Properties

Label 8034.257
Modulus $8034$
Conductor $4017$
Order $102$
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([51,85,7]))
 
pari: [g,chi] = znchar(Mod(257,8034))
 

Basic properties

Modulus: \(8034\)
Conductor: \(4017\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(102\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{4017}(257,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 8034.dm

\(\chi_{8034}(257,\cdot)\) \(\chi_{8034}(329,\cdot)\) \(\chi_{8034}(563,\cdot)\) \(\chi_{8034}(719,\cdot)\) \(\chi_{8034}(1187,\cdot)\) \(\chi_{8034}(1427,\cdot)\) \(\chi_{8034}(1733,\cdot)\) \(\chi_{8034}(1889,\cdot)\) \(\chi_{8034}(2825,\cdot)\) \(\chi_{8034}(3143,\cdot)\) \(\chi_{8034}(3371,\cdot)\) \(\chi_{8034}(3683,\cdot)\) \(\chi_{8034}(4229,\cdot)\) \(\chi_{8034}(4235,\cdot)\) \(\chi_{8034}(4307,\cdot)\) \(\chi_{8034}(4391,\cdot)\) \(\chi_{8034}(4469,\cdot)\) \(\chi_{8034}(4619,\cdot)\) \(\chi_{8034}(4697,\cdot)\) \(\chi_{8034}(4937,\cdot)\) \(\chi_{8034}(5015,\cdot)\) \(\chi_{8034}(5171,\cdot)\) \(\chi_{8034}(5249,\cdot)\) \(\chi_{8034}(5399,\cdot)\) \(\chi_{8034}(5945,\cdot)\) \(\chi_{8034}(6185,\cdot)\) \(\chi_{8034}(6257,\cdot)\) \(\chi_{8034}(6575,\cdot)\) \(\chi_{8034}(6809,\cdot)\) \(\chi_{8034}(7277,\cdot)\) ...

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

\((5357,1237,5773)\) → \((-1,e\left(\frac{5}{6}\right),e\left(\frac{7}{102}\right))\)

Values

\(-1\)\(1\)\(5\)\(7\)\(11\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)\(35\)
\(1\)\(1\)\(e\left(\frac{7}{102}\right)\)\(e\left(\frac{15}{34}\right)\)\(e\left(\frac{53}{102}\right)\)\(e\left(\frac{33}{34}\right)\)\(e\left(\frac{67}{102}\right)\)\(e\left(\frac{49}{102}\right)\)\(e\left(\frac{7}{51}\right)\)\(e\left(\frac{25}{34}\right)\)\(e\left(\frac{7}{17}\right)\)\(e\left(\frac{26}{51}\right)\)
value at e.g. 2

Related number fields

Field of values: $\Q(\zeta_{51})$
Fixed field: Number field defined by a degree 102 polynomial