Basic properties
| Modulus: | \(27040\) | |
| Conductor: | \(27040\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(104\) | 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 27040.mb
\(\chi_{27040}(333,\cdot)\) \(\chi_{27040}(837,\cdot)\) \(\chi_{27040}(1373,\cdot)\) \(\chi_{27040}(1877,\cdot)\) \(\chi_{27040}(2413,\cdot)\) \(\chi_{27040}(2917,\cdot)\) \(\chi_{27040}(3453,\cdot)\) \(\chi_{27040}(4997,\cdot)\) \(\chi_{27040}(5533,\cdot)\) \(\chi_{27040}(6037,\cdot)\) \(\chi_{27040}(6573,\cdot)\) \(\chi_{27040}(7077,\cdot)\) \(\chi_{27040}(7613,\cdot)\) \(\chi_{27040}(8117,\cdot)\) \(\chi_{27040}(8653,\cdot)\) \(\chi_{27040}(9157,\cdot)\) \(\chi_{27040}(9693,\cdot)\) \(\chi_{27040}(10197,\cdot)\) \(\chi_{27040}(10733,\cdot)\) \(\chi_{27040}(11237,\cdot)\) \(\chi_{27040}(11773,\cdot)\) \(\chi_{27040}(12277,\cdot)\) \(\chi_{27040}(12813,\cdot)\) \(\chi_{27040}(13317,\cdot)\) \(\chi_{27040}(13853,\cdot)\) \(\chi_{27040}(14357,\cdot)\) \(\chi_{27040}(14893,\cdot)\) \(\chi_{27040}(15397,\cdot)\) \(\chi_{27040}(15933,\cdot)\) \(\chi_{27040}(16437,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{104})$ |
| Fixed field: | Number field defined by a degree 104 polynomial (not computed) |
Values on generators
\((18591,16901,10817,12001)\) → \((1,e\left(\frac{3}{8}\right),-i,e\left(\frac{21}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 27040 }(15933, a) \) | \(1\) | \(1\) | \(e\left(\frac{47}{104}\right)\) | \(e\left(\frac{37}{52}\right)\) | \(e\left(\frac{47}{52}\right)\) | \(e\left(\frac{49}{104}\right)\) | \(e\left(\frac{11}{52}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{17}{104}\right)\) | \(1\) | \(e\left(\frac{37}{104}\right)\) | \(e\left(\frac{81}{104}\right)\) |