Basic properties
| Modulus: | \(1601\) | |
| Conductor: | \(1601\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1600\) | 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 1601.u
\(\chi_{1601}(3,\cdot)\) \(\chi_{1601}(6,\cdot)\) \(\chi_{1601}(7,\cdot)\) \(\chi_{1601}(11,\cdot)\) \(\chi_{1601}(14,\cdot)\) \(\chi_{1601}(17,\cdot)\) \(\chi_{1601}(23,\cdot)\) \(\chi_{1601}(24,\cdot)\) \(\chi_{1601}(26,\cdot)\) \(\chi_{1601}(27,\cdot)\) \(\chi_{1601}(28,\cdot)\) \(\chi_{1601}(30,\cdot)\) \(\chi_{1601}(35,\cdot)\) \(\chi_{1601}(44,\cdot)\) \(\chi_{1601}(46,\cdot)\) \(\chi_{1601}(48,\cdot)\) \(\chi_{1601}(52,\cdot)\) \(\chi_{1601}(55,\cdot)\) \(\chi_{1601}(56,\cdot)\) \(\chi_{1601}(57,\cdot)\) \(\chi_{1601}(59,\cdot)\) \(\chi_{1601}(60,\cdot)\) \(\chi_{1601}(63,\cdot)\) \(\chi_{1601}(65,\cdot)\) \(\chi_{1601}(68,\cdot)\) \(\chi_{1601}(70,\cdot)\) \(\chi_{1601}(71,\cdot)\) \(\chi_{1601}(73,\cdot)\) \(\chi_{1601}(75,\cdot)\) \(\chi_{1601}(85,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1600})$ |
| Fixed field: | Number field defined by a degree 1600 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{1519}{1600}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1601 }(23, a) \) | \(-1\) | \(1\) | \(e\left(\frac{147}{400}\right)\) | \(e\left(\frac{1519}{1600}\right)\) | \(e\left(\frac{147}{200}\right)\) | \(e\left(\frac{59}{400}\right)\) | \(e\left(\frac{507}{1600}\right)\) | \(e\left(\frac{453}{1600}\right)\) | \(e\left(\frac{41}{400}\right)\) | \(e\left(\frac{719}{800}\right)\) | \(e\left(\frac{103}{200}\right)\) | \(e\left(\frac{1527}{1600}\right)\) |