Properties

Label 7098.101
Modulus $7098$
Conductor $3549$
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([39,13,35]))
 
pari: [g,chi] = znchar(Mod(101,7098))
 

Basic properties

Modulus: \(7098\)
Conductor: \(3549\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(78\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{3549}(101,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 7098.dc

\(\chi_{7098}(101,\cdot)\) \(\chi_{7098}(173,\cdot)\) \(\chi_{7098}(647,\cdot)\) \(\chi_{7098}(719,\cdot)\) \(\chi_{7098}(1193,\cdot)\) \(\chi_{7098}(1265,\cdot)\) \(\chi_{7098}(1739,\cdot)\) \(\chi_{7098}(1811,\cdot)\) \(\chi_{7098}(2285,\cdot)\) \(\chi_{7098}(2357,\cdot)\) \(\chi_{7098}(2831,\cdot)\) \(\chi_{7098}(2903,\cdot)\) \(\chi_{7098}(3377,\cdot)\) \(\chi_{7098}(3449,\cdot)\) \(\chi_{7098}(3923,\cdot)\) \(\chi_{7098}(3995,\cdot)\) \(\chi_{7098}(4469,\cdot)\) \(\chi_{7098}(5015,\cdot)\) \(\chi_{7098}(5087,\cdot)\) \(\chi_{7098}(5561,\cdot)\) \(\chi_{7098}(5633,\cdot)\) \(\chi_{7098}(6179,\cdot)\) \(\chi_{7098}(6653,\cdot)\) \(\chi_{7098}(6725,\cdot)\)

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

\((4733,5071,6931)\) → \((-1,e\left(\frac{1}{6}\right),e\left(\frac{35}{78}\right))\)

Values

\(-1\)\(1\)\(5\)\(11\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)\(37\)\(41\)
\(1\)\(1\)\(e\left(\frac{29}{78}\right)\)\(e\left(\frac{5}{13}\right)\)\(e\left(\frac{7}{39}\right)\)\(1\)\(e\left(\frac{1}{6}\right)\)\(e\left(\frac{29}{39}\right)\)\(e\left(\frac{35}{78}\right)\)\(e\left(\frac{23}{39}\right)\)\(e\left(\frac{7}{78}\right)\)\(e\left(\frac{11}{78}\right)\)
value at e.g. 2