ListLinePlot of sum giving zeroes at nonzero values

I was using Wolfram|Alpha to graph the sums of $$\sum^k_{n=0}\frac{\sin(2^n)}{n}.$$ After querying sum n=1 to infinity of sin(2^n)/n and clicking More Terms several times, I got this result: Eager to get more terms without having to click a button so many times, clicked Open Code, which gave me ListLinePlot[Accumulate[Table[Sin[2^n]/n, {n, 1, 641}]]]. However, the plot I got looked like this instead: Is this caused by not having a plan for the Wolfram Language, or something else I'm not aware of? I also tried ListLinePlot[Table[Sum[Sin[2^i]/i,{i,1,n}], {n, 1, 641}]] which gave similar results.

I also tried using the free release of wolframscript but was unable to get a picture, the command line returned -Graphics- and I couldn't find how to output an image online.

Is there a way apart from Wolfram|Alpha to render these images?

Try with N

ListLinePlot[Table[N@Sum[Sin[2^i]/i, {i, 1, n}], {n, 1, 641}],
AspectRatio -> Full] ListLinePlot[Table[N@Sum[Sin[2^i]/i, {i, 1, n}], {n, 1, 641}],
AspectRatio -> Full] // AbsoluteTiming ListLinePlot[
Table[N@Sum[Sin[2^i]/i, {i, 1, n}], {n, 1, 1001}]] // AbsoluteTiming • I've just tried doing this with 1001 instead of 641 but it's taking a long time to load... is this because the image is large? Can I remove the AspectRatio thing? – boboquack Jul 2 at 3:09
• In my environment,AspectRatio doesn't affect on the time.(its around 3.1 seconds). anyway,you can remove AspectRatio,of course. – Xminer Jul 2 at 3:29
• by the way,If it is heavy in your environment, please use this.　cpp.sh/3mb7s – Xminer Jul 2 at 3:46