Basic properties
| Modulus: | \(1075\) | |
| Conductor: | \(1075\) | 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 1075.bt
\(\chi_{1075}(19,\cdot)\) \(\chi_{1075}(29,\cdot)\) \(\chi_{1075}(34,\cdot)\) \(\chi_{1075}(69,\cdot)\) \(\chi_{1075}(89,\cdot)\) \(\chi_{1075}(104,\cdot)\) \(\chi_{1075}(114,\cdot)\) \(\chi_{1075}(119,\cdot)\) \(\chi_{1075}(134,\cdot)\) \(\chi_{1075}(159,\cdot)\) \(\chi_{1075}(184,\cdot)\) \(\chi_{1075}(234,\cdot)\) \(\chi_{1075}(244,\cdot)\) \(\chi_{1075}(284,\cdot)\) \(\chi_{1075}(304,\cdot)\) \(\chi_{1075}(319,\cdot)\) \(\chi_{1075}(329,\cdot)\) \(\chi_{1075}(334,\cdot)\) \(\chi_{1075}(364,\cdot)\) \(\chi_{1075}(459,\cdot)\) \(\chi_{1075}(464,\cdot)\) \(\chi_{1075}(519,\cdot)\) \(\chi_{1075}(534,\cdot)\) \(\chi_{1075}(544,\cdot)\) \(\chi_{1075}(564,\cdot)\) \(\chi_{1075}(579,\cdot)\) \(\chi_{1075}(589,\cdot)\) \(\chi_{1075}(614,\cdot)\) \(\chi_{1075}(664,\cdot)\) \(\chi_{1075}(679,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((302,476)\) → \((e\left(\frac{9}{10}\right),e\left(\frac{19}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 1075 }(19, a) \) | \(-1\) | \(1\) | \(e\left(\frac{4}{35}\right)\) | \(e\left(\frac{79}{105}\right)\) | \(e\left(\frac{8}{35}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{12}{35}\right)\) | \(e\left(\frac{53}{105}\right)\) | \(e\left(\frac{34}{35}\right)\) | \(e\left(\frac{103}{105}\right)\) | \(e\left(\frac{121}{210}\right)\) |