Basic properties
| Modulus: | \(5225\) | |
| Conductor: | \(5225\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(180\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| 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.iw
\(\chi_{5225}(142,\cdot)\) \(\chi_{5225}(252,\cdot)\) \(\chi_{5225}(263,\cdot)\) \(\chi_{5225}(472,\cdot)\) \(\chi_{5225}(538,\cdot)\) \(\chi_{5225}(747,\cdot)\) \(\chi_{5225}(758,\cdot)\) \(\chi_{5225}(802,\cdot)\) \(\chi_{5225}(967,\cdot)\) \(\chi_{5225}(978,\cdot)\) \(\chi_{5225}(1088,\cdot)\) \(\chi_{5225}(1187,\cdot)\) \(\chi_{5225}(1297,\cdot)\) \(\chi_{5225}(1308,\cdot)\) \(\chi_{5225}(1517,\cdot)\) \(\chi_{5225}(1583,\cdot)\) \(\chi_{5225}(1638,\cdot)\) \(\chi_{5225}(1792,\cdot)\) \(\chi_{5225}(1803,\cdot)\) \(\chi_{5225}(1847,\cdot)\) \(\chi_{5225}(2012,\cdot)\) \(\chi_{5225}(2023,\cdot)\) \(\chi_{5225}(2133,\cdot)\) \(\chi_{5225}(2342,\cdot)\) \(\chi_{5225}(2353,\cdot)\) \(\chi_{5225}(2562,\cdot)\) \(\chi_{5225}(2628,\cdot)\) \(\chi_{5225}(2683,\cdot)\) \(\chi_{5225}(2837,\cdot)\) \(\chi_{5225}(2848,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{180})$ |
| Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((2927,2851,4676)\) → \((e\left(\frac{13}{20}\right),-1,e\left(\frac{4}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
| \( \chi_{ 5225 }(142, a) \) | \(1\) | \(1\) | \(e\left(\frac{107}{180}\right)\) | \(e\left(\frac{59}{180}\right)\) | \(e\left(\frac{17}{90}\right)\) | \(e\left(\frac{83}{90}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{59}{90}\right)\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{13}{180}\right)\) | \(e\left(\frac{1}{90}\right)\) |