Basic properties
Modulus: | \(5241\) | |
Conductor: | \(1747\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(1746\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1747}(46,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5241.v
\(\chi_{5241}(7,\cdot)\) \(\chi_{5241}(13,\cdot)\) \(\chi_{5241}(37,\cdot)\) \(\chi_{5241}(46,\cdot)\) \(\chi_{5241}(58,\cdot)\) \(\chi_{5241}(70,\cdot)\) \(\chi_{5241}(82,\cdot)\) \(\chi_{5241}(85,\cdot)\) \(\chi_{5241}(112,\cdot)\) \(\chi_{5241}(130,\cdot)\) \(\chi_{5241}(133,\cdot)\) \(\chi_{5241}(136,\cdot)\) \(\chi_{5241}(139,\cdot)\) \(\chi_{5241}(151,\cdot)\) \(\chi_{5241}(154,\cdot)\) \(\chi_{5241}(157,\cdot)\) \(\chi_{5241}(175,\cdot)\) \(\chi_{5241}(181,\cdot)\) \(\chi_{5241}(184,\cdot)\) \(\chi_{5241}(187,\cdot)\) \(\chi_{5241}(193,\cdot)\) \(\chi_{5241}(199,\cdot)\) \(\chi_{5241}(202,\cdot)\) \(\chi_{5241}(205,\cdot)\) \(\chi_{5241}(208,\cdot)\) \(\chi_{5241}(211,\cdot)\) \(\chi_{5241}(232,\cdot)\) \(\chi_{5241}(247,\cdot)\) \(\chi_{5241}(253,\cdot)\) \(\chi_{5241}(283,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{873})$ |
Fixed field: | Number field defined by a degree 1746 polynomial (not computed) |
Values on generators
\((1748,3496)\) → \((1,e\left(\frac{329}{1746}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 5241 }(46, a) \) | \(-1\) | \(1\) | \(e\left(\frac{329}{1746}\right)\) | \(e\left(\frac{329}{873}\right)\) | \(e\left(\frac{1567}{1746}\right)\) | \(e\left(\frac{1481}{1746}\right)\) | \(e\left(\frac{329}{582}\right)\) | \(e\left(\frac{25}{291}\right)\) | \(e\left(\frac{373}{582}\right)\) | \(e\left(\frac{839}{1746}\right)\) | \(e\left(\frac{32}{873}\right)\) | \(e\left(\frac{658}{873}\right)\) |