Basic properties
| Modulus: | \(8007\) | |
| Conductor: | \(2669\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(624\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2669}(10,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8007.fl
\(\chi_{8007}(10,\cdot)\) \(\chi_{8007}(31,\cdot)\) \(\chi_{8007}(148,\cdot)\) \(\chi_{8007}(160,\cdot)\) \(\chi_{8007}(190,\cdot)\) \(\chi_{8007}(193,\cdot)\) \(\chi_{8007}(199,\cdot)\) \(\chi_{8007}(214,\cdot)\) \(\chi_{8007}(262,\cdot)\) \(\chi_{8007}(277,\cdot)\) \(\chi_{8007}(295,\cdot)\) \(\chi_{8007}(436,\cdot)\) \(\chi_{8007}(454,\cdot)\) \(\chi_{8007}(481,\cdot)\) \(\chi_{8007}(496,\cdot)\) \(\chi_{8007}(547,\cdot)\) \(\chi_{8007}(598,\cdot)\) \(\chi_{8007}(619,\cdot)\) \(\chi_{8007}(670,\cdot)\) \(\chi_{8007}(685,\cdot)\) \(\chi_{8007}(745,\cdot)\) \(\chi_{8007}(853,\cdot)\) \(\chi_{8007}(895,\cdot)\) \(\chi_{8007}(907,\cdot)\) \(\chi_{8007}(925,\cdot)\) \(\chi_{8007}(1102,\cdot)\) \(\chi_{8007}(1132,\cdot)\) \(\chi_{8007}(1150,\cdot)\) \(\chi_{8007}(1204,\cdot)\) \(\chi_{8007}(1219,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{624})$ |
| Fixed field: | Number field defined by a degree 624 polynomial (not computed) |
Values on generators
\((5339,1414,7855)\) → \((1,e\left(\frac{3}{16}\right),e\left(\frac{71}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 8007 }(10, a) \) | \(-1\) | \(1\) | \(e\left(\frac{101}{104}\right)\) | \(e\left(\frac{49}{52}\right)\) | \(e\left(\frac{529}{624}\right)\) | \(e\left(\frac{181}{208}\right)\) | \(e\left(\frac{95}{104}\right)\) | \(e\left(\frac{511}{624}\right)\) | \(e\left(\frac{499}{624}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{175}{208}\right)\) | \(e\left(\frac{23}{26}\right)\) |