Basic properties
| Modulus: | \(2563\) | |
| Conductor: | \(2563\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(290\) | 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.ba
\(\chi_{2563}(2,\cdot)\) \(\chi_{2563}(8,\cdot)\) \(\chi_{2563}(19,\cdot)\) \(\chi_{2563}(46,\cdot)\) \(\chi_{2563}(51,\cdot)\) \(\chi_{2563}(63,\cdot)\) \(\chi_{2563}(74,\cdot)\) \(\chi_{2563}(117,\cdot)\) \(\chi_{2563}(128,\cdot)\) \(\chi_{2563}(184,\cdot)\) \(\chi_{2563}(204,\cdot)\) \(\chi_{2563}(237,\cdot)\) \(\chi_{2563}(249,\cdot)\) \(\chi_{2563}(270,\cdot)\) \(\chi_{2563}(271,\cdot)\) \(\chi_{2563}(304,\cdot)\) \(\chi_{2563}(325,\cdot)\) \(\chi_{2563}(359,\cdot)\) \(\chi_{2563}(381,\cdot)\) \(\chi_{2563}(437,\cdot)\) \(\chi_{2563}(468,\cdot)\) \(\chi_{2563}(470,\cdot)\) \(\chi_{2563}(503,\cdot)\) \(\chi_{2563}(512,\cdot)\) \(\chi_{2563}(530,\cdot)\) \(\chi_{2563}(558,\cdot)\) \(\chi_{2563}(568,\cdot)\) \(\chi_{2563}(601,\cdot)\) \(\chi_{2563}(618,\cdot)\) \(\chi_{2563}(701,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{145})$ |
| Fixed field: | Number field defined by a degree 290 polynomial (not computed) |
Values on generators
\((1399,2333)\) → \((e\left(\frac{1}{10}\right),e\left(\frac{9}{29}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 2563 }(2, a) \) | \(-1\) | \(1\) | \(e\left(\frac{129}{290}\right)\) | \(e\left(\frac{16}{145}\right)\) | \(e\left(\frac{129}{145}\right)\) | \(e\left(\frac{88}{145}\right)\) | \(e\left(\frac{161}{290}\right)\) | \(e\left(\frac{173}{290}\right)\) | \(e\left(\frac{97}{290}\right)\) | \(e\left(\frac{32}{145}\right)\) | \(e\left(\frac{3}{58}\right)\) | \(1\) |