Properties

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

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[52]
 
pari: [g,chi] = znchar(Mod(52,4011))
 

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.bv
Orbit index = 48

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 ]
 

\(\chi_{4011}(52,\cdot)\) \(\chi_{4011}(136,\cdot)\) \(\chi_{4011}(388,\cdot)\) \(\chi_{4011}(418,\cdot)\) \(\chi_{4011}(451,\cdot)\) \(\chi_{4011}(535,\cdot)\) \(\chi_{4011}(598,\cdot)\) \(\chi_{4011}(733,\cdot)\) \(\chi_{4011}(796,\cdot)\) \(\chi_{4011}(871,\cdot)\) \(\chi_{4011}(985,\cdot)\) \(\chi_{4011}(1132,\cdot)\) \(\chi_{4011}(1300,\cdot)\) \(\chi_{4011}(1342,\cdot)\) \(\chi_{4011}(1564,\cdot)\) \(\chi_{4011}(1678,\cdot)\) \(\chi_{4011}(1879,\cdot)\) \(\chi_{4011}(1942,\cdot)\) \(\chi_{4011}(2035,\cdot)\) \(\chi_{4011}(2131,\cdot)\) \(\chi_{4011}(2278,\cdot)\) \(\chi_{4011}(2413,\cdot)\) \(\chi_{4011}(2446,\cdot)\) \(\chi_{4011}(2488,\cdot)\) \(\chi_{4011}(2824,\cdot)\) \(\chi_{4011}(2854,\cdot)\) \(\chi_{4011}(2917,\cdot)\) \(\chi_{4011}(3001,\cdot)\) \(\chi_{4011}(3181,\cdot)\) \(\chi_{4011}(3253,\cdot)\) ...

Inducing primitive character

\(\chi_{1337}(52,\cdot)\)

Values on generators

\((2675,2866,2311)\) → \((1,e\left(\frac{1}{6}\right),e\left(\frac{1}{19}\right))\)

Values

-112458101113161719
\(-1\)\(1\)\(e\left(\frac{37}{57}\right)\)\(e\left(\frac{17}{57}\right)\)\(e\left(\frac{53}{114}\right)\)\(e\left(\frac{18}{19}\right)\)\(e\left(\frac{13}{114}\right)\)\(e\left(\frac{8}{57}\right)\)\(e\left(\frac{15}{38}\right)\)\(e\left(\frac{34}{57}\right)\)\(e\left(\frac{37}{114}\right)\)\(e\left(\frac{101}{114}\right)\)
value at  e.g. 2

Related number fields

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