Basic properties
| Modulus: | \(1519\) | |
| Conductor: | \(1519\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(210\) | 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 1519.cw
\(\chi_{1519}(11,\cdot)\) \(\chi_{1519}(53,\cdot)\) \(\chi_{1519}(65,\cdot)\) \(\chi_{1519}(86,\cdot)\) \(\chi_{1519}(137,\cdot)\) \(\chi_{1519}(198,\cdot)\) \(\chi_{1519}(207,\cdot)\) \(\chi_{1519}(228,\cdot)\) \(\chi_{1519}(270,\cdot)\) \(\chi_{1519}(282,\cdot)\) \(\chi_{1519}(296,\cdot)\) \(\chi_{1519}(303,\cdot)\) \(\chi_{1519}(354,\cdot)\) \(\chi_{1519}(415,\cdot)\) \(\chi_{1519}(424,\cdot)\) \(\chi_{1519}(445,\cdot)\) \(\chi_{1519}(487,\cdot)\) \(\chi_{1519}(499,\cdot)\) \(\chi_{1519}(513,\cdot)\) \(\chi_{1519}(571,\cdot)\) \(\chi_{1519}(632,\cdot)\) \(\chi_{1519}(641,\cdot)\) \(\chi_{1519}(662,\cdot)\) \(\chi_{1519}(730,\cdot)\) \(\chi_{1519}(737,\cdot)\) \(\chi_{1519}(788,\cdot)\) \(\chi_{1519}(849,\cdot)\) \(\chi_{1519}(858,\cdot)\) \(\chi_{1519}(879,\cdot)\) \(\chi_{1519}(921,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((1179,344)\) → \((e\left(\frac{1}{21}\right),e\left(\frac{1}{30}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 1519 }(499, a) \) | \(-1\) | \(1\) | \(e\left(\frac{4}{105}\right)\) | \(e\left(\frac{17}{210}\right)\) | \(e\left(\frac{8}{105}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{4}{35}\right)\) | \(e\left(\frac{17}{105}\right)\) | \(e\left(\frac{3}{35}\right)\) | \(e\left(\frac{47}{70}\right)\) | \(e\left(\frac{11}{70}\right)\) |