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 \(\chi_{2365}(963,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4730.dp
\(\chi_{4730}(13,\cdot)\) \(\chi_{4730}(17,\cdot)\) \(\chi_{4730}(57,\cdot)\) \(\chi_{4730}(83,\cdot)\) \(\chi_{4730}(117,\cdot)\) \(\chi_{4730}(167,\cdot)\) \(\chi_{4730}(283,\cdot)\) \(\chi_{4730}(447,\cdot)\) \(\chi_{4730}(453,\cdot)\) \(\chi_{4730}(497,\cdot)\) \(\chi_{4730}(513,\cdot)\) \(\chi_{4730}(547,\cdot)\) \(\chi_{4730}(633,\cdot)\) \(\chi_{4730}(783,\cdot)\) \(\chi_{4730}(787,\cdot)\) \(\chi_{4730}(827,\cdot)\) \(\chi_{4730}(877,\cdot)\) \(\chi_{4730}(943,\cdot)\) \(\chi_{4730}(963,\cdot)\) \(\chi_{4730}(1003,\cdot)\) \(\chi_{4730}(1047,\cdot)\) \(\chi_{4730}(1063,\cdot)\) \(\chi_{4730}(1113,\cdot)\) \(\chi_{4730}(1217,\cdot)\) \(\chi_{4730}(1227,\cdot)\) \(\chi_{4730}(1393,\cdot)\) \(\chi_{4730}(1443,\cdot)\) \(\chi_{4730}(1487,\cdot)\) \(\chi_{4730}(1493,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{420})$ |
| Fixed field: | Number field defined by a degree 420 polynomial (not computed) |
Values on generators
\((947,431,1981)\) → \((-i,e\left(\frac{9}{10}\right),e\left(\frac{19}{21}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 4730 }(963, a) \) | \(1\) | \(1\) | \(e\left(\frac{149}{420}\right)\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{149}{210}\right)\) | \(e\left(\frac{43}{420}\right)\) | \(e\left(\frac{97}{420}\right)\) | \(e\left(\frac{41}{105}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{61}{84}\right)\) | \(e\left(\frac{9}{140}\right)\) | \(e\left(\frac{94}{105}\right)\) |