Basic properties
Modulus: | \(8993\) | |
Conductor: | \(8993\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(368\) | 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 8993.bd
\(\chi_{8993}(22,\cdot)\) \(\chi_{8993}(45,\cdot)\) \(\chi_{8993}(91,\cdot)\) \(\chi_{8993}(114,\cdot)\) \(\chi_{8993}(160,\cdot)\) \(\chi_{8993}(252,\cdot)\) \(\chi_{8993}(275,\cdot)\) \(\chi_{8993}(367,\cdot)\) \(\chi_{8993}(413,\cdot)\) \(\chi_{8993}(436,\cdot)\) \(\chi_{8993}(482,\cdot)\) \(\chi_{8993}(505,\cdot)\) \(\chi_{8993}(551,\cdot)\) \(\chi_{8993}(643,\cdot)\) \(\chi_{8993}(666,\cdot)\) \(\chi_{8993}(758,\cdot)\) \(\chi_{8993}(804,\cdot)\) \(\chi_{8993}(827,\cdot)\) \(\chi_{8993}(873,\cdot)\) \(\chi_{8993}(896,\cdot)\) \(\chi_{8993}(942,\cdot)\) \(\chi_{8993}(1034,\cdot)\) \(\chi_{8993}(1149,\cdot)\) \(\chi_{8993}(1195,\cdot)\) \(\chi_{8993}(1218,\cdot)\) \(\chi_{8993}(1264,\cdot)\) \(\chi_{8993}(1287,\cdot)\) \(\chi_{8993}(1333,\cdot)\) \(\chi_{8993}(1425,\cdot)\) \(\chi_{8993}(1448,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{368})$ |
Fixed field: | Number field defined by a degree 368 polynomial (not computed) |
Values on generators
\((530,7940)\) → \((e\left(\frac{5}{16}\right),e\left(\frac{13}{46}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 8993 }(22, a) \) | \(1\) | \(1\) | \(e\left(\frac{165}{184}\right)\) | \(e\left(\frac{307}{368}\right)\) | \(e\left(\frac{73}{92}\right)\) | \(e\left(\frac{311}{368}\right)\) | \(e\left(\frac{269}{368}\right)\) | \(e\left(\frac{329}{368}\right)\) | \(e\left(\frac{127}{184}\right)\) | \(e\left(\frac{123}{184}\right)\) | \(e\left(\frac{273}{368}\right)\) | \(e\left(\frac{29}{368}\right)\) |