Basic properties
| Modulus: | \(8007\) | |
| Conductor: | \(2669\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(208\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2669}(7,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8007.et
\(\chi_{8007}(7,\cdot)\) \(\chi_{8007}(79,\cdot)\) \(\chi_{8007}(112,\cdot)\) \(\chi_{8007}(211,\cdot)\) \(\chi_{8007}(235,\cdot)\) \(\chi_{8007}(343,\cdot)\) \(\chi_{8007}(469,\cdot)\) \(\chi_{8007}(550,\cdot)\) \(\chi_{8007}(787,\cdot)\) \(\chi_{8007}(793,\cdot)\) \(\chi_{8007}(1144,\cdot)\) \(\chi_{8007}(1264,\cdot)\) \(\chi_{8007}(1297,\cdot)\) \(\chi_{8007}(1348,\cdot)\) \(\chi_{8007}(1354,\cdot)\) \(\chi_{8007}(1384,\cdot)\) \(\chi_{8007}(1516,\cdot)\) \(\chi_{8007}(1720,\cdot)\) \(\chi_{8007}(1729,\cdot)\) \(\chi_{8007}(1756,\cdot)\) \(\chi_{8007}(1792,\cdot)\) \(\chi_{8007}(1825,\cdot)\) \(\chi_{8007}(1843,\cdot)\) \(\chi_{8007}(1996,\cdot)\) \(\chi_{8007}(2086,\cdot)\) \(\chi_{8007}(2221,\cdot)\) \(\chi_{8007}(2230,\cdot)\) \(\chi_{8007}(2239,\cdot)\) \(\chi_{8007}(2290,\cdot)\) \(\chi_{8007}(2323,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{208})$ |
| Fixed field: | Number field defined by a degree 208 polynomial (not computed) |
Values on generators
\((5339,1414,7855)\) → \((1,e\left(\frac{11}{16}\right),e\left(\frac{49}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 8007 }(7, a) \) | \(1\) | \(1\) | \(e\left(\frac{51}{104}\right)\) | \(e\left(\frac{51}{52}\right)\) | \(e\left(\frac{79}{208}\right)\) | \(e\left(\frac{17}{208}\right)\) | \(e\left(\frac{49}{104}\right)\) | \(e\left(\frac{181}{208}\right)\) | \(e\left(\frac{41}{208}\right)\) | \(i\) | \(e\left(\frac{119}{208}\right)\) | \(e\left(\frac{25}{26}\right)\) |