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The Riesz Energy Database

Lowest minima located for the Riesz problem with $ s = 1$

53 configurations, N = 512 to 9913.



$ N$ Energy Point Group Voronoi Image Mollweide Image point coordinates angle coordinates
512 124673.9055677 $ C_1$ 512.gif 512.png points_512_1.dat angles_512_1.dat
516 126654.6040876 $ T$ 516.gif 516.png points_516_1.dat angles_516_1.dat
518 127650.8075930 $ D_2$ 518.gif 518.png points_518_1.dat angles_518_1.dat
522 129655.3224067 $ C_2$ 522.gif 522.png points_522_1.dat angles_522_1.dat
532 134735.0715455 $ C_2$ 532.gif 532.png points_532_1.dat angles_532_1.dat
534 135762.9106616 $ C_1$ 534.gif 534.png points_534_1.dat angles_534_1.dat
538 137830.1360893 $ C_2$ 538.gif 538.png points_538_1.dat angles_538_1.dat
542 139913.1454539 $ C_2$ 542.gif 542.png points_542_1.dat angles_542_1.dat
548 143067.0064628 $ C_1$ 548.gif 548.png points_548_1.dat angles_548_1.dat
572 156036.2385635 $ C_{2v}$ 572.gif 572.png points_572_1.dat angles_572_1.dat
612 178909.7952490 $ C_2$ 612.gif 612.png points_612_1.dat angles_612_1.dat
620 183673.0995320 $ C_1$ 620.gif 620.png points_620_1.dat angles_620_1.dat
642 197097.1993002 $ C_2$ 642.gif 642.png points_642_1.dat angles_642_1.dat
660 208434.6161288 $ T$ 660.gif 660.png points_660_1.dat angles_660_1.dat
672 216170.0403547 $ C_1$ 672.gif 672.png points_672_1.dat angles_672_1.dat
722 249926.1662872 $ C_1$ 722.gif 722.png points_722_1.dat angles_722_1.dat
732 256972.4358872 $ T$ 732.gif 732.png points_732_1.dat angles_732_1.dat
739 261963.5020771 $ C_3$ 739.gif 739.png points_739_1.dat angles_739_1.dat
740 262680.3895493 $ S_6$ 740.gif 740.png points_740_1.dat angles_740_1.dat
743 264837.5858504 $ C_1$ 743.gif 743.png points_743_1.dat angles_743_1.dat
745 266280.2589229 $ C_1$ 745.gif 745.png points_745_1.dat angles_745_1.dat
750 269904.2259635 $ C_1$ 750.gif 750.png points_750_1.dat angles_750_1.dat
752 271360.9889196 $ C_2$ 752.gif 752.png points_752_1.dat angles_752_1.dat
753 272090.8085565 $ C_2$ 753.gif 753.png points_753_1.dat angles_753_1.dat
755 273553.3317336 $ C_1$ 755.gif 755.png points_755_1.dat angles_755_1.dat
759 276490.0843822 $ C_1$ 759.gif 759.png points_759_1.dat angles_759_1.dat
762 278703.1085972 $ C_2$ 762.gif 762.png points_762_1.dat angles_762_1.dat
777 289900.8082430 $ C_1$ 777.gif 777.png points_777_1.dat angles_777_1.dat
780 292166.7658373 $ C_1$ 780.gif 780.png points_780_1.dat angles_780_1.dat
792 301319.8733917 $ T$ 792.gif 792.png points_792_1.dat angles_792_1.dat
812 316890.4580541 $ C_2$ 812.gif 812.png points_812_1.dat angles_812_1.dat
842 340985.6576387 $ C_1$ 842.gif 842.png points_842_1.dat angles_842_1.dat
900 390084.7556201 $ C_1$ 900.gif 900.png points_900_1.dat angles_900_1.dat
912 400657.6165027 $ C_1$ 912.gif 912.png points_912_1.dat angles_912_1.dat
920 407784.8388324 $ C_1$ 920.gif 920.png points_920_1.dat angles_920_1.dat
932 418594.2339500 $ C_1$ 932.gif 932.png points_932_1.dat angles_932_1.dat
960 444368.4706375 $ C_1$ 960.gif 960.png points_960_1.dat angles_960_1.dat
972 455651.0809351 $ T_h$ 972.gif 972.png points_972_1.dat angles_972_1.dat
1382 926576.1030330 $ C_1$ 1382.gif 1382.png points_1382_1.dat angles_1382_1.dat
2000 1950575.5888846 $ C_1$ 2000.gif 2000.png points_2000_1.dat angles_2000_1.dat
2192 2345721.0320489 $ C_2$ 2192.gif 2192.png points_2192_1.dat angles_2192_1.dat
2500 3055923.3717686 $ C_1$ 2500.gif 2500.png points_2500_1.dat angles_2500_1.dat
2502 3060842.3258377 $ C_1$ 2502.gif 2502.png points_2502_1.dat angles_2502_1.dat
2832 3926824.7500678 $ T$ 2832.gif 2832.png points_2832_1.dat angles_2832_1.dat
3182 4963364.7161387 $ C_1$ 3182.gif 3182.png points_3182_1.dat angles_3182_1.dat
3552 6191355.6866585 $ C_1$ 3552.gif 3552.png points_3552_1.dat angles_3552_1.dat
3942 7632894.5083689 $ C_1$ 3942.gif 3942.png points_3942_1.dat angles_3942_1.dat
4352 9311273.1820032 $ C_1$ 4352.gif 4352.png points_4352_1.dat angles_4352_1.dat
5792 16529989.7209392 $ C_1$ 5792.gif 5792.png points_5792_1.dat angles_5792_1.dat
5872 16991482.4656879 $ C_1$ 5872.gif 5872.png points_5872_1.dat angles_5872_1.dat
9911 48568535.8379516 $ C_1$ 9911.gif 9911.png points_9911_1.dat angles_9911_1.dat
9912 48578364.7656764 $ I$ 9912.gif 9912.png points_9912_1.dat angles_9912_1.dat
9913 48588194.8806764 $ C_1$ 9913.gif 9913.png points_9913_1.dat angles_9913_1.dat


Energies are for the potential r-s, with -log r at s = 0 and an overall change of sign for negative s, so that the configuration listed is the lowest minimum known in every case.

Point groups were determined with a tolerance of 0.0001. The angle files hold the 2N vector (theta0, phi0, ...) with the last point at the north pole and the penultimate one at phi = 0; the point files hold N rows of x y z on the unit sphere.

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2026-08-13 19:50:09