Basic properties
| Modulus: | \(8007\) | |
| Conductor: | \(8007\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(312\) | 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.ey
\(\chi_{8007}(53,\cdot)\) \(\chi_{8007}(83,\cdot)\) \(\chi_{8007}(212,\cdot)\) \(\chi_{8007}(230,\cdot)\) \(\chi_{8007}(332,\cdot)\) \(\chi_{8007}(383,\cdot)\) \(\chi_{8007}(410,\cdot)\) \(\chi_{8007}(491,\cdot)\) \(\chi_{8007}(671,\cdot)\) \(\chi_{8007}(689,\cdot)\) \(\chi_{8007}(716,\cdot)\) \(\chi_{8007}(722,\cdot)\) \(\chi_{8007}(767,\cdot)\) \(\chi_{8007}(848,\cdot)\) \(\chi_{8007}(869,\cdot)\) \(\chi_{8007}(899,\cdot)\) \(\chi_{8007}(1046,\cdot)\) \(\chi_{8007}(1079,\cdot)\) \(\chi_{8007}(1250,\cdot)\) \(\chi_{8007}(1328,\cdot)\) \(\chi_{8007}(1358,\cdot)\) \(\chi_{8007}(1379,\cdot)\) \(\chi_{8007}(1487,\cdot)\) \(\chi_{8007}(1532,\cdot)\) \(\chi_{8007}(1640,\cdot)\) \(\chi_{8007}(1964,\cdot)\) \(\chi_{8007}(2015,\cdot)\) \(\chi_{8007}(2174,\cdot)\) \(\chi_{8007}(2219,\cdot)\) \(\chi_{8007}(2684,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{312})$ |
| Fixed field: | Number field defined by a degree 312 polynomial (not computed) |
Values on generators
\((5339,1414,7855)\) → \((-1,e\left(\frac{7}{8}\right),e\left(\frac{59}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 8007 }(53, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{79}{312}\right)\) | \(e\left(\frac{23}{104}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{103}{312}\right)\) | \(e\left(\frac{67}{312}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{31}{104}\right)\) | \(e\left(\frac{4}{13}\right)\) |