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.z
\(\chi_{1048}(29,\cdot)\) \(\chi_{1048}(37,\cdot)\) \(\chi_{1048}(85,\cdot)\) \(\chi_{1048}(93,\cdot)\) \(\chi_{1048}(133,\cdot)\) \(\chi_{1048}(141,\cdot)\) \(\chi_{1048}(157,\cdot)\) \(\chi_{1048}(181,\cdot)\) \(\chi_{1048}(197,\cdot)\) \(\chi_{1048}(213,\cdot)\) \(\chi_{1048}(221,\cdot)\) \(\chi_{1048}(229,\cdot)\) \(\chi_{1048}(237,\cdot)\) \(\chi_{1048}(253,\cdot)\) \(\chi_{1048}(285,\cdot)\) \(\chi_{1048}(293,\cdot)\) \(\chi_{1048}(349,\cdot)\) \(\chi_{1048}(357,\cdot)\) \(\chi_{1048}(365,\cdot)\) \(\chi_{1048}(373,\cdot)\) \(\chi_{1048}(381,\cdot)\) \(\chi_{1048}(389,\cdot)\) \(\chi_{1048}(469,\cdot)\) \(\chi_{1048}(509,\cdot)\) \(\chi_{1048}(517,\cdot)\) \(\chi_{1048}(541,\cdot)\) \(\chi_{1048}(581,\cdot)\) \(\chi_{1048}(621,\cdot)\) \(\chi_{1048}(661,\cdot)\) \(\chi_{1048}(669,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{65})$ |
| Fixed field: | Number field defined by a degree 130 polynomial (not computed) |
Values on generators
\((263,525,657)\) → \((1,-1,e\left(\frac{41}{130}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 1048 }(37, a) \) | \(-1\) | \(1\) | \(e\left(\frac{27}{130}\right)\) | \(e\left(\frac{1}{130}\right)\) | \(e\left(\frac{18}{65}\right)\) | \(e\left(\frac{27}{65}\right)\) | \(e\left(\frac{21}{130}\right)\) | \(e\left(\frac{23}{130}\right)\) | \(e\left(\frac{14}{65}\right)\) | \(e\left(\frac{73}{130}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{63}{130}\right)\) |