Properties

Label 7098.97
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([0,78,17]))
 
pari: [g,chi] = znchar(Mod(97,7098))
 

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 \(\chi_{1183}(97,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 7098.en

\(\chi_{7098}(97,\cdot)\) \(\chi_{7098}(223,\cdot)\) \(\chi_{7098}(349,\cdot)\) \(\chi_{7098}(475,\cdot)\) \(\chi_{7098}(643,\cdot)\) \(\chi_{7098}(769,\cdot)\) \(\chi_{7098}(895,\cdot)\) \(\chi_{7098}(1021,\cdot)\) \(\chi_{7098}(1189,\cdot)\) \(\chi_{7098}(1315,\cdot)\) \(\chi_{7098}(1567,\cdot)\) \(\chi_{7098}(1735,\cdot)\) \(\chi_{7098}(1861,\cdot)\) \(\chi_{7098}(1987,\cdot)\) \(\chi_{7098}(2113,\cdot)\) \(\chi_{7098}(2281,\cdot)\) \(\chi_{7098}(2407,\cdot)\) \(\chi_{7098}(2533,\cdot)\) \(\chi_{7098}(2659,\cdot)\) \(\chi_{7098}(2827,\cdot)\) \(\chi_{7098}(3079,\cdot)\) \(\chi_{7098}(3205,\cdot)\) \(\chi_{7098}(3373,\cdot)\) \(\chi_{7098}(3499,\cdot)\) \(\chi_{7098}(3625,\cdot)\) \(\chi_{7098}(3751,\cdot)\) \(\chi_{7098}(3919,\cdot)\) \(\chi_{7098}(4045,\cdot)\) \(\chi_{7098}(4171,\cdot)\) \(\chi_{7098}(4297,\cdot)\) ...

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

\((4733,5071,6931)\) → \((1,-1,e\left(\frac{17}{156}\right))\)

Values

\(-1\)\(1\)\(5\)\(11\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)\(37\)\(41\)
\(1\)\(1\)\(e\left(\frac{25}{52}\right)\)\(e\left(\frac{35}{156}\right)\)\(e\left(\frac{16}{39}\right)\)\(e\left(\frac{7}{12}\right)\)\(e\left(\frac{1}{6}\right)\)\(e\left(\frac{25}{26}\right)\)\(e\left(\frac{14}{39}\right)\)\(e\left(\frac{41}{52}\right)\)\(e\left(\frac{71}{156}\right)\)\(e\left(\frac{119}{156}\right)\)
value at e.g. 2