Basic properties
| Modulus: | \(2009\) | |
| Conductor: | \(2009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(280\) | 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 2009.ch
\(\chi_{2009}(15,\cdot)\) \(\chi_{2009}(22,\cdot)\) \(\chi_{2009}(29,\cdot)\) \(\chi_{2009}(71,\cdot)\) \(\chi_{2009}(106,\cdot)\) \(\chi_{2009}(134,\cdot)\) \(\chi_{2009}(176,\cdot)\) \(\chi_{2009}(183,\cdot)\) \(\chi_{2009}(190,\cdot)\) \(\chi_{2009}(211,\cdot)\) \(\chi_{2009}(218,\cdot)\) \(\chi_{2009}(239,\cdot)\) \(\chi_{2009}(253,\cdot)\) \(\chi_{2009}(274,\cdot)\) \(\chi_{2009}(281,\cdot)\) \(\chi_{2009}(302,\cdot)\) \(\chi_{2009}(309,\cdot)\) \(\chi_{2009}(316,\cdot)\) \(\chi_{2009}(358,\cdot)\) \(\chi_{2009}(386,\cdot)\) \(\chi_{2009}(421,\cdot)\) \(\chi_{2009}(463,\cdot)\) \(\chi_{2009}(470,\cdot)\) \(\chi_{2009}(477,\cdot)\) \(\chi_{2009}(498,\cdot)\) \(\chi_{2009}(505,\cdot)\) \(\chi_{2009}(526,\cdot)\) \(\chi_{2009}(561,\cdot)\) \(\chi_{2009}(568,\cdot)\) \(\chi_{2009}(596,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{280})$ |
| Fixed field: | Number field defined by a degree 280 polynomial (not computed) |
Values on generators
\((493,785)\) → \((e\left(\frac{3}{7}\right),e\left(\frac{7}{40}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 2009 }(29, a) \) | \(-1\) | \(1\) | \(e\left(\frac{97}{140}\right)\) | \(e\left(\frac{3}{56}\right)\) | \(e\left(\frac{27}{70}\right)\) | \(e\left(\frac{39}{140}\right)\) | \(e\left(\frac{209}{280}\right)\) | \(e\left(\frac{11}{140}\right)\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{34}{35}\right)\) | \(e\left(\frac{187}{280}\right)\) | \(e\left(\frac{123}{280}\right)\) |