# ListLinePlot gives the correct values but N doesn't

I have solved a set of 6 differential equations with DSolve. When I use the table command and produce the results of one of the equations given by DSolve, the ListLinePlot command gives me the correct plot that I expect. However, if I use N function and then plot the results, incorrect values will be observed. My intention is to extract the values of ListLinePlot so that I can use them for further calculation.

The function is as following (sorry if it is huge):

 ut1[s] = {1/2 (-((263065237316028000000 RootSum[
635805494085519074310026089203000000000000000 +
384504301895102029248886600000000 #1^2 +
386620189214000 #1^4 + #1^6 &, (-48228902435000 E^((s #1)/
556815000) + E^((s #1)/556815000) #1^2)/(
384504301895102029248886600000000 #1 +
773240378428000 #1^3 +
3 #1^5) &] (-526130474632056000000 F RootSum[
635805494085519074310026089203000000000000000 +
384504301895102029248886600000000 #1^2 +
386620189214000 #1^4 + #1^6 &, (
58662093574000 E^((\[Pi] #1)/14848400) +
E^((\[Pi] #1)/14848400) #1^2)/(
384504301895102029248886600000000 +
773240378428000 #1^2 + 3 #1^4) &] RootSum[
635805494085519074310026089203000000000000000 +
384504301895102029248886600000000 #1^2 +
386620189214000 #1^4 + #1^6 &, (-48228902435000 E^((\
\[Pi] #1)/14848400) #1 + E^((\[Pi] #1)/14848400) #1^3)/(
384504301895102029248886600000000 +
773240378428000 #1^2 + 3 #1^4) &] +
263065237316028000000 F RootSum[

635805494085519074310026089203000000000000000 +
384504301895102029248886600000000 #1^2 +
386620189214000 #1^4 + #1^6 &, (
58662093574000 E^((\[Pi] #1)/14848400) +
E^((\[Pi] #1)/14848400) #1^2)/(
384504301895102029248886600000000 +
773240378428000 #1^2 + 3 #1^4) &] RootSum[
635805494085519074310026089203000000000000000 +
384504301895102029248886600000000 #1^2 +
386620189214000 #1^4 + #1^6 &, (-48228902435000 E^((\
\[Pi] #1)/14848400) #1 + E^((\[Pi] #1)/14848400) #1^3)/(
384504301895102029248886600000000 +
773240378428000 #1^2 + 3 #1^4) &] RootSum[
635805494085519074310026089203000000000000000 +
384504301895102029248886600000000 #1^2 +
386620189214000 #1^4 + #1^6 &, \
(384506509054825843402500000000000 E^((\[Pi] #1)/14848400) +
327958095640000 E^((\[Pi] #1)/14848400) #1^2 +
E^((\[Pi] #1)/
14848400) #1^4)/(384504301895102029248886600000000 \
+ 773240378428000 #1^2 + 3 #1^4) &] +
292268684265343371301878659417760000000000000 F RootSum[

635805494085519074310026089203000000000000000 +
384504301895102029248886600000000 #1^2 +
386620189214000 #1^4 + #1^6 &, (
E^((\[Pi] #1)/14848400) #1^2)/(
384504301895102029248886600000000 +
773240378428000 #1^2 + 3 #1^4) &] RootSum[
635805494085519074310026089203000000000000000 +
384504301895102029248886600000000 #1^2 +
386620189214000 #1^4 + #1^6 &, (
19729892798702100000000 E^((\[Pi] #1)/14848400) +
19303 E^((\[Pi] #1)/14848400) #1^2)/(
384504301895102029248886600000000 +
773240378428000 #1^2 + 3 #1^4) &] RootSum[
635805494085519074310026089203000000000000000 +
384504301895102029248886600000000 #1^2 +
386620189214000 #1^4 + #1^6 &, (-48228902435000 E^((\
\[Pi] #1)/14848400) +
E^((\[Pi] #1)/
14848400) #1^2)/(384504301895102029248886600000000 \
#1 + 773240378428000 #1^3 + 3 #1^5) &] -
10253506908128689157400000000000 F RootSum[
635805494085519074310026089203000000000000000 +
384504301895102029248886600000000 #1^2 +
386620189214000 #1^4 + #1^6 &, (
19729892798702100000000 E^((\[Pi] #1)/14848400) +
19303 E^((\[Pi] #1)/14848400) #1^2)/(
384504301895102029248886600000000 +
773240378428000 #1^2 + 3 #1^4) &] RootSum[
635805494085519074310026089203000000000000000 +
384504301895102029248886600000000 #1^2 +
386620189214000 #1^4 + #1^6 &, (1653562369200 \
E^((\[Pi] #1)/14848400) +
E^((\[Pi] #1)/
14848400) #1^2)/(384504301895102029248886600000000 \
#1 + 773240378428000 #1^3 + 3 #1^5) &] +
5126753454064344578700000000000 F RootSum[
635805494085519074310026089203000000000000000 +
384504301895102029248886600000000 #1^2 +
386620189214000 #1^4 + #1^6 &, (
19729892798702100000000 E^((\[Pi] #1)/14848400) +
19303 E^((\[Pi] #1)/14848400) #1^2)/(
384504301895102029248886600000000 +
773240378428000 #1^2 + 3 #1^4) &] RootSum[
635805494085519074310026089203000000000000000 +
384504301895102029248886600000000 #1^2 +
386620189214000 #1^4 + #1^6 &, \
(384506509054825843402500000000000 E^((\[Pi] #1)/14848400) +
327958095640000 E^((\[Pi] #1)/14848400) #1^2 +
E^((\[Pi] #1)/
14848400) #1^4)/(384504301895102029248886600000000 \
+ 773240378428000 #1^2 + 3 #1^4) &] RootSum[
635805494085519074310026089203000000000000000 +
384504301895102029248886600000000 #1^2 +
386620189214000 #1^4 + #1^6 &, (1653562369200 \
E^((\[Pi] #1)/14848400) +
E^((\[Pi] #1)/
14848400) #1^2)/(384504301895102029248886600000000 \
#1 + 773240378428000 #1^3 + 3 #1^5) &] +
14499825902348383627117920000000000 F RootSum[
635805494085519074310026089203000000000000000 +
384504301895102029248886600000000 #1^2 +
386620189214000 #1^4 + #1^6 &, (-48228902435000 E^((\
\[Pi] #1)/14848400) #1 + E^((\[Pi] #1)/14848400) #1^3)/(
384504301895102029248886600000000 +
773240378428000 #1^2 + 3 #1^4) &] RootSum[
635805494085519074310026089203000000000000000 +
384504301895102029248886600000000 #1^2 +
386620189214000 #1^4 + #1^6 &, (-48228902435000 E^((\
\[Pi] #1)/14848400) +
E^((\[Pi] #1)/
14848400) #1^2)/(384504301895102029248886600000000 \
#1 + 773240378428000 #1^3 + 3 #1^5) &] RootSum[
635805494085519074310026089203000000000000000 +
384504301895102029248886600000000 #1^2 +
386620189214000 #1^4 + #1^6 &, \
(-13183080310451171773800000000000 E^((\[Pi] #1)/14848400) +
45764253640000 E^((\[Pi] #1)/14848400) #1^2 +
E^((\[Pi] #1)/
14848400) #1^4)/(384504301895102029248886600000000 \
#1 + 773240378428000 #1^3 + 3 #1^5) &] +
28119305232054186819732252000000000 F RootSum[
635805494085519074310026089203000000000000000 +
384504301895102029248886600000000 #1^2 +
386620189214000 #1^4 + #1^6 &, (
E^((\[Pi] #1)/14848400) #1^2)/(
384504301895102029248886600000000 +
773240378428000 #1^2 + 3 #1^4) &] RootSum[
635805494085519074310026089203000000000000000 +
384504301895102029248886600000000 #1^2 +
386620189214000 #1^4 + #1^6 &, (
58662093574000 E^((\[Pi] #1)/14848400) +
E^((\[Pi] #1)/14848400) #1^2)/(

384504301895102029248886600000000 +
773240378428000 #1^2 + 3 #1^4) &] RootSum[
635805494085519074310026089203000000000000000 +
384504301895102029248886600000000 #1^2 +
386620189214000 #1^4 + #1^6 &, \
(179436370892252060254500000000000 E^((\[Pi] #1)/14848400) +
127325030000000 E^((\[Pi] #1)/14848400) #1^2 +
E^((\[Pi] #1)/
14848400) #1^4)/(384504301895102029248886600000000 \
#1 + 773240378428000 #1^3 + 3 #1^5) &] -
27187173566903219300846100000000000 F RootSum[
635805494085519074310026089203000000000000000 +
384504301895102029248886600000000 #1^2 +
386620189214000 #1^4 + #1^6 &, (1653562369200 \
E^((\[Pi] #1)/14848400) +
E^((\[Pi] #1)/
14848400) #1^2)/(384504301895102029248886600000000 \
#1 + 773240378428000 #1^3 + 3 #1^5) &] RootSum[
635805494085519074310026089203000000000000000 +
384504301895102029248886600000000 #1^2 +
386620189214000 #1^4 + #1^6 &, \
(-13183080310451171773800000000000 E^((\[Pi] #1)/14848400) +
45764253640000 E^((\[Pi] #1)/14848400) #1^2 +
E^((\[Pi] #1)/
14848400) #1^4)/(384504301895102029248886600000000 \
#1 + 773240378428000 #1^3 + 3 #1^5) &] RootSum[
635805494085519074310026089203000000000000000 +
384504301895102029248886600000000 #1^2 +
386620189214000 #1^4 + #1^6 &, \
(179436370892252060254500000000000 E^((\[Pi] #1)/14848400) +
127325030000000 E^((\[Pi] #1)/14848400) #1^2 +
E^((\[Pi] #1)/
14848400) #1^4)/(384504301895102029248886600000000 \
#1 + 773240378428000 #1^3 +
3 #1^5) \
&]))/(-1394910749393204308212476277803143152000000000000000 RootSum[
635805494085519074310026089203000000000000000 +
384504301895102029248886600000000 #1^2 +
386620189214000 #1^4 + #1^6 &,
E^((\[Pi] #1)/14848400)/(
384504301895102029248886600000000 +
773240378428000 #1^2 + 3 #1^4) &] RootSum[
635805494085519074310026089203000000000000000 +
384504301895102029248886600000000 #1^2 +
386620189214000 #1^4 + #1^6 &, (

58662093574000 E^((\[Pi] #1)/14848400) +
E^((\[Pi] #1)/14848400) #1^2)/(
384504301895102029248886600000000 +
773240378428000 #1^2 + 3 #1^4) &] RootSum[
635805494085519074310026089203000000000000000 +
384504301895102029248886600000000 #1^2 +
386620189214000 #1^4 + #1^6 &, (-48228902435000 \
E^((\[Pi] #1)/14848400) #1 + E^((\[Pi] #1)/14848400) #1^3)/(
384504301895102029248886600000000 +
773240378428000 #1^2 + 3 #1^4) &] +
1394910749393204308212476277803143152000000000000000 RootSum[
635805494085519074310026089203000000000000000 +
384504301895102029248886600000000 #1^2 +
386620189214000 #1^4 + #1^6 &, (
E^((\[Pi] #1)/14848400) #1^2)/(
384504301895102029248886600000000 +
773240378428000 #1^2 + 3 #1^4) &] RootSum[
635805494085519074310026089203000000000000000 +
384504301895102029248886600000000 #1^2 +
386620189214000 #1^4 + #1^6 &, (
58662093574000 E^((\[Pi] #1)/14848400) +
E^((\[Pi] #1)/14848400) #1^2)/(

384504301895102029248886600000000 +
773240378428000 #1^2 + 3 #1^4) &] RootSum[
635805494085519074310026089203000000000000000 +
384504301895102029248886600000000 #1^2 +
386620189214000 #1^4 + #1^6 &, (-48228902435000 \
E^((\[Pi] #1)/14848400) + E^((\[Pi] #1)/14848400) #1^2)/(
384504301895102029248886600000000 #1 +
773240378428000 #1^3 + 3 #1^5) &] -
2718475301231819699070654925187350039633080000000000000000000\
0 RootSum[
635805494085519074310026089203000000000000000 +
384504301895102029248886600000000 #1^2 +
386620189214000 #1^4 + #1^6 &,
E^((\[Pi] #1)/14848400)/(
384504301895102029248886600000000 +
773240378428000 #1^2 + 3 #1^4) &] RootSum[
635805494085519074310026089203000000000000000 +
384504301895102029248886600000000 #1^2 +
386620189214000 #1^4 + #1^6 &, (
19729892798702100000000 E^((\[Pi] #1)/14848400) +
19303 E^((\[Pi] #1)/14848400) #1^2)/(
384504301895102029248886600000000 +
773240378428000 #1^2 + 3 #1^4) &] RootSum[

635805494085519074310026089203000000000000000 +
384504301895102029248886600000000 #1^2 +
386620189214000 #1^4 + #1^6 &, (
1653562369200 E^((\[Pi] #1)/14848400) +
E^((\[Pi] #1)/14848400) #1^2)/(
384504301895102029248886600000000 #1 +
773240378428000 #1^3 + 3 #1^5) &] -
1348670614054203060426427340417403600000000000000000 RootSum[
635805494085519074310026089203000000000000000 +
384504301895102029248886600000000 #1^2 +
386620189214000 #1^4 + #1^6 &, (-48228902435000 \
E^((\[Pi] #1)/14848400) + E^((\[Pi] #1)/14848400) #1^2)/(
384504301895102029248886600000000 #1 +
773240378428000 #1^3 + 3 #1^5) &] RootSum[
635805494085519074310026089203000000000000000 +
384504301895102029248886600000000 #1^2 +
386620189214000 #1^4 + #1^6 &, (
1653562369200 E^((\[Pi] #1)/14848400) +
E^((\[Pi] #1)/14848400) #1^2)/(
384504301895102029248886600000000 #1 +
773240378428000 #1^3 + 3 #1^5) &] RootSum[
635805494085519074310026089203000000000000000 +
384504301895102029248886600000000 #1^2 +
386620189214000 #1^4 + #1^6 &, \
(-13183080310451171773800000000000 E^((\[Pi] #1)/14848400) +
45764253640000 E^((\[Pi] #1)/14848400) #1^2 +
E^((\[Pi] #1)/
14848400) #1^4)/(384504301895102029248886600000000 #1 \
+ 773240378428000 #1^3 + 3 #1^5) &] -
70700371442715913809120000000 RootSum[
635805494085519074310026089203000000000000000 +
384504301895102029248886600000000 #1^2 +
386620189214000 #1^4 + #1^6 &, (
E^((\[Pi] #1)/14848400) #1^2)/(
384504301895102029248886600000000 +
773240378428000 #1^2 + 3 #1^4) &] RootSum[
635805494085519074310026089203000000000000000 +
384504301895102029248886600000000 #1^2 +
386620189214000 #1^4 + #1^6 &, (
19729892798702100000000 E^((\[Pi] #1)/14848400) +
19303 E^((\[Pi] #1)/14848400) #1^2)/(
384504301895102029248886600000000 +
773240378428000 #1^2 + 3 #1^4) &] RootSum[
635805494085519074310026089203000000000000000 +
384504301895102029248886600000000 #1^2 +

386620189214000 #1^4 + #1^6 &, \
(-2207159723814153613400000000 E^((\[Pi] #1)/14848400) +
386620189214000 E^((\[Pi] #1)/14848400) #1^2 +
E^((\[Pi] #1)/
14848400) #1^4)/(384504301895102029248886600000000 #1 \
+ 773240378428000 #1^3 + 3 #1^5) &] -
3507536497547040000 RootSum[
635805494085519074310026089203000000000000000 +
384504301895102029248886600000000 #1^2 +
386620189214000 #1^4 + #1^6 &, (-48228902435000 \
E^((\[Pi] #1)/14848400) #1 + E^((\[Pi] #1)/14848400) #1^3)/(
384504301895102029248886600000000 +
773240378428000 #1^2 + 3 #1^4) &] RootSum[
635805494085519074310026089203000000000000000 +
384504301895102029248886600000000 #1^2 +
386620189214000 #1^4 + #1^6 &, \
(-13183080310451171773800000000000 E^((\[Pi] #1)/14848400) +
45764253640000 E^((\[Pi] #1)/14848400) #1^2 +
E^((\[Pi] #1)/
14848400) #1^4)/(384504301895102029248886600000000 #1 \
+ 773240378428000 #1^3 + 3 #1^5) &] RootSum[
635805494085519074310026089203000000000000000 +
384504301895102029248886600000000 #1^2 +
386620189214000 #1^4 + #1^6 &, \
(-2207159723814153613400000000 E^((\[Pi] #1)/14848400) +
386620189214000 E^((\[Pi] #1)/14848400) #1^2 +
E^((\[Pi] #1)/
14848400) #1^4)/(384504301895102029248886600000000 #1 \
+ 773240378428000 #1^3 + 3 #1^5) &])) - (RootSum[
635805494085519074310026089203000000000000000 +
384504301895102029248886600000000 #1^2 +
386620189214000 #1^4 + #1^6 &, (
19729892798702100000000 E^((s #1)/556815000) +
19303 E^((s #1)/556815000) #1^2)/(
384504301895102029248886600000000 + 773240378428000 #1^2 +
3 #1^4) &] \
(-21920151319900752847640899456332000000000000000 F RootSum[
635805494085519074310026089203000000000000000 +
384504301895102029248886600000000 #1^2 +
386620189214000 #1^4 + #1^6 &,
E^((\[Pi] #1)/14848400)/(
384504301895102029248886600000000 +
773240378428000 #1^2 + 3 #1^4) &] RootSum[
635805494085519074310026089203000000000000000 +
384504301895102029248886600000000 #1^2 +
386620189214000 #1^4 + #1^6 &, (-48228902435000 \
E^((\[Pi] #1)/14848400) #1 + E^((\[Pi] #1)/14848400) #1^3)/(
384504301895102029248886600000000 +
773240378428000 #1^2 + 3 #1^4) &] RootSum[
635805494085519074310026089203000000000000000 +
384504301895102029248886600000000 #1^2 +
386620189214000 #1^4 + #1^6 &, (-48228902435000 \
E^((\[Pi] #1)/14848400) + E^((\[Pi] #1)/14848400) #1^2)/(
384504301895102029248886600000000 #1 +
773240378428000 #1^3 + 3 #1^5) &] +
21920151319900752847640899456332000000000000000 F RootSum[
635805494085519074310026089203000000000000000 +
384504301895102029248886600000000 #1^2 +
386620189214000 #1^4 + #1^6 &, (
E^((\[Pi] #1)/14848400) #1^2)/(
384504301895102029248886600000000 +
773240378428000 #1^2 + 3 #1^4) &] RootSum[
635805494085519074310026089203000000000000000 +
384504301895102029248886600000000 #1^2 +
386620189214000 #1^4 + #1^6 &, (-48228902435000 \
E^((\[Pi] #1)/14848400) +
E^((\[Pi] #1)/
14848400) #1^2)/(384504301895102029248886600000000 #1 \
+ 773240378428000 #1^3 + 3 #1^5) &]^2 -
769013018109651686805000000000000 F RootSum[
635805494085519074310026089203000000000000000 +
384504301895102029248886600000000 #1^2 +
386620189214000 #1^4 + #1^6 &, (-48228902435000 \
E^((\[Pi] #1)/14848400) + E^((\[Pi] #1)/14848400) #1^2)/(
384504301895102029248886600000000 #1 +
773240378428000 #1^3 + 3 #1^5) &] RootSum[
635805494085519074310026089203000000000000000 +
384504301895102029248886600000000 #1^2 +
386620189214000 #1^4 + #1^6 &, (
1653562369200 E^((\[Pi] #1)/14848400) +
E^((\[Pi] #1)/14848400) #1^2)/(
384504301895102029248886600000000 #1 +
773240378428000 #1^3 + 3 #1^5) &] +
384506509054825843402500000000000 F RootSum[
635805494085519074310026089203000000000000000 +
384504301895102029248886600000000 #1^2 +
386620189214000 #1^4 + #1^6 &, \
(384506509054825843402500000000000 E^((\[Pi] #1)/14848400) +
327958095640000 E^((\[Pi] #1)/14848400) #1^2 +
E^((\[Pi] #1)/
14848400) #1^4)/(384504301895102029248886600000000 +
773240378428000 #1^2 + 3 #1^4) &] RootSum[
635805494085519074310026089203000000000000000 +
384504301895102029248886600000000 #1^2 +
386620189214000 #1^4 + #1^6 &, (-48228902435000 \
E^((\[Pi] #1)/14848400) + E^((\[Pi] #1)/14848400) #1^2)/(
384504301895102029248886600000000 #1 +
773240378428000 #1^3 + 3 #1^5) &] RootSum[
635805494085519074310026089203000000000000000 +
384504301895102029248886600000000 #1^2 +
386620189214000 #1^4 + #1^6 &, (
1653562369200 E^((\[Pi] #1)/14848400) +
E^((\[Pi] #1)/14848400) #1^2)/(
384504301895102029248886600000000 #1 +
773240378428000 #1^3 + 3 #1^5) &] +
41100283724813911589326686480622500000000000000 F RootSum[
635805494085519074310026089203000000000000000 +
384504301895102029248886600000000 #1^2 +
386620189214000 #1^4 + #1^6 &,
E^((\[Pi] #1)/14848400)/(

384504301895102029248886600000000 +
773240378428000 #1^2 + 3 #1^4) &] RootSum[
635805494085519074310026089203000000000000000 +
384504301895102029248886600000000 #1^2 +
386620189214000 #1^4 + #1^6 &, (
1653562369200 E^((\[Pi] #1)/14848400) +
E^((\[Pi] #1)/14848400) #1^2)/(
384504301895102029248886600000000 #1 +
773240378428000 #1^3 + 3 #1^5) &] RootSum[
635805494085519074310026089203000000000000000 +
384504301895102029248886600000000 #1^2 +
386620189214000 #1^4 + #1^6 &, \
(179436370892252060254500000000000 E^((\[Pi] #1)/14848400) +
127325030000000 E^((\[Pi] #1)/14848400) #1^2 +
E^((\[Pi] #1)/
14848400) #1^4)/(384504301895102029248886600000000 #1 \
+ 773240378428000 #1^3 + 3 #1^5) &] -
2 F RootSum[
635805494085519074310026089203000000000000000 +
384504301895102029248886600000000 #1^2}


Now I establish the plot as:

Re1 = Flatten[
Table[ut1[s] /. F -> 10000, {s , 0 , (r*\[Pi])/2 , (r*\[Pi])/
500}]];

xpoints1 = Table[s , {s , 0 , (r*\[Pi])/2 , (r*\[Pi])/500}];

RE7 = Transpose@{xpoints1 , Re1};


If I use ListLinePlot command, the results are perfect. But If I use

N[RE7]//ListLinePlot


I will get incorrect values. Now the question is: 1- How this happens? and 2- How to extract the correct data given by ListLinePlot?

Thanks in advance

• First, your ut1[s] was truncated (incorrect Mma expression). Next, once your see huge integers like 635805494085519074310026089203000000000000000 it imediatelly suggest that this is precision issue. So, just try N[RE7, 30]//ListLinePlot or something like to force Mathematica use precision arithmetic. – Acus Oct 13 '17 at 11:05
• This error pops up N::meprec: "Internal precision limit $MaxExtraPrecision = 50.` reached while evaluating {{0,0},<<49>>,<<201>>}." – KratosMath Oct 13 '17 at 11:15 • Increase it before evaluating N[], say$MaxExtraPrecision = 5000. – Acus Oct 13 '17 at 11:18
• The same error exists. – KratosMath Oct 13 '17 at 11:22
• Just confirms that this really is a precision issue. Increase it even more. Try to convert RootSum into Root objects (with Normal). Then again try N[ ]. Try to identify which part causes a problem,... Probably the case probably is more interesting. – Acus Oct 13 '17 at 11:34