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.dd
\(\chi_{4600}(11,\cdot)\) \(\chi_{4600}(171,\cdot)\) \(\chi_{4600}(291,\cdot)\) \(\chi_{4600}(411,\cdot)\) \(\chi_{4600}(571,\cdot)\) \(\chi_{4600}(891,\cdot)\) \(\chi_{4600}(931,\cdot)\) \(\chi_{4600}(971,\cdot)\) \(\chi_{4600}(1091,\cdot)\) \(\chi_{4600}(1171,\cdot)\) \(\chi_{4600}(1211,\cdot)\) \(\chi_{4600}(1331,\cdot)\) \(\chi_{4600}(1371,\cdot)\) \(\chi_{4600}(1491,\cdot)\) \(\chi_{4600}(1571,\cdot)\) \(\chi_{4600}(1811,\cdot)\) \(\chi_{4600}(1891,\cdot)\) \(\chi_{4600}(2011,\cdot)\) \(\chi_{4600}(2091,\cdot)\) \(\chi_{4600}(2131,\cdot)\) \(\chi_{4600}(2291,\cdot)\) \(\chi_{4600}(2411,\cdot)\) \(\chi_{4600}(2491,\cdot)\) \(\chi_{4600}(2731,\cdot)\) \(\chi_{4600}(2771,\cdot)\) \(\chi_{4600}(2811,\cdot)\) \(\chi_{4600}(2931,\cdot)\) \(\chi_{4600}(3011,\cdot)\) \(\chi_{4600}(3171,\cdot)\) \(\chi_{4600}(3211,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((1151,2301,2577,1201)\) → \((-1,-1,e\left(\frac{4}{5}\right),e\left(\frac{9}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(27\) | \(29\) |
| \( \chi_{ 4600 }(11, a) \) | \(1\) | \(1\) | \(e\left(\frac{8}{55}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{16}{55}\right)\) | \(e\left(\frac{53}{110}\right)\) | \(e\left(\frac{47}{110}\right)\) | \(e\left(\frac{29}{110}\right)\) | \(e\left(\frac{59}{110}\right)\) | \(e\left(\frac{23}{55}\right)\) | \(e\left(\frac{24}{55}\right)\) | \(e\left(\frac{51}{110}\right)\) |