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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2009.cg
\(\chi_{2009}(6,\cdot)\) \(\chi_{2009}(13,\cdot)\) \(\chi_{2009}(34,\cdot)\) \(\chi_{2009}(69,\cdot)\) \(\chi_{2009}(76,\cdot)\) \(\chi_{2009}(104,\cdot)\) \(\chi_{2009}(111,\cdot)\) \(\chi_{2009}(153,\cdot)\) \(\chi_{2009}(181,\cdot)\) \(\chi_{2009}(188,\cdot)\) \(\chi_{2009}(216,\cdot)\) \(\chi_{2009}(258,\cdot)\) \(\chi_{2009}(265,\cdot)\) \(\chi_{2009}(272,\cdot)\) \(\chi_{2009}(300,\cdot)\) \(\chi_{2009}(321,\cdot)\) \(\chi_{2009}(335,\cdot)\) \(\chi_{2009}(356,\cdot)\) \(\chi_{2009}(363,\cdot)\) \(\chi_{2009}(384,\cdot)\) \(\chi_{2009}(398,\cdot)\) \(\chi_{2009}(468,\cdot)\) \(\chi_{2009}(475,\cdot)\) \(\chi_{2009}(503,\cdot)\) \(\chi_{2009}(545,\cdot)\) \(\chi_{2009}(552,\cdot)\) \(\chi_{2009}(559,\cdot)\) \(\chi_{2009}(580,\cdot)\) \(\chi_{2009}(608,\cdot)\) \(\chi_{2009}(622,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{280})$ |
Fixed field: | Number field defined by a degree 280 polynomial (not computed) |
Values on generators
\((493,785)\) → \((e\left(\frac{3}{14}\right),e\left(\frac{39}{40}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
\( \chi_{ 2009 }(622, a) \) | \(1\) | \(1\) | \(e\left(\frac{129}{140}\right)\) | \(e\left(\frac{47}{56}\right)\) | \(e\left(\frac{59}{70}\right)\) | \(e\left(\frac{93}{140}\right)\) | \(e\left(\frac{213}{280}\right)\) | \(e\left(\frac{107}{140}\right)\) | \(e\left(\frac{19}{28}\right)\) | \(e\left(\frac{41}{70}\right)\) | \(e\left(\frac{139}{280}\right)\) | \(e\left(\frac{191}{280}\right)\) |