Basic properties
| Modulus: | \(1031\) | |
| Conductor: | \(1031\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(206\) | 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 1031.f
\(\chi_{1031}(7,\cdot)\) \(\chi_{1031}(17,\cdot)\) \(\chi_{1031}(19,\cdot)\) \(\chi_{1031}(31,\cdot)\) \(\chi_{1031}(67,\cdot)\) \(\chi_{1031}(70,\cdot)\) \(\chi_{1031}(82,\cdot)\) \(\chi_{1031}(103,\cdot)\) \(\chi_{1031}(105,\cdot)\) \(\chi_{1031}(123,\cdot)\) \(\chi_{1031}(151,\cdot)\) \(\chi_{1031}(170,\cdot)\) \(\chi_{1031}(178,\cdot)\) \(\chi_{1031}(182,\cdot)\) \(\chi_{1031}(190,\cdot)\) \(\chi_{1031}(193,\cdot)\) \(\chi_{1031}(199,\cdot)\) \(\chi_{1031}(203,\cdot)\) \(\chi_{1031}(224,\cdot)\) \(\chi_{1031}(255,\cdot)\) \(\chi_{1031}(267,\cdot)\) \(\chi_{1031}(273,\cdot)\) \(\chi_{1031}(277,\cdot)\) \(\chi_{1031}(285,\cdot)\) \(\chi_{1031}(296,\cdot)\) \(\chi_{1031}(310,\cdot)\) \(\chi_{1031}(311,\cdot)\) \(\chi_{1031}(316,\cdot)\) \(\chi_{1031}(336,\cdot)\) \(\chi_{1031}(337,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{103})$ |
| Fixed field: | Number field defined by a degree 206 polynomial (not computed) |
Values on generators
\(14\) → \(e\left(\frac{47}{206}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1031 }(7, a) \) | \(-1\) | \(1\) | \(e\left(\frac{63}{103}\right)\) | \(e\left(\frac{27}{103}\right)\) | \(e\left(\frac{23}{103}\right)\) | \(e\left(\frac{63}{103}\right)\) | \(e\left(\frac{90}{103}\right)\) | \(e\left(\frac{127}{206}\right)\) | \(e\left(\frac{86}{103}\right)\) | \(e\left(\frac{54}{103}\right)\) | \(e\left(\frac{23}{103}\right)\) | \(e\left(\frac{93}{103}\right)\) |