Basic properties
| Modulus: | \(6369\) | |
| Conductor: | \(6369\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(160\) | 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 6369.dm
\(\chi_{6369}(8,\cdot)\) \(\chi_{6369}(260,\cdot)\) \(\chi_{6369}(314,\cdot)\) \(\chi_{6369}(458,\cdot)\) \(\chi_{6369}(512,\cdot)\) \(\chi_{6369}(602,\cdot)\) \(\chi_{6369}(893,\cdot)\) \(\chi_{6369}(941,\cdot)\) \(\chi_{6369}(1007,\cdot)\) \(\chi_{6369}(1091,\cdot)\) \(\chi_{6369}(1172,\cdot)\) \(\chi_{6369}(1328,\cdot)\) \(\chi_{6369}(1337,\cdot)\) \(\chi_{6369}(1502,\cdot)\) \(\chi_{6369}(1520,\cdot)\) \(\chi_{6369}(1568,\cdot)\) \(\chi_{6369}(1586,\cdot)\) \(\chi_{6369}(1613,\cdot)\) \(\chi_{6369}(1745,\cdot)\) \(\chi_{6369}(1751,\cdot)\) \(\chi_{6369}(1916,\cdot)\) \(\chi_{6369}(1922,\cdot)\) \(\chi_{6369}(1997,\cdot)\) \(\chi_{6369}(2054,\cdot)\) \(\chi_{6369}(2081,\cdot)\) \(\chi_{6369}(2147,\cdot)\) \(\chi_{6369}(2195,\cdot)\) \(\chi_{6369}(2339,\cdot)\) \(\chi_{6369}(2576,\cdot)\) \(\chi_{6369}(2774,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{160})$ |
| Fixed field: | Number field defined by a degree 160 polynomial (not computed) |
Values on generators
\((4247,4633,2707)\) → \((-1,e\left(\frac{9}{10}\right),e\left(\frac{5}{32}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(13\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 6369 }(1007, a) \) | \(1\) | \(1\) | \(e\left(\frac{57}{80}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{41}{160}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{11}{80}\right)\) | \(e\left(\frac{31}{32}\right)\) | \(e\left(\frac{149}{160}\right)\) | \(e\left(\frac{21}{80}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{71}{160}\right)\) |