Basic properties
| Modulus: | \(5225\) | |
| Conductor: | \(1045\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(180\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1045}(118,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5225.jk
\(\chi_{5225}(118,\cdot)\) \(\chi_{5225}(282,\cdot)\) \(\chi_{5225}(332,\cdot)\) \(\chi_{5225}(557,\cdot)\) \(\chi_{5225}(568,\cdot)\) \(\chi_{5225}(1107,\cdot)\) \(\chi_{5225}(1118,\cdot)\) \(\chi_{5225}(1157,\cdot)\) \(\chi_{5225}(1168,\cdot)\) \(\chi_{5225}(1282,\cdot)\) \(\chi_{5225}(1393,\cdot)\) \(\chi_{5225}(1657,\cdot)\) \(\chi_{5225}(1707,\cdot)\) \(\chi_{5225}(1757,\cdot)\) \(\chi_{5225}(1943,\cdot)\) \(\chi_{5225}(1982,\cdot)\) \(\chi_{5225}(1993,\cdot)\) \(\chi_{5225}(2107,\cdot)\) \(\chi_{5225}(2118,\cdot)\) \(\chi_{5225}(2493,\cdot)\) \(\chi_{5225}(2532,\cdot)\) \(\chi_{5225}(2543,\cdot)\) \(\chi_{5225}(2582,\cdot)\) \(\chi_{5225}(2593,\cdot)\) \(\chi_{5225}(2657,\cdot)\) \(\chi_{5225}(2818,\cdot)\) \(\chi_{5225}(2932,\cdot)\) \(\chi_{5225}(2943,\cdot)\) \(\chi_{5225}(3082,\cdot)\) \(\chi_{5225}(3132,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{180})$ |
| Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((2927,2851,4676)\) → \((-i,e\left(\frac{3}{10}\right),e\left(\frac{1}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
| \( \chi_{ 5225 }(118, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{180}\right)\) | \(e\left(\frac{17}{180}\right)\) | \(e\left(\frac{29}{90}\right)\) | \(e\left(\frac{23}{90}\right)\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{29}{60}\right)\) | \(e\left(\frac{17}{90}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{19}{180}\right)\) | \(e\left(\frac{61}{90}\right)\) |