Basic properties
| Modulus: | \(1681\) | |
| Conductor: | \(1681\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1640\) | 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 1681.p
\(\chi_{1681}(6,\cdot)\) \(\chi_{1681}(7,\cdot)\) \(\chi_{1681}(11,\cdot)\) \(\chi_{1681}(12,\cdot)\) \(\chi_{1681}(13,\cdot)\) \(\chi_{1681}(15,\cdot)\) \(\chi_{1681}(17,\cdot)\) \(\chi_{1681}(19,\cdot)\) \(\chi_{1681}(22,\cdot)\) \(\chi_{1681}(24,\cdot)\) \(\chi_{1681}(26,\cdot)\) \(\chi_{1681}(28,\cdot)\) \(\chi_{1681}(29,\cdot)\) \(\chi_{1681}(30,\cdot)\) \(\chi_{1681}(34,\cdot)\) \(\chi_{1681}(35,\cdot)\) \(\chi_{1681}(47,\cdot)\) \(\chi_{1681}(48,\cdot)\) \(\chi_{1681}(52,\cdot)\) \(\chi_{1681}(53,\cdot)\) \(\chi_{1681}(54,\cdot)\) \(\chi_{1681}(56,\cdot)\) \(\chi_{1681}(58,\cdot)\) \(\chi_{1681}(60,\cdot)\) \(\chi_{1681}(63,\cdot)\) \(\chi_{1681}(65,\cdot)\) \(\chi_{1681}(67,\cdot)\) \(\chi_{1681}(69,\cdot)\) \(\chi_{1681}(70,\cdot)\) \(\chi_{1681}(71,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1640})$ |
| Fixed field: | Number field defined by a degree 1640 polynomial (not computed) |
Values on generators
\(6\) → \(e\left(\frac{1633}{1640}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1681 }(17, a) \) | \(-1\) | \(1\) | \(e\left(\frac{349}{820}\right)\) | \(e\left(\frac{187}{328}\right)\) | \(e\left(\frac{349}{410}\right)\) | \(e\left(\frac{503}{820}\right)\) | \(e\left(\frac{1633}{1640}\right)\) | \(e\left(\frac{1007}{1640}\right)\) | \(e\left(\frac{227}{820}\right)\) | \(e\left(\frac{23}{164}\right)\) | \(e\left(\frac{8}{205}\right)\) | \(e\left(\frac{419}{1640}\right)\) |