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.s
\(\chi_{2563}(32,\cdot)\) \(\chi_{2563}(76,\cdot)\) \(\chi_{2563}(142,\cdot)\) \(\chi_{2563}(175,\cdot)\) \(\chi_{2563}(241,\cdot)\) \(\chi_{2563}(252,\cdot)\) \(\chi_{2563}(296,\cdot)\) \(\chi_{2563}(307,\cdot)\) \(\chi_{2563}(417,\cdot)\) \(\chi_{2563}(670,\cdot)\) \(\chi_{2563}(703,\cdot)\) \(\chi_{2563}(736,\cdot)\) \(\chi_{2563}(791,\cdot)\) \(\chi_{2563}(934,\cdot)\) \(\chi_{2563}(978,\cdot)\) \(\chi_{2563}(1462,\cdot)\) \(\chi_{2563}(1550,\cdot)\) \(\chi_{2563}(1682,\cdot)\) \(\chi_{2563}(1748,\cdot)\) \(\chi_{2563}(1759,\cdot)\) \(\chi_{2563}(1880,\cdot)\) \(\chi_{2563}(1902,\cdot)\) \(\chi_{2563}(1935,\cdot)\) \(\chi_{2563}(1990,\cdot)\) \(\chi_{2563}(2012,\cdot)\) \(\chi_{2563}(2199,\cdot)\) \(\chi_{2563}(2232,\cdot)\) \(\chi_{2563}(2353,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{29})$ |
| Fixed field: | Number field defined by a degree 58 polynomial |
Values on generators
\((1399,2333)\) → \((-1,e\left(\frac{16}{29}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 2563 }(32, a) \) | \(-1\) | \(1\) | \(e\left(\frac{13}{58}\right)\) | \(e\left(\frac{16}{29}\right)\) | \(e\left(\frac{13}{29}\right)\) | \(e\left(\frac{1}{29}\right)\) | \(e\left(\frac{45}{58}\right)\) | \(e\left(\frac{57}{58}\right)\) | \(e\left(\frac{39}{58}\right)\) | \(e\left(\frac{3}{29}\right)\) | \(e\left(\frac{15}{58}\right)\) | \(1\) |