Basic properties
Modulus: | \(6336\) | |
Conductor: | \(3168\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(120\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{3168}(515,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6336.fo
\(\chi_{6336}(119,\cdot)\) \(\chi_{6336}(311,\cdot)\) \(\chi_{6336}(455,\cdot)\) \(\chi_{6336}(599,\cdot)\) \(\chi_{6336}(839,\cdot)\) \(\chi_{6336}(983,\cdot)\) \(\chi_{6336}(1127,\cdot)\) \(\chi_{6336}(1175,\cdot)\) \(\chi_{6336}(1703,\cdot)\) \(\chi_{6336}(1895,\cdot)\) \(\chi_{6336}(2039,\cdot)\) \(\chi_{6336}(2183,\cdot)\) \(\chi_{6336}(2423,\cdot)\) \(\chi_{6336}(2567,\cdot)\) \(\chi_{6336}(2711,\cdot)\) \(\chi_{6336}(2759,\cdot)\) \(\chi_{6336}(3287,\cdot)\) \(\chi_{6336}(3479,\cdot)\) \(\chi_{6336}(3623,\cdot)\) \(\chi_{6336}(3767,\cdot)\) \(\chi_{6336}(4007,\cdot)\) \(\chi_{6336}(4151,\cdot)\) \(\chi_{6336}(4295,\cdot)\) \(\chi_{6336}(4343,\cdot)\) \(\chi_{6336}(4871,\cdot)\) \(\chi_{6336}(5063,\cdot)\) \(\chi_{6336}(5207,\cdot)\) \(\chi_{6336}(5351,\cdot)\) \(\chi_{6336}(5591,\cdot)\) \(\chi_{6336}(5735,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{120})$ |
Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((4159,4357,3521,1729)\) → \((-1,e\left(\frac{3}{8}\right),e\left(\frac{1}{6}\right),e\left(\frac{3}{5}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 6336 }(119, a) \) | \(1\) | \(1\) | \(e\left(\frac{73}{120}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{67}{120}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{59}{120}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{29}{40}\right)\) |