Properties

Label 2601.19
Modulus $2601$
Conductor $289$
Order $136$
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(136))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,7]))
 
pari: [g,chi] = znchar(Mod(19,2601))
 

Basic properties

Modulus: \(2601\)
Conductor: \(289\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(136\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{289}(19,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 2601.be

\(\chi_{2601}(19,\cdot)\) \(\chi_{2601}(100,\cdot)\) \(\chi_{2601}(127,\cdot)\) \(\chi_{2601}(145,\cdot)\) \(\chi_{2601}(172,\cdot)\) \(\chi_{2601}(253,\cdot)\) \(\chi_{2601}(280,\cdot)\) \(\chi_{2601}(298,\cdot)\) \(\chi_{2601}(325,\cdot)\) \(\chi_{2601}(406,\cdot)\) \(\chi_{2601}(433,\cdot)\) \(\chi_{2601}(451,\cdot)\) \(\chi_{2601}(478,\cdot)\) \(\chi_{2601}(559,\cdot)\) \(\chi_{2601}(586,\cdot)\) \(\chi_{2601}(604,\cdot)\) \(\chi_{2601}(631,\cdot)\) \(\chi_{2601}(739,\cdot)\) \(\chi_{2601}(784,\cdot)\) \(\chi_{2601}(865,\cdot)\) \(\chi_{2601}(892,\cdot)\) \(\chi_{2601}(910,\cdot)\) \(\chi_{2601}(937,\cdot)\) \(\chi_{2601}(1018,\cdot)\) \(\chi_{2601}(1045,\cdot)\) \(\chi_{2601}(1063,\cdot)\) \(\chi_{2601}(1090,\cdot)\) \(\chi_{2601}(1171,\cdot)\) \(\chi_{2601}(1198,\cdot)\) \(\chi_{2601}(1216,\cdot)\) ...

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: $\Q(\zeta_{136})$
Fixed field: Number field defined by a degree 136 polynomial (not computed)

Values on generators

\((290,2026)\) → \((1,e\left(\frac{7}{136}\right))\)

Values

\(-1\)\(1\)\(2\)\(4\)\(5\)\(7\)\(8\)\(10\)\(11\)\(13\)\(14\)\(16\)
\(1\)\(1\)\(e\left(\frac{53}{68}\right)\)\(e\left(\frac{19}{34}\right)\)\(e\left(\frac{107}{136}\right)\)\(e\left(\frac{133}{136}\right)\)\(e\left(\frac{23}{68}\right)\)\(e\left(\frac{77}{136}\right)\)\(e\left(\frac{25}{136}\right)\)\(e\left(\frac{3}{34}\right)\)\(e\left(\frac{103}{136}\right)\)\(e\left(\frac{2}{17}\right)\)
value at e.g. 2