Basic properties
| Modulus: | \(43120\) | |
| 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 43120.xs
\(\chi_{43120}(73,\cdot)\) \(\chi_{43120}(633,\cdot)\) \(\chi_{43120}(1657,\cdot)\) \(\chi_{43120}(1977,\cdot)\) \(\chi_{43120}(1993,\cdot)\) \(\chi_{43120}(2217,\cdot)\) \(\chi_{43120}(2537,\cdot)\) \(\chi_{43120}(3097,\cdot)\) \(\chi_{43120}(4457,\cdot)\) \(\chi_{43120}(4793,\cdot)\) \(\chi_{43120}(5337,\cdot)\) \(\chi_{43120}(5353,\cdot)\) \(\chi_{43120}(5673,\cdot)\) \(\chi_{43120}(5913,\cdot)\) \(\chi_{43120}(6233,\cdot)\) \(\chi_{43120}(7257,\cdot)\) \(\chi_{43120}(7817,\cdot)\) \(\chi_{43120}(8137,\cdot)\) \(\chi_{43120}(8377,\cdot)\) \(\chi_{43120}(8697,\cdot)\) \(\chi_{43120}(9033,\cdot)\) \(\chi_{43120}(9257,\cdot)\) \(\chi_{43120}(10617,\cdot)\) \(\chi_{43120}(10953,\cdot)\) \(\chi_{43120}(11513,\cdot)\) \(\chi_{43120}(11833,\cdot)\) \(\chi_{43120}(12393,\cdot)\) \(\chi_{43120}(12953,\cdot)\) \(\chi_{43120}(13417,\cdot)\) \(\chi_{43120}(13977,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{420})$ |
| Fixed field: | Number field defined by a degree 420 polynomial (not computed) |
Values on generators
\((5391,32341,34497,42241,11761)\) → \((1,-1,-i,e\left(\frac{37}{42}\right),e\left(\frac{7}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 43120 }(73, a) \) | \(-1\) | \(1\) | \(e\left(\frac{97}{420}\right)\) | \(e\left(\frac{97}{210}\right)\) | \(e\left(\frac{73}{140}\right)\) | \(e\left(\frac{31}{420}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{61}{84}\right)\) | \(e\left(\frac{97}{140}\right)\) | \(e\left(\frac{53}{70}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{353}{420}\right)\) |