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.en
\(\chi_{8007}(38,\cdot)\) \(\chi_{8007}(191,\cdot)\) \(\chi_{8007}(242,\cdot)\) \(\chi_{8007}(701,\cdot)\) \(\chi_{8007}(761,\cdot)\) \(\chi_{8007}(803,\cdot)\) \(\chi_{8007}(854,\cdot)\) \(\chi_{8007}(1160,\cdot)\) \(\chi_{8007}(1271,\cdot)\) \(\chi_{8007}(1322,\cdot)\) \(\chi_{8007}(1475,\cdot)\) \(\chi_{8007}(1517,\cdot)\) \(\chi_{8007}(1721,\cdot)\) \(\chi_{8007}(2036,\cdot)\) \(\chi_{8007}(2138,\cdot)\) \(\chi_{8007}(2435,\cdot)\) \(\chi_{8007}(2486,\cdot)\) \(\chi_{8007}(2648,\cdot)\) \(\chi_{8007}(2690,\cdot)\) \(\chi_{8007}(2852,\cdot)\) \(\chi_{8007}(2903,\cdot)\) \(\chi_{8007}(3200,\cdot)\) \(\chi_{8007}(3302,\cdot)\) \(\chi_{8007}(3617,\cdot)\) \(\chi_{8007}(3821,\cdot)\) \(\chi_{8007}(3863,\cdot)\) \(\chi_{8007}(4016,\cdot)\) \(\chi_{8007}(4067,\cdot)\) \(\chi_{8007}(4178,\cdot)\) \(\chi_{8007}(4484,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((5339,1414,7855)\) → \((-1,-i,e\left(\frac{89}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 8007 }(2486, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{52}\right)\) | \(e\left(\frac{23}{26}\right)\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{3}{26}\right)\) | \(e\left(\frac{17}{52}\right)\) | \(e\left(\frac{41}{156}\right)\) | \(e\left(\frac{113}{156}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{29}{52}\right)\) | \(e\left(\frac{10}{13}\right)\) |