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.bv
\(\chi_{1152}(13,\cdot)\) \(\chi_{1152}(61,\cdot)\) \(\chi_{1152}(85,\cdot)\) \(\chi_{1152}(133,\cdot)\) \(\chi_{1152}(157,\cdot)\) \(\chi_{1152}(205,\cdot)\) \(\chi_{1152}(229,\cdot)\) \(\chi_{1152}(277,\cdot)\) \(\chi_{1152}(301,\cdot)\) \(\chi_{1152}(349,\cdot)\) \(\chi_{1152}(373,\cdot)\) \(\chi_{1152}(421,\cdot)\) \(\chi_{1152}(445,\cdot)\) \(\chi_{1152}(493,\cdot)\) \(\chi_{1152}(517,\cdot)\) \(\chi_{1152}(565,\cdot)\) \(\chi_{1152}(589,\cdot)\) \(\chi_{1152}(637,\cdot)\) \(\chi_{1152}(661,\cdot)\) \(\chi_{1152}(709,\cdot)\) \(\chi_{1152}(733,\cdot)\) \(\chi_{1152}(781,\cdot)\) \(\chi_{1152}(805,\cdot)\) \(\chi_{1152}(853,\cdot)\) \(\chi_{1152}(877,\cdot)\) \(\chi_{1152}(925,\cdot)\) \(\chi_{1152}(949,\cdot)\) \(\chi_{1152}(997,\cdot)\) \(\chi_{1152}(1021,\cdot)\) \(\chi_{1152}(1069,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{96})$ |
| Fixed field: | Number field defined by a degree 96 polynomial |
Values on generators
\((127,901,641)\) → \((1,e\left(\frac{27}{32}\right),e\left(\frac{2}{3}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 1152 }(925, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{96}\right)\) | \(e\left(\frac{5}{48}\right)\) | \(e\left(\frac{37}{96}\right)\) | \(e\left(\frac{95}{96}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{13}{32}\right)\) | \(e\left(\frac{7}{48}\right)\) | \(e\left(\frac{17}{48}\right)\) | \(e\left(\frac{43}{96}\right)\) | \(e\left(\frac{1}{12}\right)\) |