Basic properties
| Modulus: | \(243675\) | |
| Conductor: | \(48735\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(684\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{48735}(43,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 243675.yv
\(\chi_{243675}(43,\cdot)\) \(\chi_{243675}(682,\cdot)\) \(\chi_{243675}(1582,\cdot)\) \(\chi_{243675}(6343,\cdot)\) \(\chi_{243675}(7882,\cdot)\) \(\chi_{243675}(8293,\cdot)\) \(\chi_{243675}(8518,\cdot)\) \(\chi_{243675}(9832,\cdot)\) \(\chi_{243675}(10057,\cdot)\) \(\chi_{243675}(10093,\cdot)\) \(\chi_{243675}(11632,\cdot)\) \(\chi_{243675}(11968,\cdot)\) \(\chi_{243675}(12868,\cdot)\) \(\chi_{243675}(13507,\cdot)\) \(\chi_{243675}(14407,\cdot)\) \(\chi_{243675}(19168,\cdot)\) \(\chi_{243675}(20707,\cdot)\) \(\chi_{243675}(21118,\cdot)\) \(\chi_{243675}(21343,\cdot)\) \(\chi_{243675}(22657,\cdot)\) \(\chi_{243675}(22882,\cdot)\) \(\chi_{243675}(22918,\cdot)\) \(\chi_{243675}(24457,\cdot)\) \(\chi_{243675}(26332,\cdot)\) \(\chi_{243675}(27232,\cdot)\) \(\chi_{243675}(31993,\cdot)\) \(\chi_{243675}(33532,\cdot)\) \(\chi_{243675}(33943,\cdot)\) \(\chi_{243675}(35482,\cdot)\) \(\chi_{243675}(35707,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{684})$ |
| Fixed field: | Number field defined by a degree 684 polynomial (not computed) |
Values on generators
\((36101,77977,129601)\) → \((e\left(\frac{2}{9}\right),-i,e\left(\frac{26}{171}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(22\) |
| \( \chi_{ 243675 }(43, a) \) | \(-1\) | \(1\) | \(e\left(\frac{85}{684}\right)\) | \(e\left(\frac{85}{342}\right)\) | \(e\left(\frac{77}{684}\right)\) | \(e\left(\frac{85}{228}\right)\) | \(e\left(\frac{68}{171}\right)\) | \(e\left(\frac{35}{684}\right)\) | \(e\left(\frac{9}{38}\right)\) | \(e\left(\frac{85}{171}\right)\) | \(e\left(\frac{305}{684}\right)\) | \(e\left(\frac{119}{228}\right)\) |