Basic properties
| Modulus: | \(1601\) | |
| Conductor: | \(1601\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(320\) | 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 1601.r
\(\chi_{1601}(12,\cdot)\) \(\chi_{1601}(15,\cdot)\) \(\chi_{1601}(22,\cdot)\) \(\chi_{1601}(34,\cdot)\) \(\chi_{1601}(54,\cdot)\) \(\chi_{1601}(83,\cdot)\) \(\chi_{1601}(93,\cdot)\) \(\chi_{1601}(99,\cdot)\) \(\chi_{1601}(112,\cdot)\) \(\chi_{1601}(114,\cdot)\) \(\chi_{1601}(118,\cdot)\) \(\chi_{1601}(127,\cdot)\) \(\chi_{1601}(140,\cdot)\) \(\chi_{1601}(153,\cdot)\) \(\chi_{1601}(173,\cdot)\) \(\chi_{1601}(209,\cdot)\) \(\chi_{1601}(226,\cdot)\) \(\chi_{1601}(229,\cdot)\) \(\chi_{1601}(230,\cdot)\) \(\chi_{1601}(241,\cdot)\) \(\chi_{1601}(243,\cdot)\) \(\chi_{1601}(271,\cdot)\) \(\chi_{1601}(277,\cdot)\) \(\chi_{1601}(284,\cdot)\) \(\chi_{1601}(293,\cdot)\) \(\chi_{1601}(323,\cdot)\) \(\chi_{1601}(355,\cdot)\) \(\chi_{1601}(367,\cdot)\) \(\chi_{1601}(382,\cdot)\) \(\chi_{1601}(384,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{320})$ |
| Fixed field: | Number field defined by a degree 320 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{209}{320}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1601 }(15, a) \) | \(-1\) | \(1\) | \(e\left(\frac{77}{80}\right)\) | \(e\left(\frac{209}{320}\right)\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{69}{80}\right)\) | \(e\left(\frac{197}{320}\right)\) | \(e\left(\frac{123}{320}\right)\) | \(e\left(\frac{71}{80}\right)\) | \(e\left(\frac{49}{160}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{137}{320}\right)\) |