SLOPE FUNCTION AND HALF-SPACE INFORMATION p/q p'/q' c d Center/ Shading C-R C+R x-value 1/0 1/0 1 1 -50/1 0 21 -49/1 -49/1 1 21 -48/1 0 21 -47/1 -47/1 1 21 -46/1 0 21 -45/1 -45/1 1 21 -44/1 0 21 -43/1 -43/1 1 21 -42/1 0 21 -41/1 -41/1 1 21 -40/1 0 21 -39/1 -39/1 1 21 -38/1 0 21 -37/1 -37/1 1 21 -36/1 0 21 -35/1 -35/1 1 21 -34/1 0 21 -33/1 -33/1 1 21 -32/1 0 21 -31/1 -31/1 1 21 -30/1 0 21 -29/1 -29/1 1 21 -28/1 0 21 -27/1 -27/1 1 21 -26/1 0 21 -25/1 -25/1 1 21 -24/1 0 21 -23/1 -23/1 1 21 -22/1 0 21 -21/1 -21/1 1 21 -20/1 0 21 -19/1 -19/1 1 21 -18/1 0 21 -17/1 -17/1 1 21 -16/1 0 21 -15/1 -15/1 1 21 -14/1 0 21 -13/1 -13/1 1 21 -12/1 0 21 -11/1 -11/1 1 21 -10/1 0 21 -9/1 -9/1 1 21 -8/1 0 21 -7/1 -7/1 1 21 -6/1 0 21 -5/1 -5/1 1 21 -4/1 0 21 -3/1 -3/1 1 21 -2/1 0 21 -1/1 -1/1 1 21 0/1 0 21 1/1 1/1 1 21 2/1 0 21 3/1 3/1 1 21 4/1 0 21 5/1 5/1 1 21 6/1 0 21 7/1 7/1 1 21 8/1 0 21 9/1 9/1 1 21 10/1 0 21 11/1 11/1 1 21 12/1 0 21 13/1 13/1 1 21 14/1 0 21 15/1 15/1 1 21 16/1 0 21 17/1 17/1 1 21 18/1 0 21 19/1 19/1 1 21 20/1 0 21 21/1 21/1 1 21 22/1 0 21 23/1 23/1 1 21 24/1 0 21 25/1 25/1 1 21 26/1 0 21 27/1 27/1 1 21 28/1 0 21 29/1 29/1 1 21 30/1 0 21 31/1 31/1 1 21 32/1 0 21 33/1 33/1 1 21 34/1 0 21 35/1 35/1 1 21 36/1 0 21 37/1 37/1 1 21 38/1 0 21 39/1 39/1 1 21 40/1 0 21 41/1 41/1 1 21 42/1 0 21 43/1 43/1 1 21 44/1 0 21 45/1 45/1 1 21 46/1 0 21 47/1 47/1 1 21 48/1 0 21 49/1 49/1 1 21 50/1 0 21 -49/2 -23/1 1 21 0.040788 In 0.040513 0.041064 -47/2 -25/1 1 21 0.042588 In 0.042288 0.042888 -45/2 -21/1 1 21 0.044411 In 0.044085 0.044738 -43/2 -23/1 1 21 0.046554 In 0.046195 0.046912 -41/2 -19/1 1 21 0.048741 In 0.048347 0.049134 -39/2 -21/1 1 21 0.051333 In 0.050897 0.051770 -37/2 -17/1 1 21 0.054006 In 0.053523 0.054489 -35/2 -19/1 1 21 0.057207 In 0.056665 0.057749 -33/2 -15/1 1 21 0.060546 In 0.059939 0.061153 -31/2 -17/1 1 21 0.064599 In 0.063908 0.065290 -29/2 -13/1 1 21 0.068889 In 0.068103 0.069675 -27/2 -15/1 1 21 0.074185 In 0.073273 0.075096 -25/2 -11/1 1 21 0.079898 In 0.078841 0.080956 -23/2 -13/1 1 21 0.087112 In 0.085855 0.088368 -21/2 -9/1 1 21 0.095098 In 0.093600 0.096596 -19/2 -11/1 1 21 0.105496 In 0.103653 0.107339 -17/2 -7/1 1 21 0.117442 In 0.115158 0.119726 -15/2 -9/1 1 21 0.133721 In 0.130761 0.136681 -13/2 -5/1 1 21 0.153519 In 0.149618 0.157420 -11/2 -7/1 1 21 0.182584 In 0.177068 0.188101 -9/2 -3/1 1 21 0.221631 In 0.213506 0.229756 -7/2 -5/1 1 21 0.287849 In 0.274156 0.301542 -5/2 -1/1 1 21 0.398855 In 0.372619 0.425091 -3/2 -3/1 1 21 0.683333 In 0.606957 0.759710 -1/2 1/1 1 21 2.150000 In 1.462614 2.837386 1/2 -1/1 1 21 -2.150000 In -2.837386 -1.462614 3/2 3/1 1 21 -0.683333 In -0.759710 -0.606957 5/2 1/1 1 21 -0.398855 In -0.425091 -0.372619 7/2 5/1 1 21 -0.287849 In -0.301542 -0.274156 9/2 3/1 1 21 -0.221631 In -0.229756 -0.213506 11/2 7/1 1 21 -0.182584 In -0.188101 -0.177068 13/2 5/1 1 21 -0.153519 In -0.157420 -0.149618 15/2 9/1 1 21 -0.133721 In -0.136681 -0.130761 17/2 7/1 1 21 -0.117442 In -0.119726 -0.115158 19/2 11/1 1 21 -0.105496 In -0.107339 -0.103653 21/2 9/1 1 21 -0.095098 In -0.096596 -0.093600 23/2 13/1 1 21 -0.087112 In -0.088368 -0.085855 25/2 11/1 1 21 -0.079898 In -0.080956 -0.078841 27/2 15/1 1 21 -0.074185 In -0.075096 -0.073273 29/2 13/1 1 21 -0.068889 In -0.069675 -0.068103 31/2 17/1 1 21 -0.064599 In -0.065290 -0.063908 33/2 15/1 1 21 -0.060546 In -0.061153 -0.059939 35/2 19/1 1 21 -0.057207 In -0.057749 -0.056665 37/2 17/1 1 21 -0.054006 In -0.054489 -0.053523 39/2 21/1 1 21 -0.051333 In -0.051770 -0.050897 41/2 19/1 1 21 -0.048741 In -0.049134 -0.048347 43/2 23/1 1 21 -0.046554 In -0.046912 -0.046195 45/2 21/1 1 21 -0.044411 In -0.044738 -0.044085 47/2 25/1 1 21 -0.042588 In -0.042888 -0.042288 49/2 23/1 1 21 -0.040788 In -0.041064 -0.040513 -50/3 0 7 -49/3 0 7 -47/3 0 7 -46/3 0 7 -44/3 0 7 -43/3 0 7 -41/3 0 7 -40/3 0 7 -38/3 0 7 -37/3 0 7 -35/3 0 7 -34/3 0 7 -32/3 0 7 -31/3 0 7 -29/3 0 7 -28/3 0 7 -26/3 0 7 -25/3 0 7 -23/3 0 7 -22/3 0 7 -20/3 0 7 -19/3 0 7 -17/3 0 7 -16/3 0 7 -14/3 0 7 -13/3 0 7 -11/3 0 7 -10/3 0 7 -8/3 0 7 -7/3 0 7 -5/3 0 7 -4/3 0 7 -2/3 0 7 -1/3 0 7 1/3 0 7 2/3 0 7 4/3 0 7 5/3 0 7 7/3 0 7 8/3 0 7 10/3 0 7 11/3 0 7 13/3 0 7 14/3 0 7 16/3 0 7 17/3 0 7 19/3 0 7 20/3 0 7 22/3 0 7 23/3 0 7 25/3 0 7 26/3 0 7 28/3 0 7 29/3 0 7 31/3 0 7 32/3 0 7 34/3 0 7 35/3 0 7 37/3 0 7 38/3 0 7 40/3 0 7 41/3 0 7 43/3 0 7 44/3 0 7 46/3 0 7 47/3 0 7 49/3 0 7 50/3 0 7 -49/4 -11/1 1 21 0.081610 In 0.081155 0.082066 -47/4 -13/1 1 21 0.085136 In 0.084641 0.085632 -45/4 -11/1 1 21 0.088883 In 0.088775 0.088991 -43/4 -11/1 1 21 0.093030 In 0.092911 0.093148 -41/4 -9/1 1 21 0.097530 In 0.096879 0.098180 -39/4 -11/1 1 21 0.102608 In 0.101888 0.103329 -37/4 -9/1 1 21 0.108100 In 0.107940 0.108259 -35/4 -9/1 1 21 0.114296 In 0.114117 0.114474 -33/4 -7/1 1 21 0.121166 In 0.120162 0.122170 -31/4 -9/1 1 21 0.129104 In 0.127965 0.130244 -29/4 -7/1 1 21 0.137917 In 0.137657 0.138178 -27/4 -7/1 1 21 0.148165 In 0.147865 0.148465 -25/4 -5/1 1 21 0.159924 In 0.158175 0.161673 -23/4 -7/1 1 21 0.174051 In 0.171979 0.176122 -21/4 -5/1 1 21 0.190450 In 0.189954 0.190947 -19/4 -5/1 1 21 0.210561 In 0.209955 0.211168 -17/4 -3/1 1 21 0.235149 In 0.231368 0.238930 -15/4 -5/1 1 21 0.267021 In 0.262146 0.271896 -13/4 -3/1 1 21 0.307627 In 0.306333 0.308922 -11/4 -3/1 1 21 0.363744 In 0.361934 0.365554 -9/4 -1/1 1 21 0.444118 In 0.430639 0.457596 -7/4 -3/1 1 21 0.573529 In 0.551066 0.595993 -5/4 -1/1 1 21 0.799618 In 0.790873 0.808364 -3/4 -1/1 1 21 1.335106 In 1.310731 1.359482 -1/4 1/1 1 21 4.250000 In 3.104356 5.395644 1/4 -1/1 1 21 -4.250000 In -5.395644 -3.104356 3/4 1/1 1 21 -1.335106 In -1.359482 -1.310731 5/4 1/1 1 21 -0.799618 In -0.808364 -0.790873 7/4 3/1 1 21 -0.573529 In -0.595993 -0.551066 9/4 1/1 1 21 -0.444118 In -0.457596 -0.430639 11/4 3/1 1 21 -0.363744 In -0.365554 -0.361934 13/4 3/1 1 21 -0.307627 In -0.308922 -0.306333 15/4 5/1 1 21 -0.267021 In -0.271896 -0.262146 17/4 3/1 1 21 -0.235149 In -0.238930 -0.231368 19/4 5/1 1 21 -0.210561 In -0.211168 -0.209955 21/4 5/1 1 21 -0.190450 In -0.190947 -0.189954 23/4 7/1 1 21 -0.174051 In -0.176122 -0.171979 25/4 5/1 1 21 -0.159924 In -0.161673 -0.158175 27/4 7/1 1 21 -0.148165 In -0.148465 -0.147865 29/4 7/1 1 21 -0.137917 In -0.138178 -0.137657 31/4 9/1 1 21 -0.129104 In -0.130244 -0.127965 33/4 7/1 1 21 -0.121166 In -0.122170 -0.120162 35/4 9/1 1 21 -0.114296 In -0.114474 -0.114117 37/4 9/1 1 21 -0.108100 In -0.108259 -0.107940 39/4 11/1 1 21 -0.102608 In -0.103329 -0.101888 41/4 9/1 1 21 -0.097530 In -0.098180 -0.096879 43/4 11/1 1 21 -0.093030 In -0.093148 -0.092911 45/4 11/1 1 21 -0.088883 In -0.088991 -0.088775 47/4 13/1 1 21 -0.085136 In -0.085632 -0.084641 49/4 11/1 1 21 -0.081610 In -0.082066 -0.081155 -49/5 -9/1 1 21 0.102026 In 0.101662 0.102390 -48/5 0 21 -47/5 -9/1 1 21 0.106375 In 0.106177 0.106573 -46/5 0 21 -44/5 0 21 -43/5 -9/1 1 21 0.116290 In 0.116053 0.116526 -42/5 0 21 -41/5 -9/1 1 21 0.121976 In 0.121456 0.122497 -39/5 -7/1 1 21 0.128183 In 0.127608 0.128757 -38/5 0 21 -37/5 -7/1 1 21 0.135122 In 0.134803 0.135441 -36/5 0 21 -34/5 0 21 -33/5 -7/1 1 21 0.151534 In 0.151132 0.151935 -32/5 0 21 -31/5 -7/1 1 21 0.161335 In 0.160425 0.162246 -29/5 -5/1 1 21 0.172375 In 0.171335 0.173414 -28/5 0 21 -27/5 -5/1 1 21 0.185161 In 0.184561 0.185761 -26/5 0 21 -24/5 0 21 -23/5 -5/1 1 21 0.217431 In 0.216604 0.218257 -22/5 0 21 -21/5 -5/1 1 21 0.238198 In 0.236214 0.240183 -19/5 -3/1 1 21 0.263074 In 0.260654 0.265495 -18/5 0 21 -17/5 -3/1 1 21 0.294059 In 0.292547 0.295572 -16/5 0 21 -14/5 0 21 -13/5 -3/1 1 21 0.384746 In 0.382157 0.387335 -12/5 0 21 -11/5 -3/1 1 21 0.454976 In 0.447737 0.462216 -9/5 -1/1 1 21 0.555294 In 0.544512 0.566077 -8/5 0 21 -7/5 -1/1 1 21 0.714008 In 0.705092 0.722923 -6/5 0 21 -4/5 0 21 -3/5 -1/1 1 21 1.670213 In 1.621462 1.718964 -2/5 0 21 -1/5 -1/1 1 21 5.200000 In 4.283485 6.116515 1/5 1/1 1 21 -5.200000 In -6.116515 -4.283485 2/5 0 21 3/5 1/1 1 21 -1.670213 In -1.718964 -1.621462 4/5 0 21 6/5 0 21 7/5 1/1 1 21 -0.714008 In -0.722923 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0.215198 0.221644 -31/7 1/0 2 3 0.225963 In 0.220012 0.231915 -30/7 1/0 2 3 0.233506 In 0.227151 0.239862 -29/7 1/0 1 3 0.241475 In 0.236668 0.246282 -27/7 1/0 1 3 0.259378 In 0.253831 0.264924 -26/7 1/0 2 3 0.269497 In 0.261033 0.277960 -25/7 1/0 2 3 0.280299 In 0.271144 0.289454 -24/7 -4/1 2 3 0.292453 In 0.286676 0.298230 -23/7 -4/1 3 3 0.306043 In 0.296296 0.315789 -22/7 -3/1 2 3 0.317992 In 0.316283 0.319700 -20/7 -3/1 2 3 0.350254 In 0.348181 0.352326 -19/7 -2/1 3 3 0.366947 In 0.352941 0.380952 -18/7 -2/1 2 3 0.387967 In 0.377803 0.398131 -17/7 1/0 2 3 0.412717 In 0.392894 0.432539 -16/7 1/0 2 3 0.438642 In 0.416258 0.461027 -15/7 1/0 1 3 0.467359 In 0.449370 0.485348 -13/7 1/0 1 3 0.539526 In 0.515565 0.563487 -12/7 1/0 2 3 0.586047 In 0.546171 0.625922 -11/7 1/0 2 3 0.639889 In 0.592392 0.687386 -10/7 -2/1 2 3 0.705479 In 0.671925 0.739034 -9/7 -2/1 3 3 0.792208 In 0.727273 0.857143 -8/7 -1/1 2 3 0.873684 In 0.860792 0.886576 -6/7 -1/1 2 3 1.169811 In 1.146703 1.192920 -5/7 0/1 3 3 1.400000 In 1.200000 1.600000 -4/7 0/1 2 3 1.750000 In 1.545876 1.954124 -3/7 1/0 2 3 2.520000 In 1.834143 3.205857 -2/7 1/0 2 3 4.200000 In 2.485357 5.914643 -1/7 1/0 1 3 10.500000 In 4.437822 16.562178 1/7 1/0 1 3 -10.500000 In -16.562178 -4.437822 2/7 1/0 2 3 -4.200000 In -5.914643 -2.485357 3/7 1/0 2 3 -2.520000 In -3.205857 -1.834143 4/7 0/1 2 3 -1.750000 In -1.954124 -1.545876 5/7 0/1 3 3 -1.400000 In -1.600000 -1.200000 6/7 1/1 2 3 -1.169811 In -1.192920 -1.146703 8/7 1/1 2 3 -0.873684 In -0.886576 -0.860792 9/7 2/1 3 3 -0.792208 In -0.857143 -0.727273 10/7 2/1 2 3 -0.705479 In -0.739034 -0.671925 11/7 1/0 2 3 -0.639889 In -0.687386 -0.592392 12/7 1/0 2 3 -0.586047 In -0.625922 -0.546171 13/7 1/0 1 3 -0.539526 In -0.563487 -0.515565 15/7 1/0 1 3 -0.467359 In -0.485348 -0.449370 16/7 1/0 2 3 -0.438642 In -0.461027 -0.416258 17/7 1/0 2 3 -0.412717 In -0.432539 -0.392894 18/7 2/1 2 3 -0.387967 In -0.398131 -0.377803 19/7 2/1 3 3 -0.366947 In -0.380952 -0.352941 20/7 3/1 2 3 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