Properties

Conductor 4011
Order 114
Real No
Primitive Yes
Parity Odd
Orbit Label 4011.bq

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[32]
 
pari: [g,chi] = znchar(Mod(32,4011))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 4011
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 = Yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = Odd
Orbit label = 4011.bq
Orbit index = 43

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 ]
 

\(\chi_{4011}(32,\cdot)\) \(\chi_{4011}(107,\cdot)\) \(\chi_{4011}(221,\cdot)\) \(\chi_{4011}(368,\cdot)\) \(\chi_{4011}(536,\cdot)\) \(\chi_{4011}(578,\cdot)\) \(\chi_{4011}(800,\cdot)\) \(\chi_{4011}(914,\cdot)\) \(\chi_{4011}(1115,\cdot)\) \(\chi_{4011}(1178,\cdot)\) \(\chi_{4011}(1271,\cdot)\) \(\chi_{4011}(1367,\cdot)\) \(\chi_{4011}(1514,\cdot)\) \(\chi_{4011}(1649,\cdot)\) \(\chi_{4011}(1682,\cdot)\) \(\chi_{4011}(1724,\cdot)\) \(\chi_{4011}(2060,\cdot)\) \(\chi_{4011}(2090,\cdot)\) \(\chi_{4011}(2153,\cdot)\) \(\chi_{4011}(2237,\cdot)\) \(\chi_{4011}(2417,\cdot)\) \(\chi_{4011}(2489,\cdot)\) \(\chi_{4011}(2552,\cdot)\) \(\chi_{4011}(2636,\cdot)\) \(\chi_{4011}(2699,\cdot)\) \(\chi_{4011}(2795,\cdot)\) \(\chi_{4011}(2972,\cdot)\) \(\chi_{4011}(3236,\cdot)\) \(\chi_{4011}(3299,\cdot)\) \(\chi_{4011}(3383,\cdot)\) ...

Values on generators

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

Values

-112458101113161719
\(-1\)\(1\)\(e\left(\frac{89}{114}\right)\)\(e\left(\frac{32}{57}\right)\)\(e\left(\frac{83}{114}\right)\)\(e\left(\frac{13}{38}\right)\)\(e\left(\frac{29}{57}\right)\)\(e\left(\frac{67}{114}\right)\)\(e\left(\frac{13}{19}\right)\)\(e\left(\frac{7}{57}\right)\)\(e\left(\frac{73}{114}\right)\)\(e\left(\frac{28}{57}\right)\)
value at  e.g. 2

Related number fields

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