Properties

Label 7098.145
Modulus $7098$
Conductor $1183$
Order $156$
Real no
Primitive no
Minimal yes
Parity even

Related objects

Learn more about

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([0,130,49]))
 
pari: [g,chi] = znchar(Mod(145,7098))
 

Basic properties

Modulus: \(7098\)
Conductor: \(1183\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(156\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{1183}(145,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 7098.ea

\(\chi_{7098}(145,\cdot)\) \(\chi_{7098}(241,\cdot)\) \(\chi_{7098}(271,\cdot)\) \(\chi_{7098}(409,\cdot)\) \(\chi_{7098}(691,\cdot)\) \(\chi_{7098}(787,\cdot)\) \(\chi_{7098}(817,\cdot)\) \(\chi_{7098}(955,\cdot)\) \(\chi_{7098}(1237,\cdot)\) \(\chi_{7098}(1363,\cdot)\) \(\chi_{7098}(1501,\cdot)\) \(\chi_{7098}(1783,\cdot)\) \(\chi_{7098}(1879,\cdot)\) \(\chi_{7098}(1909,\cdot)\) \(\chi_{7098}(2329,\cdot)\) \(\chi_{7098}(2425,\cdot)\) \(\chi_{7098}(2593,\cdot)\) \(\chi_{7098}(2875,\cdot)\) \(\chi_{7098}(2971,\cdot)\) \(\chi_{7098}(3001,\cdot)\) \(\chi_{7098}(3139,\cdot)\) \(\chi_{7098}(3421,\cdot)\) \(\chi_{7098}(3517,\cdot)\) \(\chi_{7098}(3547,\cdot)\) \(\chi_{7098}(3685,\cdot)\) \(\chi_{7098}(4063,\cdot)\) \(\chi_{7098}(4093,\cdot)\) \(\chi_{7098}(4231,\cdot)\) \(\chi_{7098}(4513,\cdot)\) \(\chi_{7098}(4609,\cdot)\) ...

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

\((4733,5071,6931)\) → \((1,e\left(\frac{5}{6}\right),e\left(\frac{49}{156}\right))\)

Values

\(-1\)\(1\)\(5\)\(11\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)\(37\)\(41\)
\(1\)\(1\)\(e\left(\frac{155}{156}\right)\)\(e\left(\frac{107}{156}\right)\)\(e\left(\frac{9}{13}\right)\)\(e\left(\frac{7}{12}\right)\)\(-1\)\(e\left(\frac{77}{78}\right)\)\(e\left(\frac{22}{39}\right)\)\(e\left(\frac{67}{156}\right)\)\(e\left(\frac{5}{52}\right)\)\(e\left(\frac{31}{156}\right)\)
value at e.g. 2