Properties

Label 8034.235
Modulus $8034$
Conductor $103$
Order $51$
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([0,0,43]))
 
pari: [g,chi] = znchar(Mod(235,8034))
 

Basic properties

Modulus: \(8034\)
Conductor: \(103\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(51\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{103}(29,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 8034.ct

\(\chi_{8034}(235,\cdot)\) \(\chi_{8034}(313,\cdot)\) \(\chi_{8034}(391,\cdot)\) \(\chi_{8034}(547,\cdot)\) \(\chi_{8034}(625,\cdot)\) \(\chi_{8034}(781,\cdot)\) \(\chi_{8034}(1093,\cdot)\) \(\chi_{8034}(1171,\cdot)\) \(\chi_{8034}(1327,\cdot)\) \(\chi_{8034}(1483,\cdot)\) \(\chi_{8034}(1561,\cdot)\) \(\chi_{8034}(1873,\cdot)\) \(\chi_{8034}(1951,\cdot)\) \(\chi_{8034}(2419,\cdot)\) \(\chi_{8034}(2497,\cdot)\) \(\chi_{8034}(2809,\cdot)\) \(\chi_{8034}(3355,\cdot)\) \(\chi_{8034}(4135,\cdot)\) \(\chi_{8034}(4291,\cdot)\) \(\chi_{8034}(4447,\cdot)\) \(\chi_{8034}(4993,\cdot)\) \(\chi_{8034}(5305,\cdot)\) \(\chi_{8034}(5461,\cdot)\) \(\chi_{8034}(5617,\cdot)\) \(\chi_{8034}(5851,\cdot)\) \(\chi_{8034}(5929,\cdot)\) \(\chi_{8034}(6007,\cdot)\) \(\chi_{8034}(6319,\cdot)\) \(\chi_{8034}(6787,\cdot)\) \(\chi_{8034}(7021,\cdot)\) ...

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

\((5357,1237,5773)\) → \((1,1,e\left(\frac{43}{51}\right))\)

Values

\(-1\)\(1\)\(5\)\(7\)\(11\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)\(35\)
\(1\)\(1\)\(e\left(\frac{43}{51}\right)\)\(e\left(\frac{19}{51}\right)\)\(e\left(\frac{22}{51}\right)\)\(e\left(\frac{1}{51}\right)\)\(e\left(\frac{23}{51}\right)\)\(e\left(\frac{4}{17}\right)\)\(e\left(\frac{35}{51}\right)\)\(e\left(\frac{26}{51}\right)\)\(e\left(\frac{1}{17}\right)\)\(e\left(\frac{11}{51}\right)\)
value at e.g. 2

Related number fields

Field of values: $\Q(\zeta_{51})$
Fixed field: Number field defined by a degree 51 polynomial