Basic properties
| Modulus: | \(8752\) | |
| Conductor: | \(8752\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | 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 8752.cs
\(\chi_{8752}(21,\cdot)\) \(\chi_{8752}(181,\cdot)\) \(\chi_{8752}(325,\cdot)\) \(\chi_{8752}(445,\cdot)\) \(\chi_{8752}(949,\cdot)\) \(\chi_{8752}(1141,\cdot)\) \(\chi_{8752}(1293,\cdot)\) \(\chi_{8752}(1325,\cdot)\) \(\chi_{8752}(1333,\cdot)\) \(\chi_{8752}(2309,\cdot)\) \(\chi_{8752}(2317,\cdot)\) \(\chi_{8752}(2405,\cdot)\) \(\chi_{8752}(2421,\cdot)\) \(\chi_{8752}(2629,\cdot)\) \(\chi_{8752}(2709,\cdot)\) \(\chi_{8752}(2789,\cdot)\) \(\chi_{8752}(3037,\cdot)\) \(\chi_{8752}(3293,\cdot)\) \(\chi_{8752}(3701,\cdot)\) \(\chi_{8752}(3925,\cdot)\) \(\chi_{8752}(3965,\cdot)\) \(\chi_{8752}(4125,\cdot)\) \(\chi_{8752}(4293,\cdot)\) \(\chi_{8752}(4317,\cdot)\) \(\chi_{8752}(4397,\cdot)\) \(\chi_{8752}(4557,\cdot)\) \(\chi_{8752}(4701,\cdot)\) \(\chi_{8752}(4821,\cdot)\) \(\chi_{8752}(5325,\cdot)\) \(\chi_{8752}(5517,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((5471,6565,2737)\) → \((1,i,e\left(\frac{20}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 8752 }(3701, a) \) | \(1\) | \(1\) | \(-i\) | \(e\left(\frac{7}{156}\right)\) | \(e\left(\frac{25}{78}\right)\) | \(-1\) | \(e\left(\frac{23}{156}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{17}{39}\right)\) | \(e\left(\frac{109}{156}\right)\) | \(e\left(\frac{11}{156}\right)\) |