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 \(\chi_{2669}(691,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8007.fk
\(\chi_{8007}(73,\cdot)\) \(\chi_{8007}(163,\cdot)\) \(\chi_{8007}(175,\cdot)\) \(\chi_{8007}(226,\cdot)\) \(\chi_{8007}(244,\cdot)\) \(\chi_{8007}(334,\cdot)\) \(\chi_{8007}(352,\cdot)\) \(\chi_{8007}(367,\cdot)\) \(\chi_{8007}(388,\cdot)\) \(\chi_{8007}(394,\cdot)\) \(\chi_{8007}(397,\cdot)\) \(\chi_{8007}(445,\cdot)\) \(\chi_{8007}(466,\cdot)\) \(\chi_{8007}(505,\cdot)\) \(\chi_{8007}(532,\cdot)\) \(\chi_{8007}(541,\cdot)\) \(\chi_{8007}(556,\cdot)\) \(\chi_{8007}(568,\cdot)\) \(\chi_{8007}(649,\cdot)\) \(\chi_{8007}(691,\cdot)\) \(\chi_{8007}(724,\cdot)\) \(\chi_{8007}(742,\cdot)\) \(\chi_{8007}(805,\cdot)\) \(\chi_{8007}(889,\cdot)\) \(\chi_{8007}(1015,\cdot)\) \(\chi_{8007}(1030,\cdot)\) \(\chi_{8007}(1078,\cdot)\) \(\chi_{8007}(1081,\cdot)\) \(\chi_{8007}(1093,\cdot)\) \(\chi_{8007}(1117,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{624})$ |
| Fixed field: | Number field defined by a degree 624 polynomial (not computed) |
Values on generators
\((5339,1414,7855)\) → \((1,e\left(\frac{7}{16}\right),e\left(\frac{155}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 8007 }(691, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{104}\right)\) | \(e\left(\frac{23}{52}\right)\) | \(e\left(\frac{113}{624}\right)\) | \(e\left(\frac{181}{208}\right)\) | \(e\left(\frac{69}{104}\right)\) | \(e\left(\frac{251}{624}\right)\) | \(e\left(\frac{551}{624}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{19}{208}\right)\) | \(e\left(\frac{23}{26}\right)\) |