Basic properties
| Modulus: | \(8007\) | |
| Conductor: | \(8007\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | 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 8007.eg
\(\chi_{8007}(200,\cdot)\) \(\chi_{8007}(251,\cdot)\) \(\chi_{8007}(293,\cdot)\) \(\chi_{8007}(497,\cdot)\) \(\chi_{8007}(548,\cdot)\) \(\chi_{8007}(608,\cdot)\) \(\chi_{8007}(1016,\cdot)\) \(\chi_{8007}(1169,\cdot)\) \(\chi_{8007}(1262,\cdot)\) \(\chi_{8007}(1466,\cdot)\) \(\chi_{8007}(1823,\cdot)\) \(\chi_{8007}(2129,\cdot)\) \(\chi_{8007}(2180,\cdot)\) \(\chi_{8007}(2282,\cdot)\) \(\chi_{8007}(2393,\cdot)\) \(\chi_{8007}(2546,\cdot)\) \(\chi_{8007}(2597,\cdot)\) \(\chi_{8007}(2741,\cdot)\) \(\chi_{8007}(2792,\cdot)\) \(\chi_{8007}(2945,\cdot)\) \(\chi_{8007}(3056,\cdot)\) \(\chi_{8007}(3158,\cdot)\) \(\chi_{8007}(3209,\cdot)\) \(\chi_{8007}(3515,\cdot)\) \(\chi_{8007}(3872,\cdot)\) \(\chi_{8007}(4076,\cdot)\) \(\chi_{8007}(4169,\cdot)\) \(\chi_{8007}(4322,\cdot)\) \(\chi_{8007}(4730,\cdot)\) \(\chi_{8007}(4790,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((5339,1414,7855)\) → \((-1,i,e\left(\frac{113}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 8007 }(200, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{52}\right)\) | \(e\left(\frac{7}{26}\right)\) | \(e\left(\frac{37}{78}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{21}{52}\right)\) | \(e\left(\frac{95}{156}\right)\) | \(e\left(\frac{83}{156}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{19}{52}\right)\) | \(e\left(\frac{7}{13}\right)\) |