Basic properties
| Modulus: | \(4900\) | |
| Conductor: | \(1225\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(420\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1225}(17,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4900.dp
\(\chi_{4900}(17,\cdot)\) \(\chi_{4900}(33,\cdot)\) \(\chi_{4900}(73,\cdot)\) \(\chi_{4900}(173,\cdot)\) \(\chi_{4900}(213,\cdot)\) \(\chi_{4900}(297,\cdot)\) \(\chi_{4900}(353,\cdot)\) \(\chi_{4900}(397,\cdot)\) \(\chi_{4900}(437,\cdot)\) \(\chi_{4900}(453,\cdot)\) \(\chi_{4900}(537,\cdot)\) \(\chi_{4900}(577,\cdot)\) \(\chi_{4900}(633,\cdot)\) \(\chi_{4900}(677,\cdot)\) \(\chi_{4900}(733,\cdot)\) \(\chi_{4900}(773,\cdot)\) \(\chi_{4900}(817,\cdot)\) \(\chi_{4900}(873,\cdot)\) \(\chi_{4900}(997,\cdot)\) \(\chi_{4900}(1013,\cdot)\) \(\chi_{4900}(1053,\cdot)\) \(\chi_{4900}(1137,\cdot)\) \(\chi_{4900}(1153,\cdot)\) \(\chi_{4900}(1237,\cdot)\) \(\chi_{4900}(1277,\cdot)\) \(\chi_{4900}(1333,\cdot)\) \(\chi_{4900}(1377,\cdot)\) \(\chi_{4900}(1417,\cdot)\) \(\chi_{4900}(1433,\cdot)\) \(\chi_{4900}(1473,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{420})$ |
| Fixed field: | Number field defined by a degree 420 polynomial (not computed) |
Values on generators
\((2451,1177,101)\) → \((1,e\left(\frac{13}{20}\right),e\left(\frac{25}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) |
| \( \chi_{ 4900 }(17, a) \) | \(1\) | \(1\) | \(e\left(\frac{61}{420}\right)\) | \(e\left(\frac{61}{210}\right)\) | \(e\left(\frac{22}{105}\right)\) | \(e\left(\frac{139}{140}\right)\) | \(e\left(\frac{139}{420}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{323}{420}\right)\) | \(e\left(\frac{61}{140}\right)\) | \(e\left(\frac{1}{70}\right)\) | \(e\left(\frac{11}{30}\right)\) |