Basic properties
| Modulus: | \(6001\) | |
| Conductor: | \(6001\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(352\) | 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 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
\((2825,3180)\) → \((e\left(\frac{11}{16}\right),e\left(\frac{273}{352}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 6001 }(313, a) \) | \(1\) | \(1\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{163}{352}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{31}{352}\right)\) | \(e\left(\frac{9}{32}\right)\) | \(e\left(\frac{11}{32}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{163}{176}\right)\) | \(e\left(\frac{29}{32}\right)\) | \(e\left(\frac{61}{176}\right)\) |