Properties

Label 8034.59
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([102,187,196]))
 
pari: [g,chi] = znchar(Mod(59,8034))
 

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 \(\chi_{4017}(59,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 8034.ea

\(\chi_{8034}(59,\cdot)\) \(\chi_{8034}(401,\cdot)\) \(\chi_{8034}(461,\cdot)\) \(\chi_{8034}(635,\cdot)\) \(\chi_{8034}(929,\cdot)\) \(\chi_{8034}(977,\cdot)\) \(\chi_{8034}(995,\cdot)\) \(\chi_{8034}(1025,\cdot)\) \(\chi_{8034}(1085,\cdot)\) \(\chi_{8034}(1151,\cdot)\) \(\chi_{8034}(1319,\cdot)\) \(\chi_{8034}(1697,\cdot)\) \(\chi_{8034}(1961,\cdot)\) \(\chi_{8034}(2039,\cdot)\) \(\chi_{8034}(2165,\cdot)\) \(\chi_{8034}(2195,\cdot)\) \(\chi_{8034}(2273,\cdot)\) \(\chi_{8034}(2321,\cdot)\) \(\chi_{8034}(2555,\cdot)\) \(\chi_{8034}(2693,\cdot)\) \(\chi_{8034}(2741,\cdot)\) \(\chi_{8034}(2819,\cdot)\) \(\chi_{8034}(2975,\cdot)\) \(\chi_{8034}(3425,\cdot)\) \(\chi_{8034}(3737,\cdot)\) \(\chi_{8034}(3863,\cdot)\) \(\chi_{8034}(4067,\cdot)\) \(\chi_{8034}(4283,\cdot)\) \(\chi_{8034}(4487,\cdot)\) \(\chi_{8034}(4565,\cdot)\) ...

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

\((5357,1237,5773)\) → \((-1,e\left(\frac{11}{12}\right),e\left(\frac{49}{51}\right))\)

Values

\(-1\)\(1\)\(5\)\(7\)\(11\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)\(35\)
\(1\)\(1\)\(e\left(\frac{145}{204}\right)\)\(e\left(\frac{63}{68}\right)\)\(e\left(\frac{107}{204}\right)\)\(e\left(\frac{10}{17}\right)\)\(e\left(\frac{91}{204}\right)\)\(e\left(\frac{37}{51}\right)\)\(e\left(\frac{43}{102}\right)\)\(e\left(\frac{27}{34}\right)\)\(e\left(\frac{1}{68}\right)\)\(e\left(\frac{65}{102}\right)\)
value at e.g. 2

Related number fields

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