Basic properties
| Modulus: | \(2057\) | |
| Conductor: | \(2057\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(176\) | 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.bh
\(\chi_{2057}(10,\cdot)\) \(\chi_{2057}(54,\cdot)\) \(\chi_{2057}(65,\cdot)\) \(\chi_{2057}(109,\cdot)\) \(\chi_{2057}(131,\cdot)\) \(\chi_{2057}(142,\cdot)\) \(\chi_{2057}(164,\cdot)\) \(\chi_{2057}(175,\cdot)\) \(\chi_{2057}(197,\cdot)\) \(\chi_{2057}(252,\cdot)\) \(\chi_{2057}(296,\cdot)\) \(\chi_{2057}(318,\cdot)\) \(\chi_{2057}(329,\cdot)\) \(\chi_{2057}(351,\cdot)\) \(\chi_{2057}(384,\cdot)\) \(\chi_{2057}(428,\cdot)\) \(\chi_{2057}(439,\cdot)\) \(\chi_{2057}(505,\cdot)\) \(\chi_{2057}(516,\cdot)\) \(\chi_{2057}(538,\cdot)\) \(\chi_{2057}(549,\cdot)\) \(\chi_{2057}(571,\cdot)\) \(\chi_{2057}(615,\cdot)\) \(\chi_{2057}(626,\cdot)\) \(\chi_{2057}(670,\cdot)\) \(\chi_{2057}(692,\cdot)\) \(\chi_{2057}(703,\cdot)\) \(\chi_{2057}(736,\cdot)\) \(\chi_{2057}(758,\cdot)\) \(\chi_{2057}(802,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{176})$ |
| Fixed field: | Number field defined by a degree 176 polynomial (not computed) |
Values on generators
\((970,122)\) → \((e\left(\frac{9}{22}\right),e\left(\frac{7}{16}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 2057 }(538, a) \) | \(1\) | \(1\) | \(e\left(\frac{47}{88}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{3}{44}\right)\) | \(e\left(\frac{81}{176}\right)\) | \(e\left(\frac{171}{176}\right)\) | \(e\left(\frac{119}{176}\right)\) | \(e\left(\frac{53}{88}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{175}{176}\right)\) | \(e\left(\frac{89}{176}\right)\) |