Basic properties
| Modulus: | \(388080\) | |
| Conductor: | \(21560\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(420\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{21560}(10853,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 388080.elv
\(\chi_{388080}(73,\cdot)\) \(\chi_{388080}(1657,\cdot)\) \(\chi_{388080}(3097,\cdot)\) \(\chi_{388080}(8137,\cdot)\) \(\chi_{388080}(15193,\cdot)\) \(\chi_{388080}(25273,\cdot)\) \(\chi_{388080}(26857,\cdot)\) \(\chi_{388080}(31897,\cdot)\) \(\chi_{388080}(33337,\cdot)\) \(\chi_{388080}(38953,\cdot)\) \(\chi_{388080}(48457,\cdot)\) \(\chi_{388080}(49033,\cdot)\) \(\chi_{388080}(54073,\cdot)\) \(\chi_{388080}(55513,\cdot)\) \(\chi_{388080}(57097,\cdot)\) \(\chi_{388080}(63577,\cdot)\) \(\chi_{388080}(70633,\cdot)\) \(\chi_{388080}(72217,\cdot)\) \(\chi_{388080}(79273,\cdot)\) \(\chi_{388080}(80713,\cdot)\) \(\chi_{388080}(82297,\cdot)\) \(\chi_{388080}(85753,\cdot)\) \(\chi_{388080}(88777,\cdot)\) \(\chi_{388080}(103897,\cdot)\) \(\chi_{388080}(104473,\cdot)\) \(\chi_{388080}(109513,\cdot)\) \(\chi_{388080}(110953,\cdot)\) \(\chi_{388080}(112537,\cdot)\) \(\chi_{388080}(113977,\cdot)\) \(\chi_{388080}(119017,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{420})$ |
| Fixed field: | Number field defined by a degree 420 polynomial (not computed) |
Values on generators
\((48511,291061,43121,77617,300961,141121)\) → \((1,-1,1,-i,e\left(\frac{37}{42}\right),e\left(\frac{7}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) | \(47\) |
| \( \chi_{ 388080 }(73, a) \) | \(-1\) | \(1\) | \(e\left(\frac{73}{140}\right)\) | \(e\left(\frac{31}{420}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{61}{84}\right)\) | \(e\left(\frac{53}{70}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{353}{420}\right)\) | \(e\left(\frac{11}{35}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{317}{420}\right)\) |