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.dg
\(\chi_{8007}(98,\cdot)\) \(\chi_{8007}(965,\cdot)\) \(\chi_{8007}(1067,\cdot)\) \(\chi_{8007}(1415,\cdot)\) \(\chi_{8007}(1577,\cdot)\) \(\chi_{8007}(1772,\cdot)\) \(\chi_{8007}(1781,\cdot)\) \(\chi_{8007}(1925,\cdot)\) \(\chi_{8007}(1976,\cdot)\) \(\chi_{8007}(2384,\cdot)\) \(\chi_{8007}(2954,\cdot)\) \(\chi_{8007}(3362,\cdot)\) \(\chi_{8007}(3413,\cdot)\) \(\chi_{8007}(3557,\cdot)\) \(\chi_{8007}(3566,\cdot)\) \(\chi_{8007}(3761,\cdot)\) \(\chi_{8007}(3923,\cdot)\) \(\chi_{8007}(4271,\cdot)\) \(\chi_{8007}(4373,\cdot)\) \(\chi_{8007}(5240,\cdot)\) \(\chi_{8007}(5801,\cdot)\) \(\chi_{8007}(6515,\cdot)\) \(\chi_{8007}(6830,\cdot)\) \(\chi_{8007}(7544,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{52})$ |
| Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((5339,1414,7855)\) → \((-1,i,e\left(\frac{41}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 8007 }(98, a) \) | \(1\) | \(1\) | \(e\left(\frac{9}{52}\right)\) | \(e\left(\frac{9}{26}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{17}{26}\right)\) | \(e\left(\frac{27}{52}\right)\) | \(e\left(\frac{37}{52}\right)\) | \(e\left(\frac{17}{52}\right)\) | \(-1\) | \(e\left(\frac{43}{52}\right)\) | \(e\left(\frac{9}{13}\right)\) |