Properties

Label 7098.281
Modulus $7098$
Conductor $507$
Order $52$
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(52))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([26,0,37]))
 
pari: [g,chi] = znchar(Mod(281,7098))
 

Basic properties

Modulus: \(7098\)
Conductor: \(507\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(52\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{507}(281,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 7098.cv

\(\chi_{7098}(281,\cdot)\) \(\chi_{7098}(785,\cdot)\) \(\chi_{7098}(827,\cdot)\) \(\chi_{7098}(1331,\cdot)\) \(\chi_{7098}(1373,\cdot)\) \(\chi_{7098}(1877,\cdot)\) \(\chi_{7098}(1919,\cdot)\) \(\chi_{7098}(2423,\cdot)\) \(\chi_{7098}(2969,\cdot)\) \(\chi_{7098}(3011,\cdot)\) \(\chi_{7098}(3515,\cdot)\) \(\chi_{7098}(3557,\cdot)\) \(\chi_{7098}(4061,\cdot)\) \(\chi_{7098}(4103,\cdot)\) \(\chi_{7098}(4607,\cdot)\) \(\chi_{7098}(4649,\cdot)\) \(\chi_{7098}(5153,\cdot)\) \(\chi_{7098}(5195,\cdot)\) \(\chi_{7098}(5699,\cdot)\) \(\chi_{7098}(5741,\cdot)\) \(\chi_{7098}(6245,\cdot)\) \(\chi_{7098}(6287,\cdot)\) \(\chi_{7098}(6791,\cdot)\) \(\chi_{7098}(6833,\cdot)\)

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: $\Q(\zeta_{52})$
Fixed field: Number field defined by a degree 52 polynomial

Values on generators

\((4733,5071,6931)\) → \((-1,1,e\left(\frac{37}{52}\right))\)

Values

\(-1\)\(1\)\(5\)\(11\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)\(37\)\(41\)
\(1\)\(1\)\(e\left(\frac{47}{52}\right)\)\(e\left(\frac{41}{52}\right)\)\(e\left(\frac{5}{13}\right)\)\(i\)\(1\)\(e\left(\frac{21}{26}\right)\)\(e\left(\frac{25}{26}\right)\)\(e\left(\frac{49}{52}\right)\)\(e\left(\frac{23}{52}\right)\)\(e\left(\frac{51}{52}\right)\)
value at e.g. 2