Basic properties
| Modulus: | \(2057\) | |
| Conductor: | \(2057\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(220\) | 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 2057.bi
\(\chi_{2057}(4,\cdot)\) \(\chi_{2057}(38,\cdot)\) \(\chi_{2057}(47,\cdot)\) \(\chi_{2057}(64,\cdot)\) \(\chi_{2057}(115,\cdot)\) \(\chi_{2057}(157,\cdot)\) \(\chi_{2057}(174,\cdot)\) \(\chi_{2057}(191,\cdot)\) \(\chi_{2057}(225,\cdot)\) \(\chi_{2057}(234,\cdot)\) \(\chi_{2057}(268,\cdot)\) \(\chi_{2057}(302,\cdot)\) \(\chi_{2057}(344,\cdot)\) \(\chi_{2057}(361,\cdot)\) \(\chi_{2057}(378,\cdot)\) \(\chi_{2057}(412,\cdot)\) \(\chi_{2057}(421,\cdot)\) \(\chi_{2057}(438,\cdot)\) \(\chi_{2057}(455,\cdot)\) \(\chi_{2057}(489,\cdot)\) \(\chi_{2057}(531,\cdot)\) \(\chi_{2057}(548,\cdot)\) \(\chi_{2057}(599,\cdot)\) \(\chi_{2057}(625,\cdot)\) \(\chi_{2057}(642,\cdot)\) \(\chi_{2057}(676,\cdot)\) \(\chi_{2057}(718,\cdot)\) \(\chi_{2057}(752,\cdot)\) \(\chi_{2057}(786,\cdot)\) \(\chi_{2057}(795,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{220})$ |
| Fixed field: | Number field defined by a degree 220 polynomial (not computed) |
Values on generators
\((970,122)\) → \((e\left(\frac{1}{55}\right),-i)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 2057 }(4, a) \) | \(1\) | \(1\) | \(e\left(\frac{57}{110}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{2}{55}\right)\) | \(e\left(\frac{21}{220}\right)\) | \(e\left(\frac{191}{220}\right)\) | \(e\left(\frac{83}{220}\right)\) | \(e\left(\frac{61}{110}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{27}{44}\right)\) | \(e\left(\frac{17}{44}\right)\) |