Properties

Label 7098.2159
Modulus $7098$
Conductor $3549$
Order $78$
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(78))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([39,13,72]))
 
pari: [g,chi] = znchar(Mod(2159,7098))
 

Basic properties

Modulus: \(7098\)
Conductor: \(3549\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(78\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{3549}(2159,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 7098.dq

\(\chi_{7098}(131,\cdot)\) \(\chi_{7098}(521,\cdot)\) \(\chi_{7098}(1067,\cdot)\) \(\chi_{7098}(1223,\cdot)\) \(\chi_{7098}(1613,\cdot)\) \(\chi_{7098}(1769,\cdot)\) \(\chi_{7098}(2159,\cdot)\) \(\chi_{7098}(2315,\cdot)\) \(\chi_{7098}(2861,\cdot)\) \(\chi_{7098}(3251,\cdot)\) \(\chi_{7098}(3407,\cdot)\) \(\chi_{7098}(3797,\cdot)\) \(\chi_{7098}(3953,\cdot)\) \(\chi_{7098}(4343,\cdot)\) \(\chi_{7098}(4499,\cdot)\) \(\chi_{7098}(4889,\cdot)\) \(\chi_{7098}(5045,\cdot)\) \(\chi_{7098}(5435,\cdot)\) \(\chi_{7098}(5591,\cdot)\) \(\chi_{7098}(5981,\cdot)\) \(\chi_{7098}(6137,\cdot)\) \(\chi_{7098}(6527,\cdot)\) \(\chi_{7098}(6683,\cdot)\) \(\chi_{7098}(7073,\cdot)\)

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: $\Q(\zeta_{39})$
Fixed field: Number field defined by a degree 78 polynomial

Values on generators

\((4733,5071,6931)\) → \((-1,e\left(\frac{1}{6}\right),e\left(\frac{12}{13}\right))\)

Values

\(-1\)\(1\)\(5\)\(11\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)\(37\)\(41\)
\(1\)\(1\)\(e\left(\frac{25}{39}\right)\)\(e\left(\frac{19}{78}\right)\)\(e\left(\frac{17}{39}\right)\)\(e\left(\frac{5}{6}\right)\)\(e\left(\frac{5}{6}\right)\)\(e\left(\frac{11}{39}\right)\)\(e\left(\frac{11}{26}\right)\)\(e\left(\frac{43}{78}\right)\)\(e\left(\frac{28}{39}\right)\)\(e\left(\frac{6}{13}\right)\)
value at e.g. 2