Properties

Label 8034.191
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([51,68,91]))
 
pari: [g,chi] = znchar(Mod(191,8034))
 

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 \(\chi_{4017}(191,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 8034.ds

\(\chi_{8034}(191,\cdot)\) \(\chi_{8034}(497,\cdot)\) \(\chi_{8034}(653,\cdot)\) \(\chi_{8034}(1589,\cdot)\) \(\chi_{8034}(1907,\cdot)\) \(\chi_{8034}(2135,\cdot)\) \(\chi_{8034}(2447,\cdot)\) \(\chi_{8034}(2993,\cdot)\) \(\chi_{8034}(2999,\cdot)\) \(\chi_{8034}(3071,\cdot)\) \(\chi_{8034}(3155,\cdot)\) \(\chi_{8034}(3233,\cdot)\) \(\chi_{8034}(3383,\cdot)\) \(\chi_{8034}(3461,\cdot)\) \(\chi_{8034}(3701,\cdot)\) \(\chi_{8034}(3779,\cdot)\) \(\chi_{8034}(3935,\cdot)\) \(\chi_{8034}(4013,\cdot)\) \(\chi_{8034}(4163,\cdot)\) \(\chi_{8034}(4709,\cdot)\) \(\chi_{8034}(4949,\cdot)\) \(\chi_{8034}(5021,\cdot)\) \(\chi_{8034}(5339,\cdot)\) \(\chi_{8034}(5573,\cdot)\) \(\chi_{8034}(6041,\cdot)\) \(\chi_{8034}(6353,\cdot)\) \(\chi_{8034}(6431,\cdot)\) \(\chi_{8034}(7055,\cdot)\) \(\chi_{8034}(7127,\cdot)\) \(\chi_{8034}(7361,\cdot)\) ...

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

\((5357,1237,5773)\) → \((-1,e\left(\frac{2}{3}\right),e\left(\frac{91}{102}\right))\)

Values

\(-1\)\(1\)\(5\)\(7\)\(11\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)\(35\)
\(1\)\(1\)\(e\left(\frac{20}{51}\right)\)\(e\left(\frac{46}{51}\right)\)\(e\left(\frac{10}{17}\right)\)\(e\left(\frac{29}{102}\right)\)\(e\left(\frac{12}{17}\right)\)\(e\left(\frac{59}{102}\right)\)\(e\left(\frac{40}{51}\right)\)\(e\left(\frac{91}{102}\right)\)\(e\left(\frac{29}{34}\right)\)\(e\left(\frac{5}{17}\right)\)
value at e.g. 2

Related number fields

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