Properties

Label 8033.28
Modulus $8033$
Conductor $8033$
Order $138$
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(8033)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([69,20]))
 
pari: [g,chi] = znchar(Mod(28,8033))
 

Basic properties

Modulus: \(8033\)
Conductor: \(8033\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(138\)
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 8033.ca

\(\chi_{8033}(28,\cdot)\) \(\chi_{8033}(57,\cdot)\) \(\chi_{8033}(144,\cdot)\) \(\chi_{8033}(202,\cdot)\) \(\chi_{8033}(492,\cdot)\) \(\chi_{8033}(840,\cdot)\) \(\chi_{8033}(898,\cdot)\) \(\chi_{8033}(985,\cdot)\) \(\chi_{8033}(1072,\cdot)\) \(\chi_{8033}(1101,\cdot)\) \(\chi_{8033}(1623,\cdot)\) \(\chi_{8033}(1710,\cdot)\) \(\chi_{8033}(1942,\cdot)\) \(\chi_{8033}(2029,\cdot)\) \(\chi_{8033}(2406,\cdot)\) \(\chi_{8033}(2464,\cdot)\) \(\chi_{8033}(2841,\cdot)\) \(\chi_{8033}(2870,\cdot)\) \(\chi_{8033}(3102,\cdot)\) \(\chi_{8033}(3218,\cdot)\) \(\chi_{8033}(3334,\cdot)\) \(\chi_{8033}(3624,\cdot)\) \(\chi_{8033}(3682,\cdot)\) \(\chi_{8033}(3856,\cdot)\) \(\chi_{8033}(4204,\cdot)\) \(\chi_{8033}(4291,\cdot)\) \(\chi_{8033}(4320,\cdot)\) \(\chi_{8033}(4349,\cdot)\) \(\chi_{8033}(4407,\cdot)\) \(\chi_{8033}(4523,\cdot)\) ...

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

\((5541,1944)\) → \((-1,e\left(\frac{10}{69}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(7\)\(8\)\(9\)\(10\)\(11\)
\(1\)\(1\)\(e\left(\frac{37}{46}\right)\)\(e\left(\frac{103}{138}\right)\)\(e\left(\frac{14}{23}\right)\)\(e\left(\frac{10}{69}\right)\)\(e\left(\frac{38}{69}\right)\)\(e\left(\frac{13}{69}\right)\)\(e\left(\frac{19}{46}\right)\)\(e\left(\frac{34}{69}\right)\)\(e\left(\frac{131}{138}\right)\)\(e\left(\frac{71}{138}\right)\)
value at e.g. 2

Related number fields

Field of values: $\Q(\zeta_{69})$
Fixed field: Number field defined by a degree 138 polynomial