Label 4011.cf

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[19]
 
pari: [g,chi] = znchar(Mod(19,4011))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 1337
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 = No
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = Even
Orbit label = 4011.cf
Orbit index = 58

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 ]
 

\(\chi_{4011}(19,\cdot)\) \(\chi_{4011}(61,\cdot)\) \(\chi_{4011}(73,\cdot)\) \(\chi_{4011}(94,\cdot)\) \(\chi_{4011}(124,\cdot)\) \(\chi_{4011}(145,\cdot)\) \(\chi_{4011}(157,\cdot)\) \(\chi_{4011}(178,\cdot)\) \(\chi_{4011}(187,\cdot)\) \(\chi_{4011}(220,\cdot)\) \(\chi_{4011}(262,\cdot)\) \(\chi_{4011}(292,\cdot)\) \(\chi_{4011}(304,\cdot)\) \(\chi_{4011}(334,\cdot)\) \(\chi_{4011}(355,\cdot)\) \(\chi_{4011}(367,\cdot)\) \(\chi_{4011}(439,\cdot)\) \(\chi_{4011}(481,\cdot)\) \(\chi_{4011}(493,\cdot)\) \(\chi_{4011}(514,\cdot)\) \(\chi_{4011}(523,\cdot)\) \(\chi_{4011}(556,\cdot)\) \(\chi_{4011}(565,\cdot)\) \(\chi_{4011}(649,\cdot)\) \(\chi_{4011}(661,\cdot)\) \(\chi_{4011}(724,\cdot)\) \(\chi_{4011}(754,\cdot)\) \(\chi_{4011}(808,\cdot)\) \(\chi_{4011}(817,\cdot)\) \(\chi_{4011}(838,\cdot)\) ...

Inducing primitive character

\(\chi_{1337}(19,\cdot)\)

Values on generators

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

Values

-112458101113161719
\(1\)\(1\)\(e\left(\frac{256}{285}\right)\)\(e\left(\frac{227}{285}\right)\)\(e\left(\frac{49}{114}\right)\)\(e\left(\frac{66}{95}\right)\)\(e\left(\frac{187}{570}\right)\)\(e\left(\frac{89}{114}\right)\)\(e\left(\frac{17}{190}\right)\)\(e\left(\frac{169}{285}\right)\)\(e\left(\frac{199}{570}\right)\)\(e\left(\frac{49}{285}\right)\)
value at  e.g. 2

Related number fields

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