Basic properties
| Modulus: | \(6001\) | |
| Conductor: | \(6001\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(88\) | 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.db
\(\chi_{6001}(185,\cdot)\) \(\chi_{6001}(484,\cdot)\) \(\chi_{6001}(570,\cdot)\) \(\chi_{6001}(893,\cdot)\) \(\chi_{6001}(937,\cdot)\) \(\chi_{6001}(1199,\cdot)\) \(\chi_{6001}(1290,\cdot)\) \(\chi_{6001}(1396,\cdot)\) \(\chi_{6001}(1470,\cdot)\) \(\chi_{6001}(1668,\cdot)\) \(\chi_{6001}(1749,\cdot)\) \(\chi_{6001}(1787,\cdot)\) \(\chi_{6001}(1896,\cdot)\) \(\chi_{6001}(2021,\cdot)\) \(\chi_{6001}(2140,\cdot)\) \(\chi_{6001}(2303,\cdot)\) \(\chi_{6001}(2688,\cdot)\) \(\chi_{6001}(2882,\cdot)\) \(\chi_{6001}(3011,\cdot)\) \(\chi_{6001}(3041,\cdot)\) \(\chi_{6001}(3317,\cdot)\) \(\chi_{6001}(3364,\cdot)\) \(\chi_{6001}(3408,\cdot)\) \(\chi_{6001}(3670,\cdot)\) \(\chi_{6001}(3715,\cdot)\) \(\chi_{6001}(3867,\cdot)\) \(\chi_{6001}(4014,\cdot)\) \(\chi_{6001}(4139,\cdot)\) \(\chi_{6001}(4258,\cdot)\) \(\chi_{6001}(4367,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{88})$ |
| Fixed field: | Number field defined by a degree 88 polynomial |
Values on generators
\((2825,3180)\) → \((e\left(\frac{5}{8}\right),e\left(\frac{2}{11}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 6001 }(2303, a) \) | \(1\) | \(1\) | \(e\left(\frac{25}{44}\right)\) | \(e\left(\frac{71}{88}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{27}{88}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{31}{44}\right)\) | \(e\left(\frac{27}{44}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{25}{88}\right)\) |