****** A. LANGUASCO & A. ZACCAGNINI ******* ****** FIRST SUM VERIFICATION FOR 3 <= q <= 100 ******* ******************* START CHECK ******************** ************************** q = 3 The sum of B(q,a) over a coprime with q is = -0.243586677279059028206405469342690768751935597549563528333022030149175877964715543288385337373520030587364785287946153327 The expected value for the sum is = -0.243586677279059028206405469342690768751935597549563528333022030149175877964715543288385337373520030587364785287946153325 The difference between the sum and the expected value is = -2.349144534 E-120 ************************** q = 4 The sum of B(q,a) over a coprime with q is = -0.122571271493944767433853130015530003915092553318469138493023011466549593910601745616941104861081410957998518979429314267 The expected value for the sum is = -0.122571271493944767433853130015530003915092553318469138493023011466549593910601745616941104861081410957998518979429314266 The difference between the sum and the expected value is = -9.85522228 E-121 ************************** q = 5 The sum of B(q,a) over a coprime with q is = -0.292574900739680321084790161163872068615991602130717178942415148472551472112028127804397207757157862784036659019425808567 The expected value for the sum is = -0.292574900739680321084790161163872068615991602130717178942415148472551472112028127804397207757157862784036659019425808568 The difference between the sum and the expected value is = 7.87039779 E-121 ************************** q = 6 The sum of B(q,a) over a coprime with q is = -0.0504394967191137187891733478845142006764354631893082742123420206557822559950208276825220103771013430453633042673754675936 The expected value for the sum is = -0.0504394967191137187891733478845142006764354631893082742123420206557822559950208276825220103771013430453633042673754675910 The difference between the sum and the expected value is = -2.634669966 E-120 ************************** q = 7 The sum of B(q,a) over a coprime with q is = -0.304424915083774629701067009268371972219355793137010767152544357010394125459388018771767872222636490694052673023534553426 The expected value for the sum is = -0.304424915083774629701067009268371972219355793137010767152544357010394125459388018771767872222636490694052673023534553421 The difference between the sum and the expected value is = -4.257366328 E-120 ************************** q = 8 The sum of B(q,a) over a coprime with q is = -0.122571271493944767433853130015530003915092553318469138493023011466549593910601745616941104861081410957998518979429314265 The expected value for the sum is = -0.122571271493944767433853130015530003915092553318469138493023011466549593910601745616941104861081410957998518979429314266 The difference between the sum and the expected value is = 1.294478375 E-120 ************************** q = 9 The sum of B(q,a) over a coprime with q is = -0.243586677279059028206405469342690768751935597549563528333022030149175877964715543288385337373520030587364785287946153322 The expected value for the sum is = -0.243586677279059028206405469342690768751935597549563528333022030149175877964715543288385337373520030587364785287946153325 The difference between the sum and the expected value is = 2.420857448 E-120 ************************** q = 10 The sum of B(q,a) over a coprime with q is = -0.0994277201797350116675580397056955005404914677704619248217351389791578501423334121985338807607391752420351779988551228318 The expected value for the sum is = -0.0994277201797350116675580397056955005404914677704619248217351389791578501423334121985338807607391752420351779988551228340 The difference between the sum and the expected value is = 2.201519547 E-120 ************************** q = 11 The sum of B(q,a) over a coprime with q is = -0.311317363158656125898042219102032388860896413279171102519372303706033110735321319292837838035372696336342967245057341024 The expected value for the sum is = -0.311317363158656125898042219102032388860896413279171102519372303706033110735321319292837838035372696336342967245057341020 The difference between the sum and the expected value is = -4.255126776 E-120 ************************** q = 12 The sum of B(q,a) over a coprime with q is = -0.0504394967191137187891733478845142006764354631893082742123420206557822559950208276825220103771013430453633042673754675895 The expected value for the sum is = -0.0504394967191137187891733478845142006764354631893082742123420206557822559950208276825220103771013430453633042673754675910 The difference between the sum and the expected value is = 1.495330006 E-120 ************************** q = 13 The sum of B(q,a) over a coprime with q is = -0.312598821303430574104230366670343731060738646384854159247634939843837008790807756831649100300503150525791722091259592496 The expected value for the sum is = -0.312598821303430574104230366670343731060738646384854159247634939843837008790807756831649100300503150525791722091259592501 The difference between the sum and the expected value is = 5.125328362 E-120 ************************** q = 14 The sum of B(q,a) over a coprime with q is = -0.111277734523829320283834887810195404143855658776755513031864347517000503489693303165904545226217803152051192002963867685 The expected value for the sum is = -0.111277734523829320283834887810195404143855658776755513031864347517000503489693303165904545226217803152051192002963867688 The difference between the sum and the expected value is = 2.587107938 E-120 ************************** q = 15 The sum of B(q,a) over a coprime with q is = -0.220443125964849272440110379032856265377334512001556314661734157661784134196447209869978113273177794871401444307371961907 The expected value for the sum is = -0.220443125964849272440110379032856265377334512001556314661734157661784134196447209869978113273177794871401444307371961892 The difference between the sum and the expected value is = -1.494710067 E-119 ************************** q = 16 The sum of B(q,a) over a coprime with q is = -0.122571271493944767433853130015530003915092553318469138493023011466549593910601745616941104861081410957998518979429314267 The expected value for the sum is = -0.122571271493944767433853130015530003915092553318469138493023011466549593910601745616941104861081410957998518979429314266 The difference between the sum and the expected value is = -4.735203254 E-121 ************************** q = 17 The sum of B(q,a) over a coprime with q is = -0.313917359649219940152832060609756896939684330181059445328597085757107480899320513322398165923318959973187073799801567994 The expected value for the sum is = -0.313917359649219940152832060609756896939684330181059445328597085757107480899320513322398165923318959973187073799801567996 The difference between the sum and the expected value is = 2.697681352 E-120 ************************** q = 18 The sum of B(q,a) over a coprime with q is = -0.0504394967191137187891733478845142006764354631893082742123420206557822559950208276825220103771013430453633042673754675925 The expected value for the sum is = -0.0504394967191137187891733478845142006764354631893082742123420206557822559950208276825220103771013430453633042673754675910 The difference between the sum and the expected value is = -1.554669622 E-120 ************************** q = 19 The sum of B(q,a) over a coprime with q is = -0.314282809730982730102411993836449433176326255332718152718443040266401143275643400809109305718274646768269326984367859816 The expected value for the sum is = -0.314282809730982730102411993836449433176326255332718152718443040266401143275643400809109305718274646768269326984367859817 The difference between the sum and the expected value is = 1.187024231 E-120 ************************** q = 20 The sum of B(q,a) over a coprime with q is = -0.0994277201797350116675580397056955005404914677704619248217351389791578501423334121985338807607391752420351779988551228255 The expected value for the sum is = -0.0994277201797350116675580397056955005404914677704619248217351389791578501423334121985338807607391752420351779988551228340 The difference between the sum and the expected value is = 8.46452076 E-120 ************************** q = 21 The sum of B(q,a) over a coprime with q is = -0.232293140308943581056387227137356168980698703007849902871863366199626787543807100837348777738656422781417458311480706753 The expected value for the sum is = -0.232293140308943581056387227137356168980698703007849902871863366199626787543807100837348777738656422781417458311480706746 The difference between the sum and the expected value is = -7.07151025 E-120 ************************** q = 22 The sum of B(q,a) over a coprime with q is = -0.118170182598710816480810097643855820785396278918915848398692294212639488765626603686974511038954008794341486224486655291 The expected value for the sum is = -0.118170182598710816480810097643855820785396278918915848398692294212639488765626603686974511038954008794341486224486655287 The difference between the sum and the expected value is = -4.390652868 E-120 ************************** q = 23 The sum of B(q,a) over a coprime with q is = -0.314744950352621456914812466912903277967158491570743688649967536013960694039299156922712679051384850059041732467813329980 The expected value for the sum is = -0.314744950352621456914812466912903277967158491570743688649967536013960694039299156922712679051384850059041732467813329969 The difference between the sum and the expected value is = -1.134005070 E-119 ************************** q = 24 The sum of B(q,a) over a coprime with q is = -0.0504394967191137187891733478845142006764354631893082742123420206557822559950208276825220103771013430453633042673754675846 The expected value for the sum is = -0.0504394967191137187891733478845142006764354631893082742123420206557822559950208276825220103771013430453633042673754675910 The difference between the sum and the expected value is = 6.34533058 E-120 ************************** q = 25 The sum of B(q,a) over a coprime with q is = -0.292574900739680321084790161163872068615991602130717178942415148472551472112028127804397207757157862784036659019425808567 The expected value for the sum is = -0.292574900739680321084790161163872068615991602130717178942415148472551472112028127804397207757157862784036659019425808568 The difference between the sum and the expected value is = 1.129363172 E-120 ************************** q = 26 The sum of B(q,a) over a coprime with q is = -0.119451640743485264686998245212167162985238512024598905126954930350443386821113041225785773304084462983790241070688906756 The expected value for the sum is = -0.119451640743485264686998245212167162985238512024598905126954930350443386821113041225785773304084462983790241070688906768 The difference between the sum and the expected value is = 1.127589406 E-119 ************************** q = 27 The sum of B(q,a) over a coprime with q is = -0.243586677279059028206405469342690768751935597549563528333022030149175877964715543288385337373520030587364785287946153318 The expected value for the sum is = -0.243586677279059028206405469342690768751935597549563528333022030149175877964715543288385337373520030587364785287946153325 The difference between the sum and the expected value is = 6.45836513 E-120 ************************** q = 28 The sum of B(q,a) over a coprime with q is = -0.111277734523829320283834887810195404143855658776755513031864347517000503489693303165904545226217803152051192002963867676 The expected value for the sum is = -0.111277734523829320283834887810195404143855658776755513031864347517000503489693303165904545226217803152051192002963867688 The difference between the sum and the expected value is = 1.152710937 E-119 ************************** q = 29 The sum of B(q,a) over a coprime with q is = -0.315109890863309628780043998574776108146233737575593389703127665827736437985626964859856952378973267586237485314929125904 The expected value for the sum is = -0.315109890863309628780043998574776108146233737575593389703127665827736437985626964859856952378973267586237485314929125928 The difference between the sum and the expected value is = 2.436599898 E-119 ************************** q = 30 The sum of B(q,a) over a coprime with q is = -0.0272959454049039630228782575746796973018343776413010605410541481683905122267524942641147862767591073293999632868012761757 The expected value for the sum is = -0.0272959454049039630228782575746796973018343776413010605410541481683905122267524942641147862767591073293999632868012761586 The difference between the sum and the expected value is = -1.712263086 E-119 ************************** q = 31 The sum of B(q,a) over a coprime with q is = -0.315186693747028238593222134667271531853761932681912913141136215348093218307738934183068689457001919573089908477268785693 The expected value for the sum is = -0.315186693747028238593222134667271531853761932681912913141136215348093218307738934183068689457001919573089908477268785690 The difference between the sum and the expected value is = -3.444119662 E-120 ************************** q = 32 The sum of B(q,a) over a coprime with q is = -0.122571271493944767433853130015530003915092553318469138493023011466549593910601745616941104861081410957998518979429314269 The expected value for the sum is = -0.122571271493944767433853130015530003915092553318469138493023011466549593910601745616941104861081410957998518979429314266 The difference between the sum and the expected value is = -2.986317559 E-120 ************************** q = 33 The sum of B(q,a) over a coprime with q is = -0.239185588383825077253362436971016585622239323150010238238691312895265772819740401358418743551392628423707752533003494335 The expected value for the sum is = -0.239185588383825077253362436971016585622239323150010238238691312895265772819740401358418743551392628423707752533003494345 The difference between the sum and the expected value is = 9.93613420 E-120 ************************** q = 34 The sum of B(q,a) over a coprime with q is = -0.120770179089274630735599939151580328864184195820804191207917076263713858929625797716534838926900272431185592779230882254 The expected value for the sum is = -0.120770179089274630735599939151580328864184195820804191207917076263713858929625797716534838926900272431185592779230882263 The difference between the sum and the expected value is = 8.19915240 E-120 ************************** q = 35 The sum of B(q,a) over a coprime with q is = -0.281281363769564873934771918958537468844754707589003553481256484523002381691119685353360648122294254978089332042960361994 The expected value for the sum is = -0.281281363769564873934771918958537468844754707589003553481256484523002381691119685353360648122294254978089332042960361989 The difference between the sum and the expected value is = -5.125804046 E-120 ************************** q = 36 The sum of B(q,a) over a coprime with q is = -0.0504394967191137187891733478845142006764354631893082742123420206557822559950208276825220103771013430453633042673754675925 The expected value for the sum is = -0.0504394967191137187891733478845142006764354631893082742123420206557822559950208276825220103771013430453633042673754675910 The difference between the sum and the expected value is = -1.560668472 E-120 ************************** q = 37 The sum of B(q,a) over a coprime with q is = -0.315346504892802661134971324230690980563523511904124667706566053055756326293569787809768088832660017405161094909188462590 The expected value for the sum is = -0.315346504892802661134971324230690980563523511904124667706566053055756326293569787809768088832660017405161094909188462593 The difference between the sum and the expected value is = 3.509314832 E-120 ************************** q = 38 The sum of B(q,a) over a coprime with q is = -0.121135629171037420685179872378272865100826120972462898597763030773007521305948685203245978721855959226267845963797174080 The expected value for the sum is = -0.121135629171037420685179872378272865100826120972462898597763030773007521305948685203245978721855959226267845963797174083 The difference between the sum and the expected value is = 3.571483801 E-120 ************************** q = 39 The sum of B(q,a) over a coprime with q is = -0.240467046528599525459550584539327927822081556255693294966953949033069670875226838897230005816523082613156507379205745823 The expected value for the sum is = -0.240467046528599525459550584539327927822081556255693294966953949033069670875226838897230005816523082613156507379205745826 The difference between the sum and the expected value is = 2.865281334 E-120 ************************** q = 40 The sum of B(q,a) over a coprime with q is = -0.0994277201797350116675580397056955005404914677704619248217351389791578501423334121985338807607391752420351779988551228424 The expected value for the sum is = -0.0994277201797350116675580397056955005404914677704619248217351389791578501423334121985338807607391752420351779988551228340 The difference between the sum and the expected value is = -8.44207576 E-120 ************************** q = 41 The sum of B(q,a) over a coprime with q is = -0.315416083365957600227021478476040717610186414653096487171567055044568355530405256952113588592339204790419281078297030697 The expected value for the sum is = -0.315416083365957600227021478476040717610186414653096487171567055044568355530405256952113588592339204790419281078297030693 The difference between the sum and the expected value is = -3.513146887 E-120 ************************** q = 42 The sum of B(q,a) over a coprime with q is = -0.0391459597489982716391551056791796009051985686475946487511833567062331655741123852314854507422377352394159772909100210090 The expected value for the sum is = -0.0391459597489982716391551056791796009051985686475946487511833567062331655741123852314854507422377352394159772909100210124 The difference between the sum and the expected value is = 3.427960103 E-120 ************************** q = 43 The sum of B(q,a) over a coprime with q is = -0.315443768597184331389096095765695027163624947817848825225154342128807633901171345045373269985478603297620547180096854353 The expected value for the sum is = -0.315443768597184331389096095765695027163624947817848825225154342128807633901171345045373269985478603297620547180096854328 The difference between the sum and the expected value is = -2.480804741 E-119 ************************** q = 44 The sum of B(q,a) over a coprime with q is = -0.118170182598710816480810097643855820785396278918915848398692294212639488765626603686974511038954008794341486224486655262 The expected value for the sum is = -0.118170182598710816480810097643855820785396278918915848398692294212639488765626603686974511038954008794341486224486655287 The difference between the sum and the expected value is = 2.474975260 E-119 ************************** q = 45 The sum of B(q,a) over a coprime with q is = -0.220443125964849272440110379032856265377334512001556314661734157661784134196447209869978113273177794871401444307371961890 The expected value for the sum is = -0.220443125964849272440110379032856265377334512001556314661734157661784134196447209869978113273177794871401444307371961892 The difference between the sum and the expected value is = 2.266310681 E-120 ************************** q = 46 The sum of B(q,a) over a coprime with q is = -0.121597769792676147497580345454726709891658357210488434529287526520567072069604441316849352054966162517040251447242644250 The expected value for the sum is = -0.121597769792676147497580345454726709891658357210488434529287526520567072069604441316849352054966162517040251447242644235 The difference between the sum and the expected value is = -1.492549994 E-119 ************************** q = 47 The sum of B(q,a) over a coprime with q is = -0.315488842577607341317949322203948102803911996561319015106978146235894849052392657735528033742380385397193929201521609738 The expected value for the sum is = -0.315488842577607341317949322203948102803911996561319015106978146235894849052392657735528033742380385397193929201521609773 The difference between the sum and the expected value is = 3.503600431 E-119 ************************** q = 48 The sum of B(q,a) over a coprime with q is = -0.0504394967191137187891733478845142006764354631893082742123420206557822559950208276825220103771013430453633042673754675907 The expected value for the sum is = -0.0504394967191137187891733478845142006764354631893082742123420206557822559950208276825220103771013430453633042673754675910 The difference between the sum and the expected value is = 2.531320804 E-121 ************************** q = 49 The sum of B(q,a) over a coprime with q is = -0.304424915083774629701067009268371972219355793137010767152544357010394125459388018771767872222636490694052673023534553431 The expected value for the sum is = -0.304424915083774629701067009268371972219355793137010767152544357010394125459388018771767872222636490694052673023534553421 The difference between the sum and the expected value is = -9.35076779 E-120 ************************** q = 50 The sum of B(q,a) over a coprime with q is = -0.0994277201797350116675580397056955005404914677704619248217351389791578501423334121985338807607391752420351779988551228315 The expected value for the sum is = -0.0994277201797350116675580397056955005404914677704619248217351389791578501423334121985338807607391752420351779988551228340 The difference between the sum and the expected value is = 2.478825781 E-120 ************************** q = 51 The sum of B(q,a) over a coprime with q is = -0.241785584874388891508152278478741093701027240051898581047916094946340142983739595387979071439338892060551859087747721322 The expected value for the sum is = -0.241785584874388891508152278478741093701027240051898581047916094946340142983739595387979071439338892060551859087747721321 The difference between the sum and the expected value is = -1.344454641 E-120 ************************** q = 52 The sum of B(q,a) over a coprime with q is = -0.119451640743485264686998245212167162985238512024598905126954930350443386821113041225785773304084462983790241070688906765 The expected value for the sum is = -0.119451640743485264686998245212167162985238512024598905126954930350443386821113041225785773304084462983790241070688906768 The difference between the sum and the expected value is = 2.205299897 E-120 ************************** q = 53 The sum of B(q,a) over a coprime with q is = -0.315538181611497484387020627114999787869902016172752716112771533422379172445889232167370333106792524963977522332058513082 The expected value for the sum is = -0.315538181611497484387020627114999787869902016172752716112771533422379172445889232167370333106792524963977522332058513099 The difference between the sum and the expected value is = 1.733999475 E-119 ************************** q = 54 The sum of B(q,a) over a coprime with q is = -0.0504394967191137187891733478845142006764354631893082742123420206557822559950208276825220103771013430453633042673754675853 The expected value for the sum is = -0.0504394967191137187891733478845142006764354631893082742123420206557822559950208276825220103771013430453633042673754675910 The difference between the sum and the expected value is = 5.647131996 E-120 ************************** q = 55 The sum of B(q,a) over a coprime with q is = -0.288173811844446370131747128792197885486295327731163888848084431218641366967052985874430613935030460620379626264483149600 The expected value for the sum is = -0.288173811844446370131747128792197885486295327731163888848084431218641366967052985874430613935030460620379626264483149588 The difference between the sum and the expected value is = -1.259817035 E-119 ************************** q = 56 The sum of B(q,a) over a coprime with q is = -0.111277734523829320283834887810195404143855658776755513031864347517000503489693303165904545226217803152051192002963867670 The expected value for the sum is = -0.111277734523829320283834887810195404143855658776755513031864347517000503489693303165904545226217803152051192002963867688 The difference between the sum and the expected value is = 1.824841349 E-119 ************************** q = 57 The sum of B(q,a) over a coprime with q is = -0.242151034956151681457732211705433629937669165203557288437762049455633805360062482874690211234294578855634112272314013139 The expected value for the sum is = -0.242151034956151681457732211705433629937669165203557288437762049455633805360062482874690211234294578855634112272314013141 The difference between the sum and the expected value is = 2.561669974 E-120 ************************** q = 58 The sum of B(q,a) over a coprime with q is = -0.121962710303364319362811877116599540070733603215338135582447656334342816015932249253993625382554580044236004294358440201 The expected value for the sum is = -0.121962710303364319362811877116599540070733603215338135582447656334342816015932249253993625382554580044236004294358440195 The difference between the sum and the expected value is = -5.840255624 E-120 ************************** q = 59 The sum of B(q,a) over a coprime with q is = -0.315573171236962844191471234963927629971835217817709874110118379952171742010551625983033896919988897304675830257649168363 The expected value for the sum is = -0.315573171236962844191471234963927629971835217817709874110118379952171742010551625983033896919988897304675830257649168347 The difference between the sum and the expected value is = -1.603279998 E-119 ************************** q = 60 The sum of B(q,a) over a coprime with q is = -0.0272959454049039630228782575746796973018343776413010605410541481683905122267524942641147862767591073293999632868012761602 The expected value for the sum is = -0.0272959454049039630228782575746796973018343776413010605410541481683905122267524942641147862767591073293999632868012761586 The difference between the sum and the expected value is = -1.625130359 E-120 ************************** q = 61 The sum of B(q,a) over a coprime with q is = -0.315582592725630332602296108654141912556380174589568880417480635032406556851823564883999053640751957525515582214051081931 The expected value for the sum is = -0.315582592725630332602296108654141912556380174589568880417480635032406556851823564883999053640751957525515582214051081971 The difference between the sum and the expected value is = 3.931314250 E-119 ************************** q = 62 The sum of B(q,a) over a coprime with q is = -0.122039513187082929175990013209094963778261798321657659020456205854699596338044218577205362460583232031088427456698099962 The expected value for the sum is = -0.122039513187082929175990013209094963778261798321657659020456205854699596338044218577205362460583232031088427456698099956 The difference between the sum and the expected value is = -5.493462732 E-120 ************************** q = 63 The sum of B(q,a) over a coprime with q is = -0.232293140308943581056387227137356168980698703007849902871863366199626787543807100837348777738656422781417458311480706748 The expected value for the sum is = -0.232293140308943581056387227137356168980698703007849902871863366199626787543807100837348777738656422781417458311480706746 The difference between the sum and the expected value is = -1.605428845 E-120 ************************** q = 64 The sum of B(q,a) over a coprime with q is = -0.122571271493944767433853130015530003915092553318469138493023011466549593910601745616941104861081410957998518979429314264 The expected value for the sum is = -0.122571271493944767433853130015530003915092553318469138493023011466549593910601745616941104861081410957998518979429314266 The difference between the sum and the expected value is = 2.645461102 E-120 ************************** q = 65 The sum of B(q,a) over a coprime with q is = -0.289455269989220818337935276360509227686137560836846945576347067356445265022539423413241876200160914809828381110685401063 The expected value for the sum is = -0.289455269989220818337935276360509227686137560836846945576347067356445265022539423413241876200160914809828381110685401069 The difference between the sum and the expected value is = 5.610022808 E-120 ************************** q = 66 The sum of B(q,a) over a coprime with q is = -0.0460384078238797678361303155128400175467391887897549841180113034018721508500456857525554165549739408817062715124328086009 The expected value for the sum is = -0.0460384078238797678361303155128400175467391887897549841180113034018721508500456857525554165549739408817062715124328086112 The difference between the sum and the expected value is = 1.026440020 E-119 ************************** q = 67 The sum of B(q,a) over a coprime with q is = -0.315605947823677920264389415336412408893730464905609145505084823043151174826884288496632989073140778725650417844334893975 The expected value for the sum is = -0.315605947823677920264389415336412408893730464905609145505084823043151174826884288496632989073140778725650417844334894010 The difference between the sum and the expected value is = 3.544548469 E-119 ************************** q = 68 The sum of B(q,a) over a coprime with q is = -0.120770179089274630735599939151580328864184195820804191207917076263713858929625797716534838926900272431185592779230882278 The expected value for the sum is = -0.120770179089274630735599939151580328864184195820804191207917076263713858929625797716534838926900272431185592779230882263 The difference between the sum and the expected value is = -1.568294248 E-119 ************************** q = 69 The sum of B(q,a) over a coprime with q is = -0.242613175577790408270132684781887474728501401441582824369286545203193356123718238988293584567404782146406517755759483312 The expected value for the sum is = -0.242613175577790408270132684781887474728501401441582824369286545203193356123718238988293584567404782146406517755759483293 The difference between the sum and the expected value is = -1.842516372 E-119 ************************** q = 70 The sum of B(q,a) over a coprime with q is = -0.0881341832096195645175397975003609007692545732287482993605764750296087597214249697474973211258755674360878510223896762649 The expected value for the sum is = -0.0881341832096195645175397975003609007692545732287482993605764750296087597214249697474973211258755674360878510223896762554 The difference between the sum and the expected value is = -9.49624260 E-120 ************************** q = 71 The sum of B(q,a) over a coprime with q is = -0.315618324104187165771735480468498102610047449601327660252600903640561082893938547505568923938391128322252141986923319399 The expected value for the sum is = -0.315618324104187165771735480468498102610047449601327660252600903640561082893938547505568923938391128322252141986923319413 The difference between the sum and the expected value is = 1.409874653 E-119 ************************** q = 72 The sum of B(q,a) over a coprime with q is = -0.0504394967191137187891733478845142006764354631893082742123420206557822559950208276825220103771013430453633042673754675945 The expected value for the sum is = -0.0504394967191137187891733478845142006764354631893082742123420206557822559950208276825220103771013430453633042673754675910 The difference between the sum and the expected value is = -3.518465822 E-120 ************************** q = 73 The sum of B(q,a) over a coprime with q is = -0.315623760058540560171026245953375251593622731396405092479569845854692555319699878648282901009224458146543213778537436783 The expected value for the sum is = -0.315623760058540560171026245953375251593622731396405092479569845854692555319699878648282901009224458146543213778537436807 The difference between the sum and the expected value is = 2.392150714 E-119 ************************** q = 74 The sum of B(q,a) over a coprime with q is = -0.122199324332857351717739202772514412488023377543869413585886043562362704323875072203904761836241329863159613888617776860 The expected value for the sum is = -0.122199324332857351717739202772514412488023377543869413585886043562362704323875072203904761836241329863159613888617776860 The difference between the sum and the expected value is = -6.321517618 E-121 ************************** q = 75 The sum of B(q,a) over a coprime with q is = -0.220443125964849272440110379032856265377334512001556314661734157661784134196447209869978113273177794871401444307371961887 The expected value for the sum is = -0.220443125964849272440110379032856265377334512001556314661734157661784134196447209869978113273177794871401444307371961892 The difference between the sum and the expected value is = 5.717321838 E-120 ************************** q = 76 The sum of B(q,a) over a coprime with q is = -0.121135629171037420685179872378272865100826120972462898597763030773007521305948685203245978721855959226267845963797174094 The expected value for the sum is = -0.121135629171037420685179872378272865100826120972462898597763030773007521305948685203245978721855959226267845963797174083 The difference between the sum and the expected value is = -1.100450948 E-119 ************************** q = 77 The sum of B(q,a) over a coprime with q is = -0.300023826188540678748023976896697789089659518737457477058213639756484020314412876841801278400509088530395640268591894446 The expected value for the sum is = -0.300023826188540678748023976896697789089659518737457477058213639756484020314412876841801278400509088530395640268591894442 The difference between the sum and the expected value is = -4.319240580 E-120 ************************** q = 78 The sum of B(q,a) over a coprime with q is = -0.0473198659686542160423184630811513597465814218954380408462739395396760489055321232913666788201043950711550263586350600914 The expected value for the sum is = -0.0473198659686542160423184630811513597465814218954380408462739395396760489055321232913666788201043950711550263586350600922 The difference between the sum and the expected value is = 8.95748131 E-121 ************************** q = 79 The sum of B(q,a) over a coprime with q is = -0.315637654124561585366889320064898805826322758427174690741774542004616319547059057614145659435326579745737011265735101567 The expected value for the sum is = -0.315637654124561585366889320064898805826322758427174690741774542004616319547059057614145659435326579745737011265735101528 The difference between the sum and the expected value is = -3.882156395 E-119 ************************** q = 80 The sum of B(q,a) over a coprime with q is = -0.0994277201797350116675580397056955005404914677704619248217351389791578501423334121985338807607391752420351779988551228490 The expected value for the sum is = -0.0994277201797350116675580397056955005404914677704619248217351389791578501423334121985338807607391752420351779988551228340 The difference between the sum and the expected value is = -1.502982890 E-119 ************************** q = 81 The sum of B(q,a) over a coprime with q is = -0.243586677279059028206405469342690768751935597549563528333022030149175877964715543288385337373520030587364785287946153344 The expected value for the sum is = -0.243586677279059028206405469342690768751935597549563528333022030149175877964715543288385337373520030587364785287946153325 The difference between the sum and the expected value is = -1.947624453 E-119 ************************** q = 82 The sum of B(q,a) over a coprime with q is = -0.122268902806012290809789357017864149534686280292841233050887045551174733560710541346250261595920517248417800057726344965 The expected value for the sum is = -0.122268902806012290809789357017864149534686280292841233050887045551174733560710541346250261595920517248417800057726344959 The difference between the sum and the expected value is = -5.757707626 E-120 ************************** q = 83 The sum of B(q,a) over a coprime with q is = -0.315645284292629604009006113039366058545720355256972621009075971750640078824489402253762422532440596586978991388639126733 The expected value for the sum is = -0.315645284292629604009006113039366058545720355256972621009075971750640078824489402253762422532440596586978991388639126814 The difference between the sum and the expected value is = 8.13571282 E-119 ************************** q = 84 The sum of B(q,a) over a coprime with q is = -0.0391459597489982716391551056791796009051985686475946487511833567062331655741123852314854507422377352394159772909100209945 The expected value for the sum is = -0.0391459597489982716391551056791796009051985686475946487511833567062331655741123852314854507422377352394159772909100210124 The difference between the sum and the expected value is = 1.791076235 E-119 ************************** q = 85 The sum of B(q,a) over a coprime with q is = -0.290773808335010184386536970299922393565083244633052231657309213269715737131052179903990941822976724257223732819227376578 The expected value for the sum is = -0.290773808335010184386536970299922393565083244633052231657309213269715737131052179903990941822976724257223732819227376564 The difference between the sum and the expected value is = -1.447631479 E-119 ************************** q = 86 The sum of B(q,a) over a coprime with q is = -0.122296588037239021971863974307518459088124813457593571104474332635414011931476629439509942989059915755619066159526168588 The expected value for the sum is = -0.122296588037239021971863974307518459088124813457593571104474332635414011931476629439509942989059915755619066159526168595 The difference between the sum and the expected value is = 6.94716419 E-120 ************************** q = 87 The sum of B(q,a) over a coprime with q is = -0.242978116088478580135364216443760304907576647446432525422446675016969100070046046925437857894993199673602270602875279273 The expected value for the sum is = -0.242978116088478580135364216443760304907576647446432525422446675016969100070046046925437857894993199673602270602875279253 The difference between the sum and the expected value is = -1.976170755 E-119 ************************** q = 88 The sum of B(q,a) over a coprime with q is = -0.118170182598710816480810097643855820785396278918915848398692294212639488765626603686974511038954008794341486224486655301 The expected value for the sum is = -0.118170182598710816480810097643855820785396278918915848398692294212639488765626603686974511038954008794341486224486655287 The difference between the sum and the expected value is = -1.471670240 E-119 ************************** q = 89 The sum of B(q,a) over a coprime with q is = -0.315654851856136486127808529548010738656611467676307516649410934091732576968104894893104670023510715141409530812955749020 The expected value for the sum is = -0.315654851856136486127808529548010738656611467676307516649410934091732576968104894893104670023510715141409530812955749030 The difference between the sum and the expected value is = 9.50095659 E-120 ************************** q = 90 The sum of B(q,a) over a coprime with q is = -0.0272959454049039630228782575746796973018343776413010605410541481683905122267524942641147862767591073293999632868012761606 The expected value for the sum is = -0.0272959454049039630228782575746796973018343776413010605410541481683905122267524942641147862767591073293999632868012761586 The difference between the sum and the expected value is = -2.035229909 E-120 ************************** q = 91 The sum of B(q,a) over a coprime with q is = -0.301305284333315126954212124465009131289501751843140533786476275894287918369899314380612540665639542719844395114794145873 The expected value for the sum is = -0.301305284333315126954212124465009131289501751843140533786476275894287918369899314380612540665639542719844395114794145923 The difference between the sum and the expected value is = 5.01403655 E-119 ************************** q = 92 The sum of B(q,a) over a coprime with q is = -0.121597769792676147497580345454726709891658357210488434529287526520567072069604441316849352054966162517040251447242644234 The expected value for the sum is = -0.121597769792676147497580345454726709891658357210488434529287526520567072069604441316849352054966162517040251447242644235 The difference between the sum and the expected value is = 1.527491425 E-120 ************************** q = 93 The sum of B(q,a) over a coprime with q is = -0.243054918972197189948542352536255728615104842552752048860455224537325880392158016248649594973021851660454693765214939044 The expected value for the sum is = -0.243054918972197189948542352536255728615104842552752048860455224537325880392158016248649594973021851660454693765214939015 The difference between the sum and the expected value is = -2.902922637 E-119 ************************** q = 94 The sum of B(q,a) over a coprime with q is = -0.122341662017662031900717200745771534728411862201063760986298136742501227082697942129664706745961697855192448180950924047 The expected value for the sum is = -0.122341662017662031900717200745771534728411862201063760986298136742501227082697942129664706745961697855192448180950924039 The difference between the sum and the expected value is = -8.12999591 E-120 ************************** q = 95 The sum of B(q,a) over a coprime with q is = -0.291139258416772974336116903526614929801725169784710939047155167779009399507375067390702081617932411052305986003793668396 The expected value for the sum is = -0.291139258416772974336116903526614929801725169784710939047155167779009399507375067390702081617932411052305986003793668384 The difference between the sum and the expected value is = -1.117854892 E-119 ************************** q = 96 The sum of B(q,a) over a coprime with q is = -0.0504394967191137187891733478845142006764354631893082742123420206557822559950208276825220103771013430453633042673754675771 The expected value for the sum is = -0.0504394967191137187891733478845142006764354631893082742123420206557822559950208276825220103771013430453633042673754675910 The difference between the sum and the expected value is = 1.383783511 E-119 ************************** q = 97 The sum of B(q,a) over a coprime with q is = -0.315664943368858957133295247179029691866462829076958449697212517840310801395996004494794282804618085380305104035895505320 The expected value for the sum is = -0.315664943368858957133295247179029691866462829076958449697212517840310801395996004494794282804618085380305104035895505309 The difference between the sum and the expected value is = -1.065512028 E-119 ************************** q = 98 The sum of B(q,a) over a coprime with q is = -0.111277734523829320283834887810195404143855658776755513031864347517000503489693303165904545226217803152051192002963867711 The expected value for the sum is = -0.111277734523829320283834887810195404143855658776755513031864347517000503489693303165904545226217803152051192002963867688 The difference between the sum and the expected value is = -2.325091960 E-119 ************************** q = 99 The sum of B(q,a) over a coprime with q is = -0.239185588383825077253362436971016585622239323150010238238691312895265772819740401358418743551392628423707752533003494337 The expected value for the sum is = -0.239185588383825077253362436971016585622239323150010238238691312895265772819740401358418743551392628423707752533003494345 The difference between the sum and the expected value is = 8.34766153 E-120 ************************** q = 100 The sum of B(q,a) over a coprime with q is = -0.0994277201797350116675580397056955005404914677704619248217351389791578501423334121985338807607391752420351779988551228345 The expected value for the sum is = -0.0994277201797350116675580397056955005404914677704619248217351389791578501423334121985338807607391752420351779988551228340 The difference between the sum and the expected value is = -5.819886196 E-121 ************************** ******************* END CHECK ********************