Properties

Label 7098.547
Modulus $7098$
Conductor $169$
Order $13$
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(7098, base_ring=CyclotomicField(26))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,0,2]))
 
pari: [g,chi] = znchar(Mod(547,7098))
 

Basic properties

Modulus: \(7098\)
Conductor: \(169\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(13\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{169}(40,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 7098.ci

\(\chi_{7098}(547,\cdot)\) \(\chi_{7098}(1093,\cdot)\) \(\chi_{7098}(1639,\cdot)\) \(\chi_{7098}(2185,\cdot)\) \(\chi_{7098}(2731,\cdot)\) \(\chi_{7098}(3277,\cdot)\) \(\chi_{7098}(3823,\cdot)\) \(\chi_{7098}(4369,\cdot)\) \(\chi_{7098}(4915,\cdot)\) \(\chi_{7098}(5461,\cdot)\) \(\chi_{7098}(6007,\cdot)\) \(\chi_{7098}(6553,\cdot)\)

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: \(\Q(\zeta_{13})\)
Fixed field: 13.13.542800770374370512771595361.1

Values on generators

\((4733,5071,6931)\) → \((1,1,e\left(\frac{1}{13}\right))\)

Values

\(-1\)\(1\)\(5\)\(11\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)\(37\)\(41\)
\(1\)\(1\)\(e\left(\frac{9}{13}\right)\)\(e\left(\frac{12}{13}\right)\)\(e\left(\frac{3}{13}\right)\)\(1\)\(1\)\(e\left(\frac{5}{13}\right)\)\(e\left(\frac{1}{13}\right)\)\(e\left(\frac{8}{13}\right)\)\(e\left(\frac{8}{13}\right)\)\(e\left(\frac{7}{13}\right)\)
value at e.g. 2