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.cz
\(\chi_{6001}(121,\cdot)\) \(\chi_{6001}(162,\cdot)\) \(\chi_{6001}(474,\cdot)\) \(\chi_{6001}(671,\cdot)\) \(\chi_{6001}(740,\cdot)\) \(\chi_{6001}(852,\cdot)\) \(\chi_{6001}(971,\cdot)\) \(\chi_{6001}(995,\cdot)\) \(\chi_{6001}(1063,\cdot)\) \(\chi_{6001}(1147,\cdot)\) \(\chi_{6001}(1205,\cdot)\) \(\chi_{6001}(1266,\cdot)\) \(\chi_{6001}(1324,\cdot)\) \(\chi_{6001}(1447,\cdot)\) \(\chi_{6001}(1800,\cdot)\) \(\chi_{6001}(1997,\cdot)\) \(\chi_{6001}(2083,\cdot)\) \(\chi_{6001}(2467,\cdot)\) \(\chi_{6001}(2535,\cdot)\) \(\chi_{6001}(2559,\cdot)\) \(\chi_{6001}(2678,\cdot)\) \(\chi_{6001}(2790,\cdot)\) \(\chi_{6001}(2820,\cdot)\) \(\chi_{6001}(2888,\cdot)\) \(\chi_{6001}(3143,\cdot)\) \(\chi_{6001}(3368,\cdot)\) \(\chi_{6001}(3409,\cdot)\) \(\chi_{6001}(3721,\cdot)\) \(\chi_{6001}(3748,\cdot)\) \(\chi_{6001}(4054,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{88})$ |
| Fixed field: | Number field defined by a degree 88 polynomial |
Values on generators
\((2825,3180)\) → \((e\left(\frac{3}{8}\right),e\left(\frac{15}{44}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 6001 }(474, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{44}\right)\) | \(e\left(\frac{63}{88}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{19}{88}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{21}{44}\right)\) | \(e\left(\frac{19}{44}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{7}{88}\right)\) |