Basic properties
Modulus: | \(583\) | |
Conductor: | \(583\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(260\) | 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 583.w
\(\chi_{583}(3,\cdot)\) \(\chi_{583}(5,\cdot)\) \(\chi_{583}(14,\cdot)\) \(\chi_{583}(20,\cdot)\) \(\chi_{583}(26,\cdot)\) \(\chi_{583}(27,\cdot)\) \(\chi_{583}(31,\cdot)\) \(\chi_{583}(48,\cdot)\) \(\chi_{583}(58,\cdot)\) \(\chi_{583}(71,\cdot)\) \(\chi_{583}(75,\cdot)\) \(\chi_{583}(80,\cdot)\) \(\chi_{583}(86,\cdot)\) \(\chi_{583}(92,\cdot)\) \(\chi_{583}(103,\cdot)\) \(\chi_{583}(104,\cdot)\) \(\chi_{583}(108,\cdot)\) \(\chi_{583}(114,\cdot)\) \(\chi_{583}(124,\cdot)\) \(\chi_{583}(125,\cdot)\) \(\chi_{583}(126,\cdot)\) \(\chi_{583}(137,\cdot)\) \(\chi_{583}(141,\cdot)\) \(\chi_{583}(147,\cdot)\) \(\chi_{583}(157,\cdot)\) \(\chi_{583}(179,\cdot)\) \(\chi_{583}(180,\cdot)\) \(\chi_{583}(181,\cdot)\) \(\chi_{583}(185,\cdot)\) \(\chi_{583}(190,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{260})$ |
Fixed field: | Number field defined by a degree 260 polynomial (not computed) |
Values on generators
\((266,320)\) → \((e\left(\frac{4}{5}\right),e\left(\frac{17}{52}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 583 }(3, a) \) | \(-1\) | \(1\) | \(e\left(\frac{33}{260}\right)\) | \(e\left(\frac{249}{260}\right)\) | \(e\left(\frac{33}{130}\right)\) | \(e\left(\frac{147}{260}\right)\) | \(e\left(\frac{11}{130}\right)\) | \(e\left(\frac{23}{130}\right)\) | \(e\left(\frac{99}{260}\right)\) | \(e\left(\frac{119}{130}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{11}{52}\right)\) |