Basic properties
| Modulus: | \(2352\) | |
| Conductor: | \(784\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{784}(61,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2352.dk
\(\chi_{2352}(61,\cdot)\) \(\chi_{2352}(157,\cdot)\) \(\chi_{2352}(229,\cdot)\) \(\chi_{2352}(397,\cdot)\) \(\chi_{2352}(493,\cdot)\) \(\chi_{2352}(565,\cdot)\) \(\chi_{2352}(661,\cdot)\) \(\chi_{2352}(733,\cdot)\) \(\chi_{2352}(829,\cdot)\) \(\chi_{2352}(997,\cdot)\) \(\chi_{2352}(1069,\cdot)\) \(\chi_{2352}(1165,\cdot)\) \(\chi_{2352}(1237,\cdot)\) \(\chi_{2352}(1333,\cdot)\) \(\chi_{2352}(1405,\cdot)\) \(\chi_{2352}(1573,\cdot)\) \(\chi_{2352}(1669,\cdot)\) \(\chi_{2352}(1741,\cdot)\) \(\chi_{2352}(1837,\cdot)\) \(\chi_{2352}(1909,\cdot)\) \(\chi_{2352}(2005,\cdot)\) \(\chi_{2352}(2173,\cdot)\) \(\chi_{2352}(2245,\cdot)\) \(\chi_{2352}(2341,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1471,1765,785,2257)\) → \((1,-i,1,e\left(\frac{11}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 2352 }(61, a) \) | \(-1\) | \(1\) | \(e\left(\frac{29}{84}\right)\) | \(e\left(\frac{19}{84}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{23}{42}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{27}{28}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{11}{84}\right)\) |