Basic properties
| Modulus: | \(1152\) | |
| Conductor: | \(1152\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(96\) | 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 1152.bs
\(\chi_{1152}(11,\cdot)\) \(\chi_{1152}(59,\cdot)\) \(\chi_{1152}(83,\cdot)\) \(\chi_{1152}(131,\cdot)\) \(\chi_{1152}(155,\cdot)\) \(\chi_{1152}(203,\cdot)\) \(\chi_{1152}(227,\cdot)\) \(\chi_{1152}(275,\cdot)\) \(\chi_{1152}(299,\cdot)\) \(\chi_{1152}(347,\cdot)\) \(\chi_{1152}(371,\cdot)\) \(\chi_{1152}(419,\cdot)\) \(\chi_{1152}(443,\cdot)\) \(\chi_{1152}(491,\cdot)\) \(\chi_{1152}(515,\cdot)\) \(\chi_{1152}(563,\cdot)\) \(\chi_{1152}(587,\cdot)\) \(\chi_{1152}(635,\cdot)\) \(\chi_{1152}(659,\cdot)\) \(\chi_{1152}(707,\cdot)\) \(\chi_{1152}(731,\cdot)\) \(\chi_{1152}(779,\cdot)\) \(\chi_{1152}(803,\cdot)\) \(\chi_{1152}(851,\cdot)\) \(\chi_{1152}(875,\cdot)\) \(\chi_{1152}(923,\cdot)\) \(\chi_{1152}(947,\cdot)\) \(\chi_{1152}(995,\cdot)\) \(\chi_{1152}(1019,\cdot)\) \(\chi_{1152}(1067,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{96})$ |
| Fixed field: | Number field defined by a degree 96 polynomial |
Values on generators
\((127,901,641)\) → \((-1,e\left(\frac{21}{32}\right),e\left(\frac{1}{6}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 1152 }(11, a) \) | \(1\) | \(1\) | \(e\left(\frac{47}{96}\right)\) | \(e\left(\frac{35}{48}\right)\) | \(e\left(\frac{43}{96}\right)\) | \(e\left(\frac{17}{96}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{19}{32}\right)\) | \(e\left(\frac{25}{48}\right)\) | \(e\left(\frac{47}{48}\right)\) | \(e\left(\frac{85}{96}\right)\) | \(e\left(\frac{1}{12}\right)\) |