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.ef
\(\chi_{6001}(37,\cdot)\) \(\chi_{6001}(126,\cdot)\) \(\chi_{6001}(158,\cdot)\) \(\chi_{6001}(160,\cdot)\) \(\chi_{6001}(249,\cdot)\) \(\chi_{6001}(258,\cdot)\) \(\chi_{6001}(266,\cdot)\) \(\chi_{6001}(350,\cdot)\) \(\chi_{6001}(401,\cdot)\) \(\chi_{6001}(428,\cdot)\) \(\chi_{6001}(456,\cdot)\) \(\chi_{6001}(471,\cdot)\) \(\chi_{6001}(507,\cdot)\) \(\chi_{6001}(556,\cdot)\) \(\chi_{6001}(558,\cdot)\) \(\chi_{6001}(598,\cdot)\) \(\chi_{6001}(734,\cdot)\) \(\chi_{6001}(777,\cdot)\) \(\chi_{6001}(793,\cdot)\) \(\chi_{6001}(810,\cdot)\) \(\chi_{6001}(813,\cdot)\) \(\chi_{6001}(879,\cdot)\) \(\chi_{6001}(896,\cdot)\) \(\chi_{6001}(921,\cdot)\) \(\chi_{6001}(940,\cdot)\) \(\chi_{6001}(1178,\cdot)\) \(\chi_{6001}(1269,\cdot)\) \(\chi_{6001}(1287,\cdot)\) \(\chi_{6001}(1332,\cdot)\) \(\chi_{6001}(1338,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{352})$ |
| Fixed field: | Number field defined by a degree 352 polynomial (not computed) |
Values on generators
\((2825,3180)\) → \((e\left(\frac{9}{16}\right),e\left(\frac{291}{352}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 6001 }(813, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{137}{352}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{93}{352}\right)\) | \(e\left(\frac{27}{32}\right)\) | \(e\left(\frac{1}{32}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{137}{176}\right)\) | \(e\left(\frac{23}{32}\right)\) | \(e\left(\frac{95}{176}\right)\) |