Basic properties
| Modulus: | \(1681\) | |
| Conductor: | \(1681\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(820\) | 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 1681.o
\(\chi_{1681}(2,\cdot)\) \(\chi_{1681}(5,\cdot)\) \(\chi_{1681}(8,\cdot)\) \(\chi_{1681}(20,\cdot)\) \(\chi_{1681}(21,\cdot)\) \(\chi_{1681}(33,\cdot)\) \(\chi_{1681}(36,\cdot)\) \(\chi_{1681}(39,\cdot)\) \(\chi_{1681}(43,\cdot)\) \(\chi_{1681}(46,\cdot)\) \(\chi_{1681}(49,\cdot)\) \(\chi_{1681}(61,\cdot)\) \(\chi_{1681}(62,\cdot)\) \(\chi_{1681}(74,\cdot)\) \(\chi_{1681}(77,\cdot)\) \(\chi_{1681}(80,\cdot)\) \(\chi_{1681}(84,\cdot)\) \(\chi_{1681}(87,\cdot)\) \(\chi_{1681}(90,\cdot)\) \(\chi_{1681}(102,\cdot)\) \(\chi_{1681}(103,\cdot)\) \(\chi_{1681}(115,\cdot)\) \(\chi_{1681}(118,\cdot)\) \(\chi_{1681}(121,\cdot)\) \(\chi_{1681}(125,\cdot)\) \(\chi_{1681}(128,\cdot)\) \(\chi_{1681}(131,\cdot)\) \(\chi_{1681}(143,\cdot)\) \(\chi_{1681}(144,\cdot)\) \(\chi_{1681}(156,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{820})$ |
| Fixed field: | Number field defined by a degree 820 polynomial (not computed) |
Values on generators
\(6\) → \(e\left(\frac{489}{820}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1681 }(33, a) \) | \(1\) | \(1\) | \(e\left(\frac{337}{410}\right)\) | \(e\left(\frac{127}{164}\right)\) | \(e\left(\frac{132}{205}\right)\) | \(e\left(\frac{239}{410}\right)\) | \(e\left(\frac{489}{820}\right)\) | \(e\left(\frac{291}{820}\right)\) | \(e\left(\frac{191}{410}\right)\) | \(e\left(\frac{45}{82}\right)\) | \(e\left(\frac{83}{205}\right)\) | \(e\left(\frac{367}{820}\right)\) |