Basic properties
| Modulus: | \(8007\) | |
| Conductor: | \(8007\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(624\) | 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.fh
\(\chi_{8007}(11,\cdot)\) \(\chi_{8007}(71,\cdot)\) \(\chi_{8007}(113,\cdot)\) \(\chi_{8007}(176,\cdot)\) \(\chi_{8007}(194,\cdot)\) \(\chi_{8007}(197,\cdot)\) \(\chi_{8007}(209,\cdot)\) \(\chi_{8007}(266,\cdot)\) \(\chi_{8007}(278,\cdot)\) \(\chi_{8007}(311,\cdot)\) \(\chi_{8007}(482,\cdot)\) \(\chi_{8007}(488,\cdot)\) \(\chi_{8007}(584,\cdot)\) \(\chi_{8007}(668,\cdot)\) \(\chi_{8007}(728,\cdot)\) \(\chi_{8007}(734,\cdot)\) \(\chi_{8007}(737,\cdot)\) \(\chi_{8007}(743,\cdot)\) \(\chi_{8007}(794,\cdot)\) \(\chi_{8007}(911,\cdot)\) \(\chi_{8007}(932,\cdot)\) \(\chi_{8007}(959,\cdot)\) \(\chi_{8007}(989,\cdot)\) \(\chi_{8007}(1013,\cdot)\) \(\chi_{8007}(1031,\cdot)\) \(\chi_{8007}(1136,\cdot)\) \(\chi_{8007}(1151,\cdot)\) \(\chi_{8007}(1214,\cdot)\) \(\chi_{8007}(1253,\cdot)\) \(\chi_{8007}(1265,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{624})$ |
| Fixed field: | Number field defined by a degree 624 polynomial (not computed) |
Values on generators
\((5339,1414,7855)\) → \((-1,e\left(\frac{7}{16}\right),e\left(\frac{7}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 8007 }(11, a) \) | \(1\) | \(1\) | \(e\left(\frac{97}{104}\right)\) | \(e\left(\frac{45}{52}\right)\) | \(e\left(\frac{541}{624}\right)\) | \(e\left(\frac{41}{208}\right)\) | \(e\left(\frac{83}{104}\right)\) | \(e\left(\frac{499}{624}\right)\) | \(e\left(\frac{367}{624}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{27}{208}\right)\) | \(e\left(\frac{19}{26}\right)\) |