Basic properties
| Modulus: | \(8007\) | |
| Conductor: | \(2669\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2669}(106,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8007.ep
\(\chi_{8007}(106,\cdot)\) \(\chi_{8007}(115,\cdot)\) \(\chi_{8007}(166,\cdot)\) \(\chi_{8007}(361,\cdot)\) \(\chi_{8007}(523,\cdot)\) \(\chi_{8007}(625,\cdot)\) \(\chi_{8007}(820,\cdot)\) \(\chi_{8007}(982,\cdot)\) \(\chi_{8007}(1432,\cdot)\) \(\chi_{8007}(1534,\cdot)\) \(\chi_{8007}(1696,\cdot)\) \(\chi_{8007}(1738,\cdot)\) \(\chi_{8007}(1798,\cdot)\) \(\chi_{8007}(1840,\cdot)\) \(\chi_{8007}(1993,\cdot)\) \(\chi_{8007}(2461,\cdot)\) \(\chi_{8007}(2716,\cdot)\) \(\chi_{8007}(2758,\cdot)\) \(\chi_{8007}(3013,\cdot)\) \(\chi_{8007}(3064,\cdot)\) \(\chi_{8007}(3115,\cdot)\) \(\chi_{8007}(3175,\cdot)\) \(\chi_{8007}(3421,\cdot)\) \(\chi_{8007}(3787,\cdot)\) \(\chi_{8007}(3889,\cdot)\) \(\chi_{8007}(4093,\cdot)\) \(\chi_{8007}(4195,\cdot)\) \(\chi_{8007}(4339,\cdot)\) \(\chi_{8007}(4348,\cdot)\) \(\chi_{8007}(4543,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((5339,1414,7855)\) → \((1,-i,e\left(\frac{11}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 8007 }(106, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{26}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{5}{156}\right)\) | \(e\left(\frac{37}{52}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{47}{156}\right)\) | \(e\left(\frac{23}{156}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{51}{52}\right)\) | \(e\left(\frac{1}{13}\right)\) |