Basic properties
Modulus: | \(1049\) | |
Conductor: | \(1049\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(262\) | 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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1049.f
\(\chi_{1049}(2,\cdot)\) \(\chi_{1049}(8,\cdot)\) \(\chi_{1049}(13,\cdot)\) \(\chi_{1049}(25,\cdot)\) \(\chi_{1049}(29,\cdot)\) \(\chi_{1049}(32,\cdot)\) \(\chi_{1049}(38,\cdot)\) \(\chi_{1049}(42,\cdot)\) \(\chi_{1049}(43,\cdot)\) \(\chi_{1049}(45,\cdot)\) \(\chi_{1049}(52,\cdot)\) \(\chi_{1049}(55,\cdot)\) \(\chi_{1049}(69,\cdot)\) \(\chi_{1049}(73,\cdot)\) \(\chi_{1049}(81,\cdot)\) \(\chi_{1049}(97,\cdot)\) \(\chi_{1049}(99,\cdot)\) \(\chi_{1049}(100,\cdot)\) \(\chi_{1049}(106,\cdot)\) \(\chi_{1049}(116,\cdot)\) \(\chi_{1049}(119,\cdot)\) \(\chi_{1049}(121,\cdot)\) \(\chi_{1049}(122,\cdot)\) \(\chi_{1049}(128,\cdot)\) \(\chi_{1049}(152,\cdot)\) \(\chi_{1049}(163,\cdot)\) \(\chi_{1049}(168,\cdot)\) \(\chi_{1049}(172,\cdot)\) \(\chi_{1049}(180,\cdot)\) \(\chi_{1049}(181,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{131})$ |
Fixed field: | Number field defined by a degree 262 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{203}{262}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 1049 }(1033, a) \) | \(1\) | \(1\) | \(e\left(\frac{103}{131}\right)\) | \(e\left(\frac{203}{262}\right)\) | \(e\left(\frac{75}{131}\right)\) | \(e\left(\frac{122}{131}\right)\) | \(e\left(\frac{147}{262}\right)\) | \(e\left(\frac{151}{262}\right)\) | \(e\left(\frac{47}{131}\right)\) | \(e\left(\frac{72}{131}\right)\) | \(e\left(\frac{94}{131}\right)\) | \(e\left(\frac{114}{131}\right)\) |