Properties

Conductor 751
Order 75
Real No
Primitive No
Parity Even
Orbit Label 6008.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(6008)
 
sage: chi = H[121]
 
pari: [g,chi] = znchar(Mod(121,6008))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 751
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 75
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 = 6008.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 ]
 

\(\chi_{6008}(121,\cdot)\) \(\chi_{6008}(273,\cdot)\) \(\chi_{6008}(881,\cdot)\) \(\chi_{6008}(945,\cdot)\) \(\chi_{6008}(1129,\cdot)\) \(\chi_{6008}(1609,\cdot)\) \(\chi_{6008}(1633,\cdot)\) \(\chi_{6008}(1665,\cdot)\) \(\chi_{6008}(1801,\cdot)\) \(\chi_{6008}(1809,\cdot)\) \(\chi_{6008}(1953,\cdot)\) \(\chi_{6008}(2145,\cdot)\) \(\chi_{6008}(2305,\cdot)\) \(\chi_{6008}(2433,\cdot)\) \(\chi_{6008}(2537,\cdot)\) \(\chi_{6008}(2625,\cdot)\) \(\chi_{6008}(2753,\cdot)\) \(\chi_{6008}(2761,\cdot)\) \(\chi_{6008}(2921,\cdot)\) \(\chi_{6008}(2993,\cdot)\) \(\chi_{6008}(3065,\cdot)\) \(\chi_{6008}(3201,\cdot)\) \(\chi_{6008}(3233,\cdot)\) \(\chi_{6008}(3409,\cdot)\) \(\chi_{6008}(3641,\cdot)\) \(\chi_{6008}(3721,\cdot)\) \(\chi_{6008}(3841,\cdot)\) \(\chi_{6008}(3945,\cdot)\) \(\chi_{6008}(4129,\cdot)\) \(\chi_{6008}(4377,\cdot)\) ...

Inducing primitive character

\(\chi_{751}(121,\cdot)\)

Values on generators

\((1503,3005,1505)\) → \((1,1,e\left(\frac{68}{75}\right))\)

Values

-113579111315171921
\(1\)\(1\)\(e\left(\frac{68}{75}\right)\)\(e\left(\frac{23}{75}\right)\)\(e\left(\frac{6}{25}\right)\)\(e\left(\frac{61}{75}\right)\)\(e\left(\frac{4}{15}\right)\)\(e\left(\frac{44}{75}\right)\)\(e\left(\frac{16}{75}\right)\)\(e\left(\frac{22}{75}\right)\)\(e\left(\frac{74}{75}\right)\)\(e\left(\frac{11}{75}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{75})\)