Basic properties
Modulus: | \(5225\) | |
Conductor: | \(5225\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(180\) | 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 5225.ja
\(\chi_{5225}(53,\cdot)\) \(\chi_{5225}(97,\cdot)\) \(\chi_{5225}(192,\cdot)\) \(\chi_{5225}(223,\cdot)\) \(\chi_{5225}(488,\cdot)\) \(\chi_{5225}(603,\cdot)\) \(\chi_{5225}(763,\cdot)\) \(\chi_{5225}(773,\cdot)\) \(\chi_{5225}(808,\cdot)\) \(\chi_{5225}(922,\cdot)\) \(\chi_{5225}(927,\cdot)\) \(\chi_{5225}(1017,\cdot)\) \(\chi_{5225}(1048,\cdot)\) \(\chi_{5225}(1153,\cdot)\) \(\chi_{5225}(1313,\cdot)\) \(\chi_{5225}(1428,\cdot)\) \(\chi_{5225}(1477,\cdot)\) \(\chi_{5225}(1598,\cdot)\) \(\chi_{5225}(1687,\cdot)\) \(\chi_{5225}(1978,\cdot)\) \(\chi_{5225}(2027,\cdot)\) \(\chi_{5225}(2138,\cdot)\) \(\chi_{5225}(2237,\cdot)\) \(\chi_{5225}(2302,\cdot)\) \(\chi_{5225}(2423,\cdot)\) \(\chi_{5225}(2787,\cdot)\) \(\chi_{5225}(2803,\cdot)\) \(\chi_{5225}(2852,\cdot)\) \(\chi_{5225}(3062,\cdot)\) \(\chi_{5225}(3283,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{180})$ |
Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((2927,2851,4676)\) → \((e\left(\frac{7}{20}\right),e\left(\frac{3}{5}\right),e\left(\frac{11}{18}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
\( \chi_{ 5225 }(53, a) \) | \(1\) | \(1\) | \(e\left(\frac{101}{180}\right)\) | \(e\left(\frac{7}{36}\right)\) | \(e\left(\frac{11}{90}\right)\) | \(e\left(\frac{34}{45}\right)\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{11}{36}\right)\) | \(e\left(\frac{8}{45}\right)\) |