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.fi
\(\chi_{8007}(44,\cdot)\) \(\chi_{8007}(122,\cdot)\) \(\chi_{8007}(146,\cdot)\) \(\chi_{8007}(167,\cdot)\) \(\chi_{8007}(182,\cdot)\) \(\chi_{8007}(233,\cdot)\) \(\chi_{8007}(284,\cdot)\) \(\chi_{8007}(317,\cdot)\) \(\chi_{8007}(347,\cdot)\) \(\chi_{8007}(350,\cdot)\) \(\chi_{8007}(362,\cdot)\) \(\chi_{8007}(371,\cdot)\) \(\chi_{8007}(419,\cdot)\) \(\chi_{8007}(431,\cdot)\) \(\chi_{8007}(452,\cdot)\) \(\chi_{8007}(515,\cdot)\) \(\chi_{8007}(539,\cdot)\) \(\chi_{8007}(581,\cdot)\) \(\chi_{8007}(617,\cdot)\) \(\chi_{8007}(653,\cdot)\) \(\chi_{8007}(704,\cdot)\) \(\chi_{8007}(755,\cdot)\) \(\chi_{8007}(776,\cdot)\) \(\chi_{8007}(788,\cdot)\) \(\chi_{8007}(821,\cdot)\) \(\chi_{8007}(827,\cdot)\) \(\chi_{8007}(836,\cdot)\) \(\chi_{8007}(890,\cdot)\) \(\chi_{8007}(923,\cdot)\) \(\chi_{8007}(1010,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{624})$ |
| Fixed field: | Number field defined by a degree 624 polynomial (not computed) |
Values on generators
\((5339,1414,7855)\) → \((-1,e\left(\frac{3}{16}\right),e\left(\frac{77}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 8007 }(44, a) \) | \(1\) | \(1\) | \(e\left(\frac{33}{104}\right)\) | \(e\left(\frac{33}{52}\right)\) | \(e\left(\frac{265}{624}\right)\) | \(e\left(\frac{37}{208}\right)\) | \(e\left(\frac{99}{104}\right)\) | \(e\left(\frac{463}{624}\right)\) | \(e\left(\frac{283}{624}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{103}{208}\right)\) | \(e\left(\frac{7}{26}\right)\) |