Basic properties
Modulus: | \(6001\) | |
Conductor: | \(6001\) | 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
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6001.ec
\(\chi_{6001}(9,\cdot)\) \(\chi_{6001}(15,\cdot)\) \(\chi_{6001}(25,\cdot)\) \(\chi_{6001}(127,\cdot)\) \(\chi_{6001}(172,\cdot)\) \(\chi_{6001}(338,\cdot)\) \(\chi_{6001}(372,\cdot)\) \(\chi_{6001}(399,\cdot)\) \(\chi_{6001}(542,\cdot)\) \(\chi_{6001}(593,\cdot)\) \(\chi_{6001}(614,\cdot)\) \(\chi_{6001}(620,\cdot)\) \(\chi_{6001}(665,\cdot)\) \(\chi_{6001}(729,\cdot)\) \(\chi_{6001}(1137,\cdot)\) \(\chi_{6001}(1158,\cdot)\) \(\chi_{6001}(1215,\cdot)\) \(\chi_{6001}(1362,\cdot)\) \(\chi_{6001}(1403,\cdot)\) \(\chi_{6001}(1477,\cdot)\) \(\chi_{6001}(1556,\cdot)\) \(\chi_{6001}(1726,\cdot)\) \(\chi_{6001}(1783,\cdot)\) \(\chi_{6001}(1895,\cdot)\) \(\chi_{6001}(1930,\cdot)\) \(\chi_{6001}(1998,\cdot)\) \(\chi_{6001}(2025,\cdot)\) \(\chi_{6001}(2042,\cdot)\) \(\chi_{6001}(2212,\cdot)\) \(\chi_{6001}(2270,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{176})$ |
Fixed field: | Number field defined by a degree 176 polynomial (not computed) |
Values on generators
\((2825,3180)\) → \((e\left(\frac{3}{8}\right),e\left(\frac{147}{176}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 6001 }(1477, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{37}{176}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{169}{176}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{37}{88}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{65}{88}\right)\) |