Basic properties
| Modulus: | \(9800\) | |
| Conductor: | \(9800\) | 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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9800.hd
\(\chi_{9800}(123,\cdot)\) \(\chi_{9800}(163,\cdot)\) \(\chi_{9800}(347,\cdot)\) \(\chi_{9800}(387,\cdot)\) \(\chi_{9800}(403,\cdot)\) \(\chi_{9800}(627,\cdot)\) \(\chi_{9800}(683,\cdot)\) \(\chi_{9800}(723,\cdot)\) \(\chi_{9800}(947,\cdot)\) \(\chi_{9800}(963,\cdot)\) \(\chi_{9800}(1003,\cdot)\) \(\chi_{9800}(1187,\cdot)\) \(\chi_{9800}(1227,\cdot)\) \(\chi_{9800}(1283,\cdot)\) \(\chi_{9800}(1467,\cdot)\) \(\chi_{9800}(1523,\cdot)\) \(\chi_{9800}(1563,\cdot)\) \(\chi_{9800}(1747,\cdot)\) \(\chi_{9800}(1787,\cdot)\) \(\chi_{9800}(1803,\cdot)\) \(\chi_{9800}(2067,\cdot)\) \(\chi_{9800}(2083,\cdot)\) \(\chi_{9800}(2123,\cdot)\) \(\chi_{9800}(2347,\cdot)\) \(\chi_{9800}(2363,\cdot)\) \(\chi_{9800}(2403,\cdot)\) \(\chi_{9800}(2587,\cdot)\) \(\chi_{9800}(2683,\cdot)\) \(\chi_{9800}(2867,\cdot)\) \(\chi_{9800}(2923,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{420})$ |
| Fixed field: | Number field defined by a degree 420 polynomial (not computed) |
Values on generators
\((7351,4901,1177,5001)\) → \((-1,-1,e\left(\frac{11}{20}\right),e\left(\frac{8}{21}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) |
| \( \chi_{ 9800 }(123, a) \) | \(1\) | \(1\) | \(e\left(\frac{97}{420}\right)\) | \(e\left(\frac{97}{210}\right)\) | \(e\left(\frac{4}{105}\right)\) | \(e\left(\frac{73}{140}\right)\) | \(e\left(\frac{283}{420}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{11}{420}\right)\) | \(e\left(\frac{97}{140}\right)\) | \(e\left(\frac{16}{35}\right)\) | \(e\left(\frac{17}{30}\right)\) |