Basic properties
| Modulus: | \(8043\) | |
| Conductor: | \(2681\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(382\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2681}(643,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8043.s
\(\chi_{8043}(34,\cdot)\) \(\chi_{8043}(55,\cdot)\) \(\chi_{8043}(76,\cdot)\) \(\chi_{8043}(139,\cdot)\) \(\chi_{8043}(202,\cdot)\) \(\chi_{8043}(223,\cdot)\) \(\chi_{8043}(265,\cdot)\) \(\chi_{8043}(286,\cdot)\) \(\chi_{8043}(370,\cdot)\) \(\chi_{8043}(391,\cdot)\) \(\chi_{8043}(412,\cdot)\) \(\chi_{8043}(433,\cdot)\) \(\chi_{8043}(454,\cdot)\) \(\chi_{8043}(475,\cdot)\) \(\chi_{8043}(496,\cdot)\) \(\chi_{8043}(517,\cdot)\) \(\chi_{8043}(643,\cdot)\) \(\chi_{8043}(706,\cdot)\) \(\chi_{8043}(727,\cdot)\) \(\chi_{8043}(769,\cdot)\) \(\chi_{8043}(790,\cdot)\) \(\chi_{8043}(853,\cdot)\) \(\chi_{8043}(874,\cdot)\) \(\chi_{8043}(895,\cdot)\) \(\chi_{8043}(916,\cdot)\) \(\chi_{8043}(937,\cdot)\) \(\chi_{8043}(958,\cdot)\) \(\chi_{8043}(979,\cdot)\) \(\chi_{8043}(1042,\cdot)\) \(\chi_{8043}(1105,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{191})$ |
| Fixed field: | Number field defined by a degree 382 polynomial (not computed) |
Values on generators
\((5363,2299,6133)\) → \((1,-1,e\left(\frac{62}{191}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 8043 }(643, a) \) | \(-1\) | \(1\) | \(e\left(\frac{95}{191}\right)\) | \(e\left(\frac{190}{191}\right)\) | \(e\left(\frac{315}{382}\right)\) | \(e\left(\frac{94}{191}\right)\) | \(e\left(\frac{123}{382}\right)\) | \(e\left(\frac{172}{191}\right)\) | \(e\left(\frac{165}{382}\right)\) | \(e\left(\frac{189}{191}\right)\) | \(e\left(\frac{53}{382}\right)\) | \(e\left(\frac{267}{382}\right)\) |