Basic properties
| Modulus: | \(6369\) | |
| Conductor: | \(6369\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(120\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6369.di
\(\chi_{6369}(779,\cdot)\) \(\chi_{6369}(977,\cdot)\) \(\chi_{6369}(1103,\cdot)\) \(\chi_{6369}(1142,\cdot)\) \(\chi_{6369}(1358,\cdot)\) \(\chi_{6369}(1367,\cdot)\) \(\chi_{6369}(1406,\cdot)\) \(\chi_{6369}(1532,\cdot)\) \(\chi_{6369}(1556,\cdot)\) \(\chi_{6369}(1721,\cdot)\) \(\chi_{6369}(1730,\cdot)\) \(\chi_{6369}(1985,\cdot)\) \(\chi_{6369}(3095,\cdot)\) \(\chi_{6369}(3293,\cdot)\) \(\chi_{6369}(3419,\cdot)\) \(\chi_{6369}(3458,\cdot)\) \(\chi_{6369}(3683,\cdot)\) \(\chi_{6369}(3722,\cdot)\) \(\chi_{6369}(3848,\cdot)\) \(\chi_{6369}(3998,\cdot)\) \(\chi_{6369}(4046,\cdot)\) \(\chi_{6369}(4262,\cdot)\) \(\chi_{6369}(4427,\cdot)\) \(\chi_{6369}(4625,\cdot)\) \(\chi_{6369}(4832,\cdot)\) \(\chi_{6369}(5030,\cdot)\) \(\chi_{6369}(5195,\cdot)\) \(\chi_{6369}(5459,\cdot)\) \(\chi_{6369}(5735,\cdot)\) \(\chi_{6369}(5999,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{120})$ |
| Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((4247,4633,2707)\) → \((-1,e\left(\frac{2}{5}\right),e\left(\frac{13}{24}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(13\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 6369 }(1358, a) \) | \(-1\) | \(1\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{77}{120}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{107}{120}\right)\) |