Properties

Label 8034.49
Modulus $8034$
Conductor $1339$
Order $102$
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(8034)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,85,8]))
 
pari: [g,chi] = znchar(Mod(49,8034))
 

Basic properties

Modulus: \(8034\)
Conductor: \(1339\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(102\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{1339}(49,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 8034.dg

\(\chi_{8034}(49,\cdot)\) \(\chi_{8034}(517,\cdot)\) \(\chi_{8034}(673,\cdot)\) \(\chi_{8034}(907,\cdot)\) \(\chi_{8034}(979,\cdot)\) \(\chi_{8034}(1603,\cdot)\) \(\chi_{8034}(1681,\cdot)\) \(\chi_{8034}(1993,\cdot)\) \(\chi_{8034}(2461,\cdot)\) \(\chi_{8034}(2695,\cdot)\) \(\chi_{8034}(3013,\cdot)\) \(\chi_{8034}(3085,\cdot)\) \(\chi_{8034}(3325,\cdot)\) \(\chi_{8034}(3871,\cdot)\) \(\chi_{8034}(4021,\cdot)\) \(\chi_{8034}(4099,\cdot)\) \(\chi_{8034}(4255,\cdot)\) \(\chi_{8034}(4333,\cdot)\) \(\chi_{8034}(4573,\cdot)\) \(\chi_{8034}(4651,\cdot)\) \(\chi_{8034}(4801,\cdot)\) \(\chi_{8034}(4879,\cdot)\) \(\chi_{8034}(4963,\cdot)\) \(\chi_{8034}(5035,\cdot)\) \(\chi_{8034}(5041,\cdot)\) \(\chi_{8034}(5587,\cdot)\) \(\chi_{8034}(5899,\cdot)\) \(\chi_{8034}(6127,\cdot)\) \(\chi_{8034}(6445,\cdot)\) \(\chi_{8034}(7381,\cdot)\) ...

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

\((5357,1237,5773)\) → \((1,e\left(\frac{5}{6}\right),e\left(\frac{4}{51}\right))\)

Values

\(-1\)\(1\)\(5\)\(7\)\(11\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)\(35\)
\(1\)\(1\)\(e\left(\frac{59}{102}\right)\)\(e\left(\frac{49}{102}\right)\)\(e\left(\frac{21}{34}\right)\)\(e\left(\frac{8}{51}\right)\)\(e\left(\frac{15}{34}\right)\)\(e\left(\frac{11}{51}\right)\)\(e\left(\frac{8}{51}\right)\)\(e\left(\frac{4}{51}\right)\)\(e\left(\frac{33}{34}\right)\)\(e\left(\frac{1}{17}\right)\)
value at e.g. 2

Related number fields

Field of values: $\Q(\zeta_{51})$
Fixed field: Number field defined by a degree 102 polynomial