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.es
\(\chi_{6001}(14,\cdot)\) \(\chi_{6001}(40,\cdot)\) \(\chi_{6001}(71,\cdot)\) \(\chi_{6001}(90,\cdot)\) \(\chi_{6001}(141,\cdot)\) \(\chi_{6001}(148,\cdot)\) \(\chi_{6001}(173,\cdot)\) \(\chi_{6001}(190,\cdot)\) \(\chi_{6001}(199,\cdot)\) \(\chi_{6001}(250,\cdot)\) \(\chi_{6001}(333,\cdot)\) \(\chi_{6001}(384,\cdot)\) \(\chi_{6001}(422,\cdot)\) \(\chi_{6001}(449,\cdot)\) \(\chi_{6001}(581,\cdot)\) \(\chi_{6001}(632,\cdot)\) \(\chi_{6001}(673,\cdot)\) \(\chi_{6001}(703,\cdot)\) \(\chi_{6001}(754,\cdot)\) \(\chi_{6001}(821,\cdot)\) \(\chi_{6001}(840,\cdot)\) \(\chi_{6001}(864,\cdot)\) \(\chi_{6001}(925,\cdot)\) \(\chi_{6001}(947,\cdot)\) \(\chi_{6001}(1032,\cdot)\) \(\chi_{6001}(1234,\cdot)\) \(\chi_{6001}(1252,\cdot)\) \(\chi_{6001}(1270,\cdot)\) \(\chi_{6001}(1286,\cdot)\) \(\chi_{6001}(1297,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{352})$ |
| Fixed field: | Number field defined by a degree 352 polynomial (not computed) |
Values on generators
\((2825,3180)\) → \((e\left(\frac{1}{16}\right),e\left(\frac{191}{352}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 6001 }(190, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{213}{352}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{345}{352}\right)\) | \(e\left(\frac{15}{32}\right)\) | \(e\left(\frac{13}{32}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{37}{176}\right)\) | \(e\left(\frac{27}{32}\right)\) | \(e\left(\frac{175}{176}\right)\) |