Properties

Label 7098.25
Modulus $7098$
Conductor $1183$
Order $78$
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(78))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,52,9]))
 
pari: [g,chi] = znchar(Mod(25,7098))
 

Basic properties

Modulus: \(7098\)
Conductor: \(1183\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(78\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{1183}(25,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 7098.df

\(\chi_{7098}(25,\cdot)\) \(\chi_{7098}(415,\cdot)\) \(\chi_{7098}(571,\cdot)\) \(\chi_{7098}(961,\cdot)\) \(\chi_{7098}(1117,\cdot)\) \(\chi_{7098}(1507,\cdot)\) \(\chi_{7098}(1663,\cdot)\) \(\chi_{7098}(2053,\cdot)\) \(\chi_{7098}(2209,\cdot)\) \(\chi_{7098}(2599,\cdot)\) \(\chi_{7098}(2755,\cdot)\) \(\chi_{7098}(3145,\cdot)\) \(\chi_{7098}(3301,\cdot)\) \(\chi_{7098}(3691,\cdot)\) \(\chi_{7098}(3847,\cdot)\) \(\chi_{7098}(4237,\cdot)\) \(\chi_{7098}(4783,\cdot)\) \(\chi_{7098}(4939,\cdot)\) \(\chi_{7098}(5329,\cdot)\) \(\chi_{7098}(5485,\cdot)\) \(\chi_{7098}(5875,\cdot)\) \(\chi_{7098}(6031,\cdot)\) \(\chi_{7098}(6577,\cdot)\) \(\chi_{7098}(6967,\cdot)\)

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: Number field defined by a degree 78 polynomial

Values on generators

\((4733,5071,6931)\) → \((1,e\left(\frac{2}{3}\right),e\left(\frac{3}{26}\right))\)

Values

\(-1\)\(1\)\(5\)\(11\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)\(37\)\(41\)
\(1\)\(1\)\(e\left(\frac{29}{78}\right)\)\(e\left(\frac{43}{78}\right)\)\(e\left(\frac{20}{39}\right)\)\(e\left(\frac{5}{6}\right)\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{29}{39}\right)\)\(e\left(\frac{8}{13}\right)\)\(e\left(\frac{7}{78}\right)\)\(e\left(\frac{59}{78}\right)\)\(e\left(\frac{21}{26}\right)\)
value at e.g. 2