Basic properties
| Modulus: | \(81225\) | |
| Conductor: | \(9025\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(570\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{9025}(46,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 81225.lu
\(\chi_{81225}(46,\cdot)\) \(\chi_{81225}(316,\cdot)\) \(\chi_{81225}(1171,\cdot)\) \(\chi_{81225}(1756,\cdot)\) \(\chi_{81225}(2611,\cdot)\) \(\chi_{81225}(2881,\cdot)\) \(\chi_{81225}(3466,\cdot)\) \(\chi_{81225}(3736,\cdot)\) \(\chi_{81225}(4321,\cdot)\) \(\chi_{81225}(4591,\cdot)\) \(\chi_{81225}(5446,\cdot)\) \(\chi_{81225}(6031,\cdot)\) \(\chi_{81225}(6886,\cdot)\) \(\chi_{81225}(7156,\cdot)\) \(\chi_{81225}(7741,\cdot)\) \(\chi_{81225}(8866,\cdot)\) \(\chi_{81225}(9721,\cdot)\) \(\chi_{81225}(10306,\cdot)\) \(\chi_{81225}(11161,\cdot)\) \(\chi_{81225}(11431,\cdot)\) \(\chi_{81225}(12016,\cdot)\) \(\chi_{81225}(12286,\cdot)\) \(\chi_{81225}(12871,\cdot)\) \(\chi_{81225}(13141,\cdot)\) \(\chi_{81225}(13996,\cdot)\) \(\chi_{81225}(14581,\cdot)\) \(\chi_{81225}(15436,\cdot)\) \(\chi_{81225}(15706,\cdot)\) \(\chi_{81225}(16291,\cdot)\) \(\chi_{81225}(16561,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{285})$ |
| Fixed field: | Number field defined by a degree 570 polynomial (not computed) |
Values on generators
\((36101,77977,48376)\) → \((1,e\left(\frac{3}{5}\right),e\left(\frac{49}{114}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(22\) |
| \( \chi_{ 81225 }(46, a) \) | \(-1\) | \(1\) | \(e\left(\frac{17}{570}\right)\) | \(e\left(\frac{17}{285}\right)\) | \(e\left(\frac{9}{19}\right)\) | \(e\left(\frac{17}{190}\right)\) | \(e\left(\frac{42}{95}\right)\) | \(e\left(\frac{463}{570}\right)\) | \(e\left(\frac{287}{570}\right)\) | \(e\left(\frac{34}{285}\right)\) | \(e\left(\frac{268}{285}\right)\) | \(e\left(\frac{269}{570}\right)\) |