Basic properties
| Modulus: | \(4598\) | |
| Conductor: | \(2299\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2299}(151,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4598.bj
\(\chi_{4598}(151,\cdot)\) \(\chi_{4598}(189,\cdot)\) \(\chi_{4598}(227,\cdot)\) \(\chi_{4598}(303,\cdot)\) \(\chi_{4598}(569,\cdot)\) \(\chi_{4598}(607,\cdot)\) \(\chi_{4598}(721,\cdot)\) \(\chi_{4598}(987,\cdot)\) \(\chi_{4598}(1025,\cdot)\) \(\chi_{4598}(1063,\cdot)\) \(\chi_{4598}(1139,\cdot)\) \(\chi_{4598}(1405,\cdot)\) \(\chi_{4598}(1481,\cdot)\) \(\chi_{4598}(1557,\cdot)\) \(\chi_{4598}(1823,\cdot)\) \(\chi_{4598}(1861,\cdot)\) \(\chi_{4598}(1899,\cdot)\) \(\chi_{4598}(1975,\cdot)\) \(\chi_{4598}(2241,\cdot)\) \(\chi_{4598}(2279,\cdot)\) \(\chi_{4598}(2317,\cdot)\) \(\chi_{4598}(2697,\cdot)\) \(\chi_{4598}(2735,\cdot)\) \(\chi_{4598}(2811,\cdot)\) \(\chi_{4598}(3077,\cdot)\) \(\chi_{4598}(3115,\cdot)\) \(\chi_{4598}(3153,\cdot)\) \(\chi_{4598}(3229,\cdot)\) \(\chi_{4598}(3495,\cdot)\) \(\chi_{4598}(3533,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((3269,3631)\) → \((e\left(\frac{53}{110}\right),-1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) | \(25\) |
| \( \chi_{ 4598 }(151, a) \) | \(1\) | \(1\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{36}{55}\right)\) | \(e\left(\frac{41}{110}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{9}{55}\right)\) | \(e\left(\frac{61}{110}\right)\) | \(e\left(\frac{67}{110}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{17}{55}\right)\) |