Properties

Label 8034.67
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([0,17,26]))
 
pari: [g,chi] = znchar(Mod(67,8034))
 

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 \(\chi_{1339}(67,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 8034.eo

\(\chi_{8034}(67,\cdot)\) \(\chi_{8034}(85,\cdot)\) \(\chi_{8034}(115,\cdot)\) \(\chi_{8034}(241,\cdot)\) \(\chi_{8034}(271,\cdot)\) \(\chi_{8034}(349,\cdot)\) \(\chi_{8034}(379,\cdot)\) \(\chi_{8034}(457,\cdot)\) \(\chi_{8034}(487,\cdot)\) \(\chi_{8034}(799,\cdot)\) \(\chi_{8034}(817,\cdot)\) \(\chi_{8034}(895,\cdot)\) \(\chi_{8034}(1051,\cdot)\) \(\chi_{8034}(1081,\cdot)\) \(\chi_{8034}(1129,\cdot)\) \(\chi_{8034}(1177,\cdot)\) \(\chi_{8034}(1345,\cdot)\) \(\chi_{8034}(1423,\cdot)\) \(\chi_{8034}(1723,\cdot)\) \(\chi_{8034}(1735,\cdot)\) \(\chi_{8034}(1813,\cdot)\) \(\chi_{8034}(2035,\cdot)\) \(\chi_{8034}(2065,\cdot)\) \(\chi_{8034}(2251,\cdot)\) \(\chi_{8034}(2455,\cdot)\) \(\chi_{8034}(2515,\cdot)\) \(\chi_{8034}(2581,\cdot)\) \(\chi_{8034}(2659,\cdot)\) \(\chi_{8034}(2689,\cdot)\) \(\chi_{8034}(2971,\cdot)\) ...

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

\((5357,1237,5773)\) → \((1,e\left(\frac{1}{12}\right),e\left(\frac{13}{102}\right))\)

Values

\(-1\)\(1\)\(5\)\(7\)\(11\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)\(35\)
\(1\)\(1\)\(e\left(\frac{179}{204}\right)\)\(e\left(\frac{29}{68}\right)\)\(e\left(\frac{73}{204}\right)\)\(e\left(\frac{3}{34}\right)\)\(e\left(\frac{125}{204}\right)\)\(e\left(\frac{91}{102}\right)\)\(e\left(\frac{77}{102}\right)\)\(e\left(\frac{5}{17}\right)\)\(e\left(\frac{1}{68}\right)\)\(e\left(\frac{31}{102}\right)\)
value at e.g. 2

Related number fields

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