Basic properties
| Modulus: | \(8003\) | |
| Conductor: | \(8003\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(650\) | 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 8003.ci
\(\chi_{8003}(9,\cdot)\) \(\chi_{8003}(29,\cdot)\) \(\chi_{8003}(78,\cdot)\) \(\chi_{8003}(91,\cdot)\) \(\chi_{8003}(110,\cdot)\) \(\chi_{8003}(123,\cdot)\) \(\chi_{8003}(219,\cdot)\) \(\chi_{8003}(223,\cdot)\) \(\chi_{8003}(229,\cdot)\) \(\chi_{8003}(237,\cdot)\) \(\chi_{8003}(249,\cdot)\) \(\chi_{8003}(274,\cdot)\) \(\chi_{8003}(276,\cdot)\) \(\chi_{8003}(322,\cdot)\) \(\chi_{8003}(380,\cdot)\) \(\chi_{8003}(388,\cdot)\) \(\chi_{8003}(396,\cdot)\) \(\chi_{8003}(400,\cdot)\) \(\chi_{8003}(462,\cdot)\) \(\chi_{8003}(534,\cdot)\) \(\chi_{8003}(537,\cdot)\) \(\chi_{8003}(539,\cdot)\) \(\chi_{8003}(547,\cdot)\) \(\chi_{8003}(676,\cdot)\) \(\chi_{8003}(695,\cdot)\) \(\chi_{8003}(698,\cdot)\) \(\chi_{8003}(714,\cdot)\) \(\chi_{8003}(727,\cdot)\) \(\chi_{8003}(729,\cdot)\) \(\chi_{8003}(799,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{325})$ |
| Fixed field: | Number field defined by a degree 650 polynomial (not computed) |
Values on generators
\((4984,7103)\) → \((e\left(\frac{17}{26}\right),e\left(\frac{2}{25}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 8003 }(9, a) \) | \(1\) | \(1\) | \(e\left(\frac{33}{130}\right)\) | \(e\left(\frac{387}{650}\right)\) | \(e\left(\frac{33}{65}\right)\) | \(e\left(\frac{449}{650}\right)\) | \(e\left(\frac{276}{325}\right)\) | \(e\left(\frac{167}{325}\right)\) | \(e\left(\frac{99}{130}\right)\) | \(e\left(\frac{62}{325}\right)\) | \(e\left(\frac{307}{325}\right)\) | \(e\left(\frac{144}{325}\right)\) |