Basic properties
Modulus: | \(6001\) | |
Conductor: | \(6001\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(352\) | 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.ee
\(\chi_{6001}(56,\cdot)\) \(\chi_{6001}(96,\cdot)\) \(\chi_{6001}(210,\cdot)\) \(\chi_{6001}(241,\cdot)\) \(\chi_{6001}(248,\cdot)\) \(\chi_{6001}(284,\cdot)\) \(\chi_{6001}(313,\cdot)\) \(\chi_{6001}(326,\cdot)\) \(\chi_{6001}(329,\cdot)\) \(\chi_{6001}(415,\cdot)\) \(\chi_{6001}(430,\cdot)\) \(\chi_{6001}(486,\cdot)\) \(\chi_{6001}(487,\cdot)\) \(\chi_{6001}(564,\cdot)\) \(\chi_{6001}(572,\cdot)\) \(\chi_{6001}(583,\cdot)\) \(\chi_{6001}(592,\cdot)\) \(\chi_{6001}(686,\cdot)\) \(\chi_{6001}(692,\cdot)\) \(\chi_{6001}(737,\cdot)\) \(\chi_{6001}(758,\cdot)\) \(\chi_{6001}(760,\cdot)\) \(\chi_{6001}(772,\cdot)\) \(\chi_{6001}(785,\cdot)\) \(\chi_{6001}(796,\cdot)\) \(\chi_{6001}(845,\cdot)\) \(\chi_{6001}(847,\cdot)\) \(\chi_{6001}(857,\cdot)\) \(\chi_{6001}(908,\cdot)\) \(\chi_{6001}(930,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{352})$ |
Fixed field: | Number field defined by a degree 352 polynomial (not computed) |
Values on generators
\((2825,3180)\) → \((e\left(\frac{15}{16}\right),e\left(\frac{93}{352}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 6001 }(737, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{71}{352}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{115}{352}\right)\) | \(e\left(\frac{21}{32}\right)\) | \(e\left(\frac{15}{32}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{71}{176}\right)\) | \(e\left(\frac{25}{32}\right)\) | \(e\left(\frac{73}{176}\right)\) |