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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1075.bs
\(\chi_{1075}(9,\cdot)\) \(\chi_{1075}(14,\cdot)\) \(\chi_{1075}(109,\cdot)\) \(\chi_{1075}(139,\cdot)\) \(\chi_{1075}(144,\cdot)\) \(\chi_{1075}(154,\cdot)\) \(\chi_{1075}(169,\cdot)\) \(\chi_{1075}(189,\cdot)\) \(\chi_{1075}(229,\cdot)\) \(\chi_{1075}(239,\cdot)\) \(\chi_{1075}(289,\cdot)\) \(\chi_{1075}(314,\cdot)\) \(\chi_{1075}(339,\cdot)\) \(\chi_{1075}(354,\cdot)\) \(\chi_{1075}(359,\cdot)\) \(\chi_{1075}(369,\cdot)\) \(\chi_{1075}(384,\cdot)\) \(\chi_{1075}(404,\cdot)\) \(\chi_{1075}(439,\cdot)\) \(\chi_{1075}(444,\cdot)\) \(\chi_{1075}(454,\cdot)\) \(\chi_{1075}(504,\cdot)\) \(\chi_{1075}(529,\cdot)\) \(\chi_{1075}(539,\cdot)\) \(\chi_{1075}(554,\cdot)\) \(\chi_{1075}(569,\cdot)\) \(\chi_{1075}(584,\cdot)\) \(\chi_{1075}(619,\cdot)\) \(\chi_{1075}(654,\cdot)\) \(\chi_{1075}(659,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((302,476)\) → \((e\left(\frac{7}{10}\right),e\left(\frac{1}{21}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 1075 }(9, a) \) | \(1\) | \(1\) | \(e\left(\frac{69}{70}\right)\) | \(e\left(\frac{199}{210}\right)\) | \(e\left(\frac{34}{35}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{67}{70}\right)\) | \(e\left(\frac{94}{105}\right)\) | \(e\left(\frac{22}{35}\right)\) | \(e\left(\frac{193}{210}\right)\) | \(e\left(\frac{173}{210}\right)\) |