Basic properties
| Modulus: | \(81225\) | |
| Conductor: | \(16245\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(228\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{16245}(2743,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 81225.kb
\(\chi_{81225}(7,\cdot)\) \(\chi_{81225}(2443,\cdot)\) \(\chi_{81225}(2743,\cdot)\) \(\chi_{81225}(3982,\cdot)\) \(\chi_{81225}(4282,\cdot)\) \(\chi_{81225}(6718,\cdot)\) \(\chi_{81225}(7018,\cdot)\) \(\chi_{81225}(8257,\cdot)\) \(\chi_{81225}(8557,\cdot)\) \(\chi_{81225}(10993,\cdot)\) \(\chi_{81225}(11293,\cdot)\) \(\chi_{81225}(12532,\cdot)\) \(\chi_{81225}(12832,\cdot)\) \(\chi_{81225}(15268,\cdot)\) \(\chi_{81225}(15568,\cdot)\) \(\chi_{81225}(16807,\cdot)\) \(\chi_{81225}(17107,\cdot)\) \(\chi_{81225}(19543,\cdot)\) \(\chi_{81225}(19843,\cdot)\) \(\chi_{81225}(21082,\cdot)\) \(\chi_{81225}(21382,\cdot)\) \(\chi_{81225}(23818,\cdot)\) \(\chi_{81225}(25357,\cdot)\) \(\chi_{81225}(25657,\cdot)\) \(\chi_{81225}(28093,\cdot)\) \(\chi_{81225}(28393,\cdot)\) \(\chi_{81225}(29632,\cdot)\) \(\chi_{81225}(29932,\cdot)\) \(\chi_{81225}(32368,\cdot)\) \(\chi_{81225}(32668,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{228})$ |
| Fixed field: | Number field defined by a degree 228 polynomial (not computed) |
Values on generators
\((36101,77977,48376)\) → \((e\left(\frac{2}{3}\right),-i,e\left(\frac{13}{57}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(22\) |
| \( \chi_{ 81225 }(2743, a) \) | \(-1\) | \(1\) | \(e\left(\frac{49}{76}\right)\) | \(e\left(\frac{11}{38}\right)\) | \(e\left(\frac{143}{228}\right)\) | \(e\left(\frac{71}{76}\right)\) | \(e\left(\frac{53}{57}\right)\) | \(e\left(\frac{47}{76}\right)\) | \(e\left(\frac{31}{114}\right)\) | \(e\left(\frac{11}{19}\right)\) | \(e\left(\frac{67}{228}\right)\) | \(e\left(\frac{131}{228}\right)\) |