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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2009.ci
\(\chi_{2009}(5,\cdot)\) \(\chi_{2009}(33,\cdot)\) \(\chi_{2009}(61,\cdot)\) \(\chi_{2009}(87,\cdot)\) \(\chi_{2009}(103,\cdot)\) \(\chi_{2009}(115,\cdot)\) \(\chi_{2009}(131,\cdot)\) \(\chi_{2009}(143,\cdot)\) \(\chi_{2009}(159,\cdot)\) \(\chi_{2009}(185,\cdot)\) \(\chi_{2009}(213,\cdot)\) \(\chi_{2009}(241,\cdot)\) \(\chi_{2009}(248,\cdot)\) \(\chi_{2009}(285,\cdot)\) \(\chi_{2009}(292,\cdot)\) \(\chi_{2009}(320,\cdot)\) \(\chi_{2009}(348,\cdot)\) \(\chi_{2009}(367,\cdot)\) \(\chi_{2009}(390,\cdot)\) \(\chi_{2009}(402,\cdot)\) \(\chi_{2009}(418,\cdot)\) \(\chi_{2009}(430,\cdot)\) \(\chi_{2009}(446,\cdot)\) \(\chi_{2009}(453,\cdot)\) \(\chi_{2009}(500,\cdot)\) \(\chi_{2009}(528,\cdot)\) \(\chi_{2009}(535,\cdot)\) \(\chi_{2009}(572,\cdot)\) \(\chi_{2009}(579,\cdot)\) \(\chi_{2009}(635,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{420})$ |
| Fixed field: | Number field defined by a degree 420 polynomial (not computed) |
Values on generators
\((493,785)\) → \((e\left(\frac{29}{42}\right),e\left(\frac{11}{20}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 2009 }(5, a) \) | \(-1\) | \(1\) | \(e\left(\frac{53}{210}\right)\) | \(e\left(\frac{79}{84}\right)\) | \(e\left(\frac{53}{105}\right)\) | \(e\left(\frac{13}{105}\right)\) | \(e\left(\frac{27}{140}\right)\) | \(e\left(\frac{53}{70}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{79}{210}\right)\) | \(e\left(\frac{113}{420}\right)\) | \(e\left(\frac{187}{420}\right)\) |