Basic properties
| Modulus: | \(81225\) | |
| Conductor: | \(9025\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(380\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{9025}(37,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 81225.lf
\(\chi_{81225}(37,\cdot)\) \(\chi_{81225}(208,\cdot)\) \(\chi_{81225}(892,\cdot)\) \(\chi_{81225}(1063,\cdot)\) \(\chi_{81225}(1747,\cdot)\) \(\chi_{81225}(2602,\cdot)\) \(\chi_{81225}(2773,\cdot)\) \(\chi_{81225}(3628,\cdot)\) \(\chi_{81225}(4312,\cdot)\) \(\chi_{81225}(4483,\cdot)\) \(\chi_{81225}(5167,\cdot)\) \(\chi_{81225}(5338,\cdot)\) \(\chi_{81225}(6022,\cdot)\) \(\chi_{81225}(6877,\cdot)\) \(\chi_{81225}(7048,\cdot)\) \(\chi_{81225}(7903,\cdot)\) \(\chi_{81225}(8587,\cdot)\) \(\chi_{81225}(8758,\cdot)\) \(\chi_{81225}(9442,\cdot)\) \(\chi_{81225}(9613,\cdot)\) \(\chi_{81225}(10297,\cdot)\) \(\chi_{81225}(11152,\cdot)\) \(\chi_{81225}(11323,\cdot)\) \(\chi_{81225}(12178,\cdot)\) \(\chi_{81225}(12862,\cdot)\) \(\chi_{81225}(13033,\cdot)\) \(\chi_{81225}(13888,\cdot)\) \(\chi_{81225}(14572,\cdot)\) \(\chi_{81225}(15427,\cdot)\) \(\chi_{81225}(15598,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{380})$ |
| Fixed field: | Number field defined by a degree 380 polynomial (not computed) |
Values on generators
\((36101,77977,48376)\) → \((1,e\left(\frac{9}{20}\right),e\left(\frac{5}{38}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(22\) |
| \( \chi_{ 81225 }(37, a) \) | \(1\) | \(1\) | \(e\left(\frac{221}{380}\right)\) | \(e\left(\frac{31}{190}\right)\) | \(e\left(\frac{75}{76}\right)\) | \(e\left(\frac{283}{380}\right)\) | \(e\left(\frac{59}{95}\right)\) | \(e\left(\frac{319}{380}\right)\) | \(e\left(\frac{54}{95}\right)\) | \(e\left(\frac{31}{95}\right)\) | \(e\left(\frac{223}{380}\right)\) | \(e\left(\frac{77}{380}\right)\) |