Basic properties
| Modulus: | \(43120\) | |
| Conductor: | \(43120\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(420\) | 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 43120.yk
\(\chi_{43120}(37,\cdot)\) \(\chi_{43120}(93,\cdot)\) \(\chi_{43120}(333,\cdot)\) \(\chi_{43120}(597,\cdot)\) \(\chi_{43120}(653,\cdot)\) \(\chi_{43120}(1213,\cdot)\) \(\chi_{43120}(3133,\cdot)\) \(\chi_{43120}(3397,\cdot)\) \(\chi_{43120}(4013,\cdot)\) \(\chi_{43120}(4757,\cdot)\) \(\chi_{43120}(5317,\cdot)\) \(\chi_{43120}(5373,\cdot)\) \(\chi_{43120}(5637,\cdot)\) \(\chi_{43120}(5877,\cdot)\) \(\chi_{43120}(5933,\cdot)\) \(\chi_{43120}(6197,\cdot)\) \(\chi_{43120}(6493,\cdot)\) \(\chi_{43120}(6757,\cdot)\) \(\chi_{43120}(6813,\cdot)\) \(\chi_{43120}(7373,\cdot)\) \(\chi_{43120}(8677,\cdot)\) \(\chi_{43120}(9293,\cdot)\) \(\chi_{43120}(9557,\cdot)\) \(\chi_{43120}(10917,\cdot)\) \(\chi_{43120}(11477,\cdot)\) \(\chi_{43120}(11797,\cdot)\) \(\chi_{43120}(12037,\cdot)\) \(\chi_{43120}(12093,\cdot)\) \(\chi_{43120}(12357,\cdot)\) \(\chi_{43120}(12413,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{420})$ |
| Fixed field: | Number field defined by a degree 420 polynomial (not computed) |
Values on generators
\((5391,32341,34497,42241,11761)\) → \((1,-i,-i,e\left(\frac{4}{21}\right),e\left(\frac{2}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 43120 }(93, a) \) | \(-1\) | \(1\) | \(e\left(\frac{187}{210}\right)\) | \(e\left(\frac{82}{105}\right)\) | \(e\left(\frac{13}{70}\right)\) | \(e\left(\frac{47}{420}\right)\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{83}{84}\right)\) | \(e\left(\frac{47}{70}\right)\) | \(e\left(\frac{137}{140}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{83}{210}\right)\) |