Properties

Label 8034.53
Modulus $8034$
Conductor $309$
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([51,0,97]))
 
pari: [g,chi] = znchar(Mod(53,8034))
 

Basic properties

Modulus: \(8034\)
Conductor: \(309\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(102\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{309}(53,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 8034.dt

\(\chi_{8034}(53,\cdot)\) \(\chi_{8034}(521,\cdot)\) \(\chi_{8034}(599,\cdot)\) \(\chi_{8034}(911,\cdot)\) \(\chi_{8034}(989,\cdot)\) \(\chi_{8034}(1145,\cdot)\) \(\chi_{8034}(1301,\cdot)\) \(\chi_{8034}(1379,\cdot)\) \(\chi_{8034}(1691,\cdot)\) \(\chi_{8034}(1847,\cdot)\) \(\chi_{8034}(1925,\cdot)\) \(\chi_{8034}(2081,\cdot)\) \(\chi_{8034}(2159,\cdot)\) \(\chi_{8034}(2237,\cdot)\) \(\chi_{8034}(2549,\cdot)\) \(\chi_{8034}(3095,\cdot)\) \(\chi_{8034}(3485,\cdot)\) \(\chi_{8034}(3719,\cdot)\) \(\chi_{8034}(4187,\cdot)\) \(\chi_{8034}(4499,\cdot)\) \(\chi_{8034}(4577,\cdot)\) \(\chi_{8034}(4655,\cdot)\) \(\chi_{8034}(4889,\cdot)\) \(\chi_{8034}(5045,\cdot)\) \(\chi_{8034}(5201,\cdot)\) \(\chi_{8034}(5513,\cdot)\) \(\chi_{8034}(6059,\cdot)\) \(\chi_{8034}(6215,\cdot)\) \(\chi_{8034}(6371,\cdot)\) \(\chi_{8034}(7151,\cdot)\) ...

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

\((5357,1237,5773)\) → \((-1,1,e\left(\frac{97}{102}\right))\)

Values

\(-1\)\(1\)\(5\)\(7\)\(11\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)\(35\)
\(1\)\(1\)\(e\left(\frac{23}{51}\right)\)\(e\left(\frac{41}{51}\right)\)\(e\left(\frac{26}{51}\right)\)\(e\left(\frac{7}{102}\right)\)\(e\left(\frac{4}{51}\right)\)\(e\left(\frac{11}{34}\right)\)\(e\left(\frac{46}{51}\right)\)\(e\left(\frac{29}{102}\right)\)\(e\left(\frac{7}{34}\right)\)\(e\left(\frac{13}{51}\right)\)
value at e.g. 2

Related number fields

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