Properties

Label 4033.812
Modulus $4033$
Conductor $4033$
Order $108$
Real no
Primitive yes
Minimal yes
Parity odd

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([57,80]))
 
pari: [g,chi] = znchar(Mod(812,4033))
 

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: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 4033.ic

\(\chi_{4033}(5,\cdot)\) \(\chi_{4033}(22,\cdot)\) \(\chi_{4033}(35,\cdot)\) \(\chi_{4033}(116,\cdot)\) \(\chi_{4033}(135,\cdot)\) \(\chi_{4033}(239,\cdot)\) \(\chi_{4033}(550,\cdot)\) \(\chi_{4033}(594,\cdot)\) \(\chi_{4033}(661,\cdot)\) \(\chi_{4033}(812,\cdot)\) \(\chi_{4033}(875,\cdot)\) \(\chi_{4033}(945,\cdot)\) \(\chi_{4033}(1078,\cdot)\) \(\chi_{4033}(1317,\cdot)\) \(\chi_{4033}(1495,\cdot)\) \(\chi_{4033}(1498,\cdot)\) \(\chi_{4033}(1623,\cdot)\) \(\chi_{4033}(1683,\cdot)\) \(\chi_{4033}(1715,\cdot)\) \(\chi_{4033}(1759,\cdot)\) \(\chi_{4033}(1942,\cdot)\) \(\chi_{4033}(2092,\cdot)\) \(\chi_{4033}(2420,\cdot)\) \(\chi_{4033}(2751,\cdot)\) \(\chi_{4033}(3125,\cdot)\) \(\chi_{4033}(3130,\cdot)\) \(\chi_{4033}(3132,\cdot)\) \(\chi_{4033}(3295,\cdot)\) \(\chi_{4033}(3460,\cdot)\) \(\chi_{4033}(3491,\cdot)\) ...

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

\((1963,2295)\) → \((e\left(\frac{19}{36}\right),e\left(\frac{20}{27}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(7\)\(8\)\(9\)\(10\)\(11\)
\(-1\)\(1\)\(-i\)\(e\left(\frac{13}{54}\right)\)\(-1\)\(e\left(\frac{47}{108}\right)\)\(e\left(\frac{107}{108}\right)\)\(e\left(\frac{14}{27}\right)\)\(i\)\(e\left(\frac{13}{27}\right)\)\(e\left(\frac{5}{27}\right)\)\(e\left(\frac{17}{54}\right)\)
value at e.g. 2

Related number fields

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