{"count": 4, "status":"OK", "data":[{"pols": "[X^4, -2*(2*X+1)^2*(7*X^2+7*X+3), 324*(2*X+1)*(X+1)^2*(2*X+3)]", "text": "Hadamard product $I \\ast \\delta$", "degz": 2, "h3": null, "sol": "1 6 54 60 -19530 -755244 -17954244 -226007496 3762274230 350186668260", "n_discr_factors": "1", "c3": null, "operator": "4 2 0 0 0 0 1 -6 -38 -94 -112 -56 972 4536 7452 5184 1296", "new_number": "2.54", "id": 49, "operator_tex": "\\theta^4-2 x(2\\theta+1)^2(7\\theta^2+7\\theta+3)+2^{2} 3^{4} x^{2}(2\\theta+1)(\\theta+1)^2(2\\theta+3)", "superseek": "2 -104", "discriminant": "2 1 -56 1296", "aesz": "41", "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "a9ddeed4299f59fb9ac9f6f248383b8f", "dim_h": null, "inst": " 2 -7 -104 -588 3300 128384 1336396 -5019718 -393656474 -5619028410", "cleanlist": "True", "n_sing_real": "1", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "3", "laurent": null, "discriminant_tex": "1-56z+1296z^2", "discr_factors": "1296, 1/1296-7/162*z+z^2", "dm_basis": ["1-872284041/1000000000*I", "24", "7/6", "1", "-6", "-48", "-1", "0", "12", "72", "0", "0", "-72", "0", "0", "0"], "q": "0 1 -14 207 -1868 19671 -198834 1196141 -14261624 194353344", "yuk": "1 2 -54 -2806 -37686 412502 27728082 458383830 -2570133302 -286975572352", "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","72","1","0","0","0","1","1"]},{"re":"7/324","im":"-1/81*2^(1/2)","approx_re":"0.0216049382716","approx_im":"-0.017459","exponents":["0","1","1","2"],"monodromy":[".872284041*I","-1/6+30*lambda","-1/12+15*lambda","-1/243*3^(1/2)*ln(2)^2/(-8*I*lambda*Pi^3)^(1/6)+5*lambda","6","2","1/2","1/12-15*lambda","-12","-2","0","-1/6+30*lambda","72","12","6","2.-.872284041*I"],"monodromy_dm":["1","-22","-1","-1","0","1","0","0","0","0","1","0","0","0","0","1"]},{"re":"7/324","im":"1/81*2^(1/2)","approx_re":"0.0216049382716","approx_im":"0.017459","exponents":["0","1","1","2"],"monodromy":["2.+.872284041*I","-1/6-30*lambda","1/12+15*lambda","-1/243*3^(1/2)*ln(2)^2/(-8*I*lambda*Pi^3)^(1/6)-5*lambda","6","0","1/2","-1/12-15*lambda","12","-2","2","-1/6-30*lambda","72","-12","6","-.872284041*I"],"monodromy_dm":["-3","-38","-1333333/1000000","-1","1333333/1000000","13666667/1000000","111111/250000","333333/1000000","-64","-608","-20333333/1000000","-16","50666667/1000000","481333333/1000000","16888889/1000000","13666667/1000000"]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/2","1","1","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -6*(2*X+1)^2*(9*X^2+9*X+5), 2916*(2*X+1)*(X+1)^2*(2*X+3)]", "text": "Hadamard product $I \\ast \\iota$", "degz": 2, "h3": null, "sol": "1 30 1782 129900 10463670 894351780 79506157500 7268449719960 678536243277750 64381774028157300", "n_discr_factors": "1", "c3": null, "operator": "4 2 0 0 0 0 1 -30 -174 -390 -432 -216 8748 40824 67068 46656 11664", "new_number": "2.58", "id": 53, "operator_tex": "\\theta^4-2 3 x(2\\theta+1)^2(9\\theta^2+9\\theta+5)+2^{2} 3^{6} x^{2}(2\\theta+1)(\\theta+1)^2(2\\theta+3)", "superseek": "-6 -104", "discriminant": "2 1 -216 11664", "aesz": "46", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "2226ec115674e71c483ba2c0350e8adf", "dim_h": null, "inst": " -6 -6 -104 36 -4812 37984 -444900 7911900 -81187538 1584490908", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "2", "laurent": null, "discriminant_tex": "(108z-1)^2", "discr_factors": "11664, (z-1/108)^2", "dm_basis": ["1/2-36*lambda", "-3", "5/6", "1", "0", "12", "-1", "0", "6", "-36", "0", "0", "36", "0", "0", "0"], "q": "0 1 -54 2079 -67356 1981287 -54730890 1447035885 -37047063960 925398152064", "yuk": "1 -6 -54 -2814 2250 -601506 8201682 -152600706 4050895050 -59185718016", "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","-36","1","0","0","0","1","1"]},{"re":"1/108","im":"0","approx_re":"0.00925925925926","approx_im":"0.0","exponents":["0","1/6","5/6","1"],"monodromy":["1/2+36*lambda","1/4+6*lambda","0",".19987912e-1","0","1","0","0","-6","3","1","1/4-6*lambda","-36","-6","0","1/2-36*lambda"],"monodromy_dm":["0","1","-666667/1000000","-1","-333333/1000000","-333333/1000000","111111/1000000","0","-4","-16","2333333/1000000","0","3333333/1000000","13333333/1000000","-1111111/1000000","1"]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/2","1","1","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[49*X^4, 1876*X^4+4004*X^3+3276*X^2+1274*X+196, -7672-32900*X-54004*X^2-41064*X^3-12732*X^4, 20704*X^4+67200*X^3+82048*X^2+45192*X+9520, -8352-34416*X-54768*X^2-40704*X^3-12288*X^4, 2304*(X+1)^4]", "text": "There is a second MUM-point corresponding to Operator AESZ 117 /5.515.", "degz": 5, "h3": null, "sol": "1 -4 64 -1408 37216 -1093504 34467616 -1141889536 39261600352 -1389328714624", "n_discr_factors": "3", "c3": null, "operator": "4 5 0 0 0 0 49 196 1274 3276 4004 1876 -7672 -32900 -54004 -41064 -12732 9520 45192 82048 67200 20704 -8352 -34416 -54768 -40704 -12288 2304 9216 13824 9216 2304", "new_number": "5.31", "id": 240, "operator_tex": "7^{2} \\theta^4+2 7 x\\left(134\\theta^4+286\\theta^3+234\\theta^2+91\\theta+14\\right)-2^{2} x^{2}\\left(3183\\theta^4+10266\\theta^3+13501\\theta^2+8225\\theta+1918\\right)+2^{3} x^{3}\\left(2588\\theta^4+8400\\theta^3+10256\\theta^2+5649\\theta+1190\\right)-2^{4} 3 x^{4}\\left(256\\theta^4+848\\theta^3+1141\\theta^2+717\\theta+174\\right)+2^{8} 3^{2} x^{5}\\left((\\theta+1)^4\\right)", "superseek": "-20/7 -104", "discriminant": "5 49 1876 -12732 20704 -12288 2304", "aesz": "212", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "f72aa947ba945355102b3fef56e0af0f", "dim_h": null, "inst": " -20/7 57/4 -104 16385/14 -110508/7 487971/2 -28874844/7 522536803/7 -9957702452/7 112972467743/4", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "(4z-1)(16z^2-44z-1)(6z-7)^2", "discr_factors": "2304, z^2-11/4*z-1/16, (z-7/6)^2, z-1/4", "dm_basis": null, "q": "0 1 10 1 -20 -2412 31482 -619038 12504648 -262953732", "yuk": "1 -20/7 778/7 -19676/7 75014 -1973360 368887198/7 -9904071512/7 267539368234/7 -7259165107184/7", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"11/8-5/8*5^(1/2)","im":"0","approx_re":"-0.022542","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":"1/4","im":"0","approx_re":"0.25","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"7/6","im":"0","approx_re":"1.16666666667","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"11/8+5/8*5^(1/2)","im":"0","approx_re":"2.772542","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","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -4*(3*X^2+3*X+1)*(7*X^2+7*X+2), 1440*X^4+2688*X^3+3744*X^2+2112*X+384, -21504*X^4+129024*X^3+395264*X^2+297984*X+77824, 606208*X^4+1212416*X^3+819200*X^2+212992*X+98304, 5505024*X^4+55050240*X^3+30932992*X^2-4980736*X-6291456, 94371840*X^4+201326592*X^3+283115520*X^2+201326592*X+50331648, 67108864*(3*X^2+3*X+1)*(7*X^2+7*X+2), 4294967296*(X+1)^4]", "text": "Hadamard product $a \\ast d$. This operator has a second MUM-point at infinity with the same instanton numbers.\nIt can be reduced to an operator of degree 4 with a single MUM-point defined over\n$Q(\\sqrt{-1})$.", "degz": 8, "h3": "48", "sol": "1 8 200 6272 233896 9692608 432683264 20387430400 1000461680296 50660529892928", "n_discr_factors": "5", "c3": "12", "operator": "4 8 0 0 0 0 1 -8 -52 -136 -168 -84 384 2112 3744 2688 1440 77824 297984 395264 129024 -21504 98304 212992 819200 1212416 606208 -6291456 -4980736 30932992 55050240 5505024 50331648 201326592 283115520 201326592 94371840 134217728 872415232 2281701376 2818572288 1409286144 4294967296 17179869184 25769803776 17179869184 4294967296", "new_number": "8.3", "id": 485, "operator_tex": "\\theta^4-2^{2} x(3\\theta^2+3\\theta+1)(7\\theta^2+7\\theta+2)+2^{5} 3 x^{2}\\left(15\\theta^4+28\\theta^3+39\\theta^2+22\\theta+4\\right)-2^{10} x^{3}\\left(21\\theta^4-126\\theta^3-386\\theta^2-291\\theta-76\\right)+2^{14} x^{4}\\left(37\\theta^4+74\\theta^3+50\\theta^2+13\\theta+6\\right)+2^{18} x^{5}\\left(21\\theta^4+210\\theta^3+118\\theta^2-19\\theta-24\\right)+2^{21} 3 x^{6}\\left(15\\theta^4+32\\theta^3+45\\theta^2+32\\theta+8\\right)+2^{26} x^{7}(3\\theta^2+3\\theta+1)(7\\theta^2+7\\theta+2)+2^{32} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "8 -104", "discriminant": "8 1 -84 1440 -21504 606208 5505024 94371840 1409286144 4294967296", "aesz": "105", "n_sing_complex": "2", "inst_int": "", "c2h": "72", "hash": "7b27135451cf2016217211c633b7ab83", "dim_h": "14", "inst": " 8 71/2 -104 4202 50112 1190589/2 19232792 750651197/2 8202541856 213407759180", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "7", "n_sing": "7", "laurent": null, "discriminant_tex": "(8z+1)(64z-1)(4z+1)(32z-1)(1+256z^2)^2", "discr_factors": "4294967296, z-1/32, (1/256+z^2)^2, z+1/8, z+1/4, z-1/64", "dm_basis": null, "q": "0 1 -20 150 912 -51715 530216 -531590 -169210560 1317153558", "yuk": "1 8 292 -2800 269220 6264008 128581096 6596847664 192166975652 5979653010224", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/4","im":"0","approx_re":"-0.25","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/8","im":"0","approx_re":"-0.125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"-1/16","approx_re":"0.0","approx_im":"-0.0625","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":"0","im":"1/16","approx_re":"0.0","approx_im":"0.0625","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/64","im":"0","approx_re":"0.015625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/32","im":"0","approx_re":"0.03125","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","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}]}