Basic properties
| Modulus: | \(6272\) | |
| Conductor: | \(896\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(96\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{896}(19,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6272.cv
\(\chi_{6272}(19,\cdot)\) \(\chi_{6272}(227,\cdot)\) \(\chi_{6272}(411,\cdot)\) \(\chi_{6272}(619,\cdot)\) \(\chi_{6272}(803,\cdot)\) \(\chi_{6272}(1011,\cdot)\) \(\chi_{6272}(1195,\cdot)\) \(\chi_{6272}(1403,\cdot)\) \(\chi_{6272}(1587,\cdot)\) \(\chi_{6272}(1795,\cdot)\) \(\chi_{6272}(1979,\cdot)\) \(\chi_{6272}(2187,\cdot)\) \(\chi_{6272}(2371,\cdot)\) \(\chi_{6272}(2579,\cdot)\) \(\chi_{6272}(2763,\cdot)\) \(\chi_{6272}(2971,\cdot)\) \(\chi_{6272}(3155,\cdot)\) \(\chi_{6272}(3363,\cdot)\) \(\chi_{6272}(3547,\cdot)\) \(\chi_{6272}(3755,\cdot)\) \(\chi_{6272}(3939,\cdot)\) \(\chi_{6272}(4147,\cdot)\) \(\chi_{6272}(4331,\cdot)\) \(\chi_{6272}(4539,\cdot)\) \(\chi_{6272}(4723,\cdot)\) \(\chi_{6272}(4931,\cdot)\) \(\chi_{6272}(5115,\cdot)\) \(\chi_{6272}(5323,\cdot)\) \(\chi_{6272}(5507,\cdot)\) \(\chi_{6272}(5715,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{96})$ |
| Fixed field: | Number field defined by a degree 96 polynomial |
Values on generators
\((4607,3333,4609)\) → \((-1,e\left(\frac{23}{32}\right),e\left(\frac{5}{6}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 6272 }(19, a) \) | \(1\) | \(1\) | \(e\left(\frac{47}{96}\right)\) | \(e\left(\frac{85}{96}\right)\) | \(e\left(\frac{47}{48}\right)\) | \(e\left(\frac{89}{96}\right)\) | \(e\left(\frac{9}{32}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{19}{96}\right)\) | \(e\left(\frac{11}{48}\right)\) | \(e\left(\frac{37}{48}\right)\) |