Basic properties
| Modulus: | \(2681\) | |
| Conductor: | \(2681\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1146\) | 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 2681.n
\(\chi_{2681}(3,\cdot)\) \(\chi_{2681}(12,\cdot)\) \(\chi_{2681}(17,\cdot)\) \(\chi_{2681}(19,\cdot)\) \(\chi_{2681}(24,\cdot)\) \(\chi_{2681}(31,\cdot)\) \(\chi_{2681}(38,\cdot)\) \(\chi_{2681}(54,\cdot)\) \(\chi_{2681}(68,\cdot)\) \(\chi_{2681}(73,\cdot)\) \(\chi_{2681}(75,\cdot)\) \(\chi_{2681}(87,\cdot)\) \(\chi_{2681}(96,\cdot)\) \(\chi_{2681}(101,\cdot)\) \(\chi_{2681}(103,\cdot)\) \(\chi_{2681}(108,\cdot)\) \(\chi_{2681}(110,\cdot)\) \(\chi_{2681}(124,\cdot)\) \(\chi_{2681}(129,\cdot)\) \(\chi_{2681}(136,\cdot)\) \(\chi_{2681}(138,\cdot)\) \(\chi_{2681}(143,\cdot)\) \(\chi_{2681}(150,\cdot)\) \(\chi_{2681}(152,\cdot)\) \(\chi_{2681}(171,\cdot)\) \(\chi_{2681}(173,\cdot)\) \(\chi_{2681}(185,\cdot)\) \(\chi_{2681}(192,\cdot)\) \(\chi_{2681}(201,\cdot)\) \(\chi_{2681}(206,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{573})$ |
| Fixed field: | Number field defined by a degree 1146 polynomial (not computed) |
Values on generators
\((2299,771)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{75}{191}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 2681 }(535, a) \) | \(-1\) | \(1\) | \(e\left(\frac{545}{573}\right)\) | \(e\left(\frac{965}{1146}\right)\) | \(e\left(\frac{517}{573}\right)\) | \(e\left(\frac{259}{1146}\right)\) | \(e\left(\frac{303}{382}\right)\) | \(e\left(\frac{163}{191}\right)\) | \(e\left(\frac{392}{573}\right)\) | \(e\left(\frac{203}{1146}\right)\) | \(e\left(\frac{82}{573}\right)\) | \(e\left(\frac{853}{1146}\right)\) |