Properties

Label 2601.118
Modulus $2601$
Conductor $289$
Order $34$
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(34))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,19]))
 
pari: [g,chi] = znchar(Mod(118,2601))
 

Basic properties

Modulus: \(2601\)
Conductor: \(289\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(34\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{289}(118,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 2601.t

\(\chi_{2601}(118,\cdot)\) \(\chi_{2601}(271,\cdot)\) \(\chi_{2601}(424,\cdot)\) \(\chi_{2601}(730,\cdot)\) \(\chi_{2601}(883,\cdot)\) \(\chi_{2601}(1036,\cdot)\) \(\chi_{2601}(1189,\cdot)\) \(\chi_{2601}(1342,\cdot)\) \(\chi_{2601}(1495,\cdot)\) \(\chi_{2601}(1648,\cdot)\) \(\chi_{2601}(1801,\cdot)\) \(\chi_{2601}(1954,\cdot)\) \(\chi_{2601}(2107,\cdot)\) \(\chi_{2601}(2260,\cdot)\) \(\chi_{2601}(2413,\cdot)\) \(\chi_{2601}(2566,\cdot)\)

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: \(\Q(\zeta_{17})\)
Fixed field: 34.34.95319090450218007303742536355848761234066170796000792973413605849481890760893457.1

Values on generators

\((290,2026)\) → \((1,e\left(\frac{19}{34}\right))\)

Values

\(-1\)\(1\)\(2\)\(4\)\(5\)\(7\)\(8\)\(10\)\(11\)\(13\)\(14\)\(16\)
\(1\)\(1\)\(e\left(\frac{3}{17}\right)\)\(e\left(\frac{6}{17}\right)\)\(e\left(\frac{33}{34}\right)\)\(e\left(\frac{21}{34}\right)\)\(e\left(\frac{9}{17}\right)\)\(e\left(\frac{5}{34}\right)\)\(e\left(\frac{29}{34}\right)\)\(e\left(\frac{9}{17}\right)\)\(e\left(\frac{27}{34}\right)\)\(e\left(\frac{12}{17}\right)\)
value at e.g. 2