Basic properties
| Modulus: | \(8005\) | |
| Conductor: | \(1601\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(100\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1601}(31,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8005.bx
\(\chi_{8005}(16,\cdot)\) \(\chi_{8005}(31,\cdot)\) \(\chi_{8005}(841,\cdot)\) \(\chi_{8005}(876,\cdot)\) \(\chi_{8005}(976,\cdot)\) \(\chi_{8005}(1311,\cdot)\) \(\chi_{8005}(1351,\cdot)\) \(\chi_{8005}(1501,\cdot)\) \(\chi_{8005}(1701,\cdot)\) \(\chi_{8005}(1851,\cdot)\) \(\chi_{8005}(1891,\cdot)\) \(\chi_{8005}(2226,\cdot)\) \(\chi_{8005}(2326,\cdot)\) \(\chi_{8005}(2361,\cdot)\) \(\chi_{8005}(3171,\cdot)\) \(\chi_{8005}(3186,\cdot)\) \(\chi_{8005}(3501,\cdot)\) \(\chi_{8005}(3791,\cdot)\) \(\chi_{8005}(3796,\cdot)\) \(\chi_{8005}(3836,\cdot)\) \(\chi_{8005}(4041,\cdot)\) \(\chi_{8005}(4096,\cdot)\) \(\chi_{8005}(4131,\cdot)\) \(\chi_{8005}(4856,\cdot)\) \(\chi_{8005}(5406,\cdot)\) \(\chi_{8005}(5431,\cdot)\) \(\chi_{8005}(5471,\cdot)\) \(\chi_{8005}(5526,\cdot)\) \(\chi_{8005}(5681,\cdot)\) \(\chi_{8005}(5736,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{100})$ |
| Fixed field: | Number field defined by a degree 100 polynomial |
Values on generators
\((1602,4806)\) → \((1,e\left(\frac{19}{100}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 8005 }(31, a) \) | \(1\) | \(1\) | \(e\left(\frac{22}{25}\right)\) | \(e\left(\frac{19}{100}\right)\) | \(e\left(\frac{19}{25}\right)\) | \(e\left(\frac{7}{100}\right)\) | \(e\left(\frac{53}{100}\right)\) | \(e\left(\frac{16}{25}\right)\) | \(e\left(\frac{19}{50}\right)\) | \(e\left(\frac{27}{100}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(-i\) |