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 \(\chi_{805}(478,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4025.cz
\(\chi_{4025}(18,\cdot)\) \(\chi_{4025}(32,\cdot)\) \(\chi_{4025}(193,\cdot)\) \(\chi_{4025}(282,\cdot)\) \(\chi_{4025}(443,\cdot)\) \(\chi_{4025}(807,\cdot)\) \(\chi_{4025}(968,\cdot)\) \(\chi_{4025}(982,\cdot)\) \(\chi_{4025}(1143,\cdot)\) \(\chi_{4025}(1432,\cdot)\) \(\chi_{4025}(1507,\cdot)\) \(\chi_{4025}(1593,\cdot)\) \(\chi_{4025}(1668,\cdot)\) \(\chi_{4025}(1682,\cdot)\) \(\chi_{4025}(1843,\cdot)\) \(\chi_{4025}(1957,\cdot)\) \(\chi_{4025}(2032,\cdot)\) \(\chi_{4025}(2118,\cdot)\) \(\chi_{4025}(2132,\cdot)\) \(\chi_{4025}(2193,\cdot)\) \(\chi_{4025}(2293,\cdot)\) \(\chi_{4025}(2382,\cdot)\) \(\chi_{4025}(2543,\cdot)\) \(\chi_{4025}(2557,\cdot)\) \(\chi_{4025}(2657,\cdot)\) \(\chi_{4025}(2718,\cdot)\) \(\chi_{4025}(2732,\cdot)\) \(\chi_{4025}(2818,\cdot)\) \(\chi_{4025}(2832,\cdot)\) \(\chi_{4025}(2893,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{132})$ |
Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((2577,1151,3501)\) → \((-i,e\left(\frac{1}{3}\right),e\left(\frac{6}{11}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
\( \chi_{ 4025 }(2893, a) \) | \(-1\) | \(1\) | \(e\left(\frac{67}{132}\right)\) | \(e\left(\frac{41}{132}\right)\) | \(e\left(\frac{1}{66}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{23}{44}\right)\) | \(e\left(\frac{41}{66}\right)\) | \(e\left(\frac{8}{33}\right)\) | \(e\left(\frac{43}{132}\right)\) | \(e\left(\frac{39}{44}\right)\) | \(e\left(\frac{1}{33}\right)\) |