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
\((1399,2333)\) → \((e\left(\frac{3}{10}\right),e\left(\frac{17}{29}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 2563 }(19, a) \) | \(-1\) | \(1\) | \(e\left(\frac{147}{290}\right)\) | \(e\left(\frac{143}{145}\right)\) | \(e\left(\frac{2}{145}\right)\) | \(e\left(\frac{134}{145}\right)\) | \(e\left(\frac{143}{290}\right)\) | \(e\left(\frac{69}{290}\right)\) | \(e\left(\frac{151}{290}\right)\) | \(e\left(\frac{141}{145}\right)\) | \(e\left(\frac{25}{58}\right)\) | \(1\) |