Basic properties
| Modulus: | \(8043\) | |
| Conductor: | \(2681\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1146\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2681}(340,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8043.bd
\(\chi_{8043}(37,\cdot)\) \(\chi_{8043}(79,\cdot)\) \(\chi_{8043}(88,\cdot)\) \(\chi_{8043}(109,\cdot)\) \(\chi_{8043}(151,\cdot)\) \(\chi_{8043}(163,\cdot)\) \(\chi_{8043}(214,\cdot)\) \(\chi_{8043}(247,\cdot)\) \(\chi_{8043}(310,\cdot)\) \(\chi_{8043}(319,\cdot)\) \(\chi_{8043}(340,\cdot)\) \(\chi_{8043}(352,\cdot)\) \(\chi_{8043}(394,\cdot)\) \(\chi_{8043}(403,\cdot)\) \(\chi_{8043}(424,\cdot)\) \(\chi_{8043}(436,\cdot)\) \(\chi_{8043}(457,\cdot)\) \(\chi_{8043}(466,\cdot)\) \(\chi_{8043}(478,\cdot)\) \(\chi_{8043}(487,\cdot)\) \(\chi_{8043}(508,\cdot)\) \(\chi_{8043}(541,\cdot)\) \(\chi_{8043}(550,\cdot)\) \(\chi_{8043}(562,\cdot)\) \(\chi_{8043}(571,\cdot)\) \(\chi_{8043}(592,\cdot)\) \(\chi_{8043}(604,\cdot)\) \(\chi_{8043}(613,\cdot)\) \(\chi_{8043}(697,\cdot)\) \(\chi_{8043}(709,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{573})$ |
| Fixed field: | Number field defined by a degree 1146 polynomial (not computed) |
Values on generators
\((5363,2299,6133)\) → \((1,e\left(\frac{2}{3}\right),e\left(\frac{43}{382}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 8043 }(340, a) \) | \(-1\) | \(1\) | \(e\left(\frac{239}{573}\right)\) | \(e\left(\frac{478}{573}\right)\) | \(e\left(\frac{511}{1146}\right)\) | \(e\left(\frac{48}{191}\right)\) | \(e\left(\frac{989}{1146}\right)\) | \(e\left(\frac{401}{1146}\right)\) | \(e\left(\frac{259}{382}\right)\) | \(e\left(\frac{383}{573}\right)\) | \(e\left(\frac{130}{573}\right)\) | \(e\left(\frac{554}{573}\right)\) |