Properties

Label 8034.41
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([102,17,100]))
 
pari: [g,chi] = znchar(Mod(41,8034))
 

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 \(\chi_{4017}(41,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 8034.el

\(\chi_{8034}(41,\cdot)\) \(\chi_{8034}(119,\cdot)\) \(\chi_{8034}(431,\cdot)\) \(\chi_{8034}(509,\cdot)\) \(\chi_{8034}(773,\cdot)\) \(\chi_{8034}(839,\cdot)\) \(\chi_{8034}(1055,\cdot)\) \(\chi_{8034}(1367,\cdot)\) \(\chi_{8034}(1397,\cdot)\) \(\chi_{8034}(1475,\cdot)\) \(\chi_{8034}(1571,\cdot)\) \(\chi_{8034}(1787,\cdot)\) \(\chi_{8034}(1883,\cdot)\) \(\chi_{8034}(1913,\cdot)\) \(\chi_{8034}(2009,\cdot)\) \(\chi_{8034}(2255,\cdot)\) \(\chi_{8034}(2429,\cdot)\) \(\chi_{8034}(2489,\cdot)\) \(\chi_{8034}(2633,\cdot)\) \(\chi_{8034}(2711,\cdot)\) \(\chi_{8034}(2849,\cdot)\) \(\chi_{8034}(2879,\cdot)\) \(\chi_{8034}(3005,\cdot)\) \(\chi_{8034}(3023,\cdot)\) \(\chi_{8034}(3131,\cdot)\) \(\chi_{8034}(3209,\cdot)\) \(\chi_{8034}(3491,\cdot)\) \(\chi_{8034}(3521,\cdot)\) \(\chi_{8034}(3551,\cdot)\) \(\chi_{8034}(3599,\cdot)\) ...

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

\((5357,1237,5773)\) → \((-1,e\left(\frac{1}{12}\right),e\left(\frac{25}{51}\right))\)

Values

\(-1\)\(1\)\(5\)\(7\)\(11\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)\(35\)
\(1\)\(1\)\(e\left(\frac{151}{204}\right)\)\(e\left(\frac{179}{204}\right)\)\(e\left(\frac{67}{68}\right)\)\(e\left(\frac{50}{51}\right)\)\(e\left(\frac{43}{68}\right)\)\(e\left(\frac{5}{51}\right)\)\(e\left(\frac{49}{102}\right)\)\(e\left(\frac{101}{102}\right)\)\(e\left(\frac{47}{68}\right)\)\(e\left(\frac{21}{34}\right)\)
value at e.g. 2

Related number fields

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