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.dw
\(\chi_{4005}(68,\cdot)\) \(\chi_{4005}(218,\cdot)\) \(\chi_{4005}(227,\cdot)\) \(\chi_{4005}(257,\cdot)\) \(\chi_{4005}(338,\cdot)\) \(\chi_{4005}(392,\cdot)\) \(\chi_{4005}(632,\cdot)\) \(\chi_{4005}(707,\cdot)\) \(\chi_{4005}(848,\cdot)\) \(\chi_{4005}(932,\cdot)\) \(\chi_{4005}(1073,\cdot)\) \(\chi_{4005}(1148,\cdot)\) \(\chi_{4005}(1388,\cdot)\) \(\chi_{4005}(1442,\cdot)\) \(\chi_{4005}(1523,\cdot)\) \(\chi_{4005}(1553,\cdot)\) \(\chi_{4005}(1562,\cdot)\) \(\chi_{4005}(1712,\cdot)\) \(\chi_{4005}(1967,\cdot)\) \(\chi_{4005}(2027,\cdot)\) \(\chi_{4005}(2153,\cdot)\) \(\chi_{4005}(2183,\cdot)\) \(\chi_{4005}(2297,\cdot)\) \(\chi_{4005}(2408,\cdot)\) \(\chi_{4005}(2423,\cdot)\) \(\chi_{4005}(2723,\cdot)\) \(\chi_{4005}(2738,\cdot)\) \(\chi_{4005}(2777,\cdot)\) \(\chi_{4005}(2858,\cdot)\) \(\chi_{4005}(2927,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{132})$ |
Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((3116,802,181)\) → \((e\left(\frac{5}{6}\right),-i,e\left(\frac{19}{44}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 4005 }(68, a) \) | \(1\) | \(1\) | \(e\left(\frac{65}{132}\right)\) | \(e\left(\frac{65}{66}\right)\) | \(e\left(\frac{2}{33}\right)\) | \(e\left(\frac{21}{44}\right)\) | \(e\left(\frac{7}{66}\right)\) | \(e\left(\frac{28}{33}\right)\) | \(e\left(\frac{73}{132}\right)\) | \(e\left(\frac{32}{33}\right)\) | \(e\left(\frac{37}{44}\right)\) | \(e\left(\frac{27}{44}\right)\) |