Basic properties
Modulus: | \(1048\) | |
Conductor: | \(1048\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(130\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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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
\((263,525,657)\) → \((-1,-1,e\left(\frac{9}{65}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 1048 }(275, a) \) | \(-1\) | \(1\) | \(e\left(\frac{63}{65}\right)\) | \(e\left(\frac{113}{130}\right)\) | \(e\left(\frac{103}{130}\right)\) | \(e\left(\frac{61}{65}\right)\) | \(e\left(\frac{49}{65}\right)\) | \(e\left(\frac{129}{130}\right)\) | \(e\left(\frac{109}{130}\right)\) | \(e\left(\frac{62}{65}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{99}{130}\right)\) |