Properties

Conductor 67
Order 33
Real No
Primitive No
Parity Even
Orbit Label 4020.cm

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(4020)
 
sage: chi = H[121]
 
pari: [g,chi] = znchar(Mod(121,4020))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 67
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 33
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 = 4020.cm
Orbit index = 65

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 ]
 

\(\chi_{4020}(121,\cdot)\) \(\chi_{4020}(181,\cdot)\) \(\chi_{4020}(301,\cdot)\) \(\chi_{4020}(361,\cdot)\) \(\chi_{4020}(421,\cdot)\) \(\chi_{4020}(601,\cdot)\) \(\chi_{4020}(961,\cdot)\) \(\chi_{4020}(1021,\cdot)\) \(\chi_{4020}(1261,\cdot)\) \(\chi_{4020}(1681,\cdot)\) \(\chi_{4020}(2161,\cdot)\) \(\chi_{4020}(2221,\cdot)\) \(\chi_{4020}(2401,\cdot)\) \(\chi_{4020}(2461,\cdot)\) \(\chi_{4020}(2581,\cdot)\) \(\chi_{4020}(2701,\cdot)\) \(\chi_{4020}(2941,\cdot)\) \(\chi_{4020}(3121,\cdot)\) \(\chi_{4020}(3421,\cdot)\) \(\chi_{4020}(3721,\cdot)\)

Inducing primitive character

\(\chi_{67}(54,\cdot)\)

Values on generators

\((2011,2681,3217,1141)\) → \((1,1,1,e\left(\frac{26}{33}\right))\)

Values

-117111317192329313741
\(1\)\(1\)\(e\left(\frac{4}{33}\right)\)\(e\left(\frac{16}{33}\right)\)\(e\left(\frac{32}{33}\right)\)\(e\left(\frac{14}{33}\right)\)\(e\left(\frac{29}{33}\right)\)\(e\left(\frac{2}{33}\right)\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{1}{33}\right)\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{25}{33}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{33})\)