Basic properties
Modulus: | \(5077\) | |
Conductor: | \(5077\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(5076\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5077.x
\(\chi_{5077}(2,\cdot)\) \(\chi_{5077}(6,\cdot)\) \(\chi_{5077}(11,\cdot)\) \(\chi_{5077}(14,\cdot)\) \(\chi_{5077}(17,\cdot)\) \(\chi_{5077}(18,\cdot)\) \(\chi_{5077}(20,\cdot)\) \(\chi_{5077}(31,\cdot)\) \(\chi_{5077}(32,\cdot)\) \(\chi_{5077}(33,\cdot)\) \(\chi_{5077}(35,\cdot)\) \(\chi_{5077}(37,\cdot)\) \(\chi_{5077}(41,\cdot)\) \(\chi_{5077}(42,\cdot)\) \(\chi_{5077}(43,\cdot)\) \(\chi_{5077}(44,\cdot)\) \(\chi_{5077}(50,\cdot)\) \(\chi_{5077}(51,\cdot)\) \(\chi_{5077}(52,\cdot)\) \(\chi_{5077}(54,\cdot)\) \(\chi_{5077}(56,\cdot)\) \(\chi_{5077}(60,\cdot)\) \(\chi_{5077}(67,\cdot)\) \(\chi_{5077}(80,\cdot)\) \(\chi_{5077}(83,\cdot)\) \(\chi_{5077}(91,\cdot)\) \(\chi_{5077}(92,\cdot)\) \(\chi_{5077}(93,\cdot)\) \(\chi_{5077}(94,\cdot)\) \(\chi_{5077}(95,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{5076})$ |
Fixed field: | Number field defined by a degree 5076 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{4363}{5076}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 5077 }(6, a) \) | \(-1\) | \(1\) | \(e\left(\frac{4363}{5076}\right)\) | \(e\left(\frac{247}{846}\right)\) | \(e\left(\frac{1825}{2538}\right)\) | \(e\left(\frac{53}{188}\right)\) | \(e\left(\frac{769}{5076}\right)\) | \(e\left(\frac{358}{1269}\right)\) | \(e\left(\frac{979}{1692}\right)\) | \(e\left(\frac{247}{423}\right)\) | \(e\left(\frac{359}{2538}\right)\) | \(e\left(\frac{4691}{5076}\right)\) |