Basic properties
| Modulus: | \(4730\) | |
| Conductor: | \(2365\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(210\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2365}(1389,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4730.dl
\(\chi_{4730}(9,\cdot)\) \(\chi_{4730}(169,\cdot)\) \(\chi_{4730}(229,\cdot)\) \(\chi_{4730}(289,\cdot)\) \(\chi_{4730}(339,\cdot)\) \(\chi_{4730}(599,\cdot)\) \(\chi_{4730}(619,\cdot)\) \(\chi_{4730}(669,\cdot)\) \(\chi_{4730}(719,\cdot)\) \(\chi_{4730}(999,\cdot)\) \(\chi_{4730}(1049,\cdot)\) \(\chi_{4730}(1149,\cdot)\) \(\chi_{4730}(1219,\cdot)\) \(\chi_{4730}(1389,\cdot)\) \(\chi_{4730}(1479,\cdot)\) \(\chi_{4730}(1659,\cdot)\) \(\chi_{4730}(1819,\cdot)\) \(\chi_{4730}(1829,\cdot)\) \(\chi_{4730}(2159,\cdot)\) \(\chi_{4730}(2249,\cdot)\) \(\chi_{4730}(2259,\cdot)\) \(\chi_{4730}(2319,\cdot)\) \(\chi_{4730}(2379,\cdot)\) \(\chi_{4730}(2489,\cdot)\) \(\chi_{4730}(2589,\cdot)\) \(\chi_{4730}(2689,\cdot)\) \(\chi_{4730}(2809,\cdot)\) \(\chi_{4730}(2819,\cdot)\) \(\chi_{4730}(2869,\cdot)\) \(\chi_{4730}(2919,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((947,431,1981)\) → \((-1,e\left(\frac{4}{5}\right),e\left(\frac{16}{21}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 4730 }(1389, a) \) | \(1\) | \(1\) | \(e\left(\frac{139}{210}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{34}{105}\right)\) | \(e\left(\frac{143}{210}\right)\) | \(e\left(\frac{137}{210}\right)\) | \(e\left(\frac{92}{105}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{69}{70}\right)\) | \(e\left(\frac{88}{105}\right)\) |