Basic properties
| Modulus: | \(1005\) | |
| Conductor: | \(1005\) | 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 1005.bu
\(\chi_{1005}(2,\cdot)\) \(\chi_{1005}(32,\cdot)\) \(\chi_{1005}(98,\cdot)\) \(\chi_{1005}(113,\cdot)\) \(\chi_{1005}(128,\cdot)\) \(\chi_{1005}(152,\cdot)\) \(\chi_{1005}(182,\cdot)\) \(\chi_{1005}(197,\cdot)\) \(\chi_{1005}(203,\cdot)\) \(\chi_{1005}(212,\cdot)\) \(\chi_{1005}(233,\cdot)\) \(\chi_{1005}(242,\cdot)\) \(\chi_{1005}(302,\cdot)\) \(\chi_{1005}(347,\cdot)\) \(\chi_{1005}(353,\cdot)\) \(\chi_{1005}(383,\cdot)\) \(\chi_{1005}(392,\cdot)\) \(\chi_{1005}(398,\cdot)\) \(\chi_{1005}(413,\cdot)\) \(\chi_{1005}(422,\cdot)\) \(\chi_{1005}(443,\cdot)\) \(\chi_{1005}(452,\cdot)\) \(\chi_{1005}(482,\cdot)\) \(\chi_{1005}(497,\cdot)\) \(\chi_{1005}(503,\cdot)\) \(\chi_{1005}(548,\cdot)\) \(\chi_{1005}(587,\cdot)\) \(\chi_{1005}(593,\cdot)\) \(\chi_{1005}(623,\cdot)\) \(\chi_{1005}(647,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((671,202,136)\) → \((-1,i,e\left(\frac{1}{66}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 1005 }(2, a) \) | \(-1\) | \(1\) | \(e\left(\frac{101}{132}\right)\) | \(e\left(\frac{35}{66}\right)\) | \(e\left(\frac{79}{132}\right)\) | \(e\left(\frac{13}{44}\right)\) | \(e\left(\frac{13}{33}\right)\) | \(e\left(\frac{5}{132}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{2}{33}\right)\) | \(e\left(\frac{95}{132}\right)\) | \(e\left(\frac{43}{66}\right)\) |