Properties

Label 4033.930
Modulus $4033$
Conductor $4033$
Order $108$
Real no
Primitive yes
Minimal yes
Parity even

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(4033)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([69,91]))
 
pari: [g,chi] = znchar(Mod(930,4033))
 

Basic properties

Modulus: \(4033\)
Conductor: \(4033\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(108\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 4033.ia

\(\chi_{4033}(13,\cdot)\) \(\chi_{4033}(204,\cdot)\) \(\chi_{4033}(257,\cdot)\) \(\chi_{4033}(383,\cdot)\) \(\chi_{4033}(392,\cdot)\) \(\chi_{4033}(426,\cdot)\) \(\chi_{4033}(505,\cdot)\) \(\chi_{4033}(575,\cdot)\) \(\chi_{4033}(930,\cdot)\) \(\chi_{4033}(1053,\cdot)\) \(\chi_{4033}(1142,\cdot)\) \(\chi_{4033}(1241,\cdot)\) \(\chi_{4033}(1297,\cdot)\) \(\chi_{4033}(1367,\cdot)\) \(\chi_{4033}(1411,\cdot)\) \(\chi_{4033}(1720,\cdot)\) \(\chi_{4033}(1791,\cdot)\) \(\chi_{4033}(1835,\cdot)\) \(\chi_{4033}(2198,\cdot)\) \(\chi_{4033}(2242,\cdot)\) \(\chi_{4033}(2313,\cdot)\) \(\chi_{4033}(2622,\cdot)\) \(\chi_{4033}(2666,\cdot)\) \(\chi_{4033}(2736,\cdot)\) \(\chi_{4033}(2792,\cdot)\) \(\chi_{4033}(2891,\cdot)\) \(\chi_{4033}(2980,\cdot)\) \(\chi_{4033}(3103,\cdot)\) \(\chi_{4033}(3458,\cdot)\) \(\chi_{4033}(3528,\cdot)\) ...

sage: chi.galois_orbit()
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Values on generators

\((1963,2295)\) → \((e\left(\frac{23}{36}\right),e\left(\frac{91}{108}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(7\)\(8\)\(9\)\(10\)\(11\)
\(1\)\(1\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{23}{54}\right)\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{79}{108}\right)\)\(e\left(\frac{5}{54}\right)\)\(e\left(\frac{4}{27}\right)\)\(1\)\(e\left(\frac{23}{27}\right)\)\(e\left(\frac{43}{108}\right)\)\(e\left(\frac{11}{108}\right)\)
value at e.g. 2

Related number fields

Field of values: $\Q(\zeta_{108})$
Fixed field: Number field defined by a degree 108 polynomial