Basic properties
| Modulus: | \(1048\) | |
| Conductor: | \(1048\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(130\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1048.be
\(\chi_{1048}(3,\cdot)\) \(\chi_{1048}(11,\cdot)\) \(\chi_{1048}(27,\cdot)\) \(\chi_{1048}(35,\cdot)\) \(\chi_{1048}(43,\cdot)\) \(\chi_{1048}(59,\cdot)\) \(\chi_{1048}(75,\cdot)\) \(\chi_{1048}(91,\cdot)\) \(\chi_{1048}(123,\cdot)\) \(\chi_{1048}(147,\cdot)\) \(\chi_{1048}(179,\cdot)\) \(\chi_{1048}(195,\cdot)\) \(\chi_{1048}(267,\cdot)\) \(\chi_{1048}(275,\cdot)\) \(\chi_{1048}(283,\cdot)\) \(\chi_{1048}(339,\cdot)\) \(\chi_{1048}(363,\cdot)\) \(\chi_{1048}(371,\cdot)\) \(\chi_{1048}(379,\cdot)\) \(\chi_{1048}(387,\cdot)\) \(\chi_{1048}(427,\cdot)\) \(\chi_{1048}(467,\cdot)\) \(\chi_{1048}(507,\cdot)\) \(\chi_{1048}(531,\cdot)\) \(\chi_{1048}(539,\cdot)\) \(\chi_{1048}(579,\cdot)\) \(\chi_{1048}(659,\cdot)\) \(\chi_{1048}(667,\cdot)\) \(\chi_{1048}(675,\cdot)\) \(\chi_{1048}(683,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{65})$ |
| Fixed field: | Number field defined by a degree 130 polynomial (not computed) |
Values on generators
\((263,525,657)\) → \((-1,-1,e\left(\frac{43}{65}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 1048 }(27, a) \) | \(-1\) | \(1\) | \(e\left(\frac{41}{65}\right)\) | \(e\left(\frac{121}{130}\right)\) | \(e\left(\frac{1}{130}\right)\) | \(e\left(\frac{17}{65}\right)\) | \(e\left(\frac{3}{65}\right)\) | \(e\left(\frac{53}{130}\right)\) | \(e\left(\frac{73}{130}\right)\) | \(e\left(\frac{29}{65}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{83}{130}\right)\) |