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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 43120.xe
\(\chi_{43120}(59,\cdot)\) \(\chi_{43120}(339,\cdot)\) \(\chi_{43120}(1699,\cdot)\) \(\chi_{43120}(2259,\cdot)\) \(\chi_{43120}(2539,\cdot)\) \(\chi_{43120}(2819,\cdot)\) \(\chi_{43120}(3139,\cdot)\) \(\chi_{43120}(3419,\cdot)\) \(\chi_{43120}(3699,\cdot)\) \(\chi_{43120}(4779,\cdot)\) \(\chi_{43120}(5339,\cdot)\) \(\chi_{43120}(5619,\cdot)\) \(\chi_{43120}(5659,\cdot)\) \(\chi_{43120}(6219,\cdot)\) \(\chi_{43120}(6779,\cdot)\) \(\chi_{43120}(8419,\cdot)\) \(\chi_{43120}(8699,\cdot)\) \(\chi_{43120}(8739,\cdot)\) \(\chi_{43120}(8979,\cdot)\) \(\chi_{43120}(9299,\cdot)\) \(\chi_{43120}(9579,\cdot)\) \(\chi_{43120}(9859,\cdot)\) \(\chi_{43120}(10939,\cdot)\) \(\chi_{43120}(11499,\cdot)\) \(\chi_{43120}(11819,\cdot)\) \(\chi_{43120}(12059,\cdot)\) \(\chi_{43120}(12659,\cdot)\) \(\chi_{43120}(12939,\cdot)\) \(\chi_{43120}(14019,\cdot)\) \(\chi_{43120}(14579,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{420})$ |
| Fixed field: | Number field defined by a degree 420 polynomial (not computed) |
Values on generators
\((5391,32341,34497,42241,11761)\) → \((-1,i,-1,e\left(\frac{13}{42}\right),e\left(\frac{1}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 43120 }(59, a) \) | \(1\) | \(1\) | \(e\left(\frac{277}{420}\right)\) | \(e\left(\frac{67}{210}\right)\) | \(e\left(\frac{93}{140}\right)\) | \(e\left(\frac{4}{105}\right)\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{137}{140}\right)\) | \(e\left(\frac{101}{140}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{23}{420}\right)\) |