Basic properties
Modulus: | \(4005\) | |
Conductor: | \(4005\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(264\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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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 4005.ec
\(\chi_{4005}(43,\cdot)\) \(\chi_{4005}(103,\cdot)\) \(\chi_{4005}(232,\cdot)\) \(\chi_{4005}(313,\cdot)\) \(\chi_{4005}(328,\cdot)\) \(\chi_{4005}(337,\cdot)\) \(\chi_{4005}(382,\cdot)\) \(\chi_{4005}(448,\cdot)\) \(\chi_{4005}(472,\cdot)\) \(\chi_{4005}(493,\cdot)\) \(\chi_{4005}(547,\cdot)\) \(\chi_{4005}(592,\cdot)\) \(\chi_{4005}(652,\cdot)\) \(\chi_{4005}(682,\cdot)\) \(\chi_{4005}(688,\cdot)\) \(\chi_{4005}(697,\cdot)\) \(\chi_{4005}(718,\cdot)\) \(\chi_{4005}(727,\cdot)\) \(\chi_{4005}(742,\cdot)\) \(\chi_{4005}(772,\cdot)\) \(\chi_{4005}(778,\cdot)\) \(\chi_{4005}(808,\cdot)\) \(\chi_{4005}(832,\cdot)\) \(\chi_{4005}(877,\cdot)\) \(\chi_{4005}(913,\cdot)\) \(\chi_{4005}(952,\cdot)\) \(\chi_{4005}(1003,\cdot)\) \(\chi_{4005}(1042,\cdot)\) \(\chi_{4005}(1087,\cdot)\) \(\chi_{4005}(1192,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{264})$ |
Fixed field: | Number field defined by a degree 264 polynomial (not computed) |
Values on generators
\((3116,802,181)\) → \((e\left(\frac{2}{3}\right),-i,e\left(\frac{29}{88}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 4005 }(43, a) \) | \(1\) | \(1\) | \(e\left(\frac{91}{132}\right)\) | \(e\left(\frac{25}{66}\right)\) | \(e\left(\frac{29}{264}\right)\) | \(e\left(\frac{3}{44}\right)\) | \(e\left(\frac{23}{66}\right)\) | \(e\left(\frac{43}{264}\right)\) | \(e\left(\frac{211}{264}\right)\) | \(e\left(\frac{25}{33}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{3}{88}\right)\) |