Basic properties
| Modulus: | \(8007\) | |
| Conductor: | \(2669\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(104\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2669}(49,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8007.dy
\(\chi_{8007}(49,\cdot)\) \(\chi_{8007}(247,\cdot)\) \(\chi_{8007}(298,\cdot)\) \(\chi_{8007}(457,\cdot)\) \(\chi_{8007}(529,\cdot)\) \(\chi_{8007}(535,\cdot)\) \(\chi_{8007}(553,\cdot)\) \(\chi_{8007}(655,\cdot)\) \(\chi_{8007}(739,\cdot)\) \(\chi_{8007}(841,\cdot)\) \(\chi_{8007}(1471,\cdot)\) \(\chi_{8007}(1477,\cdot)\) \(\chi_{8007}(1681,\cdot)\) \(\chi_{8007}(1783,\cdot)\) \(\chi_{8007}(2473,\cdot)\) \(\chi_{8007}(2830,\cdot)\) \(\chi_{8007}(2875,\cdot)\) \(\chi_{8007}(3283,\cdot)\) \(\chi_{8007}(3415,\cdot)\) \(\chi_{8007}(3544,\cdot)\) \(\chi_{8007}(3595,\cdot)\) \(\chi_{8007}(3772,\cdot)\) \(\chi_{8007}(3817,\cdot)\) \(\chi_{8007}(3850,\cdot)\) \(\chi_{8007}(3952,\cdot)\) \(\chi_{8007}(4225,\cdot)\) \(\chi_{8007}(4303,\cdot)\) \(\chi_{8007}(4486,\cdot)\) \(\chi_{8007}(4507,\cdot)\) \(\chi_{8007}(4537,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{104})$ |
| Fixed field: | Number field defined by a degree 104 polynomial (not computed) |
Values on generators
\((5339,1414,7855)\) → \((1,e\left(\frac{3}{8}\right),e\left(\frac{23}{26}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 8007 }(49, a) \) | \(1\) | \(1\) | \(e\left(\frac{51}{52}\right)\) | \(e\left(\frac{25}{26}\right)\) | \(e\left(\frac{79}{104}\right)\) | \(e\left(\frac{17}{104}\right)\) | \(e\left(\frac{49}{52}\right)\) | \(e\left(\frac{77}{104}\right)\) | \(e\left(\frac{41}{104}\right)\) | \(-1\) | \(e\left(\frac{15}{104}\right)\) | \(e\left(\frac{12}{13}\right)\) |