Basic properties
| Modulus: | \(6369\) | |
| Conductor: | \(6369\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(480\) | 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.ea
\(\chi_{6369}(2,\cdot)\) \(\chi_{6369}(83,\cdot)\) \(\chi_{6369}(95,\cdot)\) \(\chi_{6369}(101,\cdot)\) \(\chi_{6369}(107,\cdot)\) \(\chi_{6369}(128,\cdot)\) \(\chi_{6369}(161,\cdot)\) \(\chi_{6369}(293,\cdot)\) \(\chi_{6369}(332,\cdot)\) \(\chi_{6369}(380,\cdot)\) \(\chi_{6369}(392,\cdot)\) \(\chi_{6369}(404,\cdot)\) \(\chi_{6369}(479,\cdot)\) \(\chi_{6369}(611,\cdot)\) \(\chi_{6369}(635,\cdot)\) \(\chi_{6369}(644,\cdot)\) \(\chi_{6369}(662,\cdot)\) \(\chi_{6369}(677,\cdot)\) \(\chi_{6369}(689,\cdot)\) \(\chi_{6369}(959,\cdot)\) \(\chi_{6369}(1019,\cdot)\) \(\chi_{6369}(1040,\cdot)\) \(\chi_{6369}(1058,\cdot)\) \(\chi_{6369}(1190,\cdot)\) \(\chi_{6369}(1223,\cdot)\) \(\chi_{6369}(1250,\cdot)\) \(\chi_{6369}(1256,\cdot)\) \(\chi_{6369}(1295,\cdot)\) \(\chi_{6369}(1349,\cdot)\) \(\chi_{6369}(1382,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{480})$ |
| Fixed field: | Number field defined by a degree 480 polynomial (not computed) |
Values on generators
\((4247,4633,2707)\) → \((-1,e\left(\frac{1}{10}\right),e\left(\frac{67}{96}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(13\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 6369 }(101, a) \) | \(1\) | \(1\) | \(e\left(\frac{79}{240}\right)\) | \(e\left(\frac{79}{120}\right)\) | \(e\left(\frac{287}{480}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{79}{80}\right)\) | \(e\left(\frac{89}{96}\right)\) | \(e\left(\frac{81}{160}\right)\) | \(e\left(\frac{49}{80}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{17}{480}\right)\) |