Basic properties
| Modulus: | \(81225\) | |
| Conductor: | \(81225\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(570\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 81225.mb
\(\chi_{81225}(11,\cdot)\) \(\chi_{81225}(311,\cdot)\) \(\chi_{81225}(866,\cdot)\) \(\chi_{81225}(1166,\cdot)\) \(\chi_{81225}(1721,\cdot)\) \(\chi_{81225}(2021,\cdot)\) \(\chi_{81225}(3431,\cdot)\) \(\chi_{81225}(3731,\cdot)\) \(\chi_{81225}(4286,\cdot)\) \(\chi_{81225}(4586,\cdot)\) \(\chi_{81225}(5141,\cdot)\) \(\chi_{81225}(5441,\cdot)\) \(\chi_{81225}(5996,\cdot)\) \(\chi_{81225}(6296,\cdot)\) \(\chi_{81225}(7706,\cdot)\) \(\chi_{81225}(8006,\cdot)\) \(\chi_{81225}(8561,\cdot)\) \(\chi_{81225}(8861,\cdot)\) \(\chi_{81225}(9416,\cdot)\) \(\chi_{81225}(9716,\cdot)\) \(\chi_{81225}(10271,\cdot)\) \(\chi_{81225}(10571,\cdot)\) \(\chi_{81225}(12281,\cdot)\) \(\chi_{81225}(12836,\cdot)\) \(\chi_{81225}(13136,\cdot)\) \(\chi_{81225}(13691,\cdot)\) \(\chi_{81225}(13991,\cdot)\) \(\chi_{81225}(14546,\cdot)\) \(\chi_{81225}(14846,\cdot)\) \(\chi_{81225}(16256,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{285})$ |
| Fixed field: | Number field defined by a degree 570 polynomial (not computed) |
Values on generators
\((36101,77977,48376)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{4}{5}\right),e\left(\frac{17}{57}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(22\) |
| \( \chi_{ 81225 }(11, a) \) | \(-1\) | \(1\) | \(e\left(\frac{151}{570}\right)\) | \(e\left(\frac{151}{285}\right)\) | \(e\left(\frac{23}{57}\right)\) | \(e\left(\frac{151}{190}\right)\) | \(e\left(\frac{221}{570}\right)\) | \(e\left(\frac{187}{285}\right)\) | \(e\left(\frac{127}{190}\right)\) | \(e\left(\frac{17}{285}\right)\) | \(e\left(\frac{173}{570}\right)\) | \(e\left(\frac{62}{95}\right)\) |