Properties

Conductor 4001
Order 125
Real No
Primitive No
Parity Even
Orbit Label 8002.o

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(8002)
 
sage: chi = H[35]
 
pari: [g,chi] = znchar(Mod(35,8002))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 4001
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 125
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 = 8002.o
Orbit index = 15

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 ]
 

\(\chi_{8002}(35,\cdot)\) \(\chi_{8002}(71,\cdot)\) \(\chi_{8002}(405,\cdot)\) \(\chi_{8002}(417,\cdot)\) \(\chi_{8002}(463,\cdot)\) \(\chi_{8002}(501,\cdot)\) \(\chi_{8002}(615,\cdot)\) \(\chi_{8002}(785,\cdot)\) \(\chi_{8002}(865,\cdot)\) \(\chi_{8002}(1013,\cdot)\) \(\chi_{8002}(1023,\cdot)\) \(\chi_{8002}(1095,\cdot)\) \(\chi_{8002}(1219,\cdot)\) \(\chi_{8002}(1225,\cdot)\) \(\chi_{8002}(1385,\cdot)\) \(\chi_{8002}(1535,\cdot)\) \(\chi_{8002}(1823,\cdot)\) \(\chi_{8002}(1913,\cdot)\) \(\chi_{8002}(2131,\cdot)\) \(\chi_{8002}(2163,\cdot)\) \(\chi_{8002}(2485,\cdot)\) \(\chi_{8002}(2499,\cdot)\) \(\chi_{8002}(2539,\cdot)\) \(\chi_{8002}(2567,\cdot)\) \(\chi_{8002}(2655,\cdot)\) \(\chi_{8002}(2855,\cdot)\) \(\chi_{8002}(2859,\cdot)\) \(\chi_{8002}(2865,\cdot)\) \(\chi_{8002}(2939,\cdot)\) \(\chi_{8002}(3007,\cdot)\) ...

Inducing primitive character

\(\chi_{4001}(35,\cdot)\)

Values on generators

\(3\) → \(e\left(\frac{44}{125}\right)\)

Values

-113579111315171921
\(1\)\(1\)\(e\left(\frac{44}{125}\right)\)\(e\left(\frac{9}{25}\right)\)\(e\left(\frac{32}{125}\right)\)\(e\left(\frac{88}{125}\right)\)\(e\left(\frac{3}{5}\right)\)\(e\left(\frac{91}{125}\right)\)\(e\left(\frac{89}{125}\right)\)\(e\left(\frac{89}{125}\right)\)\(e\left(\frac{31}{125}\right)\)\(e\left(\frac{76}{125}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{125})\)