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.ds
\(\chi_{4005}(203,\cdot)\) \(\chi_{4005}(263,\cdot)\) \(\chi_{4005}(317,\cdot)\) \(\chi_{4005}(437,\cdot)\) \(\chi_{4005}(443,\cdot)\) \(\chi_{4005}(518,\cdot)\) \(\chi_{4005}(578,\cdot)\) \(\chi_{4005}(797,\cdot)\) \(\chi_{4005}(812,\cdot)\) \(\chi_{4005}(947,\cdot)\) \(\chi_{4005}(977,\cdot)\) \(\chi_{4005}(1112,\cdot)\) \(\chi_{4005}(1118,\cdot)\) \(\chi_{4005}(1238,\cdot)\) \(\chi_{4005}(1598,\cdot)\) \(\chi_{4005}(1613,\cdot)\) \(\chi_{4005}(1652,\cdot)\) \(\chi_{4005}(1748,\cdot)\) \(\chi_{4005}(1778,\cdot)\) \(\chi_{4005}(1802,\cdot)\) \(\chi_{4005}(1913,\cdot)\) \(\chi_{4005}(2072,\cdot)\) \(\chi_{4005}(2147,\cdot)\) \(\chi_{4005}(2282,\cdot)\) \(\chi_{4005}(2387,\cdot)\) \(\chi_{4005}(2453,\cdot)\) \(\chi_{4005}(2603,\cdot)\) \(\chi_{4005}(2873,\cdot)\) \(\chi_{4005}(2948,\cdot)\) \(\chi_{4005}(3083,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{132})$ |
Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((3116,802,181)\) → \((e\left(\frac{5}{6}\right),-i,e\left(\frac{13}{22}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 4005 }(203, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{132}\right)\) | \(e\left(\frac{5}{66}\right)\) | \(e\left(\frac{125}{132}\right)\) | \(e\left(\frac{5}{44}\right)\) | \(e\left(\frac{31}{66}\right)\) | \(e\left(\frac{67}{132}\right)\) | \(e\left(\frac{65}{66}\right)\) | \(e\left(\frac{5}{33}\right)\) | \(e\left(\frac{35}{44}\right)\) | \(e\left(\frac{2}{11}\right)\) |