Basic properties
| Modulus: | \(8023\) | |
| Conductor: | \(8023\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(80\) | 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 8023.ek
\(\chi_{8023}(492,\cdot)\) \(\chi_{8023}(756,\cdot)\) \(\chi_{8023}(869,\cdot)\) \(\chi_{8023}(969,\cdot)\) \(\chi_{8023}(1082,\cdot)\) \(\chi_{8023}(1434,\cdot)\) \(\chi_{8023}(1647,\cdot)\) \(\chi_{8023}(1963,\cdot)\) \(\chi_{8023}(2076,\cdot)\) \(\chi_{8023}(2105,\cdot)\) \(\chi_{8023}(2218,\cdot)\) \(\chi_{8023}(2338,\cdot)\) \(\chi_{8023}(2551,\cdot)\) \(\chi_{8023}(2641,\cdot)\) \(\chi_{8023}(2783,\cdot)\) \(\chi_{8023}(3099,\cdot)\) \(\chi_{8023}(3212,\cdot)\) \(\chi_{8023}(3312,\cdot)\) \(\chi_{8023}(3425,\cdot)\) \(\chi_{8023}(3545,\cdot)\) \(\chi_{8023}(3687,\cdot)\) \(\chi_{8023}(3777,\cdot)\) \(\chi_{8023}(3990,\cdot)\) \(\chi_{8023}(4681,\cdot)\) \(\chi_{8023}(4894,\cdot)\) \(\chi_{8023}(5158,\cdot)\) \(\chi_{8023}(5271,\cdot)\) \(\chi_{8023}(5836,\cdot)\) \(\chi_{8023}(6740,\cdot)\) \(\chi_{8023}(6933,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((6894,3054)\) → \((e\left(\frac{9}{10}\right),e\left(\frac{1}{16}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 8023 }(492, a) \) | \(1\) | \(1\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{37}{80}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{31}{80}\right)\) | \(e\left(\frac{49}{80}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{43}{80}\right)\) | \(e\left(\frac{21}{40}\right)\) |