Basic properties
| Modulus: | \(8005\) | |
| Conductor: | \(8005\) | 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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8005.bv
\(\chi_{8005}(32,\cdot)\) \(\chi_{8005}(77,\cdot)\) \(\chi_{8005}(122,\cdot)\) \(\chi_{8005}(248,\cdot)\) \(\chi_{8005}(607,\cdot)\) \(\chi_{8005}(748,\cdot)\) \(\chi_{8005}(853,\cdot)\) \(\chi_{8005}(1353,\cdot)\) \(\chi_{8005}(1922,\cdot)\) \(\chi_{8005}(2598,\cdot)\) \(\chi_{8005}(2692,\cdot)\) \(\chi_{8005}(2703,\cdot)\) \(\chi_{8005}(2803,\cdot)\) \(\chi_{8005}(2888,\cdot)\) \(\chi_{8005}(2937,\cdot)\) \(\chi_{8005}(3467,\cdot)\) \(\chi_{8005}(3712,\cdot)\) \(\chi_{8005}(4482,\cdot)\) \(\chi_{8005}(4658,\cdot)\) \(\chi_{8005}(4753,\cdot)\) \(\chi_{8005}(4853,\cdot)\) \(\chi_{8005}(4948,\cdot)\) \(\chi_{8005}(5797,\cdot)\) \(\chi_{8005}(6282,\cdot)\) \(\chi_{8005}(6327,\cdot)\) \(\chi_{8005}(6372,\cdot)\) \(\chi_{8005}(6718,\cdot)\) \(\chi_{8005}(6803,\cdot)\) \(\chi_{8005}(6817,\cdot)\) \(\chi_{8005}(6903,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((1602,4806)\) → \((i,e\left(\frac{13}{80}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 8005 }(32, a) \) | \(-1\) | \(1\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{73}{80}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{49}{80}\right)\) | \(e\left(\frac{51}{80}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{69}{80}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{5}{16}\right)\) |