Basic properties
| Modulus: | \(2563\) | |
| Conductor: | \(233\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(58\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{233}(105,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2563.r
\(\chi_{2563}(210,\cdot)\) \(\chi_{2563}(331,\cdot)\) \(\chi_{2563}(364,\cdot)\) \(\chi_{2563}(551,\cdot)\) \(\chi_{2563}(573,\cdot)\) \(\chi_{2563}(628,\cdot)\) \(\chi_{2563}(661,\cdot)\) \(\chi_{2563}(683,\cdot)\) \(\chi_{2563}(804,\cdot)\) \(\chi_{2563}(815,\cdot)\) \(\chi_{2563}(881,\cdot)\) \(\chi_{2563}(1013,\cdot)\) \(\chi_{2563}(1101,\cdot)\) \(\chi_{2563}(1585,\cdot)\) \(\chi_{2563}(1629,\cdot)\) \(\chi_{2563}(1772,\cdot)\) \(\chi_{2563}(1827,\cdot)\) \(\chi_{2563}(1860,\cdot)\) \(\chi_{2563}(1893,\cdot)\) \(\chi_{2563}(2146,\cdot)\) \(\chi_{2563}(2256,\cdot)\) \(\chi_{2563}(2267,\cdot)\) \(\chi_{2563}(2311,\cdot)\) \(\chi_{2563}(2322,\cdot)\) \(\chi_{2563}(2388,\cdot)\) \(\chi_{2563}(2421,\cdot)\) \(\chi_{2563}(2487,\cdot)\) \(\chi_{2563}(2531,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{29})$ |
| Fixed field: | Number field defined by a degree 58 polynomial |
Values on generators
\((1399,2333)\) → \((1,e\left(\frac{39}{58}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 2563 }(804, a) \) | \(1\) | \(1\) | \(e\left(\frac{12}{29}\right)\) | \(e\left(\frac{39}{58}\right)\) | \(e\left(\frac{24}{29}\right)\) | \(e\left(\frac{55}{58}\right)\) | \(e\left(\frac{5}{58}\right)\) | \(e\left(\frac{8}{29}\right)\) | \(e\left(\frac{7}{29}\right)\) | \(e\left(\frac{10}{29}\right)\) | \(e\left(\frac{21}{58}\right)\) | \(-1\) |