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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 805.bt
\(\chi_{805}(2,\cdot)\) \(\chi_{805}(18,\cdot)\) \(\chi_{805}(32,\cdot)\) \(\chi_{805}(58,\cdot)\) \(\chi_{805}(72,\cdot)\) \(\chi_{805}(123,\cdot)\) \(\chi_{805}(128,\cdot)\) \(\chi_{805}(142,\cdot)\) \(\chi_{805}(163,\cdot)\) \(\chi_{805}(177,\cdot)\) \(\chi_{805}(193,\cdot)\) \(\chi_{805}(233,\cdot)\) \(\chi_{805}(242,\cdot)\) \(\chi_{805}(282,\cdot)\) \(\chi_{805}(303,\cdot)\) \(\chi_{805}(312,\cdot)\) \(\chi_{805}(317,\cdot)\) \(\chi_{805}(338,\cdot)\) \(\chi_{805}(347,\cdot)\) \(\chi_{805}(403,\cdot)\) \(\chi_{805}(417,\cdot)\) \(\chi_{805}(422,\cdot)\) \(\chi_{805}(443,\cdot)\) \(\chi_{805}(473,\cdot)\) \(\chi_{805}(478,\cdot)\) \(\chi_{805}(487,\cdot)\) \(\chi_{805}(492,\cdot)\) \(\chi_{805}(508,\cdot)\) \(\chi_{805}(522,\cdot)\) \(\chi_{805}(578,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((162,346,281)\) → \((-i,e\left(\frac{2}{3}\right),e\left(\frac{6}{11}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
| \( \chi_{ 805 }(18, a) \) | \(-1\) | \(1\) | \(e\left(\frac{23}{132}\right)\) | \(e\left(\frac{85}{132}\right)\) | \(e\left(\frac{23}{66}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{23}{44}\right)\) | \(e\left(\frac{19}{66}\right)\) | \(e\left(\frac{19}{33}\right)\) | \(e\left(\frac{131}{132}\right)\) | \(e\left(\frac{39}{44}\right)\) | \(e\left(\frac{23}{33}\right)\) |