Basic properties
Modulus: | \(4005\) | |
Conductor: | \(4005\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(132\) | 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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4005.dt
\(\chi_{4005}(2,\cdot)\) \(\chi_{4005}(32,\cdot)\) \(\chi_{4005}(128,\cdot)\) \(\chi_{4005}(167,\cdot)\) \(\chi_{4005}(182,\cdot)\) \(\chi_{4005}(542,\cdot)\) \(\chi_{4005}(662,\cdot)\) \(\chi_{4005}(668,\cdot)\) \(\chi_{4005}(803,\cdot)\) \(\chi_{4005}(833,\cdot)\) \(\chi_{4005}(968,\cdot)\) \(\chi_{4005}(983,\cdot)\) \(\chi_{4005}(1202,\cdot)\) \(\chi_{4005}(1262,\cdot)\) \(\chi_{4005}(1337,\cdot)\) \(\chi_{4005}(1343,\cdot)\) \(\chi_{4005}(1463,\cdot)\) \(\chi_{4005}(1517,\cdot)\) \(\chi_{4005}(1577,\cdot)\) \(\chi_{4005}(1847,\cdot)\) \(\chi_{4005}(1877,\cdot)\) \(\chi_{4005}(2003,\cdot)\) \(\chi_{4005}(2063,\cdot)\) \(\chi_{4005}(2138,\cdot)\) \(\chi_{4005}(2318,\cdot)\) \(\chi_{4005}(2378,\cdot)\) \(\chi_{4005}(2597,\cdot)\) \(\chi_{4005}(2648,\cdot)\) \(\chi_{4005}(2678,\cdot)\) \(\chi_{4005}(2702,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{132})$ |
Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((3116,802,181)\) → \((e\left(\frac{1}{6}\right),i,e\left(\frac{2}{11}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 4005 }(2, a) \) | \(1\) | \(1\) | \(e\left(\frac{43}{132}\right)\) | \(e\left(\frac{43}{66}\right)\) | \(e\left(\frac{85}{132}\right)\) | \(e\left(\frac{43}{44}\right)\) | \(e\left(\frac{29}{66}\right)\) | \(e\left(\frac{35}{132}\right)\) | \(e\left(\frac{32}{33}\right)\) | \(e\left(\frac{10}{33}\right)\) | \(e\left(\frac{37}{44}\right)\) | \(e\left(\frac{19}{22}\right)\) |