Properties

Label 7098.4577
Modulus $7098$
Conductor $3549$
Order $26$
Real no
Primitive no
Minimal yes
Parity even

Related objects

Learn more

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([13,13,18]))
 
pari: [g,chi] = znchar(Mod(4577,7098))
 

Basic properties

Modulus: \(7098\)
Conductor: \(3549\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(26\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{3549}(1028,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 7098.ck

\(\chi_{7098}(209,\cdot)\) \(\chi_{7098}(755,\cdot)\) \(\chi_{7098}(1301,\cdot)\) \(\chi_{7098}(1847,\cdot)\) \(\chi_{7098}(2393,\cdot)\) \(\chi_{7098}(2939,\cdot)\) \(\chi_{7098}(3485,\cdot)\) \(\chi_{7098}(4031,\cdot)\) \(\chi_{7098}(4577,\cdot)\) \(\chi_{7098}(5123,\cdot)\) \(\chi_{7098}(5669,\cdot)\) \(\chi_{7098}(6215,\cdot)\)

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: Number field defined by a degree 26 polynomial

Values on generators

\((4733,5071,6931)\) → \((-1,-1,e\left(\frac{9}{13}\right))\)

Values

\(-1\)\(1\)\(5\)\(11\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)\(37\)\(41\)
\(1\)\(1\)\(e\left(\frac{3}{13}\right)\)\(e\left(\frac{21}{26}\right)\)\(e\left(\frac{1}{13}\right)\)\(-1\)\(-1\)\(e\left(\frac{6}{13}\right)\)\(e\left(\frac{5}{26}\right)\)\(e\left(\frac{1}{26}\right)\)\(e\left(\frac{7}{13}\right)\)\(e\left(\frac{11}{13}\right)\)
value at e.g. 2