Basic properties
| Modulus: | \(1061\) | |
| Conductor: | \(1061\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1060\) | 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 1061.l
\(\chi_{1061}(2,\cdot)\) \(\chi_{1061}(3,\cdot)\) \(\chi_{1061}(8,\cdot)\) \(\chi_{1061}(12,\cdot)\) \(\chi_{1061}(15,\cdot)\) \(\chi_{1061}(21,\cdot)\) \(\chi_{1061}(22,\cdot)\) \(\chi_{1061}(27,\cdot)\) \(\chi_{1061}(33,\cdot)\) \(\chi_{1061}(38,\cdot)\) \(\chi_{1061}(40,\cdot)\) \(\chi_{1061}(43,\cdot)\) \(\chi_{1061}(46,\cdot)\) \(\chi_{1061}(48,\cdot)\) \(\chi_{1061}(50,\cdot)\) \(\chi_{1061}(52,\cdot)\) \(\chi_{1061}(56,\cdot)\) \(\chi_{1061}(60,\cdot)\) \(\chi_{1061}(62,\cdot)\) \(\chi_{1061}(65,\cdot)\) \(\chi_{1061}(68,\cdot)\) \(\chi_{1061}(70,\cdot)\) \(\chi_{1061}(71,\cdot)\) \(\chi_{1061}(72,\cdot)\) \(\chi_{1061}(74,\cdot)\) \(\chi_{1061}(78,\cdot)\) \(\chi_{1061}(79,\cdot)\) \(\chi_{1061}(82,\cdot)\) \(\chi_{1061}(85,\cdot)\) \(\chi_{1061}(89,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1060})$ |
| Fixed field: | Number field defined by a degree 1060 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{531}{1060}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1061 }(1059, a) \) | \(-1\) | \(1\) | \(e\left(\frac{531}{1060}\right)\) | \(e\left(\frac{697}{1060}\right)\) | \(e\left(\frac{1}{530}\right)\) | \(e\left(\frac{61}{265}\right)\) | \(e\left(\frac{42}{265}\right)\) | \(e\left(\frac{119}{265}\right)\) | \(e\left(\frac{533}{1060}\right)\) | \(e\left(\frac{167}{530}\right)\) | \(e\left(\frac{155}{212}\right)\) | \(e\left(\frac{301}{530}\right)\) |