Basic properties
Modulus: | \(4025\) | |
Conductor: | \(4025\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(110\) | 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 4025.cv
\(\chi_{4025}(111,\cdot)\) \(\chi_{4025}(181,\cdot)\) \(\chi_{4025}(286,\cdot)\) \(\chi_{4025}(356,\cdot)\) \(\chi_{4025}(566,\cdot)\) \(\chi_{4025}(636,\cdot)\) \(\chi_{4025}(741,\cdot)\) \(\chi_{4025}(881,\cdot)\) \(\chi_{4025}(916,\cdot)\) \(\chi_{4025}(986,\cdot)\) \(\chi_{4025}(1056,\cdot)\) \(\chi_{4025}(1091,\cdot)\) \(\chi_{4025}(1161,\cdot)\) \(\chi_{4025}(1371,\cdot)\) \(\chi_{4025}(1441,\cdot)\) \(\chi_{4025}(1546,\cdot)\) \(\chi_{4025}(1581,\cdot)\) \(\chi_{4025}(1686,\cdot)\) \(\chi_{4025}(1721,\cdot)\) \(\chi_{4025}(1791,\cdot)\) \(\chi_{4025}(1861,\cdot)\) \(\chi_{4025}(1896,\cdot)\) \(\chi_{4025}(1966,\cdot)\) \(\chi_{4025}(2246,\cdot)\) \(\chi_{4025}(2386,\cdot)\) \(\chi_{4025}(2491,\cdot)\) \(\chi_{4025}(2596,\cdot)\) \(\chi_{4025}(2666,\cdot)\) \(\chi_{4025}(2771,\cdot)\) \(\chi_{4025}(2981,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{55})$ |
Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((2577,1151,3501)\) → \((e\left(\frac{3}{5}\right),-1,e\left(\frac{9}{22}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
\( \chi_{ 4025 }(2771, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{55}\right)\) | \(e\left(\frac{27}{110}\right)\) | \(e\left(\frac{46}{55}\right)\) | \(e\left(\frac{73}{110}\right)\) | \(e\left(\frac{14}{55}\right)\) | \(e\left(\frac{27}{55}\right)\) | \(e\left(\frac{31}{110}\right)\) | \(e\left(\frac{9}{110}\right)\) | \(e\left(\frac{69}{110}\right)\) | \(e\left(\frac{37}{55}\right)\) |