Basic properties
| Modulus: | \(2563\) | |
| Conductor: | \(2563\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(116\) | 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.v
\(\chi_{2563}(109,\cdot)\) \(\chi_{2563}(120,\cdot)\) \(\chi_{2563}(197,\cdot)\) \(\chi_{2563}(208,\cdot)\) \(\chi_{2563}(219,\cdot)\) \(\chi_{2563}(263,\cdot)\) \(\chi_{2563}(285,\cdot)\) \(\chi_{2563}(362,\cdot)\) \(\chi_{2563}(406,\cdot)\) \(\chi_{2563}(494,\cdot)\) \(\chi_{2563}(516,\cdot)\) \(\chi_{2563}(538,\cdot)\) \(\chi_{2563}(637,\cdot)\) \(\chi_{2563}(681,\cdot)\) \(\chi_{2563}(692,\cdot)\) \(\chi_{2563}(714,\cdot)\) \(\chi_{2563}(725,\cdot)\) \(\chi_{2563}(901,\cdot)\) \(\chi_{2563}(923,\cdot)\) \(\chi_{2563}(945,\cdot)\) \(\chi_{2563}(1033,\cdot)\) \(\chi_{2563}(1044,\cdot)\) \(\chi_{2563}(1055,\cdot)\) \(\chi_{2563}(1099,\cdot)\) \(\chi_{2563}(1110,\cdot)\) \(\chi_{2563}(1132,\cdot)\) \(\chi_{2563}(1198,\cdot)\) \(\chi_{2563}(1220,\cdot)\) \(\chi_{2563}(1231,\cdot)\) \(\chi_{2563}(1275,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{116})$ |
| Fixed field: | Number field defined by a degree 116 polynomial (not computed) |
Values on generators
\((1399,2333)\) → \((-1,e\left(\frac{105}{116}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 2563 }(109, a) \) | \(-1\) | \(1\) | \(e\left(\frac{39}{58}\right)\) | \(e\left(\frac{105}{116}\right)\) | \(e\left(\frac{10}{29}\right)\) | \(e\left(\frac{41}{116}\right)\) | \(e\left(\frac{67}{116}\right)\) | \(e\left(\frac{13}{29}\right)\) | \(e\left(\frac{1}{58}\right)\) | \(e\left(\frac{47}{58}\right)\) | \(e\left(\frac{3}{116}\right)\) | \(i\) |