{"count": 6, "status":"OK", "data":[{"pols": "[X^4, -3*(3*X+1)*(3*X+2)*(10*X^2+10*X+3), 81*(3*X+1)*(3*X+2)*(3*X+4)*(3*X+5)]", "text": "Hadamard product $B\\ast c$.", "degz": 2, "h3": "18", "sol": "1 18 1350 156240 22141350 3521185668 603258639984 108881071041600 20424293211323430 3946730690210665500", "n_discr_factors": "2", "c3": "-156", "operator": "4 2 0 0 0 0 1 -18 -141 -411 -540 -270 3240 18954 35721 26244 6561", "new_number": "2.10", "id": 1, "operator_tex": "\\theta^4-3 x(3\\theta+1)(3\\theta+2)(10\\theta^2+10\\theta+3)+3^{4} x^{2}(3\\theta+1)(3\\theta+2)(3\\theta+4)(3\\theta+5)", "superseek": "27 18089", "discriminant": "2 1 -270 6561", "aesz": "70", "n_sing_complex": "0", "inst_int": "", "c2h": "72", "hash": "3d2adae6eaf26a56c76b8b67d92cc5df", "dim_h": "9", "inst": " 27 432 18089 997785 68438142 5372412653 462553061328 42629254956495 4139005487642537 418758418475154936", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "A_{n}=\\dbinom{2n}{n}\\dbinom{3n}{n}\\sum_{k=0}^{n}\\dbinom{n}{k}^{2}\\dbinom{2k}{k}", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "(243z-1)(27z-1)", "discr_factors": "6561, z-1/243, z-1/27", "dm_basis": ["-377989751/500000000*I", "6", "1", "1", "-3", "-9", "-1", "0", "0", "18", "0", "0", "-18", "0", "0", "0"], "q": "0 1 -69 2196 -90131 1380525 -161041824 -7106675719 -979853201733 -98506835149437", "yuk": "1 27 3483 488430 63861723 8554767777 1160441624934 158655700035531 21826178601587163 3017335000491897903", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":["1","-1","1/2","-1/6","0","1","-1","1/2","0","0","1","-1","0","0","0","1"],"monodromy_dm":["1","0","0","0","1","1","0","0","0","18","1","0","0","0","1","1"]},{"re":"1/243","im":"0","approx_re":"0.00411522633745","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["1.+.755979502*I","0","26*lambda",".31750278e-1","3","1","1/2","-26*lambda","0","0","1","0","18","0","3","1.-.755979502*I"],"monodromy_dm":["1","-9","-1","-1","0","1","0","0","0","0","1","0","0","0","0","1"]},{"re":"1/27","im":"0","approx_re":"0.037037037037","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["4+468*lambda","-1.-.755979502*I","1/2+78*lambda","-.71415832e-1-52*lambda","9","-2","3/2","-1/2-78*lambda","18","-6","4","-1.-.755979502*I","54","-18","9","-2-468*lambda"],"monodromy_dm":["-5","-36","-4","-3","2","13","1333333/1000000","1","-18","-108","-11","-9","12","72","8","7"]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/3","2/3","4/3","5/3"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -3*(3*X+1)*(3*X+2)*(7*X^2+7*X+2), -72*(3*X+1)*(3*X+2)*(3*X+4)*(3*X+5)]", "text": "Hadamard product $B\\ast a$.\n\nA-Incarnation: diagonal of (3,3)-intersection in $P^2 \\times P^2$", "degz": 2, "h3": "18", "sol": "1 12 900 94080 11988900 1704214512 260453217024 41886697881600 6996546610936740 1203384096358158000", "n_discr_factors": "2", "c3": "-162", "operator": "4 2 0 0 0 0 1 -12 -96 -285 -378 -189 -2880 -16848 -31752 -23328 -5832", "new_number": "2.2", "id": 22, "operator_tex": "\\theta^4-3 x(3\\theta+1)(3\\theta+2)(7\\theta^2+7\\theta+2)-2^{3} 3^{2} x^{2}(3\\theta+1)(3\\theta+2)(3\\theta+4)(3\\theta+5)", "superseek": "21 15894", "discriminant": "2 1 -189 -5832", "aesz": "15", "n_sing_complex": "0", "inst_int": "", "c2h": "72", "hash": "c8053e0e9c05ef468263fafd5e3fc764", "dim_h": "9", "inst": " 21 480 15894 894075 58703151 4482271260 373469554929 33373998306933 3140252369423073 307963083118697496", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "A_{n}=\\dbinom{2n}{n}\\dbinom{3n}{n}\\sum_{k=0}^{n}\\dbinom{n}{k}^3", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "-(27z+1)(216z-1)", "discr_factors": "-5832, z-1/216, z+1/27", "dm_basis": ["-162*lambda", "6", "1", "1", "-3", "-9", "-1", "0", "0", "18", "0", "0", "-18", "0", "0", "0"], "q": "0 1 -48 -18 7976 -1697115 -90056880 -9049527514 -907472920848 -94324071435966", "yuk": "1 21 3861 429159 57224661 7337893896 968171025159 128100057340668 17087487190374357 2289243977309849376", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/27","im":"0","approx_re":"-0.037037037037","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["4+324*lambda","-3/2-162*lambda","3/4+81*lambda","-222/1223-54*lambda","9","-7/2","9/4","-3/4-81*lambda","18","-9","11/2","-3/2-162*lambda","36","-18","9","-2-324*lambda"],"monodromy_dm":["-5","-30","-3","-2","3","16","3/2","1","-36","-180","-17","-12","27","135","27/2","10"]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":["1","-1","1/2","-1/6","0","1","-1","1/2","0","0","1","-1","0","0","0","1"],"monodromy_dm":["1","0","0","0","1","1","0","0","0","18","1","0","0","0","1","1"]},{"re":"1/216","im":"0","approx_re":"0.00462962962963","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["1+162*lambda","0","27*lambda",".34239575e-1","3","1","1/2","-27*lambda","0","0","1","0","18","0","3","1-162*lambda"],"monodromy_dm":["1","-9","-1","-1","0","1","0","0","0","0","1","0","0","0","0","1"]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/3","2/3","4/3","5/3"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -24-184*X-545*X^2-722*X^3-289*X^4, 5136*X^4+65616*X^3+116664*X^2+63360*X+11232, 72576+746496*X+2449152*X^2+2985984*X^3+801216*X^4, 746496*(2*X+1)^4]", "text": "Sporadic Operator. There is a second MUM-point hiding at infinity, corresponding to Operator AESZ 351/4.70", "degz": 4, "h3": "18", "sol": "1 24 1944 232800 34133400 5649061824 1011627229536 191367704601216 37683808295304600 7651704687834292800", "n_discr_factors": "3", "c3": "-64", "operator": "4 4 0 0 0 0 1 -24 -184 -545 -722 -289 11232 63360 116664 65616 5136 72576 746496 2449152 2985984 801216 746496 5971968 17915904 23887872 11943936", "new_number": "4.69", "id": 169, "operator_tex": "\\theta^4-x\\left(24+184\\theta+545\\theta^2+722\\theta^3+289\\theta^4\\right)+2^{3} 3 x^{2}\\left(214\\theta^4+2734\\theta^3+4861\\theta^2+2640\\theta+468\\right)+2^{6} 3^{2} x^{3}\\left(1391\\theta^4+5184\\theta^3+4252\\theta^2+1296\\theta+126\\right)+2^{10} 3^{6} x^{4}\\left((2\\theta+1)^4\\right)", "superseek": "49 173876/9", "discriminant": "4 1 -289 5136 801216 11943936", "aesz": "350", "n_sing_complex": "0", "inst_int": "", "c2h": "60", "hash": "e6de16eb3758d2ed5687f4b2a2abf36b", "dim_h": "8", "inst": " 49 136 173876/9 781152 57087750 12201523592/3 338790123846 29537353606592 24592780153285625/9 262707875156521480", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "(256z-1)(81z-1)(1+24z)^2", "discr_factors": "11943936, z-1/256, (1/24+z)^2, z-1/81", "dm_basis": null, "q": "0 1 -88 4980 -282064 12865650 -690703872 23666776560 -1799987151264 3529620262935", "yuk": "1 49 1137 521677 49994865 7135968799 878510221389 116205012479227 15123125096569969 1992015192416657302", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/24","im":"0","approx_re":"-0.0416666666667","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/256","im":"0","approx_re":"0.00390625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/81","im":"0","approx_re":"0.0123456790123","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/2","1/2","1/2","1/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -3*X*(2+11*X+18*X^2+27*X^3), -3456-17820*X-32562*X^2-22356*X^3-3888*X^4, -178848-688176*X-699840*X^2+90396*X^4, 17496*(2*X+1)*(54*X^3+405*X^2+544*X+200), -944784*(2*X+1)*(3*X+2)*(3*X+4)*(2*X+3)]", "text": "This is operator \"5.33\" from ...", "degz": 5, "h3": "18", "sol": "1 0 216 7200 567000 38102400 2992096800 239740300800 20126947440600 1733218043356800", "n_discr_factors": "4", "c3": "-52", "operator": "4 5 0 0 0 0 1 0 -6 -33 -54 -81 -3456 -17820 -32562 -22356 -3888 -178848 -688176 -699840 0 90396 3499200 16516224 26121528 15116544 1889568 -22674816 -111484512 -191791152 -136048896 -34012224", "new_number": "5.33", "id": 242, "operator_tex": "\\theta^4-3 x\\theta(2+11\\theta+18\\theta^2+27\\theta^3)-2 3^{3} x^{2}\\left(72\\theta^4+414\\theta^3+603\\theta^2+330\\theta+64\\right)+2^{2} 3^{5} x^{3}\\left(93\\theta^4-720\\theta^2-708\\theta-184\\right)+2^{3} 3^{7} x^{4}(2\\theta+1)(54\\theta^3+405\\theta^2+544\\theta+200)-2^{4} 3^{10} x^{5}(2\\theta+1)(3\\theta+2)(3\\theta+4)(2\\theta+3)", "superseek": "9 14201/3", "discriminant": "5 1 -81 -3888 90396 1889568 -34012224", "aesz": "216", "n_sing_complex": "0", "inst_int": "", "c2h": "48", "hash": "af7027bf24acce4fd0ed5b09e575e2a5", "dim_h": "7", "inst": " 9 225 14201/3 154800 6298596 891120368/3 15388571196 854854622028 150149352094538/3 3054637162639620", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "5", "n_sing": "5", "laurent": null, "discriminant_tex": "-(27z+1)(108z-1)(36z+1)(-1+18z)^2", "discr_factors": "-34012224, z+1/36, (-1/18+z)^2, z+1/27, z-1/108", "dm_basis": null, "q": "0 1 -6 -693 -12452 -197823 -12446514 -891867937 -56452162728 -3600417678813", "yuk": "1 9 1809 127818 9909009 787324509 64160796114 5278279920237 437685576387345 36486292559100552", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/27","im":"0","approx_re":"-0.037037037037","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/36","im":"0","approx_re":"-0.0277777777778","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/108","im":"0","approx_re":"0.00925925925926","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/18","im":"0","approx_re":"0.0555555555556","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/2","2/3","4/3","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[81*X^4, -17937*X^4-28962*X^3-21933*X^2-7452*X-972, 559552*X^4+805888*X^3+391648*X^2+89280*X+9504, -6046720*X^4-8902656*X^3-7399680*X^2-3186432*X-539136, 32768*(2*X+1)*(340*X^3+618*X^2+455*X+129), -4194304*(2*X+1)*(X+1)^2*(2*X+3)]", "text": "This is operator \"5.75\" from ...", "degz": 5, "h3": "18", "sol": "1 12 708 63840 6989220 855982512 112786041984 15645580194816 2254801269803940 334669706566543920", "n_discr_factors": "3", "c3": "-92", "operator": "4 5 0 0 0 0 81 -972 -7452 -21933 -28962 -17937 9504 89280 391648 805888 559552 -539136 -3186432 -7399680 -8902656 -6046720 4227072 23363584 50069504 51642368 22282240 -12582912 -58720256 -96468992 -67108864 -16777216", "new_number": "5.75", "id": 288, "operator_tex": "3^{4} \\theta^4-3^{2} x\\left(1993\\theta^4+3218\\theta^3+2437\\theta^2+828\\theta+108\\right)+2^{5} x^{2}\\left(17486\\theta^4+25184\\theta^3+12239\\theta^2+2790\\theta+297\\right)-2^{8} x^{3}\\left(23620\\theta^4+34776\\theta^3+28905\\theta^2+12447\\theta+2106\\right)+2^{15} x^{4}(2\\theta+1)(340\\theta^3+618\\theta^2+455\\theta+129)-2^{22} x^{5}(2\\theta+1)(\\theta+1)^2(2\\theta+3)", "superseek": "205/9 97622/9", "discriminant": "5 81 -17937 559552 -6046720 22282240 -16777216", "aesz": "298", "n_sing_complex": "0", "inst_int": "", "c2h": "12", "hash": "e52d50673ec5c795512e2bc3e1017b12", "dim_h": "4", "inst": " 205/9 3206/9 97622/9 496806 254037095/9 16476340418/9 1172722066057/9 9930597861190 7176881517850505/9 200193418895368288/3", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "-(z-1)(1024z^2-192z+1)(-9+128z)^2", "discr_factors": "-16777216, (-9/128+z)^2, z^2-3/16*z+1/1024, z-1", "dm_basis": null, "q": "0 1 -44 350 -10696 -567579 -43127416 -3457085002 -294469950256 -26124408525758", "yuk": "1 205/9 25853/9 2635999/9 286186109/9 31754637080/9 3558892191935/9 402243668657756/9 45760195230549629/9 5231946626515654144/9", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"3/32-1/16*2^(1/2)","im":"0","approx_re":"0.005362","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"9/128","im":"0","approx_re":"0.0703125","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"3/32+1/16*2^(1/2)","im":"0","approx_re":"0.182138","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1","im":"0","approx_re":"1.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/2","1","1","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[9*X^4, -1776*X^4-3300*X^3-2487*X^2-837*X-108, 13801*X^4+6652*X^3-18041*X^2-14904*X-3312, -2*X*(8461*X^3-29160*X^2-28365*X-7236), -43092*X^4-72576*X^3-40908*X^2-5376*X+1344, -1176*(X+1)^2*(3*X+2)*(3*X+4)]", "text": "This is operator \"5.76\" from ...", "degz": 5, "h3": "18", "sol": "1 12 732 67080 7456140 926920512 123962745144 17452988516304 2552819496885900 384553561286809200", "n_discr_factors": "3", "c3": "-90", "operator": "4 5 0 0 0 0 9 -108 -837 -2487 -3300 -1776 -3312 -14904 -18041 6652 13801 0 14472 56730 58320 -16922 1344 -5376 -40908 -72576 -43092 -9408 -39984 -62328 -42336 -10584", "new_number": "5.76", "id": 289, "operator_tex": "3^{2} \\theta^4-3 x\\left(592\\theta^4+1100\\theta^3+829\\theta^2+279\\theta+36\\right)+x^{2}\\left(13801\\theta^4+6652\\theta^3-18041\\theta^2-14904\\theta-3312\\right)-2 x^{3}\\theta(8461\\theta^3-29160\\theta^2-28365\\theta-7236)-2^{2} 3 7 x^{4}\\left(513\\theta^4+864\\theta^3+487\\theta^2+64\\theta-16\\right)-2^{3} 3 7^{2} x^{5}(\\theta+1)^2(3\\theta+2)(3\\theta+4)", "superseek": "73/3 11119", "discriminant": "5 9 -1776 13801 -16922 -43092 -10584", "aesz": "306", "n_sing_complex": "0", "inst_int": "", "c2h": "60", "hash": "d14307aa38b16c728ee31e5936937c44", "dim_h": "8", "inst": " 73/3 2131/6 11119 518671 29749701 3901038259/2 140360129678 10814052859404 877844110264408 445563524466054257/6", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "-(z+1)(54z^2+189z-1)(-3+14z)^2", "discr_factors": "-10584, z+1, (-3/14+z)^2, z^2+7/2*z-1/54", "dm_basis": null, "q": "0 1 -45 378 -10275 -622278 -44377758 -3650207751 -314202691197 -28179105875892", "yuk": "1 73/3 8597/3 900712/3 99593429/3 11156137948/3 1263937305152/3 144430573438735/3 16610385291637973/3 1919845069149161008/3", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-7/4-11/36*33^(1/2)","im":"0","approx_re":"-3.505283","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1","im":"0","approx_re":"-1.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"-7/4+11/36*33^(1/2)","im":"0","approx_re":"0.005283","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"3/14","im":"0","approx_re":"0.214285714286","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["2/3","1","1","4/3"],"monodromy":[],"monodromy_dm":[]}]}]}