Basic properties
| Modulus: | \(805\) | |
| Conductor: | \(805\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(132\) | 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 805.bs
\(\chi_{805}(37,\cdot)\) \(\chi_{805}(53,\cdot)\) \(\chi_{805}(67,\cdot)\) \(\chi_{805}(88,\cdot)\) \(\chi_{805}(102,\cdot)\) \(\chi_{805}(107,\cdot)\) \(\chi_{805}(158,\cdot)\) \(\chi_{805}(172,\cdot)\) \(\chi_{805}(198,\cdot)\) \(\chi_{805}(212,\cdot)\) \(\chi_{805}(228,\cdot)\) \(\chi_{805}(247,\cdot)\) \(\chi_{805}(263,\cdot)\) \(\chi_{805}(268,\cdot)\) \(\chi_{805}(333,\cdot)\) \(\chi_{805}(352,\cdot)\) \(\chi_{805}(373,\cdot)\) \(\chi_{805}(382,\cdot)\) \(\chi_{805}(387,\cdot)\) \(\chi_{805}(408,\cdot)\) \(\chi_{805}(452,\cdot)\) \(\chi_{805}(457,\cdot)\) \(\chi_{805}(513,\cdot)\) \(\chi_{805}(527,\cdot)\) \(\chi_{805}(543,\cdot)\) \(\chi_{805}(548,\cdot)\) \(\chi_{805}(557,\cdot)\) \(\chi_{805}(562,\cdot)\) \(\chi_{805}(592,\cdot)\) \(\chi_{805}(613,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((162,346,281)\) → \((i,e\left(\frac{1}{3}\right),e\left(\frac{21}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
| \( \chi_{ 805 }(37, a) \) | \(1\) | \(1\) | \(e\left(\frac{109}{132}\right)\) | \(e\left(\frac{47}{132}\right)\) | \(e\left(\frac{43}{66}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{21}{44}\right)\) | \(e\left(\frac{47}{66}\right)\) | \(e\left(\frac{61}{66}\right)\) | \(e\left(\frac{1}{132}\right)\) | \(e\left(\frac{5}{44}\right)\) | \(e\left(\frac{10}{33}\right)\) |