Basic properties
| Modulus: | \(2681\) | |
| Conductor: | \(2681\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(573\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2681.m
\(\chi_{2681}(2,\cdot)\) \(\chi_{2681}(4,\cdot)\) \(\chi_{2681}(9,\cdot)\) \(\chi_{2681}(16,\cdot)\) \(\chi_{2681}(18,\cdot)\) \(\chi_{2681}(23,\cdot)\) \(\chi_{2681}(25,\cdot)\) \(\chi_{2681}(32,\cdot)\) \(\chi_{2681}(46,\cdot)\) \(\chi_{2681}(51,\cdot)\) \(\chi_{2681}(58,\cdot)\) \(\chi_{2681}(65,\cdot)\) \(\chi_{2681}(67,\cdot)\) \(\chi_{2681}(72,\cdot)\) \(\chi_{2681}(81,\cdot)\) \(\chi_{2681}(86,\cdot)\) \(\chi_{2681}(93,\cdot)\) \(\chi_{2681}(100,\cdot)\) \(\chi_{2681}(102,\cdot)\) \(\chi_{2681}(114,\cdot)\) \(\chi_{2681}(116,\cdot)\) \(\chi_{2681}(121,\cdot)\) \(\chi_{2681}(128,\cdot)\) \(\chi_{2681}(130,\cdot)\) \(\chi_{2681}(137,\cdot)\) \(\chi_{2681}(142,\cdot)\) \(\chi_{2681}(144,\cdot)\) \(\chi_{2681}(149,\cdot)\) \(\chi_{2681}(165,\cdot)\) \(\chi_{2681}(172,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{573})$ |
| Fixed field: | Number field defined by a degree 573 polynomial (not computed) |
Values on generators
\((2299,771)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{160}{191}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 2681 }(226, a) \) | \(1\) | \(1\) | \(e\left(\frac{526}{573}\right)\) | \(e\left(\frac{329}{573}\right)\) | \(e\left(\frac{479}{573}\right)\) | \(e\left(\frac{289}{573}\right)\) | \(e\left(\frac{94}{191}\right)\) | \(e\left(\frac{144}{191}\right)\) | \(e\left(\frac{85}{573}\right)\) | \(e\left(\frac{242}{573}\right)\) | \(e\left(\frac{506}{573}\right)\) | \(e\left(\frac{235}{573}\right)\) |