# sandtable generator spiral_arms arms=8 turns=0.6 0.00000 0.00000 0.00000 0.00000 0.01995 0.00529 0.03989 0.01058 0.05984 0.01587 0.07979 0.02116 0.09973 0.02646 0.11968 0.03175 0.13963 0.03704 0.15957 0.04233 0.17952 0.04762 0.19947 0.05291 0.21941 0.05820 0.23936 0.06349 0.25931 0.06878 0.27925 0.07407 0.29920 0.07937 0.31915 0.08466 0.33909 0.08995 0.35904 0.09524 0.37899 0.10053 0.39893 0.10582 0.41888 0.11111 0.43883 0.11640 0.45877 0.12169 0.47872 0.12698 0.49867 0.13228 0.51861 0.13757 0.53856 0.14286 0.55851 0.14815 0.57845 0.15344 0.59840 0.15873 0.61835 0.16402 0.63829 0.16931 0.65824 0.17460 0.67819 0.17989 0.69813 0.18519 0.71808 0.19048 0.73802 0.19577 0.75797 0.20106 0.77792 0.20635 0.79786 0.21164 0.81781 0.21693 0.83776 0.22222 0.85770 0.22751 0.87765 0.23280 0.89760 0.23810 0.91754 0.24339 0.93749 0.24868 0.95744 0.25397 0.97738 0.25926 0.99733 0.26455 1.01728 0.26984 1.03722 0.27513 1.05717 0.28042 1.07712 0.28571 1.09706 0.29101 1.11701 0.29630 1.13696 0.30159 1.15690 0.30688 1.17685 0.31217 1.19680 0.31746 1.21674 0.32275 1.23669 0.32804 1.25664 0.33333 1.27658 0.33862 1.29653 0.34392 1.31648 0.34921 1.33642 0.35450 1.35637 0.35979 1.37632 0.36508 1.39626 0.37037 1.41621 0.37566 1.43616 0.38095 1.45610 0.38624 1.47605 0.39153 1.49600 0.39683 1.51594 0.40212 1.53589 0.40741 1.55584 0.41270 1.57578 0.41799 1.59573 0.42328 1.61568 0.42857 1.63562 0.43386 1.65557 0.43915 1.67552 0.44444 1.69546 0.44974 1.71541 0.45503 1.73536 0.46032 1.75530 0.46561 1.77525 0.47090 1.79520 0.47619 1.81514 0.48148 1.83509 0.48677 1.85504 0.49206 1.87498 0.49735 1.89493 0.50265 1.91488 0.50794 1.93482 0.51323 1.95477 0.51852 1.97472 0.52381 1.99466 0.52910 2.01461 0.53439 2.03456 0.53968 2.05450 0.54497 2.07445 0.55026 2.09440 0.55556 2.11434 0.56085 2.13429 0.56614 2.15423 0.57143 2.17418 0.57672 2.19413 0.58201 2.21407 0.58730 2.23402 0.59259 2.25397 0.59788 2.27391 0.60317 2.29386 0.60847 2.31381 0.61376 2.33375 0.61905 2.35370 0.62434 2.37365 0.62963 2.39359 0.63492 2.41354 0.64021 2.43349 0.64550 2.45343 0.65079 2.47338 0.65608 2.49333 0.66138 2.51327 0.66667 2.53322 0.67196 2.55317 0.67725 2.57311 0.68254 2.59306 0.68783 2.61301 0.69312 2.63295 0.69841 2.65290 0.70370 2.67285 0.70899 2.69279 0.71429 2.71274 0.71958 2.73269 0.72487 2.75263 0.73016 2.77258 0.73545 2.79253 0.74074 2.81247 0.74603 2.83242 0.75132 2.85237 0.75661 2.87231 0.76190 2.89226 0.76720 2.91221 0.77249 2.93215 0.77778 2.95210 0.78307 2.97205 0.78836 2.99199 0.79365 3.01194 0.79894 3.03189 0.80423 3.05183 0.80952 3.07178 0.81481 3.09173 0.82011 3.11167 0.82540 3.13162 0.83069 3.15157 0.83598 3.17151 0.84127 3.19146 0.84656 3.21141 0.85185 3.23135 0.85714 3.25130 0.86243 3.27125 0.86772 3.29119 0.87302 3.31114 0.87831 3.33109 0.88360 3.35103 0.88889 3.37098 0.89418 3.39093 0.89947 3.41087 0.90476 3.43082 0.91005 3.45077 0.91534 3.47071 0.92063 3.49066 0.92593 3.51061 0.93122 3.53055 0.93651 3.55050 0.94180 3.57044 0.94709 3.59039 0.95238 3.61034 0.95767 3.63028 0.96296 3.65023 0.96825 3.67018 0.97354 3.69012 0.97884 3.71007 0.98413 3.73002 0.98942 3.74996 0.99471 3.76991 1.00000 3.78955 1.00000 3.80918 1.00000 3.82882 1.00000 3.84845 1.00000 3.86809 1.00000 3.88772 1.00000 3.90736 1.00000 3.92699 1.00000 3.94663 1.00000 3.96626 1.00000 3.98590 1.00000 4.00553 1.00000 4.02517 1.00000 4.04480 1.00000 4.06444 1.00000 4.08407 1.00000 4.10371 1.00000 4.12334 1.00000 4.14298 1.00000 4.16261 1.00000 4.18225 1.00000 4.20188 1.00000 4.22152 1.00000 4.24115 1.00000 4.26079 1.00000 4.28042 1.00000 4.30005 1.00000 4.31969 1.00000 4.33932 1.00000 4.35896 1.00000 4.37859 1.00000 4.39823 1.00000 4.41786 1.00000 4.43750 1.00000 4.45713 1.00000 4.47677 1.00000 4.49640 1.00000 4.51604 1.00000 4.53567 1.00000 4.55531 1.00000 4.53536 0.99471 4.51542 0.98942 4.49547 0.98413 4.47552 0.97884 4.45558 0.97354 4.43563 0.96825 4.41568 0.96296 4.39574 0.95767 4.37579 0.95238 4.35584 0.94709 4.33590 0.94180 4.31595 0.93651 4.29600 0.93122 4.27606 0.92593 4.25611 0.92063 4.23616 0.91534 4.21622 0.91005 4.19627 0.90476 4.17632 0.89947 4.15638 0.89418 4.13643 0.88889 4.11648 0.88360 4.09654 0.87831 4.07659 0.87302 4.05664 0.86772 4.03670 0.86243 4.01675 0.85714 3.99680 0.85185 3.97686 0.84656 3.95691 0.84127 3.93696 0.83598 3.91702 0.83069 3.89707 0.82540 3.87712 0.82011 3.85718 0.81481 3.83723 0.80952 3.81728 0.80423 3.79734 0.79894 3.77739 0.79365 3.75744 0.78836 3.73750 0.78307 3.71755 0.77778 3.69760 0.77249 3.67766 0.76720 3.65771 0.76190 3.63776 0.75661 3.61782 0.75132 3.59787 0.74603 3.57792 0.74074 3.55798 0.73545 3.53803 0.73016 3.51809 0.72487 3.49814 0.71958 3.47819 0.71429 3.45825 0.70899 3.43830 0.70370 3.41835 0.69841 3.39841 0.69312 3.37846 0.68783 3.35851 0.68254 3.33857 0.67725 3.31862 0.67196 3.29867 0.66667 3.27873 0.66138 3.25878 0.65608 3.23883 0.65079 3.21889 0.64550 3.19894 0.64021 3.17899 0.63492 3.15905 0.62963 3.13910 0.62434 3.11915 0.61905 3.09921 0.61376 3.07926 0.60847 3.05931 0.60317 3.03937 0.59788 3.01942 0.59259 2.99947 0.58730 2.97953 0.58201 2.95958 0.57672 2.93963 0.57143 2.91969 0.56614 2.89974 0.56085 2.87979 0.55556 2.85985 0.55026 2.83990 0.54497 2.81995 0.53968 2.80001 0.53439 2.78006 0.52910 2.76011 0.52381 2.74017 0.51852 2.72022 0.51323 2.70027 0.50794 2.68033 0.50265 2.66038 0.49735 2.64043 0.49206 2.62049 0.48677 2.60054 0.48148 2.58059 0.47619 2.56065 0.47090 2.54070 0.46561 2.52075 0.46032 2.50081 0.45503 2.48086 0.44974 2.46091 0.44444 2.44097 0.43915 2.42102 0.43386 2.40107 0.42857 2.38113 0.42328 2.36118 0.41799 2.34123 0.41270 2.32129 0.40741 2.30134 0.40212 2.28139 0.39683 2.26145 0.39153 2.24150 0.38624 2.22155 0.38095 2.20161 0.37566 2.18166 0.37037 2.16171 0.36508 2.14177 0.35979 2.12182 0.35450 2.10188 0.34921 2.08193 0.34392 2.06198 0.33862 2.04204 0.33333 2.02209 0.32804 2.00214 0.32275 1.98220 0.31746 1.96225 0.31217 1.94230 0.30688 1.92236 0.30159 1.90241 0.29630 1.88246 0.29101 1.86252 0.28571 1.84257 0.28042 1.82262 0.27513 1.80268 0.26984 1.78273 0.26455 1.76278 0.25926 1.74284 0.25397 1.72289 0.24868 1.70294 0.24339 1.68300 0.23810 1.66305 0.23280 1.64310 0.22751 1.62316 0.22222 1.60321 0.21693 1.58326 0.21164 1.56332 0.20635 1.54337 0.20106 1.52342 0.19577 1.50348 0.19048 1.48353 0.18519 1.46358 0.17989 1.44364 0.17460 1.42369 0.16931 1.40374 0.16402 1.38380 0.15873 1.36385 0.15344 1.34390 0.14815 1.32396 0.14286 1.30401 0.13757 1.28406 0.13228 1.26412 0.12698 1.24417 0.12169 1.22422 0.11640 1.20428 0.11111 1.18433 0.10582 1.16438 0.10053 1.14444 0.09524 1.12449 0.08995 1.10454 0.08466 1.08460 0.07937 1.06465 0.07407 1.04470 0.06878 1.02476 0.06349 1.00481 0.05820 0.98486 0.05291 0.96492 0.04762 0.94497 0.04233 0.92502 0.03704 0.90508 0.03175 0.88513 0.02646 0.86518 0.02116 0.84524 0.01587 0.82529 0.01058 0.80534 0.00529 0.78540 0.00000 1.57080 0.00000 1.59074 0.00529 1.61069 0.01058 1.63064 0.01587 1.65058 0.02116 1.67053 0.02646 1.69048 0.03175 1.71042 0.03704 1.73037 0.04233 1.75032 0.04762 1.77026 0.05291 1.79021 0.05820 1.81016 0.06349 1.83010 0.06878 1.85005 0.07407 1.87000 0.07937 1.88994 0.08466 1.90989 0.08995 1.92984 0.09524 1.94978 0.10053 1.96973 0.10582 1.98968 0.11111 2.00962 0.11640 2.02957 0.12169 2.04952 0.12698 2.06946 0.13228 2.08941 0.13757 2.10936 0.14286 2.12930 0.14815 2.14925 0.15344 2.16919 0.15873 2.18914 0.16402 2.20909 0.16931 2.22903 0.17460 2.24898 0.17989 2.26893 0.18519 2.28887 0.19048 2.30882 0.19577 2.32877 0.20106 2.34871 0.20635 2.36866 0.21164 2.38861 0.21693 2.40855 0.22222 2.42850 0.22751 2.44845 0.23280 2.46839 0.23810 2.48834 0.24339 2.50829 0.24868 2.52823 0.25397 2.54818 0.25926 2.56813 0.26455 2.58807 0.26984 2.60802 0.27513 2.62797 0.28042 2.64791 0.28571 2.66786 0.29101 2.68781 0.29630 2.70775 0.30159 2.72770 0.30688 2.74765 0.31217 2.76759 0.31746 2.78754 0.32275 2.80749 0.32804 2.82743 0.33333 2.84738 0.33862 2.86733 0.34392 2.88727 0.34921 2.90722 0.35450 2.92717 0.35979 2.94711 0.36508 2.96706 0.37037 2.98701 0.37566 3.00695 0.38095 3.02690 0.38624 3.04685 0.39153 3.06679 0.39683 3.08674 0.40212 3.10669 0.40741 3.12663 0.41270 3.14658 0.41799 3.16653 0.42328 3.18647 0.42857 3.20642 0.43386 3.22637 0.43915 3.24631 0.44444 3.26626 0.44974 3.28621 0.45503 3.30615 0.46032 3.32610 0.46561 3.34605 0.47090 3.36599 0.47619 3.38594 0.48148 3.40589 0.48677 3.42583 0.49206 3.44578 0.49735 3.46573 0.50265 3.48567 0.50794 3.50562 0.51323 3.52557 0.51852 3.54551 0.52381 3.56546 0.52910 3.58540 0.53439 3.60535 0.53968 3.62530 0.54497 3.64524 0.55026 3.66519 0.55556 3.68514 0.56085 3.70508 0.56614 3.72503 0.57143 3.74498 0.57672 3.76492 0.58201 3.78487 0.58730 3.80482 0.59259 3.82476 0.59788 3.84471 0.60317 3.86466 0.60847 3.88460 0.61376 3.90455 0.61905 3.92450 0.62434 3.94444 0.62963 3.96439 0.63492 3.98434 0.64021 4.00428 0.64550 4.02423 0.65079 4.04418 0.65608 4.06412 0.66138 4.08407 0.66667 4.10402 0.67196 4.12396 0.67725 4.14391 0.68254 4.16386 0.68783 4.18380 0.69312 4.20375 0.69841 4.22370 0.70370 4.24364 0.70899 4.26359 0.71429 4.28354 0.71958 4.30348 0.72487 4.32343 0.73016 4.34338 0.73545 4.36332 0.74074 4.38327 0.74603 4.40322 0.75132 4.42316 0.75661 4.44311 0.76190 4.46306 0.76720 4.48300 0.77249 4.50295 0.77778 4.52290 0.78307 4.54284 0.78836 4.56279 0.79365 4.58274 0.79894 4.60268 0.80423 4.62263 0.80952 4.64258 0.81481 4.66252 0.82011 4.68247 0.82540 4.70242 0.83069 4.72236 0.83598 4.74231 0.84127 4.76226 0.84656 4.78220 0.85185 4.80215 0.85714 4.82210 0.86243 4.84204 0.86772 4.86199 0.87302 4.88194 0.87831 4.90188 0.88360 4.92183 0.88889 4.94178 0.89418 4.96172 0.89947 4.98167 0.90476 5.00161 0.91005 5.02156 0.91534 5.04151 0.92063 5.06145 0.92593 5.08140 0.93122 5.10135 0.93651 5.12129 0.94180 5.14124 0.94709 5.16119 0.95238 5.18113 0.95767 5.20108 0.96296 5.22103 0.96825 5.24097 0.97354 5.26092 0.97884 5.28087 0.98413 5.30081 0.98942 5.32076 0.99471 5.34071 1.00000 5.36034 1.00000 5.37998 1.00000 5.39961 1.00000 5.41925 1.00000 5.43888 1.00000 5.45852 1.00000 5.47815 1.00000 5.49779 1.00000 5.51742 1.00000 5.53706 1.00000 5.55669 1.00000 5.57633 1.00000 5.59596 1.00000 5.61560 1.00000 5.63523 1.00000 5.65487 1.00000 5.67450 1.00000 5.69414 1.00000 5.71377 1.00000 5.73341 1.00000 5.75304 1.00000 5.77268 1.00000 5.79231 1.00000 5.81195 1.00000 5.83158 1.00000 5.85122 1.00000 5.87085 1.00000 5.89049 1.00000 5.91012 1.00000 5.92976 1.00000 5.94939 1.00000 5.96903 1.00000 5.98866 1.00000 6.00830 1.00000 6.02793 1.00000 6.04757 1.00000 6.06720 1.00000 6.08684 1.00000 6.10647 1.00000 6.12611 1.00000 6.10616 0.99471 6.08621 0.98942 6.06627 0.98413 6.04632 0.97884 6.02637 0.97354 6.00643 0.96825 5.98648 0.96296 5.96653 0.95767 5.94659 0.95238 5.92664 0.94709 5.90669 0.94180 5.88675 0.93651 5.86680 0.93122 5.84685 0.92593 5.82691 0.92063 5.80696 0.91534 5.78701 0.91005 5.76707 0.90476 5.74712 0.89947 5.72717 0.89418 5.70723 0.88889 5.68728 0.88360 5.66733 0.87831 5.64739 0.87302 5.62744 0.86772 5.60749 0.86243 5.58755 0.85714 5.56760 0.85185 5.54765 0.84656 5.52771 0.84127 5.50776 0.83598 5.48781 0.83069 5.46787 0.82540 5.44792 0.82011 5.42797 0.81481 5.40803 0.80952 5.38808 0.80423 5.36813 0.79894 5.34819 0.79365 5.32824 0.78836 5.30829 0.78307 5.28835 0.77778 5.26840 0.77249 5.24845 0.76720 5.22851 0.76190 5.20856 0.75661 5.18861 0.75132 5.16867 0.74603 5.14872 0.74074 5.12877 0.73545 5.10883 0.73016 5.08888 0.72487 5.06893 0.71958 5.04899 0.71429 5.02904 0.70899 5.00909 0.70370 4.98915 0.69841 4.96920 0.69312 4.94926 0.68783 4.92931 0.68254 4.90936 0.67725 4.88942 0.67196 4.86947 0.66667 4.84952 0.66138 4.82958 0.65608 4.80963 0.65079 4.78968 0.64550 4.76974 0.64021 4.74979 0.63492 4.72984 0.62963 4.70990 0.62434 4.68995 0.61905 4.67000 0.61376 4.65006 0.60847 4.63011 0.60317 4.61016 0.59788 4.59022 0.59259 4.57027 0.58730 4.55032 0.58201 4.53038 0.57672 4.51043 0.57143 4.49048 0.56614 4.47054 0.56085 4.45059 0.55556 4.43064 0.55026 4.41070 0.54497 4.39075 0.53968 4.37080 0.53439 4.35086 0.52910 4.33091 0.52381 4.31096 0.51852 4.29102 0.51323 4.27107 0.50794 4.25112 0.50265 4.23118 0.49735 4.21123 0.49206 4.19128 0.48677 4.17134 0.48148 4.15139 0.47619 4.13144 0.47090 4.11150 0.46561 4.09155 0.46032 4.07160 0.45503 4.05166 0.44974 4.03171 0.44444 4.01176 0.43915 3.99182 0.43386 3.97187 0.42857 3.95192 0.42328 3.93198 0.41799 3.91203 0.41270 3.89208 0.40741 3.87214 0.40212 3.85219 0.39683 3.83224 0.39153 3.81230 0.38624 3.79235 0.38095 3.77240 0.37566 3.75246 0.37037 3.73251 0.36508 3.71256 0.35979 3.69262 0.35450 3.67267 0.34921 3.65272 0.34392 3.63278 0.33862 3.61283 0.33333 3.59288 0.32804 3.57294 0.32275 3.55299 0.31746 3.53305 0.31217 3.51310 0.30688 3.49315 0.30159 3.47321 0.29630 3.45326 0.29101 3.43331 0.28571 3.41337 0.28042 3.39342 0.27513 3.37347 0.26984 3.35353 0.26455 3.33358 0.25926 3.31363 0.25397 3.29369 0.24868 3.27374 0.24339 3.25379 0.23810 3.23385 0.23280 3.21390 0.22751 3.19395 0.22222 3.17401 0.21693 3.15406 0.21164 3.13411 0.20635 3.11417 0.20106 3.09422 0.19577 3.07427 0.19048 3.05433 0.18519 3.03438 0.17989 3.01443 0.17460 2.99449 0.16931 2.97454 0.16402 2.95459 0.15873 2.93465 0.15344 2.91470 0.14815 2.89475 0.14286 2.87481 0.13757 2.85486 0.13228 2.83491 0.12698 2.81497 0.12169 2.79502 0.11640 2.77507 0.11111 2.75513 0.10582 2.73518 0.10053 2.71523 0.09524 2.69529 0.08995 2.67534 0.08466 2.65539 0.07937 2.63545 0.07407 2.61550 0.06878 2.59555 0.06349 2.57561 0.05820 2.55566 0.05291 2.53571 0.04762 2.51577 0.04233 2.49582 0.03704 2.47587 0.03175 2.45593 0.02646 2.43598 0.02116 2.41603 0.01587 2.39609 0.01058 2.37614 0.00529 2.35619 0.00000 3.14159 0.00000 3.16154 0.00529 3.18149 0.01058 3.20143 0.01587 3.22138 0.02116 3.24133 0.02646 3.26127 0.03175 3.28122 0.03704 3.30117 0.04233 3.32111 0.04762 3.34106 0.05291 3.36101 0.05820 3.38095 0.06349 3.40090 0.06878 3.42085 0.07407 3.44079 0.07937 3.46074 0.08466 3.48069 0.08995 3.50063 0.09524 3.52058 0.10053 3.54053 0.10582 3.56047 0.11111 3.58042 0.11640 3.60036 0.12169 3.62031 0.12698 3.64026 0.13228 3.66020 0.13757 3.68015 0.14286 3.70010 0.14815 3.72004 0.15344 3.73999 0.15873 3.75994 0.16402 3.77988 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