Basic properties
| Modulus: | \(1601\) | |
| Conductor: | \(1601\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(400\) | 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 1601.s
\(\chi_{1601}(2,\cdot)\) \(\chi_{1601}(5,\cdot)\) \(\chi_{1601}(8,\cdot)\) \(\chi_{1601}(20,\cdot)\) \(\chi_{1601}(21,\cdot)\) \(\chi_{1601}(38,\cdot)\) \(\chi_{1601}(51,\cdot)\) \(\chi_{1601}(58,\cdot)\) \(\chi_{1601}(62,\cdot)\) \(\chi_{1601}(80,\cdot)\) \(\chi_{1601}(81,\cdot)\) \(\chi_{1601}(84,\cdot)\) \(\chi_{1601}(91,\cdot)\) \(\chi_{1601}(95,\cdot)\) \(\chi_{1601}(106,\cdot)\) \(\chi_{1601}(125,\cdot)\) \(\chi_{1601}(128,\cdot)\) \(\chi_{1601}(138,\cdot)\) \(\chi_{1601}(151,\cdot)\) \(\chi_{1601}(152,\cdot)\) \(\chi_{1601}(155,\cdot)\) \(\chi_{1601}(158,\cdot)\) \(\chi_{1601}(187,\cdot)\) \(\chi_{1601}(197,\cdot)\) \(\chi_{1601}(200,\cdot)\) \(\chi_{1601}(204,\cdot)\) \(\chi_{1601}(210,\cdot)\) \(\chi_{1601}(221,\cdot)\) \(\chi_{1601}(232,\cdot)\) \(\chi_{1601}(269,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{400})$ |
| Fixed field: | Number field defined by a degree 400 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{261}{400}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1601 }(5, a) \) | \(1\) | \(1\) | \(e\left(\frac{93}{100}\right)\) | \(e\left(\frac{261}{400}\right)\) | \(e\left(\frac{43}{50}\right)\) | \(e\left(\frac{21}{100}\right)\) | \(e\left(\frac{233}{400}\right)\) | \(e\left(\frac{7}{400}\right)\) | \(e\left(\frac{79}{100}\right)\) | \(e\left(\frac{61}{200}\right)\) | \(e\left(\frac{7}{50}\right)\) | \(e\left(\frac{13}{400}\right)\) |