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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6001.eg
\(\chi_{6001}(26,\cdot)\) \(\chi_{6001}(53,\cdot)\) \(\chi_{6001}(138,\cdot)\) \(\chi_{6001}(161,\cdot)\) \(\chi_{6001}(274,\cdot)\) \(\chi_{6001}(325,\cdot)\) \(\chi_{6001}(365,\cdot)\) \(\chi_{6001}(461,\cdot)\) \(\chi_{6001}(485,\cdot)\) \(\chi_{6001}(495,\cdot)\) \(\chi_{6001}(502,\cdot)\) \(\chi_{6001}(536,\cdot)\) \(\chi_{6001}(559,\cdot)\) \(\chi_{6001}(631,\cdot)\) \(\chi_{6001}(654,\cdot)\) \(\chi_{6001}(655,\cdot)\) \(\chi_{6001}(661,\cdot)\) \(\chi_{6001}(733,\cdot)\) \(\chi_{6001}(757,\cdot)\) \(\chi_{6001}(763,\cdot)\) \(\chi_{6001}(780,\cdot)\) \(\chi_{6001}(801,\cdot)\) \(\chi_{6001}(818,\cdot)\) \(\chi_{6001}(831,\cdot)\) \(\chi_{6001}(876,\cdot)\) \(\chi_{6001}(910,\cdot)\) \(\chi_{6001}(926,\cdot)\) \(\chi_{6001}(927,\cdot)\) \(\chi_{6001}(1011,\cdot)\) \(\chi_{6001}(1022,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{352})$ |
| Fixed field: | Number field defined by a degree 352 polynomial (not computed) |
Values on generators
\((2825,3180)\) → \((e\left(\frac{1}{8}\right),e\left(\frac{149}{352}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 6001 }(26, a) \) | \(-1\) | \(1\) | \(e\left(\frac{15}{88}\right)\) | \(e\left(\frac{193}{352}\right)\) | \(e\left(\frac{15}{44}\right)\) | \(e\left(\frac{149}{352}\right)\) | \(e\left(\frac{23}{32}\right)\) | \(e\left(\frac{9}{32}\right)\) | \(e\left(\frac{45}{88}\right)\) | \(e\left(\frac{17}{176}\right)\) | \(e\left(\frac{19}{32}\right)\) | \(e\left(\frac{3}{11}\right)\) |