Properties

Label 8034.203
Modulus $8034$
Conductor $4017$
Order $68$
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([34,17,60]))
 
pari: [g,chi] = znchar(Mod(203,8034))
 

Basic properties

Modulus: \(8034\)
Conductor: \(4017\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(68\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{4017}(203,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 8034.cv

\(\chi_{8034}(203,\cdot)\) \(\chi_{8034}(317,\cdot)\) \(\chi_{8034}(473,\cdot)\) \(\chi_{8034}(785,\cdot)\) \(\chi_{8034}(905,\cdot)\) \(\chi_{8034}(941,\cdot)\) \(\chi_{8034}(1373,\cdot)\) \(\chi_{8034}(1451,\cdot)\) \(\chi_{8034}(1877,\cdot)\) \(\chi_{8034}(2033,\cdot)\) \(\chi_{8034}(2153,\cdot)\) \(\chi_{8034}(2345,\cdot)\) \(\chi_{8034}(3515,\cdot)\) \(\chi_{8034}(3635,\cdot)\) \(\chi_{8034}(3671,\cdot)\) \(\chi_{8034}(4025,\cdot)\) \(\chi_{8034}(4181,\cdot)\) \(\chi_{8034}(4295,\cdot)\) \(\chi_{8034}(4493,\cdot)\) \(\chi_{8034}(4529,\cdot)\) \(\chi_{8034}(4649,\cdot)\) \(\chi_{8034}(5231,\cdot)\) \(\chi_{8034}(5585,\cdot)\) \(\chi_{8034}(5699,\cdot)\) \(\chi_{8034}(5741,\cdot)\) \(\chi_{8034}(5777,\cdot)\) \(\chi_{8034}(6053,\cdot)\) \(\chi_{8034}(6479,\cdot)\) \(\chi_{8034}(7223,\cdot)\) \(\chi_{8034}(7379,\cdot)\) ...

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

\((5357,1237,5773)\) → \((-1,i,e\left(\frac{15}{17}\right))\)

Values

\(-1\)\(1\)\(5\)\(7\)\(11\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)\(35\)
\(1\)\(1\)\(e\left(\frac{43}{68}\right)\)\(e\left(\frac{19}{68}\right)\)\(e\left(\frac{5}{68}\right)\)\(e\left(\frac{13}{17}\right)\)\(e\left(\frac{57}{68}\right)\)\(e\left(\frac{3}{17}\right)\)\(e\left(\frac{9}{34}\right)\)\(e\left(\frac{13}{34}\right)\)\(e\left(\frac{37}{68}\right)\)\(e\left(\frac{31}{34}\right)\)
value at e.g. 2

Related number fields

Field of values: $\Q(\zeta_{68})$
Fixed field: Number field defined by a degree 68 polynomial