Basic properties
| Modulus: | \(16335\) | |
| Conductor: | \(121\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{121}(2,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 16335.dm
\(\chi_{16335}(271,\cdot)\) \(\chi_{16335}(541,\cdot)\) \(\chi_{16335}(811,\cdot)\) \(\chi_{16335}(1216,\cdot)\) \(\chi_{16335}(1756,\cdot)\) \(\chi_{16335}(2026,\cdot)\) \(\chi_{16335}(2701,\cdot)\) \(\chi_{16335}(3241,\cdot)\) \(\chi_{16335}(3511,\cdot)\) \(\chi_{16335}(3781,\cdot)\) \(\chi_{16335}(4186,\cdot)\) \(\chi_{16335}(4726,\cdot)\) \(\chi_{16335}(4996,\cdot)\) \(\chi_{16335}(5266,\cdot)\) \(\chi_{16335}(5671,\cdot)\) \(\chi_{16335}(6481,\cdot)\) \(\chi_{16335}(6751,\cdot)\) \(\chi_{16335}(7156,\cdot)\) \(\chi_{16335}(7696,\cdot)\) \(\chi_{16335}(7966,\cdot)\) \(\chi_{16335}(8236,\cdot)\) \(\chi_{16335}(8641,\cdot)\) \(\chi_{16335}(9181,\cdot)\) \(\chi_{16335}(9451,\cdot)\) \(\chi_{16335}(9721,\cdot)\) \(\chi_{16335}(10126,\cdot)\) \(\chi_{16335}(10666,\cdot)\) \(\chi_{16335}(10936,\cdot)\) \(\chi_{16335}(11206,\cdot)\) \(\chi_{16335}(11611,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((3026,9802,3511)\) → \((1,1,e\left(\frac{1}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) | \(23\) |
| \( \chi_{ 16335 }(3511, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1}{110}\right)\) | \(e\left(\frac{1}{55}\right)\) | \(e\left(\frac{7}{110}\right)\) | \(e\left(\frac{3}{110}\right)\) | \(e\left(\frac{101}{110}\right)\) | \(e\left(\frac{4}{55}\right)\) | \(e\left(\frac{2}{55}\right)\) | \(e\left(\frac{49}{110}\right)\) | \(e\left(\frac{83}{110}\right)\) | \(e\left(\frac{7}{11}\right)\) |