Properties

Label 7098.6005
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([13,13,17]))
 
pari: [g,chi] = znchar(Mod(6005,7098))
 

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 \(\chi_{3549}(2456,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 7098.cm

\(\chi_{7098}(545,\cdot)\) \(\chi_{7098}(1091,\cdot)\) \(\chi_{7098}(1637,\cdot)\) \(\chi_{7098}(2183,\cdot)\) \(\chi_{7098}(2729,\cdot)\) \(\chi_{7098}(3275,\cdot)\) \(\chi_{7098}(3821,\cdot)\) \(\chi_{7098}(4367,\cdot)\) \(\chi_{7098}(4913,\cdot)\) \(\chi_{7098}(5459,\cdot)\) \(\chi_{7098}(6005,\cdot)\) \(\chi_{7098}(6551,\cdot)\)

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

\((4733,5071,6931)\) → \((-1,-1,e\left(\frac{17}{26}\right))\)

Values

\(-1\)\(1\)\(5\)\(11\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)\(37\)\(41\)
\(1\)\(1\)\(e\left(\frac{23}{26}\right)\)\(e\left(\frac{11}{13}\right)\)\(e\left(\frac{6}{13}\right)\)\(1\)\(-1\)\(e\left(\frac{10}{13}\right)\)\(e\left(\frac{17}{26}\right)\)\(e\left(\frac{3}{13}\right)\)\(e\left(\frac{19}{26}\right)\)\(e\left(\frac{15}{26}\right)\)
value at e.g. 2