Basic properties
| Modulus: | \(8788\) | |
| Conductor: | \(8788\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(338\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8788.z
\(\chi_{8788}(51,\cdot)\) \(\chi_{8788}(103,\cdot)\) \(\chi_{8788}(155,\cdot)\) \(\chi_{8788}(207,\cdot)\) \(\chi_{8788}(259,\cdot)\) \(\chi_{8788}(311,\cdot)\) \(\chi_{8788}(363,\cdot)\) \(\chi_{8788}(415,\cdot)\) \(\chi_{8788}(467,\cdot)\) \(\chi_{8788}(519,\cdot)\) \(\chi_{8788}(571,\cdot)\) \(\chi_{8788}(623,\cdot)\) \(\chi_{8788}(727,\cdot)\) \(\chi_{8788}(779,\cdot)\) \(\chi_{8788}(831,\cdot)\) \(\chi_{8788}(883,\cdot)\) \(\chi_{8788}(935,\cdot)\) \(\chi_{8788}(987,\cdot)\) \(\chi_{8788}(1039,\cdot)\) \(\chi_{8788}(1091,\cdot)\) \(\chi_{8788}(1143,\cdot)\) \(\chi_{8788}(1195,\cdot)\) \(\chi_{8788}(1247,\cdot)\) \(\chi_{8788}(1299,\cdot)\) \(\chi_{8788}(1403,\cdot)\) \(\chi_{8788}(1455,\cdot)\) \(\chi_{8788}(1507,\cdot)\) \(\chi_{8788}(1559,\cdot)\) \(\chi_{8788}(1611,\cdot)\) \(\chi_{8788}(1663,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{169})$ |
| Fixed field: | Number field defined by a degree 338 polynomial (not computed) |
Values on generators
\((4395,6593)\) → \((-1,e\left(\frac{293}{338}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 8788 }(623, a) \) | \(-1\) | \(1\) | \(e\left(\frac{257}{338}\right)\) | \(e\left(\frac{323}{338}\right)\) | \(e\left(\frac{95}{169}\right)\) | \(e\left(\frac{88}{169}\right)\) | \(e\left(\frac{42}{169}\right)\) | \(e\left(\frac{121}{169}\right)\) | \(e\left(\frac{43}{169}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{109}{338}\right)\) | \(e\left(\frac{17}{26}\right)\) |