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.bv
\(\chi_{805}(3,\cdot)\) \(\chi_{805}(12,\cdot)\) \(\chi_{805}(52,\cdot)\) \(\chi_{805}(73,\cdot)\) \(\chi_{805}(82,\cdot)\) \(\chi_{805}(87,\cdot)\) \(\chi_{805}(108,\cdot)\) \(\chi_{805}(117,\cdot)\) \(\chi_{805}(173,\cdot)\) \(\chi_{805}(187,\cdot)\) \(\chi_{805}(192,\cdot)\) \(\chi_{805}(213,\cdot)\) \(\chi_{805}(243,\cdot)\) \(\chi_{805}(248,\cdot)\) \(\chi_{805}(257,\cdot)\) \(\chi_{805}(262,\cdot)\) \(\chi_{805}(278,\cdot)\) \(\chi_{805}(292,\cdot)\) \(\chi_{805}(348,\cdot)\) \(\chi_{805}(353,\cdot)\) \(\chi_{805}(397,\cdot)\) \(\chi_{805}(418,\cdot)\) \(\chi_{805}(423,\cdot)\) \(\chi_{805}(432,\cdot)\) \(\chi_{805}(453,\cdot)\) \(\chi_{805}(472,\cdot)\) \(\chi_{805}(537,\cdot)\) \(\chi_{805}(542,\cdot)\) \(\chi_{805}(558,\cdot)\) \(\chi_{805}(577,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{132})$ |
Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((162,346,281)\) → \((-i,e\left(\frac{5}{6}\right),e\left(\frac{9}{11}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
\( \chi_{ 805 }(558, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{132}\right)\) | \(e\left(\frac{23}{132}\right)\) | \(e\left(\frac{7}{66}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{7}{44}\right)\) | \(e\left(\frac{23}{66}\right)\) | \(e\left(\frac{23}{33}\right)\) | \(e\left(\frac{37}{132}\right)\) | \(e\left(\frac{9}{44}\right)\) | \(e\left(\frac{7}{33}\right)\) |