Properties

Conductor 1337
Order 114
Real No
Primitive No
Parity Odd
Orbit Label 4011.bw

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[37]
 
pari: [g,chi] = znchar(Mod(37,4011))
 

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 = Odd
Orbit label = 4011.bw
Orbit index = 49

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 ]
 

\(\chi_{4011}(37,\cdot)\) \(\chi_{4011}(205,\cdot)\) \(\chi_{4011}(352,\cdot)\) \(\chi_{4011}(466,\cdot)\) \(\chi_{4011}(541,\cdot)\) \(\chi_{4011}(604,\cdot)\) \(\chi_{4011}(739,\cdot)\) \(\chi_{4011}(802,\cdot)\) \(\chi_{4011}(886,\cdot)\) \(\chi_{4011}(919,\cdot)\) \(\chi_{4011}(949,\cdot)\) \(\chi_{4011}(1201,\cdot)\) \(\chi_{4011}(1285,\cdot)\) \(\chi_{4011}(1348,\cdot)\) \(\chi_{4011}(1612,\cdot)\) \(\chi_{4011}(1789,\cdot)\) \(\chi_{4011}(1885,\cdot)\) \(\chi_{4011}(1948,\cdot)\) \(\chi_{4011}(2032,\cdot)\) \(\chi_{4011}(2095,\cdot)\) \(\chi_{4011}(2167,\cdot)\) \(\chi_{4011}(2347,\cdot)\) \(\chi_{4011}(2431,\cdot)\) \(\chi_{4011}(2494,\cdot)\) \(\chi_{4011}(2524,\cdot)\) \(\chi_{4011}(2860,\cdot)\) \(\chi_{4011}(2902,\cdot)\) \(\chi_{4011}(2935,\cdot)\) \(\chi_{4011}(3070,\cdot)\) \(\chi_{4011}(3217,\cdot)\) ...

Inducing primitive character

\(\chi_{1337}(37,\cdot)\)

Values on generators

\((2675,2866,2311)\) → \((1,e\left(\frac{1}{3}\right),e\left(\frac{3}{38}\right))\)

Values

-112458101113161719
\(-1\)\(1\)\(e\left(\frac{8}{57}\right)\)\(e\left(\frac{16}{57}\right)\)\(e\left(\frac{35}{57}\right)\)\(e\left(\frac{8}{19}\right)\)\(e\left(\frac{43}{57}\right)\)\(e\left(\frac{5}{114}\right)\)\(e\left(\frac{16}{19}\right)\)\(e\left(\frac{32}{57}\right)\)\(e\left(\frac{4}{57}\right)\)\(e\left(\frac{85}{114}\right)\)
value at  e.g. 2

Related number fields

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