Properties

Label 7098.6241
Modulus $7098$
Conductor $1183$
Order $39$
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(78))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,52,24]))
 
pari: [g,chi] = znchar(Mod(6241,7098))
 

Basic properties

Modulus: \(7098\)
Conductor: \(1183\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(39\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{1183}(326,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 7098.ct

\(\chi_{7098}(79,\cdot)\) \(\chi_{7098}(235,\cdot)\) \(\chi_{7098}(625,\cdot)\) \(\chi_{7098}(781,\cdot)\) \(\chi_{7098}(1171,\cdot)\) \(\chi_{7098}(1327,\cdot)\) \(\chi_{7098}(1717,\cdot)\) \(\chi_{7098}(1873,\cdot)\) \(\chi_{7098}(2263,\cdot)\) \(\chi_{7098}(2419,\cdot)\) \(\chi_{7098}(2809,\cdot)\) \(\chi_{7098}(2965,\cdot)\) \(\chi_{7098}(3355,\cdot)\) \(\chi_{7098}(3511,\cdot)\) \(\chi_{7098}(3901,\cdot)\) \(\chi_{7098}(4447,\cdot)\) \(\chi_{7098}(4603,\cdot)\) \(\chi_{7098}(4993,\cdot)\) \(\chi_{7098}(5149,\cdot)\) \(\chi_{7098}(5539,\cdot)\) \(\chi_{7098}(5695,\cdot)\) \(\chi_{7098}(6241,\cdot)\) \(\chi_{7098}(6631,\cdot)\) \(\chi_{7098}(6787,\cdot)\)

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: $\Q(\zeta_{39})$
Fixed field: 39.39.1501310100540182816122902385277086845494955654696971364374430555896401217548869308777432830007194746769.1

Values on generators

\((4733,5071,6931)\) → \((1,e\left(\frac{2}{3}\right),e\left(\frac{4}{13}\right))\)

Values

\(-1\)\(1\)\(5\)\(11\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)\(37\)\(41\)
\(1\)\(1\)\(e\left(\frac{4}{39}\right)\)\(e\left(\frac{14}{39}\right)\)\(e\left(\frac{23}{39}\right)\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{8}{39}\right)\)\(e\left(\frac{4}{13}\right)\)\(e\left(\frac{5}{39}\right)\)\(e\left(\frac{31}{39}\right)\)\(e\left(\frac{2}{13}\right)\)
value at e.g. 2