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 \(\chi_{2669}(2046,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8007.fn
\(\chi_{8007}(61,\cdot)\) \(\chi_{8007}(88,\cdot)\) \(\chi_{8007}(91,\cdot)\) \(\chi_{8007}(97,\cdot)\) \(\chi_{8007}(133,\cdot)\) \(\chi_{8007}(139,\cdot)\) \(\chi_{8007}(142,\cdot)\) \(\chi_{8007}(181,\cdot)\) \(\chi_{8007}(241,\cdot)\) \(\chi_{8007}(418,\cdot)\) \(\chi_{8007}(607,\cdot)\) \(\chi_{8007}(622,\cdot)\) \(\chi_{8007}(634,\cdot)\) \(\chi_{8007}(643,\cdot)\) \(\chi_{8007}(652,\cdot)\) \(\chi_{8007}(694,\cdot)\) \(\chi_{8007}(700,\cdot)\) \(\chi_{8007}(751,\cdot)\) \(\chi_{8007}(811,\cdot)\) \(\chi_{8007}(823,\cdot)\) \(\chi_{8007}(838,\cdot)\) \(\chi_{8007}(847,\cdot)\) \(\chi_{8007}(862,\cdot)\) \(\chi_{8007}(904,\cdot)\) \(\chi_{8007}(976,\cdot)\) \(\chi_{8007}(997,\cdot)\) \(\chi_{8007}(1027,\cdot)\) \(\chi_{8007}(1195,\cdot)\) \(\chi_{8007}(1336,\cdot)\) \(\chi_{8007}(1387,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{624})$ |
| Fixed field: | Number field defined by a degree 624 polynomial (not computed) |
Values on generators
\((5339,1414,7855)\) → \((1,e\left(\frac{15}{16}\right),e\left(\frac{1}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 8007 }(7384, a) \) | \(1\) | \(1\) | \(e\left(\frac{3}{104}\right)\) | \(e\left(\frac{3}{52}\right)\) | \(e\left(\frac{433}{624}\right)\) | \(e\left(\frac{53}{208}\right)\) | \(e\left(\frac{9}{104}\right)\) | \(e\left(\frac{451}{624}\right)\) | \(e\left(\frac{463}{624}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{59}{208}\right)\) | \(e\left(\frac{3}{26}\right)\) |