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 \(\chi_{2365}(1293,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4730.dr
\(\chi_{4730}(63,\cdot)\) \(\chi_{4730}(73,\cdot)\) \(\chi_{4730}(227,\cdot)\) \(\chi_{4730}(233,\cdot)\) \(\chi_{4730}(277,\cdot)\) \(\chi_{4730}(327,\cdot)\) \(\chi_{4730}(347,\cdot)\) \(\chi_{4730}(413,\cdot)\) \(\chi_{4730}(503,\cdot)\) \(\chi_{4730}(607,\cdot)\) \(\chi_{4730}(657,\cdot)\) \(\chi_{4730}(673,\cdot)\) \(\chi_{4730}(717,\cdot)\) \(\chi_{4730}(743,\cdot)\) \(\chi_{4730}(777,\cdot)\) \(\chi_{4730}(843,\cdot)\) \(\chi_{4730}(893,\cdot)\) \(\chi_{4730}(937,\cdot)\) \(\chi_{4730}(1007,\cdot)\) \(\chi_{4730}(1173,\cdot)\) \(\chi_{4730}(1207,\cdot)\) \(\chi_{4730}(1223,\cdot)\) \(\chi_{4730}(1267,\cdot)\) \(\chi_{4730}(1273,\cdot)\) \(\chi_{4730}(1293,\cdot)\) \(\chi_{4730}(1437,\cdot)\) \(\chi_{4730}(1447,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{420})$ |
| Fixed field: | Number field defined by a degree 420 polynomial (not computed) |
Values on generators
\((947,431,1981)\) → \((-i,e\left(\frac{9}{10}\right),e\left(\frac{1}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 4730 }(1293, a) \) | \(-1\) | \(1\) | \(e\left(\frac{199}{420}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{199}{210}\right)\) | \(e\left(\frac{383}{420}\right)\) | \(e\left(\frac{317}{420}\right)\) | \(e\left(\frac{137}{210}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{53}{84}\right)\) | \(e\left(\frac{59}{140}\right)\) | \(e\left(\frac{163}{210}\right)\) |