Basic properties
Modulus: | \(2009\) | |
Conductor: | \(2009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(420\) | 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.cj
\(\chi_{2009}(2,\cdot)\) \(\chi_{2009}(39,\cdot)\) \(\chi_{2009}(46,\cdot)\) \(\chi_{2009}(74,\cdot)\) \(\chi_{2009}(102,\cdot)\) \(\chi_{2009}(121,\cdot)\) \(\chi_{2009}(144,\cdot)\) \(\chi_{2009}(156,\cdot)\) \(\chi_{2009}(172,\cdot)\) \(\chi_{2009}(184,\cdot)\) \(\chi_{2009}(200,\cdot)\) \(\chi_{2009}(207,\cdot)\) \(\chi_{2009}(254,\cdot)\) \(\chi_{2009}(282,\cdot)\) \(\chi_{2009}(289,\cdot)\) \(\chi_{2009}(326,\cdot)\) \(\chi_{2009}(333,\cdot)\) \(\chi_{2009}(389,\cdot)\) \(\chi_{2009}(408,\cdot)\) \(\chi_{2009}(415,\cdot)\) \(\chi_{2009}(431,\cdot)\) \(\chi_{2009}(443,\cdot)\) \(\chi_{2009}(487,\cdot)\) \(\chi_{2009}(494,\cdot)\) \(\chi_{2009}(513,\cdot)\) \(\chi_{2009}(541,\cdot)\) \(\chi_{2009}(576,\cdot)\) \(\chi_{2009}(613,\cdot)\) \(\chi_{2009}(620,\cdot)\) \(\chi_{2009}(648,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{420})$ |
Fixed field: | Number field defined by a degree 420 polynomial (not computed) |
Values on generators
\((493,785)\) → \((e\left(\frac{2}{21}\right),e\left(\frac{11}{20}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
\( \chi_{ 2009 }(620, a) \) | \(1\) | \(1\) | \(e\left(\frac{163}{210}\right)\) | \(e\left(\frac{29}{84}\right)\) | \(e\left(\frac{58}{105}\right)\) | \(e\left(\frac{181}{210}\right)\) | \(e\left(\frac{17}{140}\right)\) | \(e\left(\frac{23}{70}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{67}{105}\right)\) | \(e\left(\frac{193}{420}\right)\) | \(e\left(\frac{377}{420}\right)\) |