Properties

Label 8034.77
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([51,51,65]))
 
pari: [g,chi] = znchar(Mod(77,8034))
 

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 \(\chi_{4017}(77,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 8034.dd

\(\chi_{8034}(77,\cdot)\) \(\chi_{8034}(623,\cdot)\) \(\chi_{8034}(1013,\cdot)\) \(\chi_{8034}(1247,\cdot)\) \(\chi_{8034}(1715,\cdot)\) \(\chi_{8034}(2027,\cdot)\) \(\chi_{8034}(2105,\cdot)\) \(\chi_{8034}(2183,\cdot)\) \(\chi_{8034}(2417,\cdot)\) \(\chi_{8034}(2573,\cdot)\) \(\chi_{8034}(2729,\cdot)\) \(\chi_{8034}(3041,\cdot)\) \(\chi_{8034}(3587,\cdot)\) \(\chi_{8034}(3743,\cdot)\) \(\chi_{8034}(3899,\cdot)\) \(\chi_{8034}(4679,\cdot)\) \(\chi_{8034}(5225,\cdot)\) \(\chi_{8034}(5537,\cdot)\) \(\chi_{8034}(5615,\cdot)\) \(\chi_{8034}(6083,\cdot)\) \(\chi_{8034}(6161,\cdot)\) \(\chi_{8034}(6473,\cdot)\) \(\chi_{8034}(6551,\cdot)\) \(\chi_{8034}(6707,\cdot)\) \(\chi_{8034}(6863,\cdot)\) \(\chi_{8034}(6941,\cdot)\) \(\chi_{8034}(7253,\cdot)\) \(\chi_{8034}(7409,\cdot)\) \(\chi_{8034}(7487,\cdot)\) \(\chi_{8034}(7643,\cdot)\) ...

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

\((5357,1237,5773)\) → \((-1,-1,e\left(\frac{65}{102}\right))\)

Values

\(-1\)\(1\)\(5\)\(7\)\(11\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)\(35\)
\(1\)\(1\)\(e\left(\frac{65}{102}\right)\)\(e\left(\frac{5}{102}\right)\)\(e\left(\frac{89}{102}\right)\)\(e\left(\frac{11}{102}\right)\)\(e\left(\frac{49}{102}\right)\)\(e\left(\frac{27}{34}\right)\)\(e\left(\frac{14}{51}\right)\)\(e\left(\frac{31}{102}\right)\)\(e\left(\frac{14}{17}\right)\)\(e\left(\frac{35}{51}\right)\)
value at e.g. 2

Related number fields

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