Basic properties
| Modulus: | \(29645\) | |
| Conductor: | \(29645\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(924\) | 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 29645.gq
\(\chi_{29645}(32,\cdot)\) \(\chi_{29645}(142,\cdot)\) \(\chi_{29645}(417,\cdot)\) \(\chi_{29645}(527,\cdot)\) \(\chi_{29645}(648,\cdot)\) \(\chi_{29645}(758,\cdot)\) \(\chi_{29645}(1033,\cdot)\) \(\chi_{29645}(1143,\cdot)\) \(\chi_{29645}(1187,\cdot)\) \(\chi_{29645}(1297,\cdot)\) \(\chi_{29645}(1418,\cdot)\) \(\chi_{29645}(1528,\cdot)\) \(\chi_{29645}(1682,\cdot)\) \(\chi_{29645}(1803,\cdot)\) \(\chi_{29645}(1913,\cdot)\) \(\chi_{29645}(1957,\cdot)\) \(\chi_{29645}(2067,\cdot)\) \(\chi_{29645}(2188,\cdot)\) \(\chi_{29645}(2342,\cdot)\) \(\chi_{29645}(2452,\cdot)\) \(\chi_{29645}(2573,\cdot)\) \(\chi_{29645}(2683,\cdot)\) \(\chi_{29645}(2727,\cdot)\) \(\chi_{29645}(2837,\cdot)\) \(\chi_{29645}(3112,\cdot)\) \(\chi_{29645}(3222,\cdot)\) \(\chi_{29645}(3343,\cdot)\) \(\chi_{29645}(3453,\cdot)\) \(\chi_{29645}(3728,\cdot)\) \(\chi_{29645}(3838,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{924})$ |
| Fixed field: | Number field defined by a degree 924 polynomial (not computed) |
Values on generators
\((23717,1816,19846)\) → \((i,e\left(\frac{2}{21}\right),e\left(\frac{1}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(12\) | \(13\) | \(16\) | \(17\) |
| \( \chi_{ 29645 }(32, a) \) | \(1\) | \(1\) | \(e\left(\frac{713}{924}\right)\) | \(e\left(\frac{71}{84}\right)\) | \(e\left(\frac{251}{462}\right)\) | \(e\left(\frac{95}{154}\right)\) | \(e\left(\frac{97}{308}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{359}{924}\right)\) | \(e\left(\frac{149}{308}\right)\) | \(e\left(\frac{20}{231}\right)\) | \(e\left(\frac{793}{924}\right)\) |