Properties

Conductor 1337
Order 57
Real No
Primitive No
Parity Even
Orbit Label 4011.bo

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[25]
 
pari: [g,chi] = znchar(Mod(25,4011))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 1337
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 57
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.bo
Orbit index = 41

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 ]
 

\(\chi_{4011}(25,\cdot)\) \(\chi_{4011}(121,\cdot)\) \(\chi_{4011}(298,\cdot)\) \(\chi_{4011}(562,\cdot)\) \(\chi_{4011}(625,\cdot)\) \(\chi_{4011}(709,\cdot)\) \(\chi_{4011}(961,\cdot)\) \(\chi_{4011}(991,\cdot)\) \(\chi_{4011}(1024,\cdot)\) \(\chi_{4011}(1108,\cdot)\) \(\chi_{4011}(1171,\cdot)\) \(\chi_{4011}(1306,\cdot)\) \(\chi_{4011}(1369,\cdot)\) \(\chi_{4011}(1444,\cdot)\) \(\chi_{4011}(1558,\cdot)\) \(\chi_{4011}(1705,\cdot)\) \(\chi_{4011}(1873,\cdot)\) \(\chi_{4011}(1915,\cdot)\) \(\chi_{4011}(2137,\cdot)\) \(\chi_{4011}(2251,\cdot)\) \(\chi_{4011}(2452,\cdot)\) \(\chi_{4011}(2515,\cdot)\) \(\chi_{4011}(2608,\cdot)\) \(\chi_{4011}(2704,\cdot)\) \(\chi_{4011}(2851,\cdot)\) \(\chi_{4011}(2986,\cdot)\) \(\chi_{4011}(3019,\cdot)\) \(\chi_{4011}(3061,\cdot)\) \(\chi_{4011}(3397,\cdot)\) \(\chi_{4011}(3427,\cdot)\) ...

Inducing primitive character

\(\chi_{1337}(25,\cdot)\)

Values on generators

\((2675,2866,2311)\) → \((1,e\left(\frac{2}{3}\right),e\left(\frac{10}{19}\right))\)

Values

-112458101113161719
\(1\)\(1\)\(e\left(\frac{28}{57}\right)\)\(e\left(\frac{56}{57}\right)\)\(e\left(\frac{37}{57}\right)\)\(e\left(\frac{9}{19}\right)\)\(e\left(\frac{8}{57}\right)\)\(e\left(\frac{23}{57}\right)\)\(e\left(\frac{18}{19}\right)\)\(e\left(\frac{55}{57}\right)\)\(e\left(\frac{14}{57}\right)\)\(e\left(\frac{49}{57}\right)\)
value at  e.g. 2

Related number fields

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