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 \(\chi_{2365}(534,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4730.dh
\(\chi_{4730}(19,\cdot)\) \(\chi_{4730}(29,\cdot)\) \(\chi_{4730}(149,\cdot)\) \(\chi_{4730}(249,\cdot)\) \(\chi_{4730}(349,\cdot)\) \(\chi_{4730}(459,\cdot)\) \(\chi_{4730}(519,\cdot)\) \(\chi_{4730}(579,\cdot)\) \(\chi_{4730}(589,\cdot)\) \(\chi_{4730}(679,\cdot)\) \(\chi_{4730}(1009,\cdot)\) \(\chi_{4730}(1019,\cdot)\) \(\chi_{4730}(1179,\cdot)\) \(\chi_{4730}(1359,\cdot)\) \(\chi_{4730}(1449,\cdot)\) \(\chi_{4730}(1619,\cdot)\) \(\chi_{4730}(1689,\cdot)\) \(\chi_{4730}(1789,\cdot)\) \(\chi_{4730}(1839,\cdot)\) \(\chi_{4730}(2119,\cdot)\) \(\chi_{4730}(2169,\cdot)\) \(\chi_{4730}(2219,\cdot)\) \(\chi_{4730}(2239,\cdot)\) \(\chi_{4730}(2499,\cdot)\) \(\chi_{4730}(2549,\cdot)\) \(\chi_{4730}(2609,\cdot)\) \(\chi_{4730}(2669,\cdot)\) \(\chi_{4730}(2829,\cdot)\) \(\chi_{4730}(2899,\cdot)\) \(\chi_{4730}(3099,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((947,431,1981)\) → \((-1,e\left(\frac{9}{10}\right),e\left(\frac{29}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 4730 }(2899, a) \) | \(1\) | \(1\) | \(e\left(\frac{41}{105}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{82}{105}\right)\) | \(e\left(\frac{52}{105}\right)\) | \(e\left(\frac{88}{105}\right)\) | \(e\left(\frac{86}{105}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{23}{42}\right)\) | \(e\left(\frac{6}{35}\right)\) | \(e\left(\frac{64}{105}\right)\) |