Basic properties
| Modulus: | \(8007\) | |
| Conductor: | \(471\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{471}(137,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8007.ei
\(\chi_{8007}(137,\cdot)\) \(\chi_{8007}(290,\cdot)\) \(\chi_{8007}(545,\cdot)\) \(\chi_{8007}(698,\cdot)\) \(\chi_{8007}(800,\cdot)\) \(\chi_{8007}(851,\cdot)\) \(\chi_{8007}(1004,\cdot)\) \(\chi_{8007}(1565,\cdot)\) \(\chi_{8007}(1667,\cdot)\) \(\chi_{8007}(1922,\cdot)\) \(\chi_{8007}(2075,\cdot)\) \(\chi_{8007}(2126,\cdot)\) \(\chi_{8007}(2177,\cdot)\) \(\chi_{8007}(2381,\cdot)\) \(\chi_{8007}(2432,\cdot)\) \(\chi_{8007}(2585,\cdot)\) \(\chi_{8007}(2687,\cdot)\) \(\chi_{8007}(2738,\cdot)\) \(\chi_{8007}(3044,\cdot)\) \(\chi_{8007}(3146,\cdot)\) \(\chi_{8007}(3350,\cdot)\) \(\chi_{8007}(3401,\cdot)\) \(\chi_{8007}(3605,\cdot)\) \(\chi_{8007}(3707,\cdot)\) \(\chi_{8007}(4013,\cdot)\) \(\chi_{8007}(4064,\cdot)\) \(\chi_{8007}(4166,\cdot)\) \(\chi_{8007}(4319,\cdot)\) \(\chi_{8007}(4370,\cdot)\) \(\chi_{8007}(4574,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((5339,1414,7855)\) → \((-1,1,e\left(\frac{49}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 8007 }(137, a) \) | \(1\) | \(1\) | \(e\left(\frac{41}{52}\right)\) | \(e\left(\frac{15}{26}\right)\) | \(e\left(\frac{127}{156}\right)\) | \(e\left(\frac{9}{52}\right)\) | \(e\left(\frac{19}{52}\right)\) | \(e\left(\frac{47}{78}\right)\) | \(e\left(\frac{23}{78}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{25}{26}\right)\) | \(e\left(\frac{2}{13}\right)\) |