Basic properties
| Modulus: | \(2352\) | |
| Conductor: | \(2352\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(84\) | 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 2352.dl
\(\chi_{2352}(11,\cdot)\) \(\chi_{2352}(107,\cdot)\) \(\chi_{2352}(179,\cdot)\) \(\chi_{2352}(347,\cdot)\) \(\chi_{2352}(443,\cdot)\) \(\chi_{2352}(515,\cdot)\) \(\chi_{2352}(611,\cdot)\) \(\chi_{2352}(683,\cdot)\) \(\chi_{2352}(779,\cdot)\) \(\chi_{2352}(947,\cdot)\) \(\chi_{2352}(1019,\cdot)\) \(\chi_{2352}(1115,\cdot)\) \(\chi_{2352}(1187,\cdot)\) \(\chi_{2352}(1283,\cdot)\) \(\chi_{2352}(1355,\cdot)\) \(\chi_{2352}(1523,\cdot)\) \(\chi_{2352}(1619,\cdot)\) \(\chi_{2352}(1691,\cdot)\) \(\chi_{2352}(1787,\cdot)\) \(\chi_{2352}(1859,\cdot)\) \(\chi_{2352}(1955,\cdot)\) \(\chi_{2352}(2123,\cdot)\) \(\chi_{2352}(2195,\cdot)\) \(\chi_{2352}(2291,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1471,1765,785,2257)\) → \((-1,i,-1,e\left(\frac{1}{21}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 2352 }(107, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{84}\right)\) | \(e\left(\frac{13}{84}\right)\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{65}{84}\right)\) |