Properties

Label 7098.1081
Modulus $7098$
Conductor $1183$
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([0,26,37]))
 
pari: [g,chi] = znchar(Mod(1081,7098))
 

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 \(\chi_{1183}(1081,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 7098.em

\(\chi_{7098}(115,\cdot)\) \(\chi_{7098}(397,\cdot)\) \(\chi_{7098}(535,\cdot)\) \(\chi_{7098}(565,\cdot)\) \(\chi_{7098}(661,\cdot)\) \(\chi_{7098}(943,\cdot)\) \(\chi_{7098}(1081,\cdot)\) \(\chi_{7098}(1111,\cdot)\) \(\chi_{7098}(1207,\cdot)\) \(\chi_{7098}(1489,\cdot)\) \(\chi_{7098}(1627,\cdot)\) \(\chi_{7098}(1657,\cdot)\) \(\chi_{7098}(1753,\cdot)\) \(\chi_{7098}(2035,\cdot)\) \(\chi_{7098}(2173,\cdot)\) \(\chi_{7098}(2203,\cdot)\) \(\chi_{7098}(2299,\cdot)\) \(\chi_{7098}(2581,\cdot)\) \(\chi_{7098}(2719,\cdot)\) \(\chi_{7098}(2749,\cdot)\) \(\chi_{7098}(2845,\cdot)\) \(\chi_{7098}(3127,\cdot)\) \(\chi_{7098}(3265,\cdot)\) \(\chi_{7098}(3295,\cdot)\) \(\chi_{7098}(3391,\cdot)\) \(\chi_{7098}(3673,\cdot)\) \(\chi_{7098}(3811,\cdot)\) \(\chi_{7098}(3841,\cdot)\) \(\chi_{7098}(3937,\cdot)\) \(\chi_{7098}(4219,\cdot)\) ...

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

\((4733,5071,6931)\) → \((1,e\left(\frac{1}{6}\right),e\left(\frac{37}{156}\right))\)

Values

\(-1\)\(1\)\(5\)\(11\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)\(37\)\(41\)
\(1\)\(1\)\(e\left(\frac{151}{156}\right)\)\(e\left(\frac{5}{52}\right)\)\(e\left(\frac{31}{39}\right)\)\(i\)\(e\left(\frac{1}{6}\right)\)\(e\left(\frac{73}{78}\right)\)\(e\left(\frac{19}{39}\right)\)\(e\left(\frac{23}{156}\right)\)\(e\left(\frac{23}{156}\right)\)\(e\left(\frac{103}{156}\right)\)
value at e.g. 2