Properties

Label 7098.31
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([0,26,21]))
 
pari: [g,chi] = znchar(Mod(31,7098))
 

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 \(\chi_{1183}(31,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 7098.el

\(\chi_{7098}(31,\cdot)\) \(\chi_{7098}(73,\cdot)\) \(\chi_{7098}(187,\cdot)\) \(\chi_{7098}(229,\cdot)\) \(\chi_{7098}(619,\cdot)\) \(\chi_{7098}(733,\cdot)\) \(\chi_{7098}(1123,\cdot)\) \(\chi_{7098}(1165,\cdot)\) \(\chi_{7098}(1279,\cdot)\) \(\chi_{7098}(1321,\cdot)\) \(\chi_{7098}(1669,\cdot)\) \(\chi_{7098}(1711,\cdot)\) \(\chi_{7098}(1825,\cdot)\) \(\chi_{7098}(1867,\cdot)\) \(\chi_{7098}(2215,\cdot)\) \(\chi_{7098}(2257,\cdot)\) \(\chi_{7098}(2371,\cdot)\) \(\chi_{7098}(2413,\cdot)\) \(\chi_{7098}(2761,\cdot)\) \(\chi_{7098}(2917,\cdot)\) \(\chi_{7098}(2959,\cdot)\) \(\chi_{7098}(3307,\cdot)\) \(\chi_{7098}(3349,\cdot)\) \(\chi_{7098}(3463,\cdot)\) \(\chi_{7098}(3505,\cdot)\) \(\chi_{7098}(3853,\cdot)\) \(\chi_{7098}(3895,\cdot)\) \(\chi_{7098}(4009,\cdot)\) \(\chi_{7098}(4051,\cdot)\) \(\chi_{7098}(4399,\cdot)\) ...

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

\((4733,5071,6931)\) → \((1,e\left(\frac{1}{6}\right),e\left(\frac{7}{52}\right))\)

Values

\(-1\)\(1\)\(5\)\(11\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)\(37\)\(41\)
\(1\)\(1\)\(e\left(\frac{7}{156}\right)\)\(e\left(\frac{83}{156}\right)\)\(e\left(\frac{32}{39}\right)\)\(e\left(\frac{7}{12}\right)\)\(e\left(\frac{5}{6}\right)\)\(e\left(\frac{7}{78}\right)\)\(e\left(\frac{5}{13}\right)\)\(e\left(\frac{155}{156}\right)\)\(e\left(\frac{103}{156}\right)\)\(e\left(\frac{49}{52}\right)\)
value at e.g. 2