National Weather Service Weather Forecast Office

• Home
• Site Map
• News
• Organization
• Search for: NWS All NOAA 

000
FXUS04 KWBC 192151
QPFPFD

QUANTITATIVE PRECIPITATION FORECAST DISCUSSION
NWS WEATHER PREDICTION CENTER COLLEGE PARK MD
550 PM EDT WED JUN 19 2013


FINAL DAY 1...DAY 2 AND DAY 3 QPF DISCUSSION
VALID JUN 20/0000 UTC THRU JUN 23/0000 UTC
REFERENCE AWIPS GRAPHICS UNDER...PRECIP ACCUM - 24HR


DAY 1...

18Z UPDATE...
ADDED SOME PCPN AHEAD OF PERSISTANT SMALL MCS THAT CONTINUES TO
DROP SEWD ACRS N TX.  MODELS HAVE NOT HANDLED THIS SYSTEM VERY
WELL AND EVEN THE LATEST RAP WHICH SHOWS LESS FAVORABLE LOW LEVEL
CONVERGENCE TO THE SOUTH OF IT IS SOMEWHAT IN QUESTION.
ELSEWHERE...ONLY MINOR ADJUSTMENTS WERE MADE TO PRELIM GUIDANCE
BASED ON LASTEST SATL/RADAR TRENDS.

...CENTRAL/EASTERN GULF COAST AND SE ATLC COASTAL STATES...

A FRONTAL BAND IS EXPECTED TO REMAIN NEARLY STATIONARY ACROSS THIS
REGION AND IS EXPECTED TO BE THE FOCUS FOR WIDESPREAD SHWRS.  MOST
WIDESPREAD ACTVTY IS EXPECTED ALONG THE SE ATLC COAST WHERE COOL
CYCLONIC FLOW ALOFT ASOCTD WITH A WEAK SHRTWV WILL TRIGGER SHWRS
AIDED BY INITIALLY FVBL RT ENTRANCE REGION JET DYNAMICS.  SYNOPTIC
SCALE FORCING IS LESS PRONOUNCED ALONG THE ERN AND CNTRL GULF
COASTS BUT THE AVBLTY OF HI PWS SEEMS TO ASSURE WIDESPREAD BUT
LESS ORGANIZED SHWRS THERE.

...PAC NW TO THE N CNTRL U.S...

MODELS ARE IN GOOD AGREEMENT IN SHOWING SHRTWV ENERGY/HGT FALLS
ROTATING NORTH/NORTHEASTWARD FROM THE PAC NW CLOSED UPPER LO WHICH
SHOULD BE AVBL TO FIRE WIDESPREAD SHWRS FM THE NRN ROCKIES EWD
INTO THE N CNTRL U.S. THRU THE FCST PD.  MODEL QPFS ARE IN DECENT
AGREEMENT ON THE OVERALL PLACEMENT BUT SOME SGFNT DIFFERENCES
EXIST IN REGARDS TO WHERE TO MAXIMIZE PCPN..PARTICULARLY OVR THE
NRN PLAINS.  TODAYS GEM REGIONAL AND THE 19/00Z ECMWF HAD PROBABLY
HAD THE BEST ACCORD IN REGARD TO SPECIFICS SO LEANED IN THEIR
DIRECTION FOR THE MOMENT.  GIVEN THE VERY DIFFLUENT UPPER FLOW
EXPECTED WITH THE HGT FALLS..AND AVERAGE PW VALUES..1-2+ STANDARD
DEVIATIONS ABOVE THE MEAN..WIDESPREAD HVY PCPN TOTALS ARE LIKELY.

MEANWHILE...CD CYCLONIC FLOW ALOFT AND CONTG LLVL WLY UPSLOPE FLOW
FM THE PAC NW TO THE MTNS OF NRN ID SHOULD SUPPORT MDT TO LCLY HVY
PCPN AMTS OVR FAVORED TERRAIN THERE.

...UPPER MS VLY SSWWD TO THE LWR MO RIV VLY...

BROAD SLY LLVL FLOW WILL PERSIST THRU THE CNTRL U.S. AND WILL
SUPPORT AREAS OF SHWRS IN ASOCTN WITH WEAK PIECES OF ENERGY MOVG
THRU THE CNTRL U.S. UPPER RIDGE PSN.  MODEL QPFS UNFORTUNATELY ARE
ALL OVER THE PLACE IN REGARDS TO PLACEMENT THOUGH IN GNRL THEY
FAVOR MORE ORGANIZED SHWRS INVOF A WEAK FRONT FM NERN MN EWD
ACROSS LK SUPERIOR..AND ALSO OVR THE UPPER MIDWEST WHERE WEAK
ISENTROPIC LIFT WILL BE AIDED UNDER BROADLY DIFFLUENT FLOW ALOFT.


DAYS 2/3...


...PACIFIC NORTHWEST/NORTHERN ROCKIES/NORTHERN PLAINS/NORTHERN
MISSISSIPPI VALLEY/GREAT LAKES...

AN UPPER CLOSED LOW WITH SEVERAL SHORTWAVE SPOKES WILL CONTINUE TO
SPIN SLOWLY EASTWARD ON DAYS 2/3 WITH THE MAIN AXIS OF THE LOW
BECOMING ELONGATED ON A SOUTH TO NORTH NORTHEAST AXIS BY EARLY ON
SATURDAY/DAY 3. BY THE END OF DAY 3...SATURDAY EVENING...THE UPPER
LOW LIFTS NORTHEASTWARD TOWARD WYOMING/EASTERN MONTANA...POSSIBLY
BRINGING A PERIOD OF HEAVIER RAIN FOR THAT AREA LATER IN THE
FORECAST FOR DAY 3. THE MAJORITY OF THE 12Z MODELS DO LIFT THIS
SYSTEM NORTHEASTWARD ON DAY 3...WITH THE NAM TRENDING SLIGHTLY
FASTER THAN THE OTHER MODELS AND WITH THE 12Z CANADIAN REMAINING
THE SLOWEST.

THE PRECIPITATION PATTERNS ON DAYS 2 AND 3 VARY GREATLY FROM RUN
TO RUN WITH THE NAM SOMEWHAT SIMILAR TO THE GFS BUT QUITE
DIFFERENT FROM THE OTHER OPERATIONAL MODELS. THE ECMWF/GEFS AND
SREF ENSEMBLE MEANS WERE USED AS A FIRST GUESS AND THEN THE
OPERATIONAL MODELS WERE MATCHED TO SEE WHERE SOME CONTINUITY WITH
THE MEANS AND WITH EACH OTHER COULD BE OBSERVED...WITH LESS
ATTENTION GIVEN TO THE 12Z CANADIAN AND 12Z NAM...ALTHOUGH THE 12Z
NAM BORE SOME SIMILARITIES TO THE OVERNIGHT ECMWF IN PLACES. AS IS
OFTEN THE CASE THIS TIME OF THE YEAR...THERE CAN BE SIMILAR
OVERALL STRUCTURE IN THE 500 MB HEIGHT FIELDS FROM MODEL TO
MODEL...AS WELL AS GENERAL AGREEMENT WITH THE SURFACE PRESSURE
PATTERN AS WELL...BUT THE PRECIPITATION FIELDS LOOK QUITE
DIFFERENT.  THIS IS THE CASE HERE.

IN GENERAL...THE LATEST VERSIONS OF THE ECMWF/GEFS ENSEMBLE MEANS
BOTH SHOW THE AREA OF HEAVIEST PRECIPITATION FROM EASTERN NORTH
DAKOTA ACROSS MUCH OF MINNESOTA INTO NORTHERN WISCONSIN.  ON DAY
2...THE GFS BASED MODELS SHOW THE HEAVIEST PRECIPITATION ACROSS
NORTHERN WISCONSIN WITH THE LATEST MEAN SHOWING NEARLY 1.7 INCHES
WHILE THE 12Z GFS SHOWS 1.25 INCHES AND OUR WPC BIAS CORRECTED
GEFS MEAN AT A WHOPPING 3 INCHES.  WITH THE 12Z ECMWF/00Z ECMWF
ENSEMBLE MEANS SHOWING LOWER TOTALS WITH MAXIMUM PRECIPITATION
FARTHER WEST OVER SOUTHERN MINNESOTA WHILE MAXIMUM RAINFALL ON THE
12Z GFS IS SHOWN OVER THE NORTH DAKOTA AND NORTHERN MINNESOTA
BORDER WITH AROUND 2 INCHES.  AN AREAL AVERAGE TOOK ACCOUNT OF
THESE VALUES AND THE WPC FORECAST SHOWS TWO AREAS OF GREATER THAN
ONE INCH FORECAST ON DAY 2...WITH A MAXIMUM NEAR 1.5 INCHES NEAR
THE NORTH DAKOTA/MINNESOTA BORDER AND THE OTHER MAXIMA OF ONE INCH
PLUS OVER NORTHERN WISCONSIN.  WHILE THE 1.5 INCH TOTAL NEARS THE
3 HOURLY FLASH FLOOD GUIDANCE IN PLACES...HAVE OPTED TO KEEP THE
REGION LESS THAN GUIDANCE VALUES FOR NOW ALTHOUGH VALUES LOCALLY
COULD EXCEED GUIDANCE ACROSS MINNESOTA INTO NORTHERN WISCONSIN.

THE HEAVY RAINS ACROSS NORTH DAKOTA TO WISCONSIN ON DAY 2 APPEAR
TO BE DRIVEN BY A STRONG SOUTHERLY LOW LEVEL JET OVER THE CENTRAL
PLAINS DIRECTED TOWARD A CONVERGENT BOUNDARY THAT SETS UP FROM
NORTH DAKOTA TOWARD NORTHERN WISCONSIN. THE AREA OF HEAVY RAINFALL
IS LOCATED JUST UPWIND FROM THE UPPER RIDGE AXIS IN AN AREA OF
UPPER LEVEL DIFFLUENCE DOWNWIND OF A 70 KT JET STREAK MOVING
TOWARD WESTERN NORTH DAKOTA.

BY DAY 3...WEAK SHORTWAVES FUELED BY WITHIN THE EXIT REGION OF THE
UPPER JET ON DAY 2 CONTINUE EASTWARD INTO THE UPPER MIDWEST WHILE
THE CONVERGENT FRONTAL BOUNDARY SHIFTS EASTWARD FROM THE NORTHERN
MISSISSIPPI VALLEY ACROSS MICHIGAN. THE WPC FORECAST SHOWS A
FAIRLY WIDESPREAD AREA OF RAINFALL EXCEEDING .5 INCHES ON DAY 3
FROM SOUTHERN MINNESOTA ACROSS NORTHERN IOWA AND ILLINOIS INTO
WISCONSIN AND ACROSS MUCH OF MICHIGAN WITH MAXIMUM AMOUNTS OF
AROUND AN INCH ACROSS WISCONSIN AND LAKE MICHIGAN.  THESE VALUES
REMAIN SHORT OF FLASH FLOOD GUIDANCE VALUES SO NO EXCESSIVE
RAINFALL FORECAST IS ISSUED.  LOCAL FLASH FLOODING IS OF COURSE A
POSSIBILITY SINCE LOCALIZED RAINFALL AMOUNTS WELL IN EXCESS OF AN
INCH IS LIKELY AT SOME LOCATIONS IN THIS SETTING.

FARTHER WEST...THE NORTHEASTWARD LIFTING OF THE PRIMARY SHORTWAVE
TROUGH OVER MONTANA AND WYOMING APPEARS TO LEAD TO INCREASING
RAINFALL AMOUNTS OF .5 TO 1 INCH ACROSS EASTERN MONTANA INTO
WESTERN NORTH DAKOTA.  ONE INCH RAINFALL APPROACHES AND EXCEEDS
SOME FLASH FLOOD GUIDANCE VALUES ACROSS PORTIONS OF EASTERN
MONTANA PROMPTING SLIGHT CHANCE FOR EXCESSIVE RAINFALL OVER
EASTERN MONTANA ON DAY 3.


...SOUTHEAST/FL/NORTHERN GULF COAST...

AS A POSITIVELY TILTED TROUGH CROSSES THE EASTERN UNITED
STATES...A COLD FRONT WILL BECOME STATIONARY ACROSS THE SOUTHEAST
UNITED STATES OVER THE NEXT SEVERAL DAYS.  WITH THE NORTHERN
PORTION OF THE FRONT MOVING EASTWARD FASTER THAN THE SOUTHERN
BRANCH...HEIGHTS WILL START TO RISE OVER MUCH OF THE EASTERN
UNITED STATES BUT A PORTION OF THE TROUGH WILL REMAIN STATIONARY
OVER THE SOUTHEAST US.  THE COMBINATION OF THE WEAKENING FRONTAL
BOUNDARY AND THE RELATIVELY WEAK UPPER LOW THAT RESULTS WILL
BECOME THE FOCUS FOR QPF ACROSS PORTIONS OF THE SOUTHEAST STATES
ON DAYS 2 INTO 3. THERE ARE SOME SLIGHT DIFFERENCES IN THE
POSITION OF THE FRONT OFF THE SOUTHEAST COAST ON DAYS 2 INTO
DAY...WHILE THE FRONT BEGINS TO DISSIPATE LATER ON SATURDAY AS THE
LARGE ATLANTIC SURFACE ANTICYCLONE BEGINS TO DOMINATE THE WEATHER
ACROSS MUCH OF THE EASTERN UNITED STATES. THE ENSEMBLE MEANS AND
12Z RUNS WERE USED  AS A GUIDE FOR THE QPF FORECAST.

WHILE THERE WILL BE AN INCREASE IN DIURNALLY FORCED SHOWERS AND
THUNDERSHOWERS SOUTH OF THE BOUNDARY ACROSS FLORIDA ON BOTH DAYS 2
AND 3...THE BOUNDARY SHOULD HELP FOCUS CONVECTIVE DEVELOPMENT MUCH
OF THE DAY ACROSS NORTHERN FLORIDA INTO SOUTHERN GEORGIA AND THEN
POSSIBLY SPREAD NORTHEASTWARD ON DAY 3 TOWARD THE NORTH CAROLINA
COAST.  MAXIMUM AREAL AVERAGED AMOUNTS OF .5 TO 1 INCH IS DEPICTED
ACROSS NORTHERN FLORIDA AND SOUTHERN GEORGIA ON DAY 2...WHILE
THOSE AMOUNTS ARE EXTENDED NORTHWARD ON DAY 3 INTO EASTERN NORTH
CAROLINA. WHILE VERY HEAVY RAINS ARE LIKELY IN ISOLATED INDIVIDUAL
STORMS...IT IS NOT LIKELY THAT WIDESPREAD FLASH FLOODING WILL
OCCUR WITH THIS SYSTEM AS GUIDANCE VALUES FOR 3 HOURS REMAIN FROM
AT LEAST 3 TO GREATER THAN 5 INCHES FROM FLORIDA TO EASTERN NORTH
CAROLINA.

KORTY/SULLIVAN/KOCIN

GRAPHICS AVAILABLE ON THE WEB AT WWW.WPC.NCEP.NOAA.GOV

24HR QP VT 21/00Z
 0.01 546183 547159 547148 546142 546135 546124 545116 544101
      542093 541079 539073 539059 537050 535040 533033 531022
      529014 527005 524996 519979 516968 514961 511951 509943
      506922 503897 503888 502877 499856 498851 499847 498839
      495827 492819 490813 488810 484804 480800 477804 470815
      465827 463834 459840 457857 456865 455868 452871 443881
      432906 428911 425916 419926 414931 406932 396928 392924
      387923 384924 382927 380933 377940 373945 367947 367953
      365960 362968 360970 361973 366975 369976 373973 376972
      380973 385973 394979 397983 397989 398990 402990 417988
      425986 429984 436983 439987 432999 430004 430012 432017
      440018 447017 454018 460020 466023 467025 468029 469039
      471046 469054 468060 467063 466068 465075 465085 462092
      461097 457101 459107 460113 458117 445133 439136 435140
      434149 435157 438162 442166 445172 446174 445178 441185
      441187 443190 446191 450194 455193 457189 461184 467181
      470184 471187 474194 475200 471204 465207 455214 443215
      435212 431215 429223 429228 430230 430235 428236 423240
      421242 419247 420250 423251 428252 434250 436249 440251
      443253 446254 448252 459250 470254 476256 480262 488273
      491278 496282 499286 505289 509289 514286
 0.01 456043 456039 453035 449030 447027 443026 440023 438023
      429024 426024 423028 420029 418033 415040 415049 421049
      427045 435044 441044 447044 456043 456043
 0.01 387790 386786 384781 383780 374790 359811 357815 353821
      348830 346837 345842 344848 344857 345871 347884 349891
      352893 353897 360902 365906 370907 372906 372904 370895
      367890 365882 362865 361861 362858 361850 364838 369826
      371821 375815 377810 379807 381805 385795 387790
 0.01 354734 352727 346729 341730 338732 337734 331739 328745
      324754 320765 312776 306785 296792 290795 283796 271796
      261796 257796 250799 248803 249809 252813 252818 251823
      252829 256833 257834 260834 265836 271836 283837 287840
      289848 288853 289861 289873 287885 287911 286923 286932
      284939 279947 280954 281962 302960 301965 300968 301973
      306982 310987 312991 315997 317000 317004 312015 309026
      309030 307033 304036 301040 298043 298046 297053 294057
      288067 285071 283075 290083 294085 299085 310080 320074
      322070 324067 327065 335059 336055 334053 333051 335048
      339047 343048 354043 363037 371026 371022 366021 363021
      361020 360016 362012 362008 358004 353006 348012 344015
      341015 340011 342004 339998 337993 333988 330985 326979
      322975 321973 319967 312960 304956 305953 308952 311948
      314943 320940 328938 331934 330930 326925 325922 323918
      322909 320891 321879 324868 327859 335834 337828 338822
      339816 339809 347789 350782 351776 353763 354755 355747
      354734
 0.25 530239 530227 531207 535190 536177 536167 536148 535134
      533121 528093 525081 523068 520055 517044 509021 501999
      497989 493977 490965 487954 483944 487934 489930 489923
      490909 490897 489881 477839 473847 470859 468870 467882
      466904 468914 469919 466923 463928 463934 464942 465951
      464953 460958 456959 456972 455979 454984 452995 452998
      454000 457001 466004 469008 471014 476041 476047 475054
      473067 470078 467093 467101 469108 474110 479111 484116
      484121 479123 454147 448150 444153 444158 449164 451166
      454165 457162 462163 464165 469170 472171 475176 476181
      482190 483195 482202 475208 469214 468217 469220 474223
      483226 489227 492230 497239 502247 504258 505268 508271
      512274 518273
 0.25 459925 457914 455909 453905 450905 446908 440922 435932
      432939 428944 424948 422954 429965 432969 436970 439968
      443964 447958 449952 452952 454945 457938 459925
 0.25 346750 346746 343744 340746 337748 334753 324768 313783
      303796 294813 286813 281816 286817 295817 301825 302847
      303858 303868 301878 301883 299888 297896 296906 297912
      299915 302920 303923 306923 308919 310913 310901 308889
      308879 309876 308869 311861 315843 319834 321823 325818
      330809 340794 342785 344774 346761 346750
 0.25 315977 314974 313972 311971 310971 309974 310977 311979
      314979 315977
 0.25 278814 277814 274814 271814 271817 272817 275816 277815
      278814
 0.50 523261 526255 526249 526238 527213 527205 529193 530189
      532185 534176 533152 530131 518101 515078 512058 508041
      505031 502022 495009 492999 490991 488980 486973 483967
      479959 475956 473959 470968 464980 463985 463990 465993
      469993 474999 475007 478032 479040 479050 476065 474077
      472085 470094 470102 473105 477106 482108 488112 488117
      488122 486125 483128 478130 475132 474135 474141 476143
      479146 476147 470145 465145 463149 464154 467161 472167
      475171 479180 483186 488191 490196 491202 490207 482208
      476211 472214 473218 477220 485222 489223 492225 494228
      498230 502229 505232 508239 510246 512256 516263 519264
      521263 523261
 0.50 486894 485890 482887 479890 477895 475902 474907 473912
      475920 477924 482924 484919 486912 486908 487898 486894
 0.50 341764 341758 339753 335757 327769 324776 320782 312792
      306804 303810 303817 313827 318817 325807 329801 333796
      337789 339783 340775 341767 341764
 1.00 531175 531162 529150 527141 526137 522129 516120 511110
      510105 507102 504098 502097 502100 500108 498111 494122
      490131 484138 490147 496153 498158 499162 500169 501177
      508194 512204 518214 520216 521213 522202 522193 523188
      526183 529179 531175
 1.00 497032 496027 496026 495023 493019 490014 490013 488010
      486007 486006 483002 481007 483011 482015 483020 483024
      484026 486028 487030 490032 493034 496032 497032
 1.00 485174 484169 484168 483165 482160 479158 476157 473157
      472158 473159 476161 477163 478165 479168 480172 481173
      483176 485174
 1.00 488090 490086 491081 490077 488073 485072 482073 481077
      479081 477085 476088 476089 475094 476097 479098 482097
      485095 486094 488090 488090
 1.00 487063 486059 485056 482058 482059 482063 482066 485066
      487063
 1.50 528169 527154 526149 524141 521137 519134 513129 507128
      502120 499123 498126 495131 495135 495140 497146 500150
      506160 508165 510175 512187 515185 518181 523178 527174
      528169
 2.00 525169 525164 524154 523149 520144 515139 510138 507136
      504135 503136 501141 501145 503150 506155 509160 512166
      516171 519173 522173 525169

24HR QP VT 22/00Z
 0.01 330686 329686 327692 321705 309737 299754 287764 274765
      249760 235756 223757 214762 205779 209792 222811 236819
      253822 263839 265858 267881 277909 287927 299936 317943
      341942 361939 378939 383947 381964 369980 348997 300034
      280039 260041 249046 243053 244068 264083 284089 309084
      346053 370031 391027 405031 424053 437071 442081 439091
      431097 434110 438118 432133 429143 438161 440176 438186
      442211 456239 470262 487275 498277 514272 524250 541191
      550132 549059 526954 515908 500856 492816 493778 501740
      512714 517693 508662 499643 487633 477632 474623 473607
      464595 454604 449628 445666 435691 421714 411736 404759
      384790 367816 354833 347845 340847 336837 342818 358775
      369725 372698 367680 357675 346678
 0.01 367885 361897 362903 371908 385903 404885 438841 453787
      456758 454738 445735 436755 422783 408794 392805 386820
      388838 384855 374877 367885
 0.01 425197 419193 413194 410201 411209 414214 419216 426212
      428205 427201 425197
 0.25 517219 527203 536185 541158 540112 541078 532026 518979
      502929 491893 484856 479832 471825 462830 452843 444862
      431888 413909 406921 409944 430972 448988 466002 488022
      505050 516076 519114 517131 505142 490148 481157 480175
      486186 484201 472208 464219 469228 474235 478246 488251
      499258 508254 509235 517219
 0.25 464013 460012 454017 449027 446039 444049 447061 458066
      462059 464052 469046 476041 480028 478020 472017 464013
 0.25 465105 467113 472116 478110 480103 477099 473098 469100
      467101 467102 465105
 0.25 357717 355709 352704 348701 344700 338704 335707 331715
      325724 320733 312750 303768 299775 296784 293793 288801
      281806 270811 263816 270823 276827 279832 283833 286838
      288844 292857 295867 296876 296883 299888 304883 307880
      308875 310865 312855 315846 318837 321827 325808 328799
      332790 344773 349763 353755 355745 357733 357725 357717
 0.50 525190 533184 537171 537159 536154 531147 525145 515147
      506157 504169 506177 511185 519190 525190
 0.50 531092 535104 533116 528117 526108 527100 531092
 0.50 517046 524050 528040 524024 520010 512992 500966 490934
      481893 479866 476847 469839 460850 452868 439892 428909
      416919 414934 428956 449974 467987 481997 494013 510036
      517046
 0.50 352719 349714 344711 337715 330724 317750 297797 289811
      284820 288828 294836 300846 306847 311840 316817 321798
      328785 335775 340769 343763 349748 351741 353732 352719
 1.00 484966 482959 477953 471950 461946 450934 438930 430934
      430944 436953 442956 451962 463973 475976 479976 481975
      484971 484966
 1.00 476904 473891 466883 458885 452897 451906 453915 457920
      464925 471928 474926 476916 476904
 1.00 346735 343731 340729 335732 333735 327745 324752 321760
      318769 318772 320775 323774 330768 336760 340753 344744
      346735
 1.50 475962 470962 463962 462967 468970 474969 479964 477962
      475962


24HR QP VT 23/00Z
 0.01 509260 531223 549134 548047 550016 551994 533966 509941
      499919 496883 505826 503772 512714 509676 495657 471659
      463662 443679 426699 411748 400792 392820 380842 366856
      359857 353848 355827 366799 373771 370748 370731 376713
      374700 365691 345689 324710 297735 274756 248770 236778
      231791 230809 231827 237848 243867 257902 273929 299948
      324949 350942 379936 394940 400951 398968 387985 367998
      358002 330020 298042 274044 253031 238028 231038 230053
      246066 270082 296089 318081 364040 381027 401023 416037
      426058 427095 427128 438156 449169 466186 477192 479199
      472203 466211 470218 482219 492228 492234 485237 475231
      465225 452230 446241 449256 460267 472283 488299 502300
      509289 505269 503266 506262 509260
 0.25 429717 426742 427778 418820 411852 407884 414919 416942
      420971 426990 440000 442000 448022 442036 440047 444068
      447095 444114 445136 452145 463143 471127 480122 495118
      508107 516095 520086 522061 516033 507006 498986 487951
      476929 471905 476866 486810 481772 465757 451753 445738
      443720 435710 430711 429717
 0.25 494170 501171 504164 503159 497140 490129 486131 486145
      487157 488161 490166 494170
 0.25 313879 328843 350804 360772 358747 351737 338736 323747
      309765 291781 258790 248795 241806 244820 259829 280837
      287848 291863 288881 288893 291902 295908 301910 306908
      311898 313879
 0.25 258060 254060 253064 262070 270073 276072 276066 270063
      263061 258060
 0.50 464957 469946 464934 462931 453912 456888 476830 474792
      458773 442773 435787 431813 432832 428841 421851 413877
      421913 425926 427951 430972 442977 451971 454967 459963
      464957
 0.50 461034 455043 451056 456070 466091 470096 478098 486090
      497082 503071 505047 503025 497011 482999 471999 464006
      462023 461034
 0.50 278817 273820 275825 282829 293834 302843 311849 319844
      325829 337810 352786 353772 345761 335762 328769 323782
      319798 310812 296817 278817
 0.50 260800 253801 250806 251812 256816 263815 267810 268802
      264800 260800
 1.00 432892 431897 433904 436910 440905 439895 434890 432892
 1.00 310824 309824 307825 307826 307827 310825 310824

$$