Basic properties
| Modulus: | \(21560\) | |
| Conductor: | \(21560\) | 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 21560.om
\(\chi_{21560}(173,\cdot)\) \(\chi_{21560}(437,\cdot)\) \(\chi_{21560}(453,\cdot)\) \(\chi_{21560}(677,\cdot)\) \(\chi_{21560}(733,\cdot)\) \(\chi_{21560}(997,\cdot)\) \(\chi_{21560}(1053,\cdot)\) \(\chi_{21560}(1333,\cdot)\) \(\chi_{21560}(1557,\cdot)\) \(\chi_{21560}(1613,\cdot)\) \(\chi_{21560}(2173,\cdot)\) \(\chi_{21560}(2637,\cdot)\) \(\chi_{21560}(2917,\cdot)\) \(\chi_{21560}(3197,\cdot)\) \(\chi_{21560}(3517,\cdot)\) \(\chi_{21560}(3533,\cdot)\) \(\chi_{21560}(3757,\cdot)\) \(\chi_{21560}(3797,\cdot)\) \(\chi_{21560}(3813,\cdot)\) \(\chi_{21560}(4077,\cdot)\) \(\chi_{21560}(4133,\cdot)\) \(\chi_{21560}(4373,\cdot)\) \(\chi_{21560}(4413,\cdot)\) \(\chi_{21560}(4693,\cdot)\) \(\chi_{21560}(5253,\cdot)\) \(\chi_{21560}(5717,\cdot)\) \(\chi_{21560}(6277,\cdot)\) \(\chi_{21560}(6333,\cdot)\) \(\chi_{21560}(6613,\cdot)\) \(\chi_{21560}(6837,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{420})$ |
| Fixed field: | Number field defined by a degree 420 polynomial (not computed) |
Values on generators
\((5391,10781,12937,20681,11761)\) → \((1,-1,-i,e\left(\frac{37}{42}\right),e\left(\frac{7}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 21560 }(10853, a) \) | \(-1\) | \(1\) | \(e\left(\frac{97}{420}\right)\) | \(e\left(\frac{97}{210}\right)\) | \(e\left(\frac{73}{140}\right)\) | \(e\left(\frac{31}{420}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{61}{84}\right)\) | \(e\left(\frac{97}{140}\right)\) | \(e\left(\frac{53}{70}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{353}{420}\right)\) |