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Obtain these four calculations with 500 decimal digits?

GROUPS:

Dear Friend

Could you help me ? I want to see the following calculation results with the ´500´ decimal digits ( Meanwhile please note, I have no any idea about computer programming)

Thank you very much for your this help.

$ s_1=0.5+it_1$ and $ s_2=0.5+it_2$ ........... (see $ t_1$ and $ t_2$ on below)

$ N_1=10^{14}$ and $ N_2=10^{18}$

enter image description here

Or if you consider, I can give the real functions instead of the above - complex function).

These total 4 calculations will be enough for me. If you have any question, please do not hesitate.

$ t_1$=14.134725141734693790457251983562470270784257115699243175685567460149 9634298092567649490103931715610127792029715487974367661426914698822545 8250536323944713778041338123720597054962195586586020055556672583601077 3700205410982661507542780517442591306254481978651072304938725629738321 5774203952157256748093321400349904680343462673144209203773854871413783 1735639699536542811307968053149168852906782082298049264338666734623320 0787587617920056048680543568014444246510655975686659032286865105448594 4432062407272703209427452221304874872092412385141835146054279015244783

$ t_2$=236.52422966581620580247550795566297868952949521218912370091896098781 9150384292332826261444604065174015827315678371311908125834666026514272 3427442710559412695531311686041161208386105258022537008648905356952178 6290474725602526826563480477997212116546341401730768688207342088012792 6644985268669489487216328558298806627153861486608112087260596055996397 4174141107331932566901602812030379738385137490926579562946886420201539 1274403467040835271042467991402807619705981381817538187168651059206275 5648099062015611059642060030641789502508561511728245696694558507994532

POSTED BY: Bahattin GUNES
Answer
3 months ago

Mathematica have built-in function ZetaZero.

 N[Im[ZetaZero[1]], 500]

(*14.1347251417346937904572519835624702707842571156992431756855674601499\
6342980925676494901039317156101277920297154879743676614269146988225458\
2505363239447137780413381237205970549621955865860200555566725836010773\
7002054109826615075427805174425913062544819786510723049387256297383215\
7742039521572567480933214003499046803434626731442092037738548714137831\
7356396995365428113079680531491688529067820822980492643386667346233200\
7875876179200560486805435680144442465106559756866590322868651054485944\
43206240727 *)

N[Im[ZetaZero[100]], 500]

(*236.524229665816205802475507955662978689529495212189123700918960987819\
1503842923328262614446040651740158273156783713119081258346660265142723\
4274427105594126955313116860411612083861052580225370086489053569521786\
2904747256025268265634804779972121165463414017307686882073420880127926\
6449852686694894872163285582988066271538614866081120872605960559963974\
1741411073319325669016028120303797383851374909265795629468864202015391\
2744034670408352710424679914028076197059813818175381871686510592062755\
64809906202*)

Regards, MI

POSTED BY: Mariusz Iwaniuk
Answer
3 months ago

Dear Mariusz Thank you very much your kind reply.
However, you gave the zeros of the Riemann zeta function.

Reality, I want see the calculation results ( only four calculations) on the above-my function with

$ s_1=0.5+it_1$ and $ s_2=0.5+it_2$ ........... (see $ t_1$ and $ t_2$ on above)

$ N_1=10^{14}$ and $ N_2=10^{18}$

We will see the zeros, but I do not know how sophisticated.

POSTED BY: Bahattin GUNES
Answer
3 months ago

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