Basic properties
Modulus: | \(4005\) | |
Conductor: | \(801\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(132\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{801}(529,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4005.dz
\(\chi_{4005}(106,\cdot)\) \(\chi_{4005}(196,\cdot)\) \(\chi_{4005}(346,\cdot)\) \(\chi_{4005}(376,\cdot)\) \(\chi_{4005}(436,\cdot)\) \(\chi_{4005}(466,\cdot)\) \(\chi_{4005}(481,\cdot)\) \(\chi_{4005}(691,\cdot)\) \(\chi_{4005}(781,\cdot)\) \(\chi_{4005}(796,\cdot)\) \(\chi_{4005}(841,\cdot)\) \(\chi_{4005}(961,\cdot)\) \(\chi_{4005}(1021,\cdot)\) \(\chi_{4005}(1051,\cdot)\) \(\chi_{4005}(1471,\cdot)\) \(\chi_{4005}(1651,\cdot)\) \(\chi_{4005}(1681,\cdot)\) \(\chi_{4005}(1696,\cdot)\) \(\chi_{4005}(1771,\cdot)\) \(\chi_{4005}(1816,\cdot)\) \(\chi_{4005}(2011,\cdot)\) \(\chi_{4005}(2056,\cdot)\) \(\chi_{4005}(2131,\cdot)\) \(\chi_{4005}(2146,\cdot)\) \(\chi_{4005}(2176,\cdot)\) \(\chi_{4005}(2356,\cdot)\) \(\chi_{4005}(2776,\cdot)\) \(\chi_{4005}(2806,\cdot)\) \(\chi_{4005}(2866,\cdot)\) \(\chi_{4005}(2986,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{132})$ |
Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((3116,802,181)\) → \((e\left(\frac{2}{3}\right),1,e\left(\frac{13}{44}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 4005 }(2131, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{33}\right)\) | \(e\left(\frac{26}{33}\right)\) | \(e\left(\frac{79}{132}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{16}{33}\right)\) | \(e\left(\frac{17}{132}\right)\) | \(e\left(\frac{131}{132}\right)\) | \(e\left(\frac{19}{33}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{15}{44}\right)\) |