Properties

Label 8034.233
Modulus $8034$
Conductor $4017$
Order $34$
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([17,17,5]))
 
pari: [g,chi] = znchar(Mod(233,8034))
 

Basic properties

Modulus: \(8034\)
Conductor: \(4017\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(34\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{4017}(233,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 8034.cp

\(\chi_{8034}(233,\cdot)\) \(\chi_{8034}(389,\cdot)\) \(\chi_{8034}(1325,\cdot)\) \(\chi_{8034}(1481,\cdot)\) \(\chi_{8034}(1793,\cdot)\) \(\chi_{8034}(1949,\cdot)\) \(\chi_{8034}(2339,\cdot)\) \(\chi_{8034}(3821,\cdot)\) \(\chi_{8034}(4523,\cdot)\) \(\chi_{8034}(4601,\cdot)\) \(\chi_{8034}(5069,\cdot)\) \(\chi_{8034}(5771,\cdot)\) \(\chi_{8034}(6005,\cdot)\) \(\chi_{8034}(6629,\cdot)\) \(\chi_{8034}(6785,\cdot)\) \(\chi_{8034}(7955,\cdot)\)

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

\((5357,1237,5773)\) → \((-1,-1,e\left(\frac{5}{34}\right))\)

Values

\(-1\)\(1\)\(5\)\(7\)\(11\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)\(35\)
\(1\)\(1\)\(e\left(\frac{5}{34}\right)\)\(e\left(\frac{3}{34}\right)\)\(e\left(\frac{33}{34}\right)\)\(e\left(\frac{27}{34}\right)\)\(e\left(\frac{9}{34}\right)\)\(e\left(\frac{1}{34}\right)\)\(e\left(\frac{5}{17}\right)\)\(e\left(\frac{5}{34}\right)\)\(e\left(\frac{15}{17}\right)\)\(e\left(\frac{4}{17}\right)\)
value at e.g. 2

Related number fields

Field of values: \(\Q(\zeta_{17})\)
Fixed field: Number field defined by a degree 34 polynomial