Properties

Label 4017.1715
Modulus $4017$
Conductor $4017$
Order $102$
Real no
Primitive yes
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(4017, base_ring=CyclotomicField(102))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([51,51,13]))
 
pari: [g,chi] = znchar(Mod(1715,4017))
 

Basic properties

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

Galois orbit 4017.dp

\(\chi_{4017}(77,\cdot)\) \(\chi_{4017}(623,\cdot)\) \(\chi_{4017}(662,\cdot)\) \(\chi_{4017}(1013,\cdot)\) \(\chi_{4017}(1208,\cdot)\) \(\chi_{4017}(1247,\cdot)\) \(\chi_{4017}(1520,\cdot)\) \(\chi_{4017}(1598,\cdot)\) \(\chi_{4017}(1715,\cdot)\) \(\chi_{4017}(2027,\cdot)\) \(\chi_{4017}(2066,\cdot)\) \(\chi_{4017}(2105,\cdot)\) \(\chi_{4017}(2144,\cdot)\) \(\chi_{4017}(2183,\cdot)\) \(\chi_{4017}(2417,\cdot)\) \(\chi_{4017}(2456,\cdot)\) \(\chi_{4017}(2534,\cdot)\) \(\chi_{4017}(2573,\cdot)\) \(\chi_{4017}(2690,\cdot)\) \(\chi_{4017}(2729,\cdot)\) \(\chi_{4017}(2846,\cdot)\) \(\chi_{4017}(2924,\cdot)\) \(\chi_{4017}(3041,\cdot)\) \(\chi_{4017}(3236,\cdot)\) \(\chi_{4017}(3392,\cdot)\) \(\chi_{4017}(3470,\cdot)\) \(\chi_{4017}(3587,\cdot)\) \(\chi_{4017}(3626,\cdot)\) \(\chi_{4017}(3704,\cdot)\) \(\chi_{4017}(3743,\cdot)\) ...

sage: chi.galois_orbit()
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Related number fields

Field of values: $\Q(\zeta_{51})$
Fixed field: Number field defined by a degree 102 polynomial (not computed)

Values on generators

\((1340,1237,1756)\) → \((-1,-1,e\left(\frac{13}{102}\right))\)

Values

\(-1\)\(1\)\(2\)\(4\)\(5\)\(7\)\(8\)\(10\)\(11\)\(14\)\(16\)\(17\)
\(1\)\(1\)\(e\left(\frac{31}{51}\right)\)\(e\left(\frac{11}{51}\right)\)\(e\left(\frac{13}{102}\right)\)\(e\left(\frac{1}{102}\right)\)\(e\left(\frac{14}{17}\right)\)\(e\left(\frac{25}{34}\right)\)\(e\left(\frac{79}{102}\right)\)\(e\left(\frac{21}{34}\right)\)\(e\left(\frac{22}{51}\right)\)\(e\left(\frac{43}{102}\right)\)
value at e.g. 2