Basic properties
| Modulus: | \(9464\) | |
| Conductor: | \(9464\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | 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 9464.jb
\(\chi_{9464}(123,\cdot)\) \(\chi_{9464}(219,\cdot)\) \(\chi_{9464}(275,\cdot)\) \(\chi_{9464}(683,\cdot)\) \(\chi_{9464}(851,\cdot)\) \(\chi_{9464}(947,\cdot)\) \(\chi_{9464}(1003,\cdot)\) \(\chi_{9464}(1411,\cdot)\) \(\chi_{9464}(1579,\cdot)\) \(\chi_{9464}(1675,\cdot)\) \(\chi_{9464}(1731,\cdot)\) \(\chi_{9464}(2139,\cdot)\) \(\chi_{9464}(2307,\cdot)\) \(\chi_{9464}(2403,\cdot)\) \(\chi_{9464}(2459,\cdot)\) \(\chi_{9464}(2867,\cdot)\) \(\chi_{9464}(3035,\cdot)\) \(\chi_{9464}(3187,\cdot)\) \(\chi_{9464}(3595,\cdot)\) \(\chi_{9464}(3763,\cdot)\) \(\chi_{9464}(3859,\cdot)\) \(\chi_{9464}(3915,\cdot)\) \(\chi_{9464}(4323,\cdot)\) \(\chi_{9464}(4491,\cdot)\) \(\chi_{9464}(4587,\cdot)\) \(\chi_{9464}(5219,\cdot)\) \(\chi_{9464}(5315,\cdot)\) \(\chi_{9464}(5371,\cdot)\) \(\chi_{9464}(5779,\cdot)\) \(\chi_{9464}(5947,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((2367,4733,2705,9297)\) → \((-1,-1,e\left(\frac{2}{3}\right),e\left(\frac{53}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 9464 }(123, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{139}{156}\right)\) | \(e\left(\frac{23}{39}\right)\) | \(e\left(\frac{103}{156}\right)\) | \(e\left(\frac{107}{156}\right)\) | \(e\left(\frac{7}{26}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(1\) | \(e\left(\frac{61}{78}\right)\) | \(e\left(\frac{5}{13}\right)\) |