Properties

Label 4033.2066
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([27,22]))
 
pari: [g,chi] = znchar(Mod(2066,4033))
 

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.il

\(\chi_{4033}(31,\cdot)\) \(\chi_{4033}(302,\cdot)\) \(\chi_{4033}(339,\cdot)\) \(\chi_{4033}(401,\cdot)\) \(\chi_{4033}(524,\cdot)\) \(\chi_{4033}(783,\cdot)\) \(\chi_{4033}(857,\cdot)\) \(\chi_{4033}(956,\cdot)\) \(\chi_{4033}(993,\cdot)\) \(\chi_{4033}(1042,\cdot)\) \(\chi_{4033}(1178,\cdot)\) \(\chi_{4033}(1190,\cdot)\) \(\chi_{4033}(1227,\cdot)\) \(\chi_{4033}(1301,\cdot)\) \(\chi_{4033}(1412,\cdot)\) \(\chi_{4033}(1437,\cdot)\) \(\chi_{4033}(1511,\cdot)\) \(\chi_{4033}(1523,\cdot)\) \(\chi_{4033}(1671,\cdot)\) \(\chi_{4033}(1696,\cdot)\) \(\chi_{4033}(1844,\cdot)\) \(\chi_{4033}(1881,\cdot)\) \(\chi_{4033}(1955,\cdot)\) \(\chi_{4033}(2066,\cdot)\) \(\chi_{4033}(2177,\cdot)\) \(\chi_{4033}(2263,\cdot)\) \(\chi_{4033}(2325,\cdot)\) \(\chi_{4033}(2485,\cdot)\) \(\chi_{4033}(2917,\cdot)\) \(\chi_{4033}(3003,\cdot)\) ...

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

\((1963,2295)\) → \((i,e\left(\frac{11}{54}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(7\)\(8\)\(9\)\(10\)\(11\)
\(-1\)\(1\)\(e\left(\frac{31}{36}\right)\)\(e\left(\frac{5}{54}\right)\)\(e\left(\frac{13}{18}\right)\)\(e\left(\frac{25}{108}\right)\)\(e\left(\frac{103}{108}\right)\)\(e\left(\frac{4}{27}\right)\)\(e\left(\frac{7}{12}\right)\)\(e\left(\frac{5}{27}\right)\)\(e\left(\frac{5}{54}\right)\)\(e\left(\frac{11}{27}\right)\)
value at e.g. 2

Related number fields

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