Properties

Label 8034.109
Modulus $8034$
Conductor $1339$
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([0,153,166]))
 
pari: [g,chi] = znchar(Mod(109,8034))
 

Basic properties

Modulus: \(8034\)
Conductor: \(1339\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(204\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{1339}(109,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 8034.eg

\(\chi_{8034}(109,\cdot)\) \(\chi_{8034}(151,\cdot)\) \(\chi_{8034}(187,\cdot)\) \(\chi_{8034}(307,\cdot)\) \(\chi_{8034}(463,\cdot)\) \(\chi_{8034}(499,\cdot)\) \(\chi_{8034}(577,\cdot)\) \(\chi_{8034}(733,\cdot)\) \(\chi_{8034}(775,\cdot)\) \(\chi_{8034}(889,\cdot)\) \(\chi_{8034}(967,\cdot)\) \(\chi_{8034}(1279,\cdot)\) \(\chi_{8034}(1321,\cdot)\) \(\chi_{8034}(1435,\cdot)\) \(\chi_{8034}(1477,\cdot)\) \(\chi_{8034}(1513,\cdot)\) \(\chi_{8034}(1633,\cdot)\) \(\chi_{8034}(1669,\cdot)\) \(\chi_{8034}(1747,\cdot)\) \(\chi_{8034}(1825,\cdot)\) \(\chi_{8034}(2137,\cdot)\) \(\chi_{8034}(2413,\cdot)\) \(\chi_{8034}(2683,\cdot)\) \(\chi_{8034}(2959,\cdot)\) \(\chi_{8034}(3073,\cdot)\) \(\chi_{8034}(3271,\cdot)\) \(\chi_{8034}(3307,\cdot)\) \(\chi_{8034}(3349,\cdot)\) \(\chi_{8034}(3775,\cdot)\) \(\chi_{8034}(3817,\cdot)\) ...

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

\((5357,1237,5773)\) → \((1,-i,e\left(\frac{83}{102}\right))\)

Values

\(-1\)\(1\)\(5\)\(7\)\(11\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)\(35\)
\(1\)\(1\)\(e\left(\frac{115}{204}\right)\)\(e\left(\frac{103}{204}\right)\)\(e\left(\frac{181}{204}\right)\)\(e\left(\frac{47}{102}\right)\)\(e\left(\frac{173}{204}\right)\)\(e\left(\frac{1}{34}\right)\)\(e\left(\frac{13}{102}\right)\)\(e\left(\frac{50}{51}\right)\)\(e\left(\frac{9}{68}\right)\)\(e\left(\frac{7}{102}\right)\)
value at e.g. 2

Related number fields

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