Basic properties
| Modulus: | \(388080\) | |
| Conductor: | \(97020\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(420\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{97020}(47,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 388080.ekm
\(\chi_{388080}(47,\cdot)\) \(\chi_{388080}(5087,\cdot)\) \(\chi_{388080}(9887,\cdot)\) \(\chi_{388080}(15167,\cdot)\) \(\chi_{388080}(16943,\cdot)\) \(\chi_{388080}(22223,\cdot)\) \(\chi_{388080}(25007,\cdot)\) \(\chi_{388080}(30287,\cdot)\) \(\chi_{388080}(32063,\cdot)\) \(\chi_{388080}(37343,\cdot)\) \(\chi_{388080}(47183,\cdot)\) \(\chi_{388080}(52463,\cdot)\) \(\chi_{388080}(55247,\cdot)\) \(\chi_{388080}(60527,\cdot)\) \(\chi_{388080}(65327,\cdot)\) \(\chi_{388080}(70607,\cdot)\) \(\chi_{388080}(72383,\cdot)\) \(\chi_{388080}(77423,\cdot)\) \(\chi_{388080}(77663,\cdot)\) \(\chi_{388080}(80447,\cdot)\) \(\chi_{388080}(82703,\cdot)\) \(\chi_{388080}(85727,\cdot)\) \(\chi_{388080}(87503,\cdot)\) \(\chi_{388080}(92783,\cdot)\) \(\chi_{388080}(102623,\cdot)\) \(\chi_{388080}(105647,\cdot)\) \(\chi_{388080}(107903,\cdot)\) \(\chi_{388080}(110687,\cdot)\) \(\chi_{388080}(110927,\cdot)\) \(\chi_{388080}(115967,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{420})$ |
| Fixed field: | Number field defined by a degree 420 polynomial (not computed) |
Values on generators
\((48511,291061,43121,77617,300961,141121)\) → \((-1,1,e\left(\frac{1}{6}\right),i,e\left(\frac{5}{42}\right),e\left(\frac{4}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) | \(47\) |
| \( \chi_{ 388080 }(47, a) \) | \(1\) | \(1\) | \(e\left(\frac{341}{420}\right)\) | \(e\left(\frac{389}{420}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{43}{105}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{277}{420}\right)\) | \(e\left(\frac{2}{105}\right)\) | \(e\left(\frac{53}{84}\right)\) | \(e\left(\frac{383}{420}\right)\) |