Basic properties
| Modulus: | \(8007\) | |
| Conductor: | \(8007\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(52\) | 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.dl
\(\chi_{8007}(149,\cdot)\) \(\chi_{8007}(599,\cdot)\) \(\chi_{8007}(863,\cdot)\) \(\chi_{8007}(1007,\cdot)\) \(\chi_{8007}(1058,\cdot)\) \(\chi_{8007}(1211,\cdot)\) \(\chi_{8007}(1568,\cdot)\) \(\chi_{8007}(3770,\cdot)\) \(\chi_{8007}(4127,\cdot)\) \(\chi_{8007}(4280,\cdot)\) \(\chi_{8007}(4331,\cdot)\) \(\chi_{8007}(4475,\cdot)\) \(\chi_{8007}(4739,\cdot)\) \(\chi_{8007}(5189,\cdot)\) \(\chi_{8007}(5750,\cdot)\) \(\chi_{8007}(5912,\cdot)\) \(\chi_{8007}(6116,\cdot)\) \(\chi_{8007}(6617,\cdot)\) \(\chi_{8007}(6626,\cdot)\) \(\chi_{8007}(6719,\cdot)\) \(\chi_{8007}(6728,\cdot)\) \(\chi_{8007}(7229,\cdot)\) \(\chi_{8007}(7433,\cdot)\) \(\chi_{8007}(7595,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{52})$ |
| Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((5339,1414,7855)\) → \((-1,i,e\left(\frac{11}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 8007 }(149, a) \) | \(1\) | \(1\) | \(e\left(\frac{43}{52}\right)\) | \(e\left(\frac{17}{26}\right)\) | \(e\left(\frac{25}{26}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{25}{52}\right)\) | \(e\left(\frac{41}{52}\right)\) | \(e\left(\frac{9}{52}\right)\) | \(-1\) | \(e\left(\frac{35}{52}\right)\) | \(e\left(\frac{4}{13}\right)\) |