Properties

Label 8034.751
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([0,85,84]))
 
pari: [g,chi] = znchar(Mod(751,8034))
 

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 \(\chi_{1339}(751,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 8034.dx

\(\chi_{8034}(751,\cdot)\) \(\chi_{8034}(1141,\cdot)\) \(\chi_{8034}(1297,\cdot)\) \(\chi_{8034}(1369,\cdot)\) \(\chi_{8034}(1609,\cdot)\) \(\chi_{8034}(1759,\cdot)\) \(\chi_{8034}(1765,\cdot)\) \(\chi_{8034}(1915,\cdot)\) \(\chi_{8034}(2227,\cdot)\) \(\chi_{8034}(2383,\cdot)\) \(\chi_{8034}(2701,\cdot)\) \(\chi_{8034}(2857,\cdot)\) \(\chi_{8034}(3169,\cdot)\) \(\chi_{8034}(3319,\cdot)\) \(\chi_{8034}(3475,\cdot)\) \(\chi_{8034}(3787,\cdot)\) \(\chi_{8034}(4339,\cdot)\) \(\chi_{8034}(4495,\cdot)\) \(\chi_{8034}(4957,\cdot)\) \(\chi_{8034}(5113,\cdot)\) \(\chi_{8034}(5119,\cdot)\) \(\chi_{8034}(5353,\cdot)\) \(\chi_{8034}(5737,\cdot)\) \(\chi_{8034}(5971,\cdot)\) \(\chi_{8034}(6055,\cdot)\) \(\chi_{8034}(6523,\cdot)\) \(\chi_{8034}(6601,\cdot)\) \(\chi_{8034}(6673,\cdot)\) \(\chi_{8034}(7141,\cdot)\) \(\chi_{8034}(7219,\cdot)\) ...

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

\((5357,1237,5773)\) → \((1,e\left(\frac{5}{6}\right),e\left(\frac{14}{17}\right))\)

Values

\(-1\)\(1\)\(5\)\(7\)\(11\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)\(35\)
\(1\)\(1\)\(e\left(\frac{11}{34}\right)\)\(e\left(\frac{47}{102}\right)\)\(e\left(\frac{7}{102}\right)\)\(e\left(\frac{16}{51}\right)\)\(e\left(\frac{5}{102}\right)\)\(e\left(\frac{5}{51}\right)\)\(e\left(\frac{11}{17}\right)\)\(e\left(\frac{8}{51}\right)\)\(e\left(\frac{15}{34}\right)\)\(e\left(\frac{40}{51}\right)\)
value at e.g. 2

Related number fields

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