Properties

Label 2601.55
Modulus $2601$
Conductor $289$
Order $68$
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(2601, base_ring=CyclotomicField(68))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,63]))
 
pari: [g,chi] = znchar(Mod(55,2601))
 

Basic properties

Modulus: \(2601\)
Conductor: \(289\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(68\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{289}(55,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 2601.ba

\(\chi_{2601}(55,\cdot)\) \(\chi_{2601}(64,\cdot)\) \(\chi_{2601}(208,\cdot)\) \(\chi_{2601}(217,\cdot)\) \(\chi_{2601}(361,\cdot)\) \(\chi_{2601}(370,\cdot)\) \(\chi_{2601}(514,\cdot)\) \(\chi_{2601}(523,\cdot)\) \(\chi_{2601}(667,\cdot)\) \(\chi_{2601}(676,\cdot)\) \(\chi_{2601}(820,\cdot)\) \(\chi_{2601}(973,\cdot)\) \(\chi_{2601}(982,\cdot)\) \(\chi_{2601}(1126,\cdot)\) \(\chi_{2601}(1135,\cdot)\) \(\chi_{2601}(1279,\cdot)\) \(\chi_{2601}(1288,\cdot)\) \(\chi_{2601}(1432,\cdot)\) \(\chi_{2601}(1441,\cdot)\) \(\chi_{2601}(1585,\cdot)\) \(\chi_{2601}(1594,\cdot)\) \(\chi_{2601}(1738,\cdot)\) \(\chi_{2601}(1747,\cdot)\) \(\chi_{2601}(1891,\cdot)\) \(\chi_{2601}(1900,\cdot)\) \(\chi_{2601}(2044,\cdot)\) \(\chi_{2601}(2053,\cdot)\) \(\chi_{2601}(2197,\cdot)\) \(\chi_{2601}(2206,\cdot)\) \(\chi_{2601}(2359,\cdot)\) ...

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: $\Q(\zeta_{68})$
Fixed field: Number field defined by a degree 68 polynomial

Values on generators

\((290,2026)\) → \((1,e\left(\frac{63}{68}\right))\)

Values

\(-1\)\(1\)\(2\)\(4\)\(5\)\(7\)\(8\)\(10\)\(11\)\(13\)\(14\)\(16\)
\(1\)\(1\)\(e\left(\frac{1}{34}\right)\)\(e\left(\frac{1}{17}\right)\)\(e\left(\frac{11}{68}\right)\)\(e\left(\frac{41}{68}\right)\)\(e\left(\frac{3}{34}\right)\)\(e\left(\frac{13}{68}\right)\)\(e\left(\frac{21}{68}\right)\)\(e\left(\frac{10}{17}\right)\)\(e\left(\frac{43}{68}\right)\)\(e\left(\frac{2}{17}\right)\)
value at e.g. 2