Properties

Label 8034.83
Modulus $8034$
Conductor $4017$
Order $204$
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([102,153,76]))
 
pari: [g,chi] = znchar(Mod(83,8034))
 

Basic properties

Modulus: \(8034\)
Conductor: \(4017\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(204\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{4017}(83,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 8034.ei

\(\chi_{8034}(83,\cdot)\) \(\chi_{8034}(161,\cdot)\) \(\chi_{8034}(239,\cdot)\) \(\chi_{8034}(359,\cdot)\) \(\chi_{8034}(437,\cdot)\) \(\chi_{8034}(551,\cdot)\) \(\chi_{8034}(749,\cdot)\) \(\chi_{8034}(1019,\cdot)\) \(\chi_{8034}(1253,\cdot)\) \(\chi_{8034}(1295,\cdot)\) \(\chi_{8034}(1643,\cdot)\) \(\chi_{8034}(2075,\cdot)\) \(\chi_{8034}(2189,\cdot)\) \(\chi_{8034}(2231,\cdot)\) \(\chi_{8034}(2387,\cdot)\) \(\chi_{8034}(2501,\cdot)\) \(\chi_{8034}(2579,\cdot)\) \(\chi_{8034}(2657,\cdot)\) \(\chi_{8034}(2813,\cdot)\) \(\chi_{8034}(2891,\cdot)\) \(\chi_{8034}(2933,\cdot)\) \(\chi_{8034}(3047,\cdot)\) \(\chi_{8034}(3245,\cdot)\) \(\chi_{8034}(3359,\cdot)\) \(\chi_{8034}(3401,\cdot)\) \(\chi_{8034}(3437,\cdot)\) \(\chi_{8034}(3557,\cdot)\) \(\chi_{8034}(3593,\cdot)\) \(\chi_{8034}(3749,\cdot)\) \(\chi_{8034}(3791,\cdot)\) ...

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

\((5357,1237,5773)\) → \((-1,-i,e\left(\frac{19}{51}\right))\)

Values

\(-1\)\(1\)\(5\)\(7\)\(11\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)\(35\)
\(1\)\(1\)\(e\left(\frac{127}{204}\right)\)\(e\left(\frac{151}{204}\right)\)\(e\left(\frac{97}{204}\right)\)\(e\left(\frac{4}{51}\right)\)\(e\left(\frac{113}{204}\right)\)\(e\left(\frac{16}{17}\right)\)\(e\left(\frac{25}{102}\right)\)\(e\left(\frac{55}{102}\right)\)\(e\left(\frac{67}{68}\right)\)\(e\left(\frac{37}{102}\right)\)
value at e.g. 2

Related number fields

Field of values: $\Q(\zeta_{204})$
Fixed field: Number field defined by a degree 204 polynomial