Basic properties
| Modulus: | \(8788\) | |
| Conductor: | \(2197\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(507\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2197}(29,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8788.bc
\(\chi_{8788}(9,\cdot)\) \(\chi_{8788}(29,\cdot)\) \(\chi_{8788}(61,\cdot)\) \(\chi_{8788}(81,\cdot)\) \(\chi_{8788}(113,\cdot)\) \(\chi_{8788}(133,\cdot)\) \(\chi_{8788}(165,\cdot)\) \(\chi_{8788}(185,\cdot)\) \(\chi_{8788}(217,\cdot)\) \(\chi_{8788}(237,\cdot)\) \(\chi_{8788}(269,\cdot)\) \(\chi_{8788}(289,\cdot)\) \(\chi_{8788}(321,\cdot)\) \(\chi_{8788}(341,\cdot)\) \(\chi_{8788}(373,\cdot)\) \(\chi_{8788}(393,\cdot)\) \(\chi_{8788}(425,\cdot)\) \(\chi_{8788}(445,\cdot)\) \(\chi_{8788}(477,\cdot)\) \(\chi_{8788}(497,\cdot)\) \(\chi_{8788}(549,\cdot)\) \(\chi_{8788}(581,\cdot)\) \(\chi_{8788}(601,\cdot)\) \(\chi_{8788}(633,\cdot)\) \(\chi_{8788}(685,\cdot)\) \(\chi_{8788}(705,\cdot)\) \(\chi_{8788}(737,\cdot)\) \(\chi_{8788}(757,\cdot)\) \(\chi_{8788}(789,\cdot)\) \(\chi_{8788}(809,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{507})$ |
| Fixed field: | Number field defined by a degree 507 polynomial (not computed) |
Values on generators
\((4395,6593)\) → \((1,e\left(\frac{478}{507}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 8788 }(29, a) \) | \(1\) | \(1\) | \(e\left(\frac{421}{507}\right)\) | \(e\left(\frac{147}{169}\right)\) | \(e\left(\frac{329}{507}\right)\) | \(e\left(\frac{335}{507}\right)\) | \(e\left(\frac{133}{507}\right)\) | \(e\left(\frac{355}{507}\right)\) | \(e\left(\frac{446}{507}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{81}{169}\right)\) | \(e\left(\frac{28}{39}\right)\) |