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 \(\chi_{539}(51,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1078.bd
\(\chi_{1078}(39,\cdot)\) \(\chi_{1078}(51,\cdot)\) \(\chi_{1078}(95,\cdot)\) \(\chi_{1078}(107,\cdot)\) \(\chi_{1078}(123,\cdot)\) \(\chi_{1078}(149,\cdot)\) \(\chi_{1078}(151,\cdot)\) \(\chi_{1078}(193,\cdot)\) \(\chi_{1078}(205,\cdot)\) \(\chi_{1078}(233,\cdot)\) \(\chi_{1078}(249,\cdot)\) \(\chi_{1078}(261,\cdot)\) \(\chi_{1078}(277,\cdot)\) \(\chi_{1078}(303,\cdot)\) \(\chi_{1078}(305,\cdot)\) \(\chi_{1078}(347,\cdot)\) \(\chi_{1078}(359,\cdot)\) \(\chi_{1078}(387,\cdot)\) \(\chi_{1078}(403,\cdot)\) \(\chi_{1078}(415,\cdot)\) \(\chi_{1078}(431,\cdot)\) \(\chi_{1078}(457,\cdot)\) \(\chi_{1078}(501,\cdot)\) \(\chi_{1078}(513,\cdot)\) \(\chi_{1078}(541,\cdot)\) \(\chi_{1078}(585,\cdot)\) \(\chi_{1078}(611,\cdot)\) \(\chi_{1078}(613,\cdot)\) \(\chi_{1078}(695,\cdot)\) \(\chi_{1078}(711,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((199,981)\) → \((e\left(\frac{13}{21}\right),e\left(\frac{7}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 1078 }(51, a) \) | \(-1\) | \(1\) | \(e\left(\frac{23}{105}\right)\) | \(e\left(\frac{79}{105}\right)\) | \(e\left(\frac{46}{105}\right)\) | \(e\left(\frac{9}{70}\right)\) | \(e\left(\frac{34}{35}\right)\) | \(e\left(\frac{163}{210}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{53}{105}\right)\) | \(e\left(\frac{23}{35}\right)\) |