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.jg
\(\chi_{5225}(3,\cdot)\) \(\chi_{5225}(148,\cdot)\) \(\chi_{5225}(262,\cdot)\) \(\chi_{5225}(433,\cdot)\) \(\chi_{5225}(553,\cdot)\) \(\chi_{5225}(642,\cdot)\) \(\chi_{5225}(698,\cdot)\) \(\chi_{5225}(713,\cdot)\) \(\chi_{5225}(812,\cdot)\) \(\chi_{5225}(983,\cdot)\) \(\chi_{5225}(1192,\cdot)\) \(\chi_{5225}(1248,\cdot)\) \(\chi_{5225}(1362,\cdot)\) \(\chi_{5225}(1378,\cdot)\) \(\chi_{5225}(1402,\cdot)\) \(\chi_{5225}(1523,\cdot)\) \(\chi_{5225}(1533,\cdot)\) \(\chi_{5225}(1637,\cdot)\) \(\chi_{5225}(1742,\cdot)\) \(\chi_{5225}(1808,\cdot)\) \(\chi_{5225}(1952,\cdot)\) \(\chi_{5225}(1972,\cdot)\) \(\chi_{5225}(2017,\cdot)\) \(\chi_{5225}(2073,\cdot)\) \(\chi_{5225}(2187,\cdot)\) \(\chi_{5225}(2358,\cdot)\) \(\chi_{5225}(2502,\cdot)\) \(\chi_{5225}(2522,\cdot)\) \(\chi_{5225}(2567,\cdot)\) \(\chi_{5225}(2777,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{180})$ |
| Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((2927,2851,4676)\) → \((e\left(\frac{7}{20}\right),e\left(\frac{4}{5}\right),e\left(\frac{13}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
| \( \chi_{ 5225 }(3, a) \) | \(1\) | \(1\) | \(e\left(\frac{157}{180}\right)\) | \(e\left(\frac{43}{180}\right)\) | \(e\left(\frac{67}{90}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{43}{90}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{11}{180}\right)\) | \(e\left(\frac{5}{9}\right)\) |