Basic properties
| Modulus: | \(1063\) | |
| Conductor: | \(1063\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1062\) | 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 1063.l
\(\chi_{1063}(3,\cdot)\) \(\chi_{1063}(6,\cdot)\) \(\chi_{1063}(10,\cdot)\) \(\chi_{1063}(20,\cdot)\) \(\chi_{1063}(21,\cdot)\) \(\chi_{1063}(24,\cdot)\) \(\chi_{1063}(29,\cdot)\) \(\chi_{1063}(31,\cdot)\) \(\chi_{1063}(33,\cdot)\) \(\chi_{1063}(35,\cdot)\) \(\chi_{1063}(39,\cdot)\) \(\chi_{1063}(45,\cdot)\) \(\chi_{1063}(48,\cdot)\) \(\chi_{1063}(51,\cdot)\) \(\chi_{1063}(53,\cdot)\) \(\chi_{1063}(54,\cdot)\) \(\chi_{1063}(55,\cdot)\) \(\chi_{1063}(58,\cdot)\) \(\chi_{1063}(61,\cdot)\) \(\chi_{1063}(62,\cdot)\) \(\chi_{1063}(69,\cdot)\) \(\chi_{1063}(70,\cdot)\) \(\chi_{1063}(75,\cdot)\) \(\chi_{1063}(78,\cdot)\) \(\chi_{1063}(79,\cdot)\) \(\chi_{1063}(80,\cdot)\) \(\chi_{1063}(82,\cdot)\) \(\chi_{1063}(84,\cdot)\) \(\chi_{1063}(86,\cdot)\) \(\chi_{1063}(95,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{531})$ |
| Fixed field: | Number field defined by a degree 1062 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{1}{1062}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1063 }(3, a) \) | \(-1\) | \(1\) | \(e\left(\frac{524}{531}\right)\) | \(e\left(\frac{1}{1062}\right)\) | \(e\left(\frac{517}{531}\right)\) | \(e\left(\frac{313}{354}\right)\) | \(e\left(\frac{1049}{1062}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{170}{177}\right)\) | \(e\left(\frac{1}{531}\right)\) | \(e\left(\frac{925}{1062}\right)\) | \(e\left(\frac{359}{531}\right)\) |