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
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Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4005.ee
\(\chi_{4005}(38,\cdot)\) \(\chi_{4005}(92,\cdot)\) \(\chi_{4005}(122,\cdot)\) \(\chi_{4005}(137,\cdot)\) \(\chi_{4005}(248,\cdot)\) \(\chi_{4005}(293,\cdot)\) \(\chi_{4005}(362,\cdot)\) \(\chi_{4005}(383,\cdot)\) \(\chi_{4005}(452,\cdot)\) \(\chi_{4005}(527,\cdot)\) \(\chi_{4005}(563,\cdot)\) \(\chi_{4005}(608,\cdot)\) \(\chi_{4005}(617,\cdot)\) \(\chi_{4005}(653,\cdot)\) \(\chi_{4005}(743,\cdot)\) \(\chi_{4005}(788,\cdot)\) \(\chi_{4005}(842,\cdot)\) \(\chi_{4005}(857,\cdot)\) \(\chi_{4005}(887,\cdot)\) \(\chi_{4005}(1022,\cdot)\) \(\chi_{4005}(1082,\cdot)\) \(\chi_{4005}(1103,\cdot)\) \(\chi_{4005}(1208,\cdot)\) \(\chi_{4005}(1292,\cdot)\) \(\chi_{4005}(1307,\cdot)\) \(\chi_{4005}(1373,\cdot)\) \(\chi_{4005}(1427,\cdot)\) \(\chi_{4005}(1472,\cdot)\) \(\chi_{4005}(1478,\cdot)\) \(\chi_{4005}(1667,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{264})$ |
Fixed field: | Number field defined by a degree 264 polynomial (not computed) |
Values on generators
\((3116,802,181)\) → \((e\left(\frac{1}{6}\right),-i,e\left(\frac{51}{88}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 4005 }(38, a) \) | \(-1\) | \(1\) | \(e\left(\frac{25}{132}\right)\) | \(e\left(\frac{25}{66}\right)\) | \(e\left(\frac{95}{264}\right)\) | \(e\left(\frac{25}{44}\right)\) | \(e\left(\frac{28}{33}\right)\) | \(e\left(\frac{241}{264}\right)\) | \(e\left(\frac{145}{264}\right)\) | \(e\left(\frac{25}{33}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{69}{88}\right)\) |