Basic properties
| Modulus: | \(4730\) | |
| Conductor: | \(2365\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(420\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2365}(53,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4730.dq
\(\chi_{4730}(53,\cdot)\) \(\chi_{4730}(103,\cdot)\) \(\chi_{4730}(203,\cdot)\) \(\chi_{4730}(267,\cdot)\) \(\chi_{4730}(273,\cdot)\) \(\chi_{4730}(357,\cdot)\) \(\chi_{4730}(367,\cdot)\) \(\chi_{4730}(427,\cdot)\) \(\chi_{4730}(443,\cdot)\) \(\chi_{4730}(487,\cdot)\) \(\chi_{4730}(533,\cdot)\) \(\chi_{4730}(597,\cdot)\) \(\chi_{4730}(697,\cdot)\) \(\chi_{4730}(713,\cdot)\) \(\chi_{4730}(797,\cdot)\) \(\chi_{4730}(873,\cdot)\) \(\chi_{4730}(883,\cdot)\) \(\chi_{4730}(917,\cdot)\) \(\chi_{4730}(927,\cdot)\) \(\chi_{4730}(977,\cdot)\) \(\chi_{4730}(1027,\cdot)\) \(\chi_{4730}(1127,\cdot)\) \(\chi_{4730}(1213,\cdot)\) \(\chi_{4730}(1257,\cdot)\) \(\chi_{4730}(1303,\cdot)\) \(\chi_{4730}(1307,\cdot)\) \(\chi_{4730}(1313,\cdot)\) \(\chi_{4730}(1347,\cdot)\) \(\chi_{4730}(1357,\cdot)\) \(\chi_{4730}(1373,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{420})$ |
| Fixed field: | Number field defined by a degree 420 polynomial (not computed) |
Values on generators
\((947,431,1981)\) → \((-i,e\left(\frac{3}{5}\right),e\left(\frac{5}{21}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 4730 }(53, a) \) | \(-1\) | \(1\) | \(e\left(\frac{121}{420}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{121}{210}\right)\) | \(e\left(\frac{197}{420}\right)\) | \(e\left(\frac{83}{420}\right)\) | \(e\left(\frac{173}{210}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{5}{84}\right)\) | \(e\left(\frac{121}{140}\right)\) | \(e\left(\frac{97}{210}\right)\) |