Properties

Label 7098.11
Modulus $7098$
Conductor $3549$
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([78,104,103]))
 
pari: [g,chi] = znchar(Mod(11,7098))
 

Basic properties

Modulus: \(7098\)
Conductor: \(3549\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(156\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{3549}(11,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 7098.ei

\(\chi_{7098}(11,\cdot)\) \(\chi_{7098}(149,\cdot)\) \(\chi_{7098}(431,\cdot)\) \(\chi_{7098}(527,\cdot)\) \(\chi_{7098}(557,\cdot)\) \(\chi_{7098}(977,\cdot)\) \(\chi_{7098}(1073,\cdot)\) \(\chi_{7098}(1241,\cdot)\) \(\chi_{7098}(1523,\cdot)\) \(\chi_{7098}(1619,\cdot)\) \(\chi_{7098}(1649,\cdot)\) \(\chi_{7098}(1787,\cdot)\) \(\chi_{7098}(2069,\cdot)\) \(\chi_{7098}(2165,\cdot)\) \(\chi_{7098}(2195,\cdot)\) \(\chi_{7098}(2333,\cdot)\) \(\chi_{7098}(2711,\cdot)\) \(\chi_{7098}(2741,\cdot)\) \(\chi_{7098}(2879,\cdot)\) \(\chi_{7098}(3161,\cdot)\) \(\chi_{7098}(3257,\cdot)\) \(\chi_{7098}(3287,\cdot)\) \(\chi_{7098}(3425,\cdot)\) \(\chi_{7098}(3707,\cdot)\) \(\chi_{7098}(3803,\cdot)\) \(\chi_{7098}(3833,\cdot)\) \(\chi_{7098}(3971,\cdot)\) \(\chi_{7098}(4253,\cdot)\) \(\chi_{7098}(4349,\cdot)\) \(\chi_{7098}(4379,\cdot)\) ...

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

\((4733,5071,6931)\) → \((-1,e\left(\frac{2}{3}\right),e\left(\frac{103}{156}\right))\)

Values

\(-1\)\(1\)\(5\)\(11\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)\(37\)\(41\)
\(1\)\(1\)\(e\left(\frac{121}{156}\right)\)\(e\left(\frac{9}{52}\right)\)\(e\left(\frac{22}{39}\right)\)\(i\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{43}{78}\right)\)\(e\left(\frac{71}{78}\right)\)\(e\left(\frac{83}{156}\right)\)\(e\left(\frac{5}{156}\right)\)\(e\left(\frac{97}{156}\right)\)
value at e.g. 2