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 \(\chi_{9025}(1272,\cdot)\) | 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
\((36101,77977,48376)\) → \((1,e\left(\frac{17}{20}\right),e\left(\frac{25}{38}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(22\) |
\( \chi_{ 81225 }(10297, a) \) | \(1\) | \(1\) | \(e\left(\frac{193}{380}\right)\) | \(e\left(\frac{3}{190}\right)\) | \(e\left(\frac{71}{76}\right)\) | \(e\left(\frac{199}{380}\right)\) | \(e\left(\frac{67}{95}\right)\) | \(e\left(\frac{227}{380}\right)\) | \(e\left(\frac{42}{95}\right)\) | \(e\left(\frac{3}{95}\right)\) | \(e\left(\frac{279}{380}\right)\) | \(e\left(\frac{81}{380}\right)\) |