Properties

Label 8034.35
Modulus $8034$
Conductor $4017$
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([51,68,5]))
 
pari: [g,chi] = znchar(Mod(35,8034))
 

Basic properties

Modulus: \(8034\)
Conductor: \(4017\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(102\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{4017}(35,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 8034.dn

\(\chi_{8034}(35,\cdot)\) \(\chi_{8034}(809,\cdot)\) \(\chi_{8034}(971,\cdot)\) \(\chi_{8034}(1517,\cdot)\) \(\chi_{8034}(1829,\cdot)\) \(\chi_{8034}(2375,\cdot)\) \(\chi_{8034}(2453,\cdot)\) \(\chi_{8034}(2525,\cdot)\) \(\chi_{8034}(2765,\cdot)\) \(\chi_{8034}(2843,\cdot)\) \(\chi_{8034}(3545,\cdot)\) \(\chi_{8034}(3617,\cdot)\) \(\chi_{8034}(3773,\cdot)\) \(\chi_{8034}(3851,\cdot)\) \(\chi_{8034}(4091,\cdot)\) \(\chi_{8034}(4319,\cdot)\) \(\chi_{8034}(4397,\cdot)\) \(\chi_{8034}(4403,\cdot)\) \(\chi_{8034}(4553,\cdot)\) \(\chi_{8034}(4631,\cdot)\) \(\chi_{8034}(5567,\cdot)\) \(\chi_{8034}(5957,\cdot)\) \(\chi_{8034}(6191,\cdot)\) \(\chi_{8034}(6509,\cdot)\) \(\chi_{8034}(6659,\cdot)\) \(\chi_{8034}(6743,\cdot)\) \(\chi_{8034}(6899,\cdot)\) \(\chi_{8034}(6971,\cdot)\) \(\chi_{8034}(7049,\cdot)\) \(\chi_{8034}(7367,\cdot)\) ...

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

\((5357,1237,5773)\) → \((-1,e\left(\frac{2}{3}\right),e\left(\frac{5}{102}\right))\)

Values

\(-1\)\(1\)\(5\)\(7\)\(11\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)\(35\)
\(1\)\(1\)\(e\left(\frac{28}{51}\right)\)\(e\left(\frac{9}{17}\right)\)\(e\left(\frac{8}{51}\right)\)\(e\left(\frac{9}{34}\right)\)\(e\left(\frac{13}{51}\right)\)\(e\left(\frac{35}{102}\right)\)\(e\left(\frac{5}{51}\right)\)\(e\left(\frac{13}{34}\right)\)\(e\left(\frac{27}{34}\right)\)\(e\left(\frac{4}{51}\right)\)
value at e.g. 2

Related number fields

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