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.el
\(\chi_{8007}(152,\cdot)\) \(\chi_{8007}(254,\cdot)\) \(\chi_{8007}(509,\cdot)\) \(\chi_{8007}(662,\cdot)\) \(\chi_{8007}(713,\cdot)\) \(\chi_{8007}(764,\cdot)\) \(\chi_{8007}(968,\cdot)\) \(\chi_{8007}(1019,\cdot)\) \(\chi_{8007}(1172,\cdot)\) \(\chi_{8007}(1274,\cdot)\) \(\chi_{8007}(1325,\cdot)\) \(\chi_{8007}(1631,\cdot)\) \(\chi_{8007}(1733,\cdot)\) \(\chi_{8007}(1937,\cdot)\) \(\chi_{8007}(1988,\cdot)\) \(\chi_{8007}(2192,\cdot)\) \(\chi_{8007}(2294,\cdot)\) \(\chi_{8007}(2600,\cdot)\) \(\chi_{8007}(2651,\cdot)\) \(\chi_{8007}(2753,\cdot)\) \(\chi_{8007}(2906,\cdot)\) \(\chi_{8007}(2957,\cdot)\) \(\chi_{8007}(3161,\cdot)\) \(\chi_{8007}(3212,\cdot)\) \(\chi_{8007}(3263,\cdot)\) \(\chi_{8007}(3416,\cdot)\) \(\chi_{8007}(3671,\cdot)\) \(\chi_{8007}(3773,\cdot)\) \(\chi_{8007}(4334,\cdot)\) \(\chi_{8007}(4487,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((5339,1414,7855)\) → \((-1,-1,e\left(\frac{79}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 8007 }(152, a) \) | \(1\) | \(1\) | \(e\left(\frac{47}{52}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{79}{156}\right)\) | \(e\left(\frac{49}{52}\right)\) | \(e\left(\frac{37}{52}\right)\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{8}{13}\right)\) |