Basic properties
| Modulus: | \(8007\) | |
| Conductor: | \(8007\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(104\) | 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.ed
\(\chi_{8007}(2,\cdot)\) \(\chi_{8007}(8,\cdot)\) \(\chi_{8007}(32,\cdot)\) \(\chi_{8007}(128,\cdot)\) \(\chi_{8007}(134,\cdot)\) \(\chi_{8007}(359,\cdot)\) \(\chi_{8007}(512,\cdot)\) \(\chi_{8007}(536,\cdot)\) \(\chi_{8007}(563,\cdot)\) \(\chi_{8007}(569,\cdot)\) \(\chi_{8007}(587,\cdot)\) \(\chi_{8007}(740,\cdot)\) \(\chi_{8007}(971,\cdot)\) \(\chi_{8007}(1001,\cdot)\) \(\chi_{8007}(1097,\cdot)\) \(\chi_{8007}(1436,\cdot)\) \(\chi_{8007}(1538,\cdot)\) \(\chi_{8007}(1562,\cdot)\) \(\chi_{8007}(2048,\cdot)\) \(\chi_{8007}(2144,\cdot)\) \(\chi_{8007}(2252,\cdot)\) \(\chi_{8007}(2276,\cdot)\) \(\chi_{8007}(2348,\cdot)\) \(\chi_{8007}(2858,\cdot)\) \(\chi_{8007}(2960,\cdot)\) \(\chi_{8007}(3425,\cdot)\) \(\chi_{8007}(3827,\cdot)\) \(\chi_{8007}(3833,\cdot)\) \(\chi_{8007}(3884,\cdot)\) \(\chi_{8007}(4004,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{104})$ |
| Fixed field: | Number field defined by a degree 104 polynomial (not computed) |
Values on generators
\((5339,1414,7855)\) → \((-1,e\left(\frac{3}{8}\right),e\left(\frac{27}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 8007 }(32, a) \) | \(1\) | \(1\) | \(e\left(\frac{25}{26}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{93}{104}\right)\) | \(e\left(\frac{47}{104}\right)\) | \(e\left(\frac{23}{26}\right)\) | \(e\left(\frac{89}{104}\right)\) | \(e\left(\frac{69}{104}\right)\) | \(1\) | \(e\left(\frac{43}{104}\right)\) | \(e\left(\frac{11}{13}\right)\) |