Properties

Label 7098.4411
Modulus $7098$
Conductor $169$
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([0,0,73]))
 
pari: [g,chi] = znchar(Mod(4411,7098))
 

Basic properties

Modulus: \(7098\)
Conductor: \(169\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(78\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{169}(17,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 7098.dx

\(\chi_{7098}(43,\cdot)\) \(\chi_{7098}(127,\cdot)\) \(\chi_{7098}(589,\cdot)\) \(\chi_{7098}(673,\cdot)\) \(\chi_{7098}(1135,\cdot)\) \(\chi_{7098}(1219,\cdot)\) \(\chi_{7098}(1681,\cdot)\) \(\chi_{7098}(1765,\cdot)\) \(\chi_{7098}(2227,\cdot)\) \(\chi_{7098}(2311,\cdot)\) \(\chi_{7098}(2773,\cdot)\) \(\chi_{7098}(2857,\cdot)\) \(\chi_{7098}(3319,\cdot)\) \(\chi_{7098}(3949,\cdot)\) \(\chi_{7098}(4411,\cdot)\) \(\chi_{7098}(4495,\cdot)\) \(\chi_{7098}(4957,\cdot)\) \(\chi_{7098}(5041,\cdot)\) \(\chi_{7098}(5503,\cdot)\) \(\chi_{7098}(5587,\cdot)\) \(\chi_{7098}(6049,\cdot)\) \(\chi_{7098}(6133,\cdot)\) \(\chi_{7098}(6595,\cdot)\) \(\chi_{7098}(6679,\cdot)\)

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

\((4733,5071,6931)\) → \((1,1,e\left(\frac{73}{78}\right))\)

Values

\(-1\)\(1\)\(5\)\(11\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)\(37\)\(41\)
\(1\)\(1\)\(e\left(\frac{11}{26}\right)\)\(e\left(\frac{31}{78}\right)\)\(e\left(\frac{25}{39}\right)\)\(e\left(\frac{5}{6}\right)\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{11}{13}\right)\)\(e\left(\frac{17}{39}\right)\)\(e\left(\frac{17}{26}\right)\)\(e\left(\frac{25}{78}\right)\)\(e\left(\frac{43}{78}\right)\)
value at e.g. 2