Basic properties
| Modulus: | \(4067\) | |
| Conductor: | \(581\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(246\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{581}(18,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4067.w
\(\chi_{4067}(18,\cdot)\) \(\chi_{4067}(67,\cdot)\) \(\chi_{4067}(79,\cdot)\) \(\chi_{4067}(128,\cdot)\) \(\chi_{4067}(226,\cdot)\) \(\chi_{4067}(263,\cdot)\) \(\chi_{4067}(471,\cdot)\) \(\chi_{4067}(520,\cdot)\) \(\chi_{4067}(569,\cdot)\) \(\chi_{4067}(655,\cdot)\) \(\chi_{4067}(716,\cdot)\) \(\chi_{4067}(753,\cdot)\) \(\chi_{4067}(765,\cdot)\) \(\chi_{4067}(802,\cdot)\) \(\chi_{4067}(814,\cdot)\) \(\chi_{4067}(998,\cdot)\) \(\chi_{4067}(1010,\cdot)\) \(\chi_{4067}(1145,\cdot)\) \(\chi_{4067}(1194,\cdot)\) \(\chi_{4067}(1292,\cdot)\) \(\chi_{4067}(1341,\cdot)\) \(\chi_{4067}(1390,\cdot)\) \(\chi_{4067}(1402,\cdot)\) \(\chi_{4067}(1500,\cdot)\) \(\chi_{4067}(1537,\cdot)\) \(\chi_{4067}(1549,\cdot)\) \(\chi_{4067}(1635,\cdot)\) \(\chi_{4067}(1684,\cdot)\) \(\chi_{4067}(1733,\cdot)\) \(\chi_{4067}(1745,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{123})$ |
| Fixed field: | Number field defined by a degree 246 polynomial (not computed) |
Values on generators
\((2159,2990)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{63}{82}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 4067 }(18, a) \) | \(-1\) | \(1\) | \(e\left(\frac{25}{246}\right)\) | \(e\left(\frac{121}{123}\right)\) | \(e\left(\frac{25}{123}\right)\) | \(e\left(\frac{19}{246}\right)\) | \(e\left(\frac{7}{82}\right)\) | \(e\left(\frac{25}{82}\right)\) | \(e\left(\frac{119}{123}\right)\) | \(e\left(\frac{22}{123}\right)\) | \(e\left(\frac{13}{123}\right)\) | \(e\left(\frac{23}{123}\right)\) |