Properties

Label 8033.88
Modulus $8033$
Conductor $277$
Order $69$
Real no
Primitive no
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([0,43]))
 
pari: [g,chi] = znchar(Mod(88,8033))
 

Basic properties

Modulus: \(8033\)
Conductor: \(277\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(69\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{277}(88,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 8033.bm

\(\chi_{8033}(88,\cdot)\) \(\chi_{8033}(465,\cdot)\) \(\chi_{8033}(639,\cdot)\) \(\chi_{8033}(784,\cdot)\) \(\chi_{8033}(987,\cdot)\) \(\chi_{8033}(1016,\cdot)\) \(\chi_{8033}(1045,\cdot)\) \(\chi_{8033}(1074,\cdot)\) \(\chi_{8033}(1741,\cdot)\) \(\chi_{8033}(2176,\cdot)\) \(\chi_{8033}(2640,\cdot)\) \(\chi_{8033}(3075,\cdot)\) \(\chi_{8033}(3104,\cdot)\) \(\chi_{8033}(3191,\cdot)\) \(\chi_{8033}(3249,\cdot)\) \(\chi_{8033}(3539,\cdot)\) \(\chi_{8033}(3887,\cdot)\) \(\chi_{8033}(3945,\cdot)\) \(\chi_{8033}(4032,\cdot)\) \(\chi_{8033}(4119,\cdot)\) \(\chi_{8033}(4148,\cdot)\) \(\chi_{8033}(4670,\cdot)\) \(\chi_{8033}(4757,\cdot)\) \(\chi_{8033}(4989,\cdot)\) \(\chi_{8033}(5076,\cdot)\) \(\chi_{8033}(5453,\cdot)\) \(\chi_{8033}(5511,\cdot)\) \(\chi_{8033}(5888,\cdot)\) \(\chi_{8033}(5917,\cdot)\) \(\chi_{8033}(6149,\cdot)\) ...

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

\((5541,1944)\) → \((1,e\left(\frac{43}{69}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(7\)\(8\)\(9\)\(10\)\(11\)
\(1\)\(1\)\(e\left(\frac{14}{23}\right)\)\(e\left(\frac{11}{69}\right)\)\(e\left(\frac{5}{23}\right)\)\(e\left(\frac{43}{69}\right)\)\(e\left(\frac{53}{69}\right)\)\(e\left(\frac{49}{69}\right)\)\(e\left(\frac{19}{23}\right)\)\(e\left(\frac{22}{69}\right)\)\(e\left(\frac{16}{69}\right)\)\(e\left(\frac{25}{69}\right)\)
value at e.g. 2

Related number fields

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