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 \(\chi_{48735}(7,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 243675.yj
\(\chi_{243675}(7,\cdot)\) \(\chi_{243675}(2443,\cdot)\) \(\chi_{243675}(2743,\cdot)\) \(\chi_{243675}(3982,\cdot)\) \(\chi_{243675}(4282,\cdot)\) \(\chi_{243675}(6718,\cdot)\) \(\chi_{243675}(7018,\cdot)\) \(\chi_{243675}(8257,\cdot)\) \(\chi_{243675}(8557,\cdot)\) \(\chi_{243675}(10993,\cdot)\) \(\chi_{243675}(11293,\cdot)\) \(\chi_{243675}(12532,\cdot)\) \(\chi_{243675}(12832,\cdot)\) \(\chi_{243675}(15268,\cdot)\) \(\chi_{243675}(15568,\cdot)\) \(\chi_{243675}(16807,\cdot)\) \(\chi_{243675}(17107,\cdot)\) \(\chi_{243675}(19543,\cdot)\) \(\chi_{243675}(19843,\cdot)\) \(\chi_{243675}(21082,\cdot)\) \(\chi_{243675}(21382,\cdot)\) \(\chi_{243675}(23818,\cdot)\) \(\chi_{243675}(25357,\cdot)\) \(\chi_{243675}(25657,\cdot)\) \(\chi_{243675}(28093,\cdot)\) \(\chi_{243675}(28393,\cdot)\) \(\chi_{243675}(29632,\cdot)\) \(\chi_{243675}(29932,\cdot)\) \(\chi_{243675}(32368,\cdot)\) \(\chi_{243675}(32668,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{684})$ |
| Fixed field: | Number field defined by a degree 684 polynomial (not computed) |
Values on generators
\((36101,77977,129601)\) → \((e\left(\frac{8}{9}\right),i,e\left(\frac{25}{57}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(22\) |
| \( \chi_{ 243675 }(7, a) \) | \(-1\) | \(1\) | \(e\left(\frac{395}{684}\right)\) | \(e\left(\frac{53}{342}\right)\) | \(e\left(\frac{179}{684}\right)\) | \(e\left(\frac{167}{228}\right)\) | \(e\left(\frac{50}{171}\right)\) | \(e\left(\frac{109}{684}\right)\) | \(e\left(\frac{287}{342}\right)\) | \(e\left(\frac{53}{171}\right)\) | \(e\left(\frac{161}{228}\right)\) | \(e\left(\frac{595}{684}\right)\) |