Properties

Label 7098.853
Modulus $7098$
Conductor $1183$
Order $52$
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(52))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,26,1]))
 
pari: [g,chi] = znchar(Mod(853,7098))
 

Basic properties

Modulus: \(7098\)
Conductor: \(1183\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(52\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{1183}(853,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 7098.cu

\(\chi_{7098}(265,\cdot)\) \(\chi_{7098}(307,\cdot)\) \(\chi_{7098}(811,\cdot)\) \(\chi_{7098}(853,\cdot)\) \(\chi_{7098}(1357,\cdot)\) \(\chi_{7098}(1399,\cdot)\) \(\chi_{7098}(1903,\cdot)\) \(\chi_{7098}(1945,\cdot)\) \(\chi_{7098}(2449,\cdot)\) \(\chi_{7098}(2491,\cdot)\) \(\chi_{7098}(2995,\cdot)\) \(\chi_{7098}(3037,\cdot)\) \(\chi_{7098}(3541,\cdot)\) \(\chi_{7098}(3583,\cdot)\) \(\chi_{7098}(4087,\cdot)\) \(\chi_{7098}(4129,\cdot)\) \(\chi_{7098}(4675,\cdot)\) \(\chi_{7098}(5179,\cdot)\) \(\chi_{7098}(5221,\cdot)\) \(\chi_{7098}(5725,\cdot)\) \(\chi_{7098}(5767,\cdot)\) \(\chi_{7098}(6271,\cdot)\) \(\chi_{7098}(6313,\cdot)\) \(\chi_{7098}(6817,\cdot)\)

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

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

Values

\(-1\)\(1\)\(5\)\(11\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)\(37\)\(41\)
\(1\)\(1\)\(e\left(\frac{35}{52}\right)\)\(e\left(\frac{51}{52}\right)\)\(e\left(\frac{4}{13}\right)\)\(-i\)\(-1\)\(e\left(\frac{9}{26}\right)\)\(e\left(\frac{10}{13}\right)\)\(e\left(\frac{47}{52}\right)\)\(e\left(\frac{47}{52}\right)\)\(e\left(\frac{7}{52}\right)\)
value at e.g. 2