Properties

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

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[38]
 
pari: [g,chi] = znchar(Mod(38,4011))
 

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.bt
Orbit index = 46

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 ]
 

\(\chi_{4011}(38,\cdot)\) \(\chi_{4011}(122,\cdot)\) \(\chi_{4011}(185,\cdot)\) \(\chi_{4011}(257,\cdot)\) \(\chi_{4011}(437,\cdot)\) \(\chi_{4011}(521,\cdot)\) \(\chi_{4011}(584,\cdot)\) \(\chi_{4011}(614,\cdot)\) \(\chi_{4011}(950,\cdot)\) \(\chi_{4011}(992,\cdot)\) \(\chi_{4011}(1025,\cdot)\) \(\chi_{4011}(1160,\cdot)\) \(\chi_{4011}(1307,\cdot)\) \(\chi_{4011}(1403,\cdot)\) \(\chi_{4011}(1496,\cdot)\) \(\chi_{4011}(1559,\cdot)\) \(\chi_{4011}(1760,\cdot)\) \(\chi_{4011}(1874,\cdot)\) \(\chi_{4011}(2096,\cdot)\) \(\chi_{4011}(2138,\cdot)\) \(\chi_{4011}(2306,\cdot)\) \(\chi_{4011}(2453,\cdot)\) \(\chi_{4011}(2567,\cdot)\) \(\chi_{4011}(2642,\cdot)\) \(\chi_{4011}(2705,\cdot)\) \(\chi_{4011}(2840,\cdot)\) \(\chi_{4011}(2903,\cdot)\) \(\chi_{4011}(2987,\cdot)\) \(\chi_{4011}(3020,\cdot)\) \(\chi_{4011}(3050,\cdot)\) ...

Values on generators

\((2675,2866,2311)\) → \((-1,e\left(\frac{1}{6}\right),e\left(\frac{9}{38}\right))\)

Values

-112458101113161719
\(-1\)\(1\)\(e\left(\frac{29}{114}\right)\)\(e\left(\frac{29}{57}\right)\)\(e\left(\frac{10}{57}\right)\)\(e\left(\frac{29}{38}\right)\)\(e\left(\frac{49}{114}\right)\)\(e\left(\frac{17}{57}\right)\)\(e\left(\frac{1}{38}\right)\)\(e\left(\frac{1}{57}\right)\)\(e\left(\frac{50}{57}\right)\)\(e\left(\frac{4}{57}\right)\)
value at  e.g. 2

Related number fields

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