Properties

Label 8034.95
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([51,17,81]))
 
pari: [g,chi] = znchar(Mod(95,8034))
 

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 \(\chi_{4017}(95,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 8034.dw

\(\chi_{8034}(95,\cdot)\) \(\chi_{8034}(485,\cdot)\) \(\chi_{8034}(1349,\cdot)\) \(\chi_{8034}(1967,\cdot)\) \(\chi_{8034}(2051,\cdot)\) \(\chi_{8034}(2129,\cdot)\) \(\chi_{8034}(2597,\cdot)\) \(\chi_{8034}(2669,\cdot)\) \(\chi_{8034}(2747,\cdot)\) \(\chi_{8034}(3215,\cdot)\) \(\chi_{8034}(3299,\cdot)\) \(\chi_{8034}(3533,\cdot)\) \(\chi_{8034}(3917,\cdot)\) \(\chi_{8034}(4151,\cdot)\) \(\chi_{8034}(4157,\cdot)\) \(\chi_{8034}(4313,\cdot)\) \(\chi_{8034}(4775,\cdot)\) \(\chi_{8034}(4931,\cdot)\) \(\chi_{8034}(5483,\cdot)\) \(\chi_{8034}(5795,\cdot)\) \(\chi_{8034}(5951,\cdot)\) \(\chi_{8034}(6101,\cdot)\) \(\chi_{8034}(6413,\cdot)\) \(\chi_{8034}(6569,\cdot)\) \(\chi_{8034}(6887,\cdot)\) \(\chi_{8034}(7043,\cdot)\) \(\chi_{8034}(7355,\cdot)\) \(\chi_{8034}(7505,\cdot)\) \(\chi_{8034}(7511,\cdot)\) \(\chi_{8034}(7661,\cdot)\) ...

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

\((5357,1237,5773)\) → \((-1,e\left(\frac{1}{6}\right),e\left(\frac{27}{34}\right))\)

Values

\(-1\)\(1\)\(5\)\(7\)\(11\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)\(35\)
\(1\)\(1\)\(e\left(\frac{27}{34}\right)\)\(e\left(\frac{1}{102}\right)\)\(e\left(\frac{11}{102}\right)\)\(e\left(\frac{43}{102}\right)\)\(e\left(\frac{37}{102}\right)\)\(e\left(\frac{23}{102}\right)\)\(e\left(\frac{10}{17}\right)\)\(e\left(\frac{47}{102}\right)\)\(e\left(\frac{13}{17}\right)\)\(e\left(\frac{41}{51}\right)\)
value at e.g. 2

Related number fields

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