Basic properties
| Modulus: | \(16335\) | |
| Conductor: | \(363\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{363}(26,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 16335.dp
\(\chi_{16335}(26,\cdot)\) \(\chi_{16335}(566,\cdot)\) \(\chi_{16335}(1241,\cdot)\) \(\chi_{16335}(1511,\cdot)\) \(\chi_{16335}(2051,\cdot)\) \(\chi_{16335}(2456,\cdot)\) \(\chi_{16335}(2726,\cdot)\) \(\chi_{16335}(2996,\cdot)\) \(\chi_{16335}(3941,\cdot)\) \(\chi_{16335}(4211,\cdot)\) \(\chi_{16335}(4481,\cdot)\) \(\chi_{16335}(5021,\cdot)\) \(\chi_{16335}(5426,\cdot)\) \(\chi_{16335}(5966,\cdot)\) \(\chi_{16335}(6506,\cdot)\) \(\chi_{16335}(6911,\cdot)\) \(\chi_{16335}(7181,\cdot)\) \(\chi_{16335}(7451,\cdot)\) \(\chi_{16335}(7991,\cdot)\) \(\chi_{16335}(8396,\cdot)\) \(\chi_{16335}(8666,\cdot)\) \(\chi_{16335}(8936,\cdot)\) \(\chi_{16335}(9476,\cdot)\) \(\chi_{16335}(9881,\cdot)\) \(\chi_{16335}(10151,\cdot)\) \(\chi_{16335}(10421,\cdot)\) \(\chi_{16335}(10961,\cdot)\) \(\chi_{16335}(11366,\cdot)\) \(\chi_{16335}(11636,\cdot)\) \(\chi_{16335}(11906,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((3026,9802,3511)\) → \((-1,1,e\left(\frac{51}{55}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) | \(23\) |
| \( \chi_{ 16335 }(26, a) \) | \(-1\) | \(1\) | \(e\left(\frac{47}{110}\right)\) | \(e\left(\frac{47}{55}\right)\) | \(e\left(\frac{27}{55}\right)\) | \(e\left(\frac{31}{110}\right)\) | \(e\left(\frac{36}{55}\right)\) | \(e\left(\frac{101}{110}\right)\) | \(e\left(\frac{39}{55}\right)\) | \(e\left(\frac{103}{110}\right)\) | \(e\left(\frac{53}{55}\right)\) | \(e\left(\frac{9}{22}\right)\) |