Basic properties
| Modulus: | \(6016\) | |
| Conductor: | \(3008\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(368\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3008}(211,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6016.bq
\(\chi_{6016}(23,\cdot)\) \(\chi_{6016}(39,\cdot)\) \(\chi_{6016}(87,\cdot)\) \(\chi_{6016}(135,\cdot)\) \(\chi_{6016}(151,\cdot)\) \(\chi_{6016}(167,\cdot)\) \(\chi_{6016}(199,\cdot)\) \(\chi_{6016}(231,\cdot)\) \(\chi_{6016}(279,\cdot)\) \(\chi_{6016}(295,\cdot)\) \(\chi_{6016}(311,\cdot)\) \(\chi_{6016}(327,\cdot)\) \(\chi_{6016}(359,\cdot)\) \(\chi_{6016}(391,\cdot)\) \(\chi_{6016}(407,\cdot)\) \(\chi_{6016}(503,\cdot)\) \(\chi_{6016}(583,\cdot)\) \(\chi_{6016}(599,\cdot)\) \(\chi_{6016}(631,\cdot)\) \(\chi_{6016}(663,\cdot)\) \(\chi_{6016}(727,\cdot)\) \(\chi_{6016}(743,\cdot)\) \(\chi_{6016}(775,\cdot)\) \(\chi_{6016}(791,\cdot)\) \(\chi_{6016}(839,\cdot)\) \(\chi_{6016}(887,\cdot)\) \(\chi_{6016}(903,\cdot)\) \(\chi_{6016}(919,\cdot)\) \(\chi_{6016}(951,\cdot)\) \(\chi_{6016}(983,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{368})$ |
| Fixed field: | Number field defined by a degree 368 polynomial (not computed) |
Values on generators
\((4607,2821,3201)\) → \((-1,e\left(\frac{7}{16}\right),e\left(\frac{5}{46}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 6016 }(23, a) \) | \(1\) | \(1\) | \(e\left(\frac{363}{368}\right)\) | \(e\left(\frac{201}{368}\right)\) | \(e\left(\frac{65}{184}\right)\) | \(e\left(\frac{179}{184}\right)\) | \(e\left(\frac{165}{368}\right)\) | \(e\left(\frac{279}{368}\right)\) | \(e\left(\frac{49}{92}\right)\) | \(e\left(\frac{91}{92}\right)\) | \(e\left(\frac{167}{368}\right)\) | \(e\left(\frac{125}{368}\right)\) |