# sandtable generator spiral_arms arms=4 turns=1.0 0.00000 0.00000 0.00000 0.00000 0.01995 0.00317 0.03989 0.00635 0.05984 0.00952 0.07979 0.01270 0.09973 0.01587 0.11968 0.01905 0.13963 0.02222 0.15957 0.02540 0.17952 0.02857 0.19947 0.03175 0.21941 0.03492 0.23936 0.03810 0.25931 0.04127 0.27925 0.04444 0.29920 0.04762 0.31915 0.05079 0.33909 0.05397 0.35904 0.05714 0.37899 0.06032 0.39893 0.06349 0.41888 0.06667 0.43883 0.06984 0.45877 0.07302 0.47872 0.07619 0.49867 0.07937 0.51861 0.08254 0.53856 0.08571 0.55851 0.08889 0.57845 0.09206 0.59840 0.09524 0.61835 0.09841 0.63829 0.10159 0.65824 0.10476 0.67819 0.10794 0.69813 0.11111 0.71808 0.11429 0.73802 0.11746 0.75797 0.12063 0.77792 0.12381 0.79786 0.12698 0.81781 0.13016 0.83776 0.13333 0.85770 0.13651 0.87765 0.13968 0.89760 0.14286 0.91754 0.14603 0.93749 0.14921 0.95744 0.15238 0.97738 0.15556 0.99733 0.15873 1.01728 0.16190 1.03722 0.16508 1.05717 0.16825 1.07712 0.17143 1.09706 0.17460 1.11701 0.17778 1.13696 0.18095 1.15690 0.18413 1.17685 0.18730 1.19680 0.19048 1.21674 0.19365 1.23669 0.19683 1.25664 0.20000 1.27658 0.20317 1.29653 0.20635 1.31648 0.20952 1.33642 0.21270 1.35637 0.21587 1.37632 0.21905 1.39626 0.22222 1.41621 0.22540 1.43616 0.22857 1.45610 0.23175 1.47605 0.23492 1.49600 0.23810 1.51594 0.24127 1.53589 0.24444 1.55584 0.24762 1.57578 0.25079 1.59573 0.25397 1.61568 0.25714 1.63562 0.26032 1.65557 0.26349 1.67552 0.26667 1.69546 0.26984 1.71541 0.27302 1.73536 0.27619 1.75530 0.27937 1.77525 0.28254 1.79520 0.28571 1.81514 0.28889 1.83509 0.29206 1.85504 0.29524 1.87498 0.29841 1.89493 0.30159 1.91488 0.30476 1.93482 0.30794 1.95477 0.31111 1.97472 0.31429 1.99466 0.31746 2.01461 0.32063 2.03456 0.32381 2.05450 0.32698 2.07445 0.33016 2.09440 0.33333 2.11434 0.33651 2.13429 0.33968 2.15423 0.34286 2.17418 0.34603 2.19413 0.34921 2.21407 0.35238 2.23402 0.35556 2.25397 0.35873 2.27391 0.36190 2.29386 0.36508 2.31381 0.36825 2.33375 0.37143 2.35370 0.37460 2.37365 0.37778 2.39359 0.38095 2.41354 0.38413 2.43349 0.38730 2.45343 0.39048 2.47338 0.39365 2.49333 0.39683 2.51327 0.40000 2.53322 0.40317 2.55317 0.40635 2.57311 0.40952 2.59306 0.41270 2.61301 0.41587 2.63295 0.41905 2.65290 0.42222 2.67285 0.42540 2.69279 0.42857 2.71274 0.43175 2.73269 0.43492 2.75263 0.43810 2.77258 0.44127 2.79253 0.44444 2.81247 0.44762 2.83242 0.45079 2.85237 0.45397 2.87231 0.45714 2.89226 0.46032 2.91221 0.46349 2.93215 0.46667 2.95210 0.46984 2.97205 0.47302 2.99199 0.47619 3.01194 0.47937 3.03189 0.48254 3.05183 0.48571 3.07178 0.48889 3.09173 0.49206 3.11167 0.49524 3.13162 0.49841 3.15157 0.50159 3.17151 0.50476 3.19146 0.50794 3.21141 0.51111 3.23135 0.51429 3.25130 0.51746 3.27125 0.52063 3.29119 0.52381 3.31114 0.52698 3.33109 0.53016 3.35103 0.53333 3.37098 0.53651 3.39093 0.53968 3.41087 0.54286 3.43082 0.54603 3.45077 0.54921 3.47071 0.55238 3.49066 0.55556 3.51061 0.55873 3.53055 0.56190 3.55050 0.56508 3.57044 0.56825 3.59039 0.57143 3.61034 0.57460 3.63028 0.57778 3.65023 0.58095 3.67018 0.58413 3.69012 0.58730 3.71007 0.59048 3.73002 0.59365 3.74996 0.59683 3.76991 0.60000 3.78986 0.60317 3.80980 0.60635 3.82975 0.60952 3.84970 0.61270 3.86964 0.61587 3.88959 0.61905 3.90954 0.62222 3.92948 0.62540 3.94943 0.62857 3.96938 0.63175 3.98932 0.63492 4.00927 0.63810 4.02922 0.64127 4.04916 0.64444 4.06911 0.64762 4.08906 0.65079 4.10900 0.65397 4.12895 0.65714 4.14890 0.66032 4.16884 0.66349 4.18879 0.66667 4.20874 0.66984 4.22868 0.67302 4.24863 0.67619 4.26858 0.67937 4.28852 0.68254 4.30847 0.68571 4.32842 0.68889 4.34836 0.69206 4.36831 0.69524 4.38826 0.69841 4.40820 0.70159 4.42815 0.70476 4.44810 0.70794 4.46804 0.71111 4.48799 0.71429 4.50794 0.71746 4.52788 0.72063 4.54783 0.72381 4.56778 0.72698 4.58772 0.73016 4.60767 0.73333 4.62762 0.73651 4.64756 0.73968 4.66751 0.74286 4.68746 0.74603 4.70740 0.74921 4.72735 0.75238 4.74730 0.75556 4.76724 0.75873 4.78719 0.76190 4.80714 0.76508 4.82708 0.76825 4.84703 0.77143 4.86698 0.77460 4.88692 0.77778 4.90687 0.78095 4.92682 0.78413 4.94676 0.78730 4.96671 0.79048 4.98666 0.79365 5.00660 0.79683 5.02655 0.80000 5.04649 0.80317 5.06644 0.80635 5.08639 0.80952 5.10633 0.81270 5.12628 0.81587 5.14623 0.81905 5.16617 0.82222 5.18612 0.82540 5.20607 0.82857 5.22601 0.83175 5.24596 0.83492 5.26591 0.83810 5.28585 0.84127 5.30580 0.84444 5.32575 0.84762 5.34569 0.85079 5.36564 0.85397 5.38559 0.85714 5.40553 0.86032 5.42548 0.86349 5.44543 0.86667 5.46537 0.86984 5.48532 0.87302 5.50527 0.87619 5.52521 0.87937 5.54516 0.88254 5.56511 0.88571 5.58505 0.88889 5.60500 0.89206 5.62495 0.89524 5.64489 0.89841 5.66484 0.90159 5.68479 0.90476 5.70473 0.90794 5.72468 0.91111 5.74463 0.91429 5.76457 0.91746 5.78452 0.92063 5.80447 0.92381 5.82441 0.92698 5.84436 0.93016 5.86431 0.93333 5.88425 0.93651 5.90420 0.93968 5.92415 0.94286 5.94409 0.94603 5.96404 0.94921 5.98399 0.95238 6.00393 0.95556 6.02388 0.95873 6.04383 0.96190 6.06377 0.96508 6.08372 0.96825 6.10367 0.97143 6.12361 0.97460 6.14356 0.97778 6.16351 0.98095 6.18345 0.98413 6.20340 0.98730 6.22335 0.99048 6.24329 0.99365 6.26324 0.99683 6.28319 1.00000 6.30307 1.00000 6.32295 1.00000 6.34284 1.00000 6.36272 1.00000 6.38260 1.00000 6.40249 1.00000 6.42237 1.00000 6.44225 1.00000 6.46214 1.00000 6.48202 1.00000 6.50190 1.00000 6.52179 1.00000 6.54167 1.00000 6.56155 1.00000 6.58144 1.00000 6.60132 1.00000 6.62120 1.00000 6.64109 1.00000 6.66097 1.00000 6.68086 1.00000 6.70074 1.00000 6.72062 1.00000 6.74051 1.00000 6.76039 1.00000 6.78027 1.00000 6.80016 1.00000 6.82004 1.00000 6.83992 1.00000 6.85981 1.00000 6.87969 1.00000 6.89957 1.00000 6.91946 1.00000 6.93934 1.00000 6.95922 1.00000 6.97911 1.00000 6.99899 1.00000 7.01887 1.00000 7.03876 1.00000 7.05864 1.00000 7.07853 1.00000 7.09841 1.00000 7.11829 1.00000 7.13818 1.00000 7.15806 1.00000 7.17794 1.00000 7.19783 1.00000 7.21771 1.00000 7.23759 1.00000 7.25748 1.00000 7.27736 1.00000 7.29724 1.00000 7.31713 1.00000 7.33701 1.00000 7.35689 1.00000 7.37678 1.00000 7.39666 1.00000 7.41654 1.00000 7.43643 1.00000 7.45631 1.00000 7.47620 1.00000 7.49608 1.00000 7.51596 1.00000 7.53585 1.00000 7.55573 1.00000 7.57561 1.00000 7.59550 1.00000 7.61538 1.00000 7.63526 1.00000 7.65515 1.00000 7.67503 1.00000 7.69491 1.00000 7.71480 1.00000 7.73468 1.00000 7.75456 1.00000 7.77445 1.00000 7.79433 1.00000 7.81421 1.00000 7.83410 1.00000 7.85398 1.00000 7.83404 0.99683 7.81409 0.99365 7.79414 0.99048 7.77420 0.98730 7.75425 0.98413 7.73430 0.98095 7.71436 0.97778 7.69441 0.97460 7.67446 0.97143 7.65452 0.96825 7.63457 0.96508 7.61462 0.96190 7.59468 0.95873 7.57473 0.95556 7.55478 0.95238 7.53484 0.94921 7.51489 0.94603 7.49494 0.94286 7.47500 0.93968 7.45505 0.93651 7.43510 0.93333 7.41516 0.93016 7.39521 0.92698 7.37526 0.92381 7.35532 0.92063 7.33537 0.91746 7.31542 0.91429 7.29548 0.91111 7.27553 0.90794 7.25558 0.90476 7.23564 0.90159 7.21569 0.89841 7.19574 0.89524 7.17580 0.89206 7.15585 0.88889 7.13590 0.88571 7.11596 0.88254 7.09601 0.87937 7.07606 0.87619 7.05612 0.87302 7.03617 0.86984 7.01622 0.86667 6.99628 0.86349 6.97633 0.86032 6.95638 0.85714 6.93644 0.85397 6.91649 0.85079 6.89654 0.84762 6.87660 0.84444 6.85665 0.84127 6.83670 0.83810 6.81676 0.83492 6.79681 0.83175 6.77686 0.82857 6.75692 0.82540 6.73697 0.82222 6.71702 0.81905 6.69708 0.81587 6.67713 0.81270 6.65718 0.80952 6.63724 0.80635 6.61729 0.80317 6.59734 0.80000 6.57740 0.79683 6.55745 0.79365 6.53750 0.79048 6.51756 0.78730 6.49761 0.78413 6.47766 0.78095 6.45772 0.77778 6.43777 0.77460 6.41782 0.77143 6.39788 0.76825 6.37793 0.76508 6.35799 0.76190 6.33804 0.75873 6.31809 0.75556 6.29815 0.75238 6.27820 0.74921 6.25825 0.74603 6.23831 0.74286 6.21836 0.73968 6.19841 0.73651 6.17847 0.73333 6.15852 0.73016 6.13857 0.72698 6.11863 0.72381 6.09868 0.72063 6.07873 0.71746 6.05879 0.71429 6.03884 0.71111 6.01889 0.70794 5.99895 0.70476 5.97900 0.70159 5.95905 0.69841 5.93911 0.69524 5.91916 0.69206 5.89921 0.68889 5.87927 0.68571 5.85932 0.68254 5.83937 0.67937 5.81943 0.67619 5.79948 0.67302 5.77953 0.66984 5.75959 0.66667 5.73964 0.66349 5.71969 0.66032 5.69975 0.65714 5.67980 0.65397 5.65985 0.65079 5.63991 0.64762 5.61996 0.64444 5.60001 0.64127 5.58007 0.63810 5.56012 0.63492 5.54017 0.63175 5.52023 0.62857 5.50028 0.62540 5.48033 0.62222 5.46039 0.61905 5.44044 0.61587 5.42049 0.61270 5.40055 0.60952 5.38060 0.60635 5.36065 0.60317 5.34071 0.60000 5.32076 0.59683 5.30081 0.59365 5.28087 0.59048 5.26092 0.58730 5.24097 0.58413 5.22103 0.58095 5.20108 0.57778 5.18113 0.57460 5.16119 0.57143 5.14124 0.56825 5.12129 0.56508 5.10135 0.56190 5.08140 0.55873 5.06145 0.55556 5.04151 0.55238 5.02156 0.54921 5.00161 0.54603 4.98167 0.54286 4.96172 0.53968 4.94178 0.53651 4.92183 0.53333 4.90188 0.53016 4.88194 0.52698 4.86199 0.52381 4.84204 0.52063 4.82210 0.51746 4.80215 0.51429 4.78220 0.51111 4.76226 0.50794 4.74231 0.50476 4.72236 0.50159 4.70242 0.49841 4.68247 0.49524 4.66252 0.49206 4.64258 0.48889 4.62263 0.48571 4.60268 0.48254 4.58274 0.47937 4.56279 0.47619 4.54284 0.47302 4.52290 0.46984 4.50295 0.46667 4.48300 0.46349 4.46306 0.46032 4.44311 0.45714 4.42316 0.45397 4.40322 0.45079 4.38327 0.44762 4.36332 0.44444 4.34338 0.44127 4.32343 0.43810 4.30348 0.43492 4.28354 0.43175 4.26359 0.42857 4.24364 0.42540 4.22370 0.42222 4.20375 0.41905 4.18380 0.41587 4.16386 0.41270 4.14391 0.40952 4.12396 0.40635 4.10402 0.40317 4.08407 0.40000 4.06412 0.39683 4.04418 0.39365 4.02423 0.39048 4.00428 0.38730 3.98434 0.38413 3.96439 0.38095 3.94444 0.37778 3.92450 0.37460 3.90455 0.37143 3.88460 0.36825 3.86466 0.36508 3.84471 0.36190 3.82476 0.35873 3.80482 0.35556 3.78487 0.35238 3.76492 0.34921 3.74498 0.34603 3.72503 0.34286 3.70508 0.33968 3.68514 0.33651 3.66519 0.33333 3.64524 0.33016 3.62530 0.32698 3.60535 0.32381 3.58540 0.32063 3.56546 0.31746 3.54551 0.31429 3.52557 0.31111 3.50562 0.30794 3.48567 0.30476 3.46573 0.30159 3.44578 0.29841 3.42583 0.29524 3.40589 0.29206 3.38594 0.28889 3.36599 0.28571 3.34605 0.28254 3.32610 0.27937 3.30615 0.27619 3.28621 0.27302 3.26626 0.26984 3.24631 0.26667 3.22637 0.26349 3.20642 0.26032 3.18647 0.25714 3.16653 0.25397 3.14658 0.25079 3.12663 0.24762 3.10669 0.24444 3.08674 0.24127 3.06679 0.23810 3.04685 0.23492 3.02690 0.23175 3.00695 0.22857 2.98701 0.22540 2.96706 0.22222 2.94711 0.21905 2.92717 0.21587 2.90722 0.21270 2.88727 0.20952 2.86733 0.20635 2.84738 0.20317 2.82743 0.20000 2.80749 0.19683 2.78754 0.19365 2.76759 0.19048 2.74765 0.18730 2.72770 0.18413 2.70775 0.18095 2.68781 0.17778 2.66786 0.17460 2.64791 0.17143 2.62797 0.16825 2.60802 0.16508 2.58807 0.16190 2.56813 0.15873 2.54818 0.15556 2.52823 0.15238 2.50829 0.14921 2.48834 0.14603 2.46839 0.14286 2.44845 0.13968 2.42850 0.13651 2.40855 0.13333 2.38861 0.13016 2.36866 0.12698 2.34871 0.12381 2.32877 0.12063 2.30882 0.11746 2.28887 0.11429 2.26893 0.11111 2.24898 0.10794 2.22903 0.10476 2.20909 0.10159 2.18914 0.09841 2.16919 0.09524 2.14925 0.09206 2.12930 0.08889 2.10936 0.08571 2.08941 0.08254 2.06946 0.07937 2.04952 0.07619 2.02957 0.07302 2.00962 0.06984 1.98968 0.06667 1.96973 0.06349 1.94978 0.06032 1.92984 0.05714 1.90989 0.05397 1.88994 0.05079 1.87000 0.04762 1.85005 0.04444 1.83010 0.04127 1.81016 0.03810 1.79021 0.03492 1.77026 0.03175 1.75032 0.02857 1.73037 0.02540 1.71042 0.02222 1.69048 0.01905 1.67053 0.01587 1.65058 0.01270 1.63064 0.00952 1.61069 0.00635 1.59074 0.00317 1.57080 0.00000 3.14159 0.00000 3.16154 0.00317 3.18149 0.00635 3.20143 0.00952 3.22138 0.01270 3.24133 0.01587 3.26127 0.01905 3.28122 0.02222 3.30117 0.02540 3.32111 0.02857 3.34106 0.03175 3.36101 0.03492 3.38095 0.03810 3.40090 0.04127 3.42085 0.04444 3.44079 0.04762 3.46074 0.05079 3.48069 0.05397 3.50063 0.05714 3.52058 0.06032 3.54053 0.06349 3.56047 0.06667 3.58042 0.06984 3.60036 0.07302 3.62031 0.07619 3.64026 0.07937 3.66020 0.08254 3.68015 0.08571 3.70010 0.08889 3.72004 0.09206 3.73999 0.09524 3.75994 0.09841 3.77988 0.10159 3.79983 0.10476 3.81978 0.10794 3.83972 0.11111 3.85967 0.11429 3.87962 0.11746 3.89956 0.12063 3.91951 0.12381 3.93946 0.12698 3.95940 0.13016 3.97935 0.13333 3.99930 0.13651 4.01924 0.13968 4.03919 0.14286 4.05914 0.14603 4.07908 0.14921 4.09903 0.15238 4.11898 0.15556 4.13892 0.15873 4.15887 0.16190 4.17882 0.16508 4.19876 0.16825 4.21871 0.17143 4.23866 0.17460 4.25860 0.17778 4.27855 0.18095 4.29850 0.18413 4.31844 0.18730 4.33839 0.19048 4.35834 0.19365 4.37828 0.19683 4.39823 0.20000 4.41818 0.20317 4.43812 0.20635 4.45807 0.20952 4.47802 0.21270 4.49796 0.21587 4.51791 0.21905 4.53786 0.22222 4.55780 0.22540 4.57775 0.22857 4.59770 0.23175 4.61764 0.23492 4.63759 0.23810 4.65754 0.24127 4.67748 0.24444 4.69743 0.24762 4.71738 0.25079 4.73732 0.25397 4.75727 0.25714 4.77722 0.26032 4.79716 0.26349 4.81711 0.26667 4.83706 0.26984 4.85700 0.27302 4.87695 0.27619 4.89690 0.27937 4.91684 0.28254 4.93679 0.28571 4.95674 0.28889 4.97668 0.29206 4.99663 0.29524 5.01657 0.29841 5.03652 0.30159 5.05647 0.30476 5.07641 0.30794 5.09636 0.31111 5.11631 0.31429 5.13625 0.31746 5.15620 0.32063 5.17615 0.32381 5.19609 0.32698 5.21604 0.33016 5.23599 0.33333 5.25593 0.33651 5.27588 0.33968 5.29583 0.34286 5.31577 0.34603 5.33572 0.34921 5.35567 0.35238 5.37561 0.35556 5.39556 0.35873 5.41551 0.36190 5.43545 0.36508 5.45540 0.36825 5.47535 0.37143 5.49529 0.37460 5.51524 0.37778 5.53519 0.38095 5.55513 0.38413 5.57508 0.38730 5.59503 0.39048 5.61497 0.39365 5.63492 0.39683 5.65487 0.40000 5.67481 0.40317 5.69476 0.40635 5.71471 0.40952 5.73465 0.41270 5.75460 0.41587 5.77455 0.41905 5.79449 0.42222 5.81444 0.42540 5.83439 0.42857 5.85433 0.43175 5.87428 0.43492 5.89423 0.43810 5.91417 0.44127 5.93412 0.44444 5.95407 0.44762 5.97401 0.45079 5.99396 0.45397 6.01391 0.45714 6.03385 0.46032 6.05380 0.46349 6.07375 0.46667 6.09369 0.46984 6.11364 0.47302 6.13359 0.47619 6.15353 0.47937 6.17348 0.48254 6.19343 0.48571 6.21337 0.48889 6.23332 0.49206 6.25327 0.49524 6.27321 0.49841 6.29316 0.50159 6.31311 0.50476 6.33305 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