Basic properties
Modulus: | \(4235\) | |
Conductor: | \(4235\) | 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
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4235.da
\(\chi_{4235}(12,\cdot)\) \(\chi_{4235}(353,\cdot)\) \(\chi_{4235}(397,\cdot)\) \(\chi_{4235}(507,\cdot)\) \(\chi_{4235}(628,\cdot)\) \(\chi_{4235}(738,\cdot)\) \(\chi_{4235}(782,\cdot)\) \(\chi_{4235}(892,\cdot)\) \(\chi_{4235}(1013,\cdot)\) \(\chi_{4235}(1123,\cdot)\) \(\chi_{4235}(1167,\cdot)\) \(\chi_{4235}(1277,\cdot)\) \(\chi_{4235}(1398,\cdot)\) \(\chi_{4235}(1508,\cdot)\) \(\chi_{4235}(1552,\cdot)\) \(\chi_{4235}(1662,\cdot)\) \(\chi_{4235}(1783,\cdot)\) \(\chi_{4235}(1893,\cdot)\) \(\chi_{4235}(2047,\cdot)\) \(\chi_{4235}(2168,\cdot)\) \(\chi_{4235}(2278,\cdot)\) \(\chi_{4235}(2322,\cdot)\) \(\chi_{4235}(2432,\cdot)\) \(\chi_{4235}(2553,\cdot)\) \(\chi_{4235}(2707,\cdot)\) \(\chi_{4235}(2817,\cdot)\) \(\chi_{4235}(2938,\cdot)\) \(\chi_{4235}(3048,\cdot)\) \(\chi_{4235}(3092,\cdot)\) \(\chi_{4235}(3202,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{132})$ |
Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((2542,1816,2906)\) → \((-i,e\left(\frac{1}{6}\right),e\left(\frac{8}{11}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(12\) | \(13\) | \(16\) | \(17\) |
\( \chi_{ 4235 }(1893, a) \) | \(1\) | \(1\) | \(e\left(\frac{107}{132}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{41}{66}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{19}{44}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{132}\right)\) | \(e\left(\frac{9}{44}\right)\) | \(e\left(\frac{8}{33}\right)\) | \(e\left(\frac{73}{132}\right)\) |