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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2352.dm
\(\chi_{2352}(53,\cdot)\) \(\chi_{2352}(149,\cdot)\) \(\chi_{2352}(221,\cdot)\) \(\chi_{2352}(317,\cdot)\) \(\chi_{2352}(389,\cdot)\) \(\chi_{2352}(485,\cdot)\) \(\chi_{2352}(653,\cdot)\) \(\chi_{2352}(725,\cdot)\) \(\chi_{2352}(821,\cdot)\) \(\chi_{2352}(893,\cdot)\) \(\chi_{2352}(989,\cdot)\) \(\chi_{2352}(1061,\cdot)\) \(\chi_{2352}(1229,\cdot)\) \(\chi_{2352}(1325,\cdot)\) \(\chi_{2352}(1397,\cdot)\) \(\chi_{2352}(1493,\cdot)\) \(\chi_{2352}(1565,\cdot)\) \(\chi_{2352}(1661,\cdot)\) \(\chi_{2352}(1829,\cdot)\) \(\chi_{2352}(1901,\cdot)\) \(\chi_{2352}(1997,\cdot)\) \(\chi_{2352}(2069,\cdot)\) \(\chi_{2352}(2165,\cdot)\) \(\chi_{2352}(2237,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1471,1765,785,2257)\) → \((1,i,-1,e\left(\frac{5}{21}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 2352 }(53, a) \) | \(-1\) | \(1\) | \(e\left(\frac{55}{84}\right)\) | \(e\left(\frac{23}{84}\right)\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{73}{84}\right)\) |