Basic properties
| Modulus: | \(6005\) | |
| Conductor: | \(6005\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(80\) | 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 6005.cq
\(\chi_{6005}(83,\cdot)\) \(\chi_{6005}(308,\cdot)\) \(\chi_{6005}(592,\cdot)\) \(\chi_{6005}(893,\cdot)\) \(\chi_{6005}(1017,\cdot)\) \(\chi_{6005}(1118,\cdot)\) \(\chi_{6005}(1157,\cdot)\) \(\chi_{6005}(1288,\cdot)\) \(\chi_{6005}(1312,\cdot)\) \(\chi_{6005}(1447,\cdot)\) \(\chi_{6005}(1767,\cdot)\) \(\chi_{6005}(1782,\cdot)\) \(\chi_{6005}(1938,\cdot)\) \(\chi_{6005}(1978,\cdot)\) \(\chi_{6005}(2043,\cdot)\) \(\chi_{6005}(2047,\cdot)\) \(\chi_{6005}(2757,\cdot)\) \(\chi_{6005}(2923,\cdot)\) \(\chi_{6005}(2943,\cdot)\) \(\chi_{6005}(3022,\cdot)\) \(\chi_{6005}(3037,\cdot)\) \(\chi_{6005}(3357,\cdot)\) \(\chi_{6005}(3492,\cdot)\) \(\chi_{6005}(3647,\cdot)\) \(\chi_{6005}(3787,\cdot)\) \(\chi_{6005}(4212,\cdot)\) \(\chi_{6005}(4263,\cdot)\) \(\chi_{6005}(4283,\cdot)\) \(\chi_{6005}(5163,\cdot)\) \(\chi_{6005}(5228,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((1202,11)\) → \((i,e\left(\frac{67}{80}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 6005 }(1767, a) \) | \(1\) | \(1\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(1\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{67}{80}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{3}{80}\right)\) |