Properties

Label 4033.10
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([72,25]))
 
pari: [g,chi] = znchar(Mod(10,4033))
 

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.ir

\(\chi_{4033}(10,\cdot)\) \(\chi_{4033}(174,\cdot)\) \(\chi_{4033}(232,\cdot)\) \(\chi_{4033}(248,\cdot)\) \(\chi_{4033}(269,\cdot)\) \(\chi_{4033}(285,\cdot)\) \(\chi_{4033}(380,\cdot)\) \(\chi_{4033}(602,\cdot)\) \(\chi_{4033}(750,\cdot)\) \(\chi_{4033}(787,\cdot)\) \(\chi_{4033}(914,\cdot)\) \(\chi_{4033}(951,\cdot)\) \(\chi_{4033}(1025,\cdot)\) \(\chi_{4033}(1210,\cdot)\) \(\chi_{4033}(1268,\cdot)\) \(\chi_{4033}(1358,\cdot)\) \(\chi_{4033}(1617,\cdot)\) \(\chi_{4033}(1675,\cdot)\) \(\chi_{4033}(2024,\cdot)\) \(\chi_{4033}(2156,\cdot)\) \(\chi_{4033}(2193,\cdot)\) \(\chi_{4033}(2341,\cdot)\) \(\chi_{4033}(2468,\cdot)\) \(\chi_{4033}(2563,\cdot)\) \(\chi_{4033}(2579,\cdot)\) \(\chi_{4033}(2653,\cdot)\) \(\chi_{4033}(2674,\cdot)\) \(\chi_{4033}(2711,\cdot)\) \(\chi_{4033}(2764,\cdot)\) \(\chi_{4033}(2933,\cdot)\) ...

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

\((1963,2295)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{25}{108}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(7\)\(8\)\(9\)\(10\)\(11\)
\(-1\)\(1\)\(e\left(\frac{31}{36}\right)\)\(e\left(\frac{10}{27}\right)\)\(e\left(\frac{13}{18}\right)\)\(e\left(\frac{25}{27}\right)\)\(e\left(\frac{25}{108}\right)\)\(e\left(\frac{16}{27}\right)\)\(e\left(\frac{7}{12}\right)\)\(e\left(\frac{20}{27}\right)\)\(e\left(\frac{85}{108}\right)\)\(e\left(\frac{23}{108}\right)\)
value at e.g. 2

Related number fields

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