QUANTITATIVE PRECIPITATION FORECAST DISCUSSION NWS HYDROMETEOROLOGICAL PREDICTION CENTER CAMP SPRINGS MD 542 AM EDT WED APR 28 2010 FINAL DAY 1...DAY 2 AND DAY 3 QPF DISCUSSION VALID APR 28/1200 UTC THRU MAY 01/1200 UTC REFERENCE AWIPS GRAPHICS UNDER...PRECIP ACCUM - 24HR ...DAY 1... ...UPDATE... MINOR CHNGS IN BOTH THE WEST AND NE DUE TO ONGOING RDR/SATL TRENDS. ECKERT ...SYNOPSIS... LRG SCALE HIER LAT BLOCKG HAS RESULTED IN A LWR LAT OMEGA BLOCK SETTING OVR MUCH OF THE CONUS/SRN CANADA THIS PD. ANCHORING VORTICES ARE OVR THE CANADIAN MARITIMES AND THE NWRN U.S.. LATEST SREF 5H ANOMALIES ARE ARND 3 STDS BLO NRML FOR BOTH VORTICES. NUMEROUS SMALLER SCALE SHRTWVS ARE CAUGHT IN THE LRG SCALE FLOW REGIME THAT IS RESULTING IN DIFFERENCES DVLPG NEAR THE END OF THE DAY 1 PD. RDGG THRU THE CNTRL U.S. WL CONT TO BUILD NWD INTO SCNTRL CAN. MSTR REMAINS LIMITED THIS PD AS THE FLOW ACRS THE GULF OF MEX REMAINS ANTI-CYCLONIC...BUT SATL DERIVED PW LOOPS SHOWS DEEP CARIBBEAN MSTR HAS MOVD TO THE NRN EXTENT OF THE YUCATAN CHANNEL WITH VALUES ARND TWO INCHES. THIS SHLD CONT TO ADVECT NWD BEYOND DAY 1 WITH AN INCRSG THREAT FOR HVY RNFL. ...NEW ENG STS... POTENT VORTEX OVR THE REGION WL SLOLY RELOCATE NEWD AS A SCND SYS DROPS SWD FM ERN CAN AND THEY FUJIWHARA ARND THE MAIN CIRCULATION CENTER NR THE MOUTH OF THE ST LAWRENCE RVR. DEEPER ATLC MSTR HAS BEEN CUTOFF BUT THE MIDLVL DYNAMICS/UPR DEFORMATION ZONE WL CONT TO PROVIDE STG DEEP LYRD LIFT...WHILE ERLY/NERLY LOLVL FLOW PROVIDE UPSLOPE INTO THE HIER ELEVS. XPCT LGT PCPN ACRS THE REGION WITH THE HVIER OVR THE HIER ELEVS WHERE IT SHLD CONT TO FALL AS SNW. SEE QPFHSD FOR ACCUMS. ...WRN U.S. INTO NRN PLNS... BROAD NEG TILTED MID/UPR TROF...WITH SVRL EMBEDDED SHRTWVS...WL EVOLVE INTO A CLSD 5H LOW BY THE END OF THE PD OVR ERN MT...WITH THE ASSOCD TROF CONTG TO DIG SEWD INTO THE GRT BASIN/ROCKIES. MDLS ARE SHOWG SVRL STG SHRTWVS THAT WL PROVIDE POCKETS OF STGR LIFT AND ASSOCD ORGANIZED PCPN...WHILE THE HIER ELEVS WL ALSO HELP TO FOCUS PCPN. THE TONGUE OF DEEP EPAC MSTR HAS BEEN SHOVED INTO SRN CA ERLY THIS MRNG AND WL BE CUTOFF FM THE SYS BY LATER TDA...BUT PERSISTENT WRLY FLOW OFF THE EPAC WL CONT TO PROVIDE SOME MSTR INTO THE REGION. SERIES OF LEADING SHRTWVS OVR THE NRN ROCKIES/NRN GRT BASIN WL EVOLVE INTO THE MT 5H CLSD LOW WITH STG LEFT EXIT REGION UPR JET DYNAMICS/DIFL THAT WL PROVIDE A STG REGION OF DEEP LYRD ASCENT OVR SWRN CAN THAT SHLD BUILD INTO THE HIER ELEVS OF WRN MT. ALL THE GUID HAS SHOWN A TREND TWD INCRSG PCPN AMTS INTO WRN MT THIS PD. SREF SPAGHETTI PLOTS OF HALF TO ONE INCH LIQ QPF ARE VRY CLUSTERED OVR THE HIER ELEVS OF NWRN MT. HI-RES ARW QPF IS MUCH HIER THAN THE LRG SCALE GUID...BUT THIS IS PROBABLY RELATED TO THE TERRAIN MDLG. NOT SOLD ON GRTR THAN TWO INCH LIQ AT THIS POINT W/OUT A STG MSTR LINK TO THE GULF OF MEX...BUT ISOLD AMTS JUST ABV ONE INCH ARE PSBL...ESPCLY WHERE UPSLOPE IS MAXIMIZED. MDLS ARE SHOWG A NARROW TONGUE OF HIER PWS FEEDG INTO/ARND THE SYS THAT SEEMS TO BE INITIALLY RELATED TO EPAC MSTR THAT IS MOVG THRU SRN MT THIS MRNG...WHILE SATL DERIVED PW LOOPS SHOW A VRY NARROW RIBBON OF HIER PWS THRU THE CNTRL PLNS THAT SEEMS TO BE MARGINALLY LINKED TO THE WRN GULF...SO THE MDLS DEPICTION OF INCRSG MSTR INTO THE REGION THRU THE FCST PD SEEMS LOGICAL. NEED TO WATCH THIS CAREFULLY AND COULD PSBLY SEE AN INCRS WITH LATER ARRIVING GUID. PCPN WL CHNG TO SNW THRU THE PD WITH HVY ACCUMS LKLY. SEE QPFHSD FOR TOTALS. SHRTWV TROF/UPR JET STREAK DIGG INTO THE WRN U.S. THEN THE GRT BASIN/CNTRL ROCKIES WL SPLIT OFF FM THE MORE NRN SYS AND CREATE A SEPARATE REGION OF ORGANIZED PCPN ACRS THE HIER ELEVS OF THE WASATCH INTO THE CNTRL ROCKIES. MDLS SHOW INCRSG LEFT EXIT REGION UPR JET SUPPORT THRU THE PD. A RIBBON OF DEEPER MSTR AT 8H/7H REMAINS DRAPED ACRS THE REGION AND PROVIDE FUEL FOR INCRSG PCPN. MDLS ALSO SHOW INCRSG CVRG IN THE 8H/7H LYR THAT WL COMBINE WITH UPSLOPE TO INCRS LIFT OVR THE HIER ELEVS. HAVE BEEFED UP AMTS OVR MUCH OF THE GUID DUE TO OROGRAPHIC ENHANCEMENT WITH LCL ONE INCH TOTALS PSBL. SNOW LVLS SHLD FALL THRU THE PD. WCST FM WA TO CA WL SEE MARGINAL MID/UPR LVL DYNAMICS THAT WL PROVIDE SOME LRG SCALE LIFT ACRS THE REGION. THE MAIN SUPPORT FOR PCPN WL BE THE PERSISTENT WRLY FLOW INTO THE CSTL RNGS/CASCADES/SIERRA WITH MOD OROGRAPHIC LIFT THRU THE PD. XPCT MOST AREAS TO SEE AT LEAST LGT PCPN...WITH MOD/HVY AMTS OVR THE PREFERRED HIER ELEVS. DAYS 2 AND 3... ...GREAT BASIN/INTER-MOUNTAIN WEST THRU NRN/CNTRL PLAINS/MS VLY/OH-TN VALLEY... AN ANOMALOUSLY DEEP AMPLIFIED LONG WAVE UPPER TROUGH WILL PERSIST OVER THE ROCKIES AND DRIFT OUT ON TO THE PLAINS THIS PERIOD. A CLOSED LOW OVER NERN MT EXTENDING INTO CENTRAL CANADA WILL BE THE MAIN SYNOPTIC SCALE FEATURE ALONG WITH AN IMPRESSIVE UPPER JET CARVING THROUGH THE BASE OF THE UPPER TROUGH ACROSS THE DESERT SOUTHWEST AND ADVANCING INTO THE CENTRAL PLAINS/UPPER MIDWEST. IT IS THIS UPPER LOW AND POWERFUL JET THAT WILL STEER A NUMBER OF SHORT WAVE IMPULSES... ONE WITH A SFC LOW MOVING INTO MN ON THURS AND THEN ANOTHER THU NIGHT STARTING IN THE CENTRAL PLAINS AND MOVING INTO THE UPPER MS VALLEY ON FRI EVENING. OVERALL HPC CONTINUED TO FOLLOW A LAGGED AVERAGE FORECAST OF THE ECMWF WITH THE 00Z NAM/UKMET/21 SREF MEAN FOR MOST OF THE FCST PERIOD. EXPECT SEVERAL POCKETS OF HEAVY QPF OVER THE TWO DAY FCST PERIOD. ACROSS THE WEST THE SLOW MOVING CLOSED LOW PRODUCES PERSISTENT NORTHERLY FLOW IN CENTRAL MT. LG SCALE MOISTURE POOLED IN THE REGION TURNS UPSLOPE (I.E. SUCH AS THE LITTLE BELT MNTNS)...PRODUCING OROGRAPHIC RAIN/SNOW. THE PRECIPITATION IS AIDED BY PERSISTENT UPPER DIVERGENCE MAXIMA ON DAY TWO INTO EARLY DAY THREE DOWN INTO THE BIGHORNS. THE MODELS CONSENSUS HERE SHOWS LG MAXIMA...WITH THE ECMWF BLENDED WITH THE NAM AND ECMWF ENSEMBLE MEAN TO COMPOSE EVENT TOTALS. SEE THE WINTER WEATHER FORECASTS FOR THE SNOW THREATS/DISCUSSION. AN IMPULSE ARRIVING INTO INTO THE DAKOTAS/MN ON THURS WILL IN THE VERY DIFLUENT UPPER-LEVEL FLOW ALOFT AND INTERACT WITH AN ACTIVE LL JET. UPPER DIVERGENCE MAXIMA WILL LIKELY RESULT IN A BURST OF ACTIVE CONVECTION ACROSS ERN ND/SD INTO MN. FINALLY THE STRONGEST SHORT WAVE IMPULSE WILL LEAVE THE CO ROCKIES AND ARRIVE INTO THE CENTRAL PLAINS INDUCING A SURFACE WAVE WHICH WILL DEEPEN RAPIDLY AS IT LIFTS NORTH INTO THE UPPER MIDWEST... THUS EXPECT DEVELOPING SHOWERS/STORMS ACROSS NE INTO IA AND SPREADING NORTH INTO THE ERN DAKOTAS/MN. TO THE SOUTH OF THIS AREA ON FRI... THE ASSOCIATED SURFACE COLD FRONT WILL BEGIN TO INTERACT WITH A RETURNING NORTH WARM FRONTAL BOUNDARY. THE MODELS/ECMWF ENSEMBLE MEAN/00Z GEFS MEAN SHOW A V SHAPED NOTCH IN THE UPPER JET STRUCTURE WITH TWO DISTINCT WIND MAXIMA. THE ECMWF BEST CAPTURES THE UPPER DIVERGENCE MAXIMA WITHIN THE NOTCH REGION IN THE LOWER MS VALLEY...SO A LAGGED 3 RUN AVERAGE OF THE ECMWF WAS USED FOR QPF. POOLING OF DEEP TROPICAL MOISTURE IN THE LOWER MS VALLEY IS EXPECTED AS THE ECMWF/GFS SHOW PW VALUES INCREASING TO 1.75 TO 2 INCHES. LOCALLY HEAVY RAIN IS EXPECTED AS THE MODELS SLOW THE EAST PROGRESSION OF THE FRONT...SO TRAINING SHOWERS/STORMS BECOME POSSIBLE. THE GFS SHOWS POTENTIAL GRID SCALE FEEDBACK/ANOMALOUSLY STRONG MOISTURE CONVERGENCE LACKING TEMPORAL CONTINUITY OVER WESTERN KY/TN SO ITS OUTPUT WAS GIVEN LESS WEIGHT 00-12Z FRI. THE 00Z NAM HAD LOWER AMOUNTS BUT ITS IT SHOWS A SIMILAR UPPER JET STRUCTURE AND A 300 MB DIVERGENCE MAXIMA CROSSING THE LOWER MS VALLEY...SO ITS QPF IS LIKELY TO INCREASE IN LATER RUNS. ECKERT/PETERSEN GRAPHICS AVAILABLE ON THE WEB AT WWW.HPC.NCEP.NOAA.GOV 24HR QP VT 29/12Z 0.01 464717 477685 474665 462651 451651 441665 434684 429692 425700 425710 427718 428725 422729 420734 416736 412740 416750 426762 432758 440763 447755 454740 462723 464717 0.01 457190 461184 459174 457170 460168 467172 478178 487184 499184 510192 518206 530205 539187 542156 538127 533088 531041 521999 507974 468961 439961 425964 420976 419996 411007 404015 408025 411030 406039 399043 390047 389053 391057 386060 383064 379063 375064 373073 375081 378085 383086 386090 388096 389101 392105 378114 375118 374123 370133 370138 371144 375145 378150 377154 379157 381158 387154 394149 401143 404136 411129 414128 417129 418135 416141 413146 409149 405151 399155 394158 391162 388166 388173 391178 396180 403183 407184 411188 409195 407198 403198 402193 394191 376184 372180 369179 360177 354178 351180 349180 347178 346174 346169 344165 335162 329159 325159 323162 323165 324168 327171 332173 335177 339184 342191 344193 347194 349193 350190 355190 360193 390217 392221 387220 382221 379222 376219 375216 373214 370213 367216 365211 361206 355205 353210 360221 382243 412256 446259 469257 492260 496256 492245 484238 480235 479230 474232 473226 478223 489229 500240 507235 502218 491204 484204 465208 460208 456210 453211 449213 439211 432208 429204 427200 427196 428192 430188 432185 430182 427179 427177 430173 433169 431164 424157 423151 424144 428135 433126 435127 435131 434137 432142 430151 432157 434163 440168 442173 443174 443178 438185 436189 437194 441198 444195 446192 448193 451195 454193 457190 0.01 431024 423029 419037 420050 426054 430061 435067 443066 454071 457082 460094 466087 472072 481065 492047 491031 473017 453016 434023 431024 0.01 438080 437082 434082 433078 429075 426077 423080 420077 417078 415082 414091 415100 419103 424102 427100 426095 423089 423086 428088 433093 436094 438091 444091 449090 449084 445080 442079 439079 438080 0.01 418207 416206 415206 415207 415210 415212 416213 417215 417217 416219 417222 418225 419224 419221 419219 421217 422215 422212 420210 419209 418207 0.25 531180 533173 534166 534150 533137 531124 526101 523091 516084 507082 499081 493079 487082 482087 478094 474099 471100 468098 465102 464102 461100 458102 458104 456102 453096 452095 448095 445098 445099 442098 439097 437100 435100 433104 432106 430109 431111 434112 437111 440112 443117 447120 449121 456119 460117 465116 469120 469125 468129 468134 469138 468141 466142 463143 460144 458146 458150 466157 476166 485171 495174 503176 514185 520188 526188 529183 531180 0.25 458702 459697 456696 453697 451700 448702 446705 444707 441709 439712 437717 437718 438719 442719 445720 447720 448720 451718 453716 453715 455712 457708 457707 458702 458702 0.25 488215 485209 479208 469212 465213 462212 460213 455215 447216 441216 438217 434217 432216 429218 424221 423224 425226 426228 426231 424233 421231 421228 419228 419229 416231 413228 414225 415221 415217 413215 409217 406215 405213 403210 401207 394201 387196 374187 370186 366187 365189 367192 377203 391213 395216 399219 402220 404223 404228 400228 394229 391232 392237 395241 402245 412248 423250 453246 460245 464243 467240 463233 462229 464226 467222 473220 479219 485218 488215 0.25 482984 480981 476978 467976 458975 446976 438980 433984 430989 429992 430001 431005 434004 439000 442999 453995 465992 474990 479988 482984 0.25 441149 444151 446152 450152 452151 454152 454154 452156 453159 454161 452163 450164 445163 440160 436156 436149 437146 439145 441149 0.25 405103 404107 402107 400104 398102 395102 396105 396109 394110 389113 386114 383114 381114 380116 378120 377124 376127 377130 380131 382133 381135 380138 380142 382145 386145 390144 390141 387138 389137 392136 390133 390130 390126 393126 396128 394129 396132 399131 399129 401128 404127 405126 405123 406123 407121 409119 412119 416118 416115 415113 413113 411111 411109 411104 409097 407095 406100 405101 405103 0.25 407057 402056 399057 397058 395062 392063 389064 389067 387070 386072 387076 389077 389081 391082 394081 394084 394088 394091 393095 395094 397090 401087 403089 407087 408082 409077 413076 415073 414070 414067 416066 416062 413062 407057 0.50 528169 529162 530153 528140 524128 519114 508100 495089 489088 486093 483099 482107 480115 477120 474126 472132 472139 474141 478141 481142 484145 486148 490151 500159 508166 514174 521177 527172 528169 528169 0.50 483212 481211 480210 478212 477211 475211 473215 474216 476215 478214 481214 483212 0.50 470104 468102 467103 466105 464105 462103 460105 462107 464108 466110 468112 470112 471111 472108 475108 476106 474104 472105 470104 0.50 436219 434219 432219 430221 429221 426221 426224 428224 430225 433225 434227 436227 438225 441224 445225 448224 453223 457222 463223 464220 462218 458217 455217 453218 451219 449218 445219 441218 440217 438219 436219 0.50 449159 445159 442157 439153 439150 441152 442154 445156 448157 449159 0.50 438107 436108 437110 438109 441110 443112 445112 448110 450109 447107 444107 442106 441106 438107 0.50 407235 405235 404236 403237 400236 398235 396235 396236 397239 401242 404242 407242 410242 416244 422246 428247 430245 432242 435242 437242 434239 431238 427237 423236 421235 419233 417232 415232 412233 411233 410230 408230 408233 407235 0.50 405217 402212 397207 391202 384197 379194 373190 370189 370192 375198 380203 385206 391211 396215 400217 404217 405217 0.50 410064 407065 405065 405062 404059 403060 403065 401065 400067 399070 397070 396068 394065 392067 390070 391075 394075 393071 395071 395073 396076 396079 395083 396087 398084 400081 403082 404079 405075 408075 410074 413074 414072 411068 410064 0.50 402117 404116 406117 407115 405114 405112 407112 408111 409107 407105 405107 404110 401110 399107 398110 396111 392113 388115 385115 384118 381117 380120 378123 378125 377127 379127 382125 384126 386126 389125 391123 393123 395121 392119 394118 396118 398118 400118 402117 0.50 411221 411223 410223 409221 411218 412218 411221 0.50 382138 384139 384141 382141 381139 382138 1.00 502114 496111 492112 489115 488120 486126 485130 484130 482129 479129 478133 481136 484138 487140 491144 494148 498151 502150 504151 509155 514160 518162 521159 520151 519144 518138 516130 510121 502114 24HR QP VT 30/12Z 0.01 552976 552966 551957 547944 545939 542929 539923 537915 530901 525893 517878 509866 504859 497852 485839 455805 448799 441795 433790 429788 423788 418789 417791 417796 417802 419809 425821 429825 434828 441830 444833 440834 438833 437836 435842 434847 434852 436856 440872 444882 441887 440889 437891 437895 436898 433909 426917 410930 406934 401937 395941 389943 381948 370954 347958 341959 329959 323959 320958 311955 304952 298950 294951 266968 262968 258970 253973 254975 262982 269986 276991 280996 289012 292015 296016 302015 306013 328005 346001 355998 365994 377989 381988 385989 389994 394002 399009 397016 393018 386026 383035 380042 378049 378053 379057 378060 376060 357054 353063 351067 351074 350079 346082 340090 332095 331102 332106 347123 371151 377157 386155 387162 385170 386178 389182 403192 404197 392194 382189 373182 367180 363179 360181 359182 357184 359187 362192 377205 395218 398222 398224 391229 390232 391237 394246 396249 400252 411257 421257 431256 455254 465254 472255 478260 487265 491271 493276 496281 499284 506285 508283 511279 514277 518274 519269 518254 514242 509231 507225 506218 507215 510215 514218 526223 528224 529220 527213 527206 526198 522167 526162 527153 526135 529097 529092 526087 520078 513071 506064 498061 489058 483057 477058 470057 464058 459056 455053 452048 449042 444030 443027 443023 446019 456014 466011 471009 477008 488008 495008 500007 508006 515006 522011 525014 527014 531014 543014 548012 549003 551987 552976 0.01 472681 470676 467673 461671 455670 449671 445673 443677 442680 443686 446689 449691 452692 454696 454700 452703 446706 442708 440711 438718 434721 430724 427728 427730 430732 434734 438734 443732 449731 455729 460724 458712 459709 462704 466697 470689 472681 0.01 500256 502252 501248 499243 494240 492234 489229 486226 481223 476225 480228 482232 488235 490238 493241 493244 496250 500256 500256 0.01 486201 489197 489193 488187 485185 482186 478186 473187 467187 464187 460190 457195 455202 456207 460207 465207 471206 474205 479204 483202 486201 0.01 472859 471855 469851 466851 465853 467857 468858 469860 471861 472859 0.01 422702 420699 417696 416695 413697 412700 414703 416706 417707 420706 422702 0.01 442084 441080 436076 433072 434068 436064 437060 437056 437052 435044 433040 430036 428036 424041 423045 422053 420056 417068 416076 413080 413083 413088 415093 418098 422095 422087 424084 427083 428084 433086 439086 442084 0.01 433140 434136 434134 431133 428135 427139 427142 430142 433140 433140 0.01 417138 417134 416133 414134 413134 410133 409137 410141 413141 416139 417138 0.01 404102 404098 403097 402095 401094 400094 398097 397098 398100 400102 401102 403103 404102 0.01 395105 396102 395101 392101 389101 388101 386105 386107 386109 389110 392109 395106 395105 0.01 357110 355107 355106 352105 351106 352107 354110 357111 357110 0.01 277833 276825 273819 268808 266800 263797 252792 248793 246798 244808 244818 244826 247832 251834 257834 261836 265839 269843 274844 277841 278838 277833 0.25 516955 515947 514938 510924 506914 504910 500908 492904 486905 482904 475898 471896 466897 436923 427928 419935 413941 408947 398963 395971 394979 397985 410995 412000 411007 407015 403025 402029 398034 394039 393043 394046 398049 402046 405043 410034 416029 423022 433006 437999 444993 449991 455991 461992 467990 476986 485982 495978 504974 508971 511967 513965 515959 516955 0.25 506155 509137 509128 508119 507104 505091 503086 498081 494079 488079 479082 469085 464095 462098 459099 456098 453098 451101 448105 446109 446113 450117 455122 456122 457126 454134 453138 452147 453155 454159 457164 461166 469171 473171 478170 485165 490162 494160 502158 506155 0.25 481244 477237 472236 470236 469240 465236 459235 452235 447234 443232 444228 447227 462221 458218 454218 445219 437221 430224 426232 420237 416246 420249 431249 438248 453244 462243 469240 478244 481244 0.25 405068 404064 403057 401054 398056 395058 389065 385068 381069 372067 370066 368068 369075 372086 374090 378092 384094 389092 395087 401076 405068 0.25 351975 350973 347973 345974 342976 339978 337980 337981 335984 337986 340986 343985 346984 348982 350978 351977 351975 0.25 252811 251809 250809 250812 251814 252811 0.50 501141 502123 502113 502109 499100 497097 490096 486094 482092 476093 467097 464101 462106 464113 466119 471128 470132 470137 474141 480147 485151 491151 496149 500145 501141 0.50 496955 496945 495937 491930 485931 474935 470939 467944 464949 461952 453960 451963 449969 449973 451977 455979 458980 464980 472976 481971 489965 493960 496955 0.50 471158 471154 470152 469149 468147 465145 462148 463152 464156 465157 467159 470159 471158 0.50 443946 444937 444933 441932 435932 429933 421939 414947 409953 403962 399970 399978 402981 406983 412983 420977 428971 433964 440955 443946 0.50 395076 395072 392069 389071 388072 387073 384075 382075 381077 379079 379083 381084 384085 386085 389085 392083 394079 395076 395076 1.00 488139 486138 483137 482138 483139 486139 488139 1.00 475111 475107 473102 470101 469102 467104 466106 466110 467112 470114 473113 475111 1.00 427953 428949 425947 420950 417952 413956 409961 407965 406969 408975 413972 416969 419966 422962 424958 427953 24HR QP VT 01/12Z 0.01 562878 559855 557842 554830 552823 549818 547811 541798 533784 529775 526770 523763 520759 515754 513749 510747 508743 505741 503737 499734 498731 491724 482713 478711 473705 469703 462704 458706 453706 451711 451718 451722 453725 456730 461737 464743 469750 469753 466756 456750 448746 445746 443749 441755 441761 445767 452780 454785 455792 446797 424808 411812 396818 389821 385822 374822 364822 355816 345810 341806 337802 325784 311765 309760 304756 304754 301759 296768 290775 254804 254813 253820 254824 268842 271846 273852 273863 274889 272898 269908 267918 265928 261950 259958 261969 268994 272007 276010 281012 290014 297019 306023 312019 318017 322014 329007 336999 343993 353988 364984 373980 380979 385980 391984 392988 390993 386998 380008 371018 350055 347058 345063 343068 339072 332071 328072 324075 321079 319085 315086 312089 308093 307098 305108 304117 304124 307127 311124 315121 317114 320109 323104 327102 329105 331111 334122 337132 340136 344139 347142 349143 352142 359137 361130 361123 358111 364108 368103 368095 370089 379094 385097 389096 392097 394099 393103 390108 381113 377117 374124 373130 373138 373145 374148 376148 380145 382141 384134 387130 391131 390136 387141 387145 391163 391168 393172 400175 404173 412165 416165 420163 423158 424152 425143 427135 429133 432133 434138 433148 433153 434158 441168 445175 445178 444181 441185 440191 440194 446197 450195 452193 454189 457170 463172 470175 478177 486185 492189 496190 500192 503192 508190 513190 517191 524193 528194 529193 532186 533182 533177 530172 526167 524160 526154 525145 525132 525123 523110 520095 519088 520080 529053 535038 540023 544007 547995 551979 554970 555964 556959 557955 559946 560927 561913 560905 561898 561885 562878 0.01 465239 464232 465228 467222 463217 452214 446213 441215 434219 430221 428223 427226 426235 424238 424243 427245 430244 433244 442243 448244 453243 457243 462242 465239 0.25 530926 530917 529907 527886 524871 522862 519853 514841 508832 501826 494824 431873 426875 423874 412873 407872 405870 398865 392856 389855 383855 364864 356867 344872 324880 320880 317878 314874 312868 309859 305850 299842 293834 290832 286834 286843 286851 288862 289871 288882 286892 286903 289922 295964 306977 311983 314985 319986 324985 330983 338980 347975 356973 375964 380959 383955 385949 386945 389942 393940 397941 404947 410953 412956 414964 420973 424981 429989 434991 439990 447993 456994 468992 473992 479994 488997 492997 494996 503990 507987 510982 516972 521962 524952 528937 530926 0.25 501095 501083 502078 502072 497054 495047 492041 486037 482037 470040 459044 444046 438048 433052 427061 423066 424073 430085 435097 438105 441109 444116 446124 452134 456139 458143 457147 456158 459160 465157 470156 473148 477146 485144 490144 492142 493136 491130 491125 491119 493111 497101 501095 0.25 418064 415062 414060 412060 410060 407064 404068 407071 408072 410073 412072 413072 414068 415067 418064 0.25 411110 409107 406109 406110 406111 409114 411110 0.25 396072 392069 387069 381070 377068 372066 371072 374075 376079 380083 383083 387081 390079 394076 396072 0.50 515907 515893 513881 510870 506863 501858 496855 490855 483858 475862 470866 466871 459876 447884 441888 435894 427904 419915 417924 416930 420936 424938 430941 438941 443944 448949 456960 464971 467972 472972 479972 484971 489968 495962 499956 508944 511937 514929 515910 515907 0.50 474115 475109 474102 471094 471089 469085 466083 462081 459076 450072 446075 447079 450088 453096 453103 452105 455108 460108 462110 467116 471118 474115 0.50 391885 378879 371877 364877 345881 337884 328889 324890 319891 313888 308884 302881 299881 296883 293889 292896 292906 294924 300940 315966 320972 326975 333974 339973 372961 374960 377955 375950 373948 368947 366946 365943 365940 376930 380924 384917 386913 385908 386898 389890 391885 1.00 367914 365910 362908 357904 354896 350894 341895 333897 320903 312907 309912 309917 309922 312931 318944 322949 328953 334950 341945 346941 351936 354932 358927 363921 367914 1.00 346958 343958 340959 337959 335960 337960 340960 343959 346958 346958 1.50 350922 350917 347913 344910 338905 335906 326908 321912 318920 320929 323936 329940 335941 341938 345934 349926 350922 2.00 344924 344920 343918 341918 339917 337917 334917 331917 328918 327921 327924 326925 326928 327931 328932 331933 331934 334934 336933 337932 339931 341928 344924 344924 $$