Basic properties
Modulus: | \(2057\) | |
Conductor: | \(2057\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(176\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
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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
\((970,122)\) → \((e\left(\frac{9}{22}\right),e\left(\frac{15}{16}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 2057 }(1264, a) \) | \(1\) | \(1\) | \(e\left(\frac{47}{88}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{3}{44}\right)\) | \(e\left(\frac{169}{176}\right)\) | \(e\left(\frac{83}{176}\right)\) | \(e\left(\frac{31}{176}\right)\) | \(e\left(\frac{53}{88}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{87}{176}\right)\) | \(e\left(\frac{1}{176}\right)\) |