Basic properties
Modulus: | \(4025\) | |
Conductor: | \(805\) | 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 \(\chi_{805}(53,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4025.cy
\(\chi_{4025}(107,\cdot)\) \(\chi_{4025}(268,\cdot)\) \(\chi_{4025}(382,\cdot)\) \(\chi_{4025}(457,\cdot)\) \(\chi_{4025}(543,\cdot)\) \(\chi_{4025}(557,\cdot)\) \(\chi_{4025}(618,\cdot)\) \(\chi_{4025}(632,\cdot)\) \(\chi_{4025}(718,\cdot)\) \(\chi_{4025}(732,\cdot)\) \(\chi_{4025}(793,\cdot)\) \(\chi_{4025}(893,\cdot)\) \(\chi_{4025}(907,\cdot)\) \(\chi_{4025}(1068,\cdot)\) \(\chi_{4025}(1157,\cdot)\) \(\chi_{4025}(1257,\cdot)\) \(\chi_{4025}(1318,\cdot)\) \(\chi_{4025}(1332,\cdot)\) \(\chi_{4025}(1418,\cdot)\) \(\chi_{4025}(1493,\cdot)\) \(\chi_{4025}(1607,\cdot)\) \(\chi_{4025}(1768,\cdot)\) \(\chi_{4025}(1782,\cdot)\) \(\chi_{4025}(1857,\cdot)\) \(\chi_{4025}(1943,\cdot)\) \(\chi_{4025}(2018,\cdot)\) \(\chi_{4025}(2307,\cdot)\) \(\chi_{4025}(2468,\cdot)\) \(\chi_{4025}(2482,\cdot)\) \(\chi_{4025}(2643,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{132})$ |
Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((2577,1151,3501)\) → \((-i,e\left(\frac{2}{3}\right),e\left(\frac{19}{22}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
\( \chi_{ 4025 }(2468, a) \) | \(1\) | \(1\) | \(e\left(\frac{107}{132}\right)\) | \(e\left(\frac{97}{132}\right)\) | \(e\left(\frac{41}{66}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{19}{44}\right)\) | \(e\left(\frac{31}{66}\right)\) | \(e\left(\frac{29}{66}\right)\) | \(e\left(\frac{47}{132}\right)\) | \(e\left(\frac{15}{44}\right)\) | \(e\left(\frac{8}{33}\right)\) |