Basic properties
| Modulus: | \(2348\) | |
| Conductor: | \(587\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(293\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{587}(53,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2348.e
\(\chi_{2348}(9,\cdot)\) \(\chi_{2348}(17,\cdot)\) \(\chi_{2348}(21,\cdot)\) \(\chi_{2348}(25,\cdot)\) \(\chi_{2348}(29,\cdot)\) \(\chi_{2348}(49,\cdot)\) \(\chi_{2348}(53,\cdot)\) \(\chi_{2348}(65,\cdot)\) \(\chi_{2348}(73,\cdot)\) \(\chi_{2348}(81,\cdot)\) \(\chi_{2348}(89,\cdot)\) \(\chi_{2348}(93,\cdot)\) \(\chi_{2348}(101,\cdot)\) \(\chi_{2348}(113,\cdot)\) \(\chi_{2348}(121,\cdot)\) \(\chi_{2348}(129,\cdot)\) \(\chi_{2348}(137,\cdot)\) \(\chi_{2348}(141,\cdot)\) \(\chi_{2348}(149,\cdot)\) \(\chi_{2348}(153,\cdot)\) \(\chi_{2348}(165,\cdot)\) \(\chi_{2348}(169,\cdot)\) \(\chi_{2348}(177,\cdot)\) \(\chi_{2348}(181,\cdot)\) \(\chi_{2348}(185,\cdot)\) \(\chi_{2348}(189,\cdot)\) \(\chi_{2348}(193,\cdot)\) \(\chi_{2348}(197,\cdot)\) \(\chi_{2348}(201,\cdot)\) \(\chi_{2348}(205,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{293})$ |
| Fixed field: | Number field defined by a degree 293 polynomial (not computed) |
Values on generators
\((1175,589)\) → \((1,e\left(\frac{106}{293}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 2348 }(53, a) \) | \(1\) | \(1\) | \(e\left(\frac{272}{293}\right)\) | \(e\left(\frac{48}{293}\right)\) | \(e\left(\frac{51}{293}\right)\) | \(e\left(\frac{251}{293}\right)\) | \(e\left(\frac{8}{293}\right)\) | \(e\left(\frac{100}{293}\right)\) | \(e\left(\frac{27}{293}\right)\) | \(e\left(\frac{219}{293}\right)\) | \(e\left(\frac{86}{293}\right)\) | \(e\left(\frac{30}{293}\right)\) |