Basic properties
| Modulus: | \(2557\) | |
| Conductor: | \(2557\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(213\) | 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 2557.l
\(\chi_{2557}(27,\cdot)\) \(\chi_{2557}(39,\cdot)\) \(\chi_{2557}(82,\cdot)\) \(\chi_{2557}(144,\cdot)\) \(\chi_{2557}(149,\cdot)\) \(\chi_{2557}(208,\cdot)\) \(\chi_{2557}(213,\cdot)\) \(\chi_{2557}(255,\cdot)\) \(\chi_{2557}(257,\cdot)\) \(\chi_{2557}(280,\cdot)\) \(\chi_{2557}(307,\cdot)\) \(\chi_{2557}(308,\cdot)\) \(\chi_{2557}(335,\cdot)\) \(\chi_{2557}(441,\cdot)\) \(\chi_{2557}(445,\cdot)\) \(\chi_{2557}(454,\cdot)\) \(\chi_{2557}(487,\cdot)\) \(\chi_{2557}(490,\cdot)\) \(\chi_{2557}(502,\cdot)\) \(\chi_{2557}(511,\cdot)\) \(\chi_{2557}(532,\cdot)\) \(\chi_{2557}(537,\cdot)\) \(\chi_{2557}(539,\cdot)\) \(\chi_{2557}(565,\cdot)\) \(\chi_{2557}(618,\cdot)\) \(\chi_{2557}(636,\cdot)\) \(\chi_{2557}(637,\cdot)\) \(\chi_{2557}(641,\cdot)\) \(\chi_{2557}(654,\cdot)\) \(\chi_{2557}(697,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{213})$ |
| Fixed field: | Number field defined by a degree 213 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{169}{213}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 2557 }(27, a) \) | \(1\) | \(1\) | \(e\left(\frac{169}{213}\right)\) | \(e\left(\frac{76}{213}\right)\) | \(e\left(\frac{125}{213}\right)\) | \(e\left(\frac{46}{213}\right)\) | \(e\left(\frac{32}{213}\right)\) | \(e\left(\frac{38}{213}\right)\) | \(e\left(\frac{27}{71}\right)\) | \(e\left(\frac{152}{213}\right)\) | \(e\left(\frac{2}{213}\right)\) | \(e\left(\frac{68}{213}\right)\) |