Give me an odd prime = Computing the primitive root for q = 4735703723 and saving on file
Primitive root generation time: 0 min, 0 sec, 0 millisec
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Now you can call the precomputation programs
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*** Generating wisdom-outplace-fftwq-estimate
*** Saving wisdom-outplace-fftwq-estimate.txt
***** Quadruple precision version: precision forced to 128 bits
main steps: COMPUTE, ODDRESULT, EVENRESULT
runComputation: steps: COMPUTE, ODDRESULT, EVENRESULT
****** GETTING DIVISORS FROM FILE
Plan generation
62.000000 min. 46.000000 sec. 537.811000 millisec.
COMPUTE ODD
LNGammaOdd computation
268.000000 min. 7.000000 sec. 638.970000 millisec.
p4735703723-LGodd.qd
1.000000 min. 22.000000 sec. 750.897000 millisec.
FFT(LGodd)
1250.000000 min. 10.000000 sec. 305.949000 millisec.
p4735703723-fftLGodd.qd
1.000000 min. 41.000000 sec. 986.693000 millisec.
AK computation
79.000000 min. 47.000000 sec. 68.156000 millisec.
p4735703723-ak.qd
1.000000 min. 50.000000 sec. 152.699000 millisec.
FFT(AK)
1349.000000 min. 32.000000 sec. 906.327000 millisec.
p4735703723-fftAK.qd
2.000000 min. 18.000000 sec. 279.004000 millisec.
Computing the sum and minmax over odd characters
*** indexes for minimal and maximal odd characters L'/L (1,chi)
chiminodd index = 1053513699
chimaxodd index = 109527127
Kummer_realcorrection = -7.6417361970796018263678225973e+10
Kummer_res = +7.6417361971339304061105974723e+10
Kummer (r) = +1.7216545866766412593076816570e+00
log r = +5.4328579742774874963741350126e-01
H_correction = -5.4393211659362118127955145875e+10
log h1 = +2.2024150311977185933150828848e+10
log Pi_odd = +5.4328579742774874963741350126e-01
*** indexes for minimal and maximal odd characters L (1,chi)
chiminoddL index = 2393547739
chimaxoddL index = 4661416525
*** indexes for minimal and maximal odd characters L'(1,chi)
chiminoddLprime index = 1053513699
chimaxoddLprime index = 4661416525
*** indexes for minimal and maximal odd characters |b_chi|
chiminoddbchi index = 167510273
chimaxoddbchi index = 3406253719
*** First: oddresult = -5718581831.426148580671585484727627566822 , (res = -1.207546368167540150963870905301 )
OddResult computation
151.000000 min. 59.000000 sec. 495.001000 millisec.
COMPUTE EVEN
loadTable(): initialize table
INFO: precomputed table allocated 138 elements
INFO: init() time (seconds) = 0.000031
S computation
513.000000 min. 16.000000 sec. 212.380000 millisec.
p4735703723-S.qd
1.000000 min. 43.000000 sec. 381.145000 millisec.
Sfft
1324.000000 min. 50.000000 sec. 959.112000 millisec.
p4735703723-fftS.qd
1.000000 min. 49.000000 sec. 702.507000 millisec.
mkLGeven
94.000000 min. 11.000000 sec. 806.308000 millisec.
p4735703723-LGeven.qd
1.000000 min. 52.000000 sec. 490.871000 millisec.
LGevenfft
1254.000000 min. 42.000000 sec. 85.884000 millisec.
p4735703723-fftLGeven.qd
1.000000 min. 48.000000 sec. 992.977000 millisec.
Computing the sum and minmax over even characters ...
*** indexes for minimal and maximal even characters L'/L (1,chi)
chimineven index = 218597746
chimaxeven index = 533164980
*** indexes for minimal and maximal even characters L(1,chi)
chiminevenL index = 2046385888
chimaxevenL index = 22876360
*** indexes for minimal and maximal even characters L'(1,chi)
chiminevenLprime index = 218597746
chimaxevenLprime index = 22876360
*** indexes for minimal and maximal even characters |b_chi|
chiminevenbchi index = 22876360
chimaxevenbchi index = 1524649012
log Pi_even = -3.3390335386229874749740014963e+00
*** Second: evenresult = -5718581802.323617811518709530948008269629 , (res = -11437163604.647235623037419061896016539259 )
EvenResult computation
97.000000 min. 14.000000 sec. 490.632000 millisec.
*** RESULTS:
--------------
gamma_Kr constants for every intermediate field
----
gammaK_1(4735703723) = 1.056428893764344022673709438089
gammaKplus_1(4735703723) = 14.160541298253937265937194351669
----
gammaK_331(4735703723) = 19.223284856734784795146394196470
gammaKplus_331(4735703723) = 18.491518772185233967931160702086
----
gammaK_7153631(4735703723) = -18.651038760350993945818912928063
gammaKplus_7153631(4735703723) = -4.984748623671112956600100779609
----
gammaK_2367851861(4735703723) = 0.464104660707815945702908514986
gammaKplus_2367851861(4735703723) = 0.577215664901532865549427242513
--------------
Other quantities
--------------
[1] EK(4735703723) = 1.056428893764344022673709438089
[2] EKplus(4735703723) = 14.160541298253937265937194351669
[3] EK(4735703723)diff = -13.104112404489593243263484086400
--------------
[4] min_even(4735703723) = 0.000012608171961461755936741663
[5] min_odd(4735703723) = 0.000036894628865902820197275954
[6] min_{chi neq chi_0}|L'/L(1,chi)|(4735703723) = 0.000012608171961461755936741663
--------------
[7] max_even(4735703723) = 3.354587420890358498148316982319
[8] max_odd(4735703723) = 3.346369634315847686770484229825
[9] max_{chi neq chi_0}|L'/L(1,chi)|(4735703723) = 3.354587420890358498148316982319
--------------
[10] Kummer_ratio(4735703723) = 1.721654586676641259307681656987
[11] log(Kummer) = log r(4735703723) = 0.543285797427748749637413501255
[12] logh_1(4735703723) = 22024150311.977185933150828848042182143339
--------------
[13] Pi(4735703723,1.0Q) = 16.374868340189785529016869523684
[14] Laurent series of zeta_{Q(zeta_q)} at 1: c_{-1} = Pi(q,1)^(-1) = 0.061069193304329795352852547185
[15] c_{0} = c_{-1} * EK = 0.064515260325574010683200358515
--------------
[16] minL_even(4735703723) = 0.228619959448219761661550623832
[17] minL_odd(4735703723) = 0.222456671429765976154836294524
[18] minL_{chi neq chi_0}|L(1,chi)|(4735703723) = 0.222456671429765976154836294524
--------------
[19] maxL_even(4735703723) = 6.833998279331400599241566426285
[20] maxL_odd(4735703723) = 6.681995275257390140738066994084
[21] maxL_{chi neq chi_0}|L(1,chi)|(4735703723) = 6.833998279331400599241566426285
--------------
[22] minLprime_even(4735703723) = 0.000016910172985514481822170484
[23] minLprime_odd(4735703723) = 0.000032613732836533921179704578
[24] minLprime_{chi neq chi_0}|Lprime(1,chi)|(4735703723) = 0.000016910172985514481822170484
--------------
[25] maxLprime_even(4735703723) = 22.446410831132053200818903562379
[26] maxLprime_odd(4735703723) = 21.968341232264072769956063032329
[27] maxLprime_{chi neq chi_0}|Lprime(1,chi)|(4735703723) = 22.446410831132053200818903562379
--------------
[28] minbchi_even(4735703723) = 16.579604675305928028091200073418
[29] minbchi_odd(4735703723) = 16.576797341308234180876086284291
[30] minbchi_{chi neq chi_0}(4735703723) = 16.576797341308234180876086284291
--------------
[31] maxbchi_even(4735703723) = 22.690679634520952395836210269263
[32] maxbchi_odd(4735703723) = 22.719898620995451864735721344389
[33] maxbchi_{chi neq chi_0}(4735703723) = 22.719898620995451864735721344389
--------------
******** the quadratic character is odd
[34] L(1,chi_quad)(4735703723) = 0.744260789346737045232640542213
[35] L(1,chi_quad)/log(4735703723) = 0.033407287649034232250708410901
[36] L(1,chi_quad)/loglog(4735703723) = 0.239804295065829288797131523537
[37] Lprime(1,chi_quad)(4735703723) = -0.084184085265017838985046004753
[38] Lderlog(1,chi_quad)(4735703723) = -0.113111004193716919846518727527
--------------
*** A priori (closed formulas) norms ***
N1LGeven = +1.6412698302965714359202758020e+09
N00LGeven = +2.1133666288233676069498725663e+01
N00LGodd = +2.2278396173839304397228845766e+01
N1Seven = +9.5015094467965930129541260553e+09
N00Seven = +4.9632693608939944747291684028e+02
N1AKodd = +1.1839259302500000000527904647e+09
N00AKodd = +9.9999999957767628276943202682e-01
N2AKodd = +2.8094197858869958015637817264e+04
TOTAL TIME
6467.000000 min. 58.000000 sec. 647.431000 millisec.
removing unneeded files for 4735703723 ...
DONE