Basic properties
| Modulus: | \(1078\) | |
| Conductor: | \(539\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(210\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{539}(47,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1078.be
\(\chi_{1078}(3,\cdot)\) \(\chi_{1078}(5,\cdot)\) \(\chi_{1078}(47,\cdot)\) \(\chi_{1078}(59,\cdot)\) \(\chi_{1078}(75,\cdot)\) \(\chi_{1078}(103,\cdot)\) \(\chi_{1078}(115,\cdot)\) \(\chi_{1078}(157,\cdot)\) \(\chi_{1078}(159,\cdot)\) \(\chi_{1078}(185,\cdot)\) \(\chi_{1078}(201,\cdot)\) \(\chi_{1078}(213,\cdot)\) \(\chi_{1078}(229,\cdot)\) \(\chi_{1078}(257,\cdot)\) \(\chi_{1078}(269,\cdot)\) \(\chi_{1078}(311,\cdot)\) \(\chi_{1078}(339,\cdot)\) \(\chi_{1078}(355,\cdot)\) \(\chi_{1078}(367,\cdot)\) \(\chi_{1078}(383,\cdot)\) \(\chi_{1078}(465,\cdot)\) \(\chi_{1078}(467,\cdot)\) \(\chi_{1078}(493,\cdot)\) \(\chi_{1078}(537,\cdot)\) \(\chi_{1078}(565,\cdot)\) \(\chi_{1078}(577,\cdot)\) \(\chi_{1078}(621,\cdot)\) \(\chi_{1078}(647,\cdot)\) \(\chi_{1078}(663,\cdot)\) \(\chi_{1078}(675,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((199,981)\) → \((e\left(\frac{5}{42}\right),e\left(\frac{4}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 1078 }(47, a) \) | \(-1\) | \(1\) | \(e\left(\frac{109}{210}\right)\) | \(e\left(\frac{137}{210}\right)\) | \(e\left(\frac{4}{105}\right)\) | \(e\left(\frac{51}{70}\right)\) | \(e\left(\frac{6}{35}\right)\) | \(e\left(\frac{37}{210}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{32}{105}\right)\) | \(e\left(\frac{39}{70}\right)\) |