Basic properties
| Modulus: | \(1601\) | |
| Conductor: | \(1601\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(100\) | 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.o
\(\chi_{1601}(16,\cdot)\) \(\chi_{1601}(31,\cdot)\) \(\chi_{1601}(53,\cdot)\) \(\chi_{1601}(100,\cdot)\) \(\chi_{1601}(250,\cdot)\) \(\chi_{1601}(290,\cdot)\) \(\chi_{1601}(299,\cdot)\) \(\chi_{1601}(589,\cdot)\) \(\chi_{1601}(594,\cdot)\) \(\chi_{1601}(603,\cdot)\) \(\chi_{1601}(625,\cdot)\) \(\chi_{1601}(628,\cdot)\) \(\chi_{1601}(634,\cdot)\) \(\chi_{1601}(668,\cdot)\) \(\chi_{1601}(672,\cdot)\) \(\chi_{1601}(707,\cdot)\) \(\chi_{1601}(723,\cdot)\) \(\chi_{1601}(725,\cdot)\) \(\chi_{1601}(760,\cdot)\) \(\chi_{1601}(762,\cdot)\) \(\chi_{1601}(839,\cdot)\) \(\chi_{1601}(841,\cdot)\) \(\chi_{1601}(876,\cdot)\) \(\chi_{1601}(878,\cdot)\) \(\chi_{1601}(894,\cdot)\) \(\chi_{1601}(929,\cdot)\) \(\chi_{1601}(933,\cdot)\) \(\chi_{1601}(967,\cdot)\) \(\chi_{1601}(973,\cdot)\) \(\chi_{1601}(976,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{100})$ |
| Fixed field: | Number field defined by a degree 100 polynomial |
Values on generators
\(3\) → \(e\left(\frac{19}{100}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1601 }(31, a) \) | \(1\) | \(1\) | \(e\left(\frac{22}{25}\right)\) | \(e\left(\frac{19}{100}\right)\) | \(e\left(\frac{19}{25}\right)\) | \(e\left(\frac{9}{25}\right)\) | \(e\left(\frac{7}{100}\right)\) | \(e\left(\frac{53}{100}\right)\) | \(e\left(\frac{16}{25}\right)\) | \(e\left(\frac{19}{50}\right)\) | \(e\left(\frac{6}{25}\right)\) | \(e\left(\frac{27}{100}\right)\) |