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.cw
\(\chi_{6001}(270,\cdot)\) \(\chi_{6001}(280,\cdot)\) \(\chi_{6001}(332,\cdot)\) \(\chi_{6001}(342,\cdot)\) \(\chi_{6001}(529,\cdot)\) \(\chi_{6001}(689,\cdot)\) \(\chi_{6001}(767,\cdot)\) \(\chi_{6001}(978,\cdot)\) \(\chi_{6001}(1521,\cdot)\) \(\chi_{6001}(1674,\cdot)\) \(\chi_{6001}(1681,\cdot)\) \(\chi_{6001}(1736,\cdot)\) \(\chi_{6001}(2229,\cdot)\) \(\chi_{6001}(2439,\cdot)\) \(\chi_{6001}(2463,\cdot)\) \(\chi_{6001}(2473,\cdot)\) \(\chi_{6001}(2599,\cdot)\) \(\chi_{6001}(2780,\cdot)\) \(\chi_{6001}(2892,\cdot)\) \(\chi_{6001}(2983,\cdot)\) \(\chi_{6001}(3018,\cdot)\) \(\chi_{6001}(3109,\cdot)\) \(\chi_{6001}(3221,\cdot)\) \(\chi_{6001}(3402,\cdot)\) \(\chi_{6001}(3528,\cdot)\) \(\chi_{6001}(3538,\cdot)\) \(\chi_{6001}(3562,\cdot)\) \(\chi_{6001}(3772,\cdot)\) \(\chi_{6001}(4265,\cdot)\) \(\chi_{6001}(4320,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{88})$ |
| Fixed field: | Number field defined by a degree 88 polynomial |
Values on generators
\((2825,3180)\) → \((e\left(\frac{3}{8}\right),e\left(\frac{31}{88}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 6001 }(270, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{44}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(-i\) | \(1\) | \(e\left(\frac{3}{44}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(-i\) | \(e\left(\frac{67}{88}\right)\) |