Properties

Label 7098.1961
Modulus $7098$
Conductor $507$
Order $156$
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(156))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([78,0,115]))
 
pari: [g,chi] = znchar(Mod(1961,7098))
 

Basic properties

Modulus: \(7098\)
Conductor: \(507\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(156\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{507}(440,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 7098.ek

\(\chi_{7098}(71,\cdot)\) \(\chi_{7098}(197,\cdot)\) \(\chi_{7098}(323,\cdot)\) \(\chi_{7098}(449,\cdot)\) \(\chi_{7098}(617,\cdot)\) \(\chi_{7098}(743,\cdot)\) \(\chi_{7098}(869,\cdot)\) \(\chi_{7098}(1163,\cdot)\) \(\chi_{7098}(1289,\cdot)\) \(\chi_{7098}(1415,\cdot)\) \(\chi_{7098}(1541,\cdot)\) \(\chi_{7098}(1835,\cdot)\) \(\chi_{7098}(1961,\cdot)\) \(\chi_{7098}(2087,\cdot)\) \(\chi_{7098}(2255,\cdot)\) \(\chi_{7098}(2381,\cdot)\) \(\chi_{7098}(2507,\cdot)\) \(\chi_{7098}(2633,\cdot)\) \(\chi_{7098}(2801,\cdot)\) \(\chi_{7098}(2927,\cdot)\) \(\chi_{7098}(3053,\cdot)\) \(\chi_{7098}(3179,\cdot)\) \(\chi_{7098}(3347,\cdot)\) \(\chi_{7098}(3473,\cdot)\) \(\chi_{7098}(3599,\cdot)\) \(\chi_{7098}(3725,\cdot)\) \(\chi_{7098}(3893,\cdot)\) \(\chi_{7098}(4019,\cdot)\) \(\chi_{7098}(4271,\cdot)\) \(\chi_{7098}(4439,\cdot)\) ...

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: $\Q(\zeta_{156})$
Fixed field: Number field defined by a degree 156 polynomial (not computed)

Values on generators

\((4733,5071,6931)\) → \((-1,1,e\left(\frac{115}{156}\right))\)

Values

\(-1\)\(1\)\(5\)\(11\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)\(37\)\(41\)
\(1\)\(1\)\(e\left(\frac{7}{52}\right)\)\(e\left(\frac{67}{156}\right)\)\(e\left(\frac{5}{39}\right)\)\(e\left(\frac{11}{12}\right)\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{7}{26}\right)\)\(e\left(\frac{77}{78}\right)\)\(e\left(\frac{25}{52}\right)\)\(e\left(\frac{49}{156}\right)\)\(e\left(\frac{25}{156}\right)\)
value at e.g. 2