Properties

Conductor 1337
Order 114
Real No
Primitive No
Parity Even
Orbit Label 4011.bu

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[31]
 
pari: [g,chi] = znchar(Mod(31,4011))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 1337
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 114
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.bu
Orbit index = 47

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 ]
 

\(\chi_{4011}(31,\cdot)\) \(\chi_{4011}(166,\cdot)\) \(\chi_{4011}(229,\cdot)\) \(\chi_{4011}(313,\cdot)\) \(\chi_{4011}(346,\cdot)\) \(\chi_{4011}(376,\cdot)\) \(\chi_{4011}(628,\cdot)\) \(\chi_{4011}(712,\cdot)\) \(\chi_{4011}(775,\cdot)\) \(\chi_{4011}(1039,\cdot)\) \(\chi_{4011}(1216,\cdot)\) \(\chi_{4011}(1312,\cdot)\) \(\chi_{4011}(1375,\cdot)\) \(\chi_{4011}(1459,\cdot)\) \(\chi_{4011}(1522,\cdot)\) \(\chi_{4011}(1594,\cdot)\) \(\chi_{4011}(1774,\cdot)\) \(\chi_{4011}(1858,\cdot)\) \(\chi_{4011}(1921,\cdot)\) \(\chi_{4011}(1951,\cdot)\) \(\chi_{4011}(2287,\cdot)\) \(\chi_{4011}(2329,\cdot)\) \(\chi_{4011}(2362,\cdot)\) \(\chi_{4011}(2497,\cdot)\) \(\chi_{4011}(2644,\cdot)\) \(\chi_{4011}(2740,\cdot)\) \(\chi_{4011}(2833,\cdot)\) \(\chi_{4011}(2896,\cdot)\) \(\chi_{4011}(3097,\cdot)\) \(\chi_{4011}(3211,\cdot)\) ...

Inducing primitive character

\(\chi_{1337}(31,\cdot)\)

Values on generators

\((2675,2866,2311)\) → \((1,e\left(\frac{1}{6}\right),e\left(\frac{35}{38}\right))\)

Values

-112458101113161719
\(1\)\(1\)\(e\left(\frac{49}{57}\right)\)\(e\left(\frac{41}{57}\right)\)\(e\left(\frac{101}{114}\right)\)\(e\left(\frac{11}{19}\right)\)\(e\left(\frac{85}{114}\right)\)\(e\left(\frac{109}{114}\right)\)\(e\left(\frac{25}{38}\right)\)\(e\left(\frac{25}{57}\right)\)\(e\left(\frac{49}{114}\right)\)\(e\left(\frac{43}{57}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{57})\)