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Table 1

From: Compressed lattice sums arising from the Poisson equation

d

minimal polynomial

3

1 − 3α

4

1 − 644α + 3,334 α 2 644 α 3 + α 4

5

1 + 20α210 α 2 + 100 α 3 + 25 α 4

6

1 − 39,368α + 309,916 α 2 + 589,192 α 3 + 639,814 α 4 + 589,192 α 5 + 309,916 α 6 39,368 α 7 + α 8

7

1 − 14α + 21 α 2 7 α 3

8

1 − 972,816α + 108,957,816 α 2 3,146,762,800 α 3 + 87,457,048,348 α 4 579,962,120,464 α 5 2,624,405,729,464 α 6 52,677,445,809,328 α 7 + 115,992,837,288,518 α 8 52,677,445,809,328 α 9 2,624,405,729,464 α 10 579,962,120,464 α 11 + 87,457,048,348 α 12 3,146,762,800 α 13 + 108,957,816 α 14 972,816 α 15 + α 16

9

1 + 438α8,997 α 2 + 8,292 α 3 + 711 α 4 954 α 5 3 α 6