Basic properties
| Modulus: | \(2563\) | |
| Conductor: | \(2563\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(58\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2563.t
\(\chi_{2563}(98,\cdot)\) \(\chi_{2563}(131,\cdot)\) \(\chi_{2563}(318,\cdot)\) \(\chi_{2563}(340,\cdot)\) \(\chi_{2563}(395,\cdot)\) \(\chi_{2563}(428,\cdot)\) \(\chi_{2563}(450,\cdot)\) \(\chi_{2563}(571,\cdot)\) \(\chi_{2563}(582,\cdot)\) \(\chi_{2563}(648,\cdot)\) \(\chi_{2563}(780,\cdot)\) \(\chi_{2563}(868,\cdot)\) \(\chi_{2563}(1352,\cdot)\) \(\chi_{2563}(1396,\cdot)\) \(\chi_{2563}(1539,\cdot)\) \(\chi_{2563}(1594,\cdot)\) \(\chi_{2563}(1627,\cdot)\) \(\chi_{2563}(1660,\cdot)\) \(\chi_{2563}(1913,\cdot)\) \(\chi_{2563}(2023,\cdot)\) \(\chi_{2563}(2034,\cdot)\) \(\chi_{2563}(2078,\cdot)\) \(\chi_{2563}(2089,\cdot)\) \(\chi_{2563}(2155,\cdot)\) \(\chi_{2563}(2188,\cdot)\) \(\chi_{2563}(2254,\cdot)\) \(\chi_{2563}(2298,\cdot)\) \(\chi_{2563}(2540,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{29})$ |
| Fixed field: | Number field defined by a degree 58 polynomial |
Values on generators
\((1399,2333)\) → \((-1,e\left(\frac{13}{58}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 2563 }(98, a) \) | \(-1\) | \(1\) | \(e\left(\frac{37}{58}\right)\) | \(e\left(\frac{13}{58}\right)\) | \(e\left(\frac{8}{29}\right)\) | \(e\left(\frac{57}{58}\right)\) | \(e\left(\frac{25}{29}\right)\) | \(e\left(\frac{15}{58}\right)\) | \(e\left(\frac{53}{58}\right)\) | \(e\left(\frac{13}{29}\right)\) | \(e\left(\frac{18}{29}\right)\) | \(-1\) |