Basic properties
| Modulus: | \(8005\) | |
| Conductor: | \(8005\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(64\) | 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 8005.bo
\(\chi_{8005}(13,\cdot)\) \(\chi_{8005}(147,\cdot)\) \(\chi_{8005}(742,\cdot)\) \(\chi_{8005}(773,\cdot)\) \(\chi_{8005}(828,\cdot)\) \(\chi_{8005}(862,\cdot)\) \(\chi_{8005}(1077,\cdot)\) \(\chi_{8005}(1417,\cdot)\) \(\chi_{8005}(1588,\cdot)\) \(\chi_{8005}(1738,\cdot)\) \(\chi_{8005}(2197,\cdot)\) \(\chi_{8005}(2278,\cdot)\) \(\chi_{8005}(2358,\cdot)\) \(\chi_{8005}(2557,\cdot)\) \(\chi_{8005}(3027,\cdot)\) \(\chi_{8005}(3063,\cdot)\) \(\chi_{8005}(3377,\cdot)\) \(\chi_{8005}(3703,\cdot)\) \(\chi_{8005}(3847,\cdot)\) \(\chi_{8005}(4207,\cdot)\) \(\chi_{8005}(4283,\cdot)\) \(\chi_{8005}(4987,\cdot)\) \(\chi_{8005}(5323,\cdot)\) \(\chi_{8005}(5327,\cdot)\) \(\chi_{8005}(5542,\cdot)\) \(\chi_{8005}(5662,\cdot)\) \(\chi_{8005}(5903,\cdot)\) \(\chi_{8005}(6257,\cdot)\) \(\chi_{8005}(6543,\cdot)\) \(\chi_{8005}(7248,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{64})$ |
| Fixed field: | Number field defined by a degree 64 polynomial |
Values on generators
\((1602,4806)\) → \((-i,e\left(\frac{9}{64}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 8005 }(13, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{25}{64}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{29}{64}\right)\) | \(e\left(\frac{19}{64}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{25}{32}\right)\) | \(e\left(\frac{1}{64}\right)\) | \(e\left(\frac{33}{64}\right)\) | \(e\left(\frac{57}{64}\right)\) |