Basic properties
| Modulus: | \(4600\) | |
| Conductor: | \(4600\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4600.cv
\(\chi_{4600}(141,\cdot)\) \(\chi_{4600}(261,\cdot)\) \(\chi_{4600}(381,\cdot)\) \(\chi_{4600}(541,\cdot)\) \(\chi_{4600}(581,\cdot)\) \(\chi_{4600}(821,\cdot)\) \(\chi_{4600}(1021,\cdot)\) \(\chi_{4600}(1061,\cdot)\) \(\chi_{4600}(1181,\cdot)\) \(\chi_{4600}(1221,\cdot)\) \(\chi_{4600}(1421,\cdot)\) \(\chi_{4600}(1461,\cdot)\) \(\chi_{4600}(1741,\cdot)\) \(\chi_{4600}(1821,\cdot)\) \(\chi_{4600}(1941,\cdot)\) \(\chi_{4600}(1981,\cdot)\) \(\chi_{4600}(2141,\cdot)\) \(\chi_{4600}(2221,\cdot)\) \(\chi_{4600}(2341,\cdot)\) \(\chi_{4600}(2381,\cdot)\) \(\chi_{4600}(2421,\cdot)\) \(\chi_{4600}(2661,\cdot)\) \(\chi_{4600}(2741,\cdot)\) \(\chi_{4600}(2861,\cdot)\) \(\chi_{4600}(3021,\cdot)\) \(\chi_{4600}(3061,\cdot)\) \(\chi_{4600}(3141,\cdot)\) \(\chi_{4600}(3261,\cdot)\) \(\chi_{4600}(3341,\cdot)\) \(\chi_{4600}(3581,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((1151,2301,2577,1201)\) → \((1,-1,e\left(\frac{1}{5}\right),e\left(\frac{8}{11}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(27\) | \(29\) |
| \( \chi_{ 4600 }(141, a) \) | \(1\) | \(1\) | \(e\left(\frac{59}{110}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{4}{55}\right)\) | \(e\left(\frac{27}{110}\right)\) | \(e\left(\frac{53}{110}\right)\) | \(e\left(\frac{38}{55}\right)\) | \(e\left(\frac{1}{110}\right)\) | \(e\left(\frac{39}{110}\right)\) | \(e\left(\frac{67}{110}\right)\) | \(e\left(\frac{109}{110}\right)\) |