{"count": 5, "status":"OK", "data":[{"pols": "[X^4, -16*(2*X+1)^2*(3*X^2+3*X+1), 512*(2*X+1)^2*(2*X+3)^2]", "text": "A*d", "degz": 2, "h3": "32", "sol": "1 16 720 44800 3312400 273321216 24329200896 2287879925760 224190869245200 22677180755257600", "n_discr_factors": "2", "c3": "-88", "operator": "4 2 0 0 0 0 1 -16 -112 -304 -384 -192 4608 24576 45056 32768 8192", "new_number": "2.13", "id": 4, "operator_tex": "\\theta^4-2^{4} x(2\\theta+1)^2(3\\theta^2+3\\theta+1)+2^{9} x^{2}(2\\theta+1)^2(2\\theta+3)^2", "superseek": "16 1232", "discriminant": "2 1 -192 8192", "aesz": "36", "n_sing_complex": "0", "inst_int": "", "c2h": "80", "hash": "dea6fdf568a5907a24ba30fef2caf124", "dim_h": "12", "inst": " 16 42 1232 32159 990128 34017058 1281309072 51913355161 2217439126912 98646336990894", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "A_{n}=\\dbinom{2n}{n}^2\\sum_{k=0}^{n}\\dbinom{n}{k}\\dbinom{2k}{k}\\dbinom{2n-2k}{n-k}", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "(128z-1)(64z-1)", "discr_factors": "8192, z-1/128, z-1/64", "dm_basis": ["-88*lambda", "26/3", "1", "1", "-10/3", "-16", "-1", "0", "0", "32", "0", "0", "-32", "0", "0", "0"], "q": "0 1 -48 1536 -44032 1041840 -25188864 473850880 -12342362112 111270160536", "yuk": "1 16 352 33280 2058528 123766016 7347718144 439489011712 26579639900960 1616513123552128", "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","32","1","0","0","0","1","1"]},{"re":"1/128","im":"0","approx_re":"0.0078125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["1+88*lambda","0","55/6*lambda",".5683112e-2","10/3","1","25/72","-55/6*lambda","0","0","1","0","32","0","10/3","1-88*lambda"],"monodromy_dm":["1","-12","-1","-1","0","1","0","0","0","0","1","0","0","0","0","1"]},{"re":"1/64","im":"0","approx_re":"0.015625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["10/3+176*lambda","-7/12-44*lambda","35/144+55/3*lambda","-.73703221e-1-77/6*lambda","20/3+1/500000000*I","-2/3+1/1000000000*I","25/36","-35/144-55/3*lambda","16+1/200000000*I","-4+1/500000000*I","8/3-1/500000000*I","-7/12-44*lambda","64.+.23e-7*I","-15.999999981+.90000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-8*I","20/3-1/125000000*I","-4/3-176*lambda"],"monodromy_dm":["-3","-32","-5/2","-2","1","9","5/8","1/2","-16","-128","-9","-8","12","96","15/2","7"]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/2","1/2","3/2","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -8*(2*X+1)^2*(3*X^2+3*X+1), 64*(2*X+1)*(X+1)^2*(2*X+3)]", "text": "Hadamard product $I \\ast \\epsilon$", "degz": 2, "h3": "32", "sol": "1 8 240 10880 597520 36667008 2419194624 167973611520 12113815119120 899573909886080", "n_discr_factors": "1", "c3": "-116", "operator": "4 2 0 0 0 0 1 -8 -56 -152 -192 -96 192 896 1472 1024 256", "new_number": "2.55", "id": 50, "operator_tex": "\\theta^4-2^{3} x(2\\theta+1)^2(3\\theta^2+3\\theta+1)+2^{6} x^{2}(2\\theta+1)(\\theta+1)^2(2\\theta+3)", "superseek": "8 1000", "discriminant": "2 1 -96 256", "aesz": "42", "n_sing_complex": "0", "inst_int": "", "c2h": "80", "hash": "c389d3bc0e31801bc4b7b3e186702bc9", "dim_h": "12", "inst": " 8 63 1000 44369/2 606168 18905795 646661320 47344559559/2 912828771904 36676701619909", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "3", "laurent": null, "discriminant_tex": "1-96z+256z^2", "discr_factors": "256, 1/256-3/8*z+z^2", "dm_basis": ["-116*lambda", "26/3", "1", "1", "-10/3", "-16", "-1", "0", "0", "32", "0", "0", "-32", "0", "0", "0"], "q": "0 1 -24 176 -2304 -17424 -1069312 -38256896 -1586413568 -67468395624", "yuk": "1 8 512 27008 1420320 75771008 4083679232 221804832768 12120208667424 665452174745024", "gv2": null, "gv0": "256 2016 32000 709904 19397376 604985440 20693162240 757512952944 29210520700928 1173654451837088", "gv1": "0 0 0 -8 1024 1220032 162833408 14777331408 1130217240064 78694846302528 5172560302047744 327326282005566904 20176313721010452992 1220386030465757244288 72791206205861642839040 4295938778371289615045936 251467438716667548418697216 14625621507763032366352580224 846303166705337157906220084736", "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","32","1","0","0","0","1","1"]},{"re":"3/16-1/8*2^(1/2)","im":"0","approx_re":"0.010723","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["1+116*lambda","0","1/343*I*5^(7/9)*7^(1/3)/ln(2)^3",".9874994e-2","10/3","1","25/72","-1/343*I*5^(7/9)*7^(1/3)/ln(2)^3","0","0","1","0","32","0","10/3","1-116*lambda"],"monodromy_dm":["1","-12","-1","-1","0","1","0","0","0","0","1","0","0","0","0","1"]},{"re":"3/16+1/8*2^(1/2)","im":"0","approx_re":"0.364277","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["9.+5.059247438*I","-8/3-348*lambda",".83333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333+.527004941*I","-.133347276-58*lambda","30","-9","25/8","-.83333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333-.527004941*I","96","-32","11","-8/3-348*lambda","288+1/1000000000*I","-96","30","-7.-5.059247438*I"],"monodromy_dm":["-17","-156","-12","-9","6","53","4","3","-96","-832","-63","-48","60","520","40","31"]},{"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, 624*X^4-672*X^3-464*X^2-128*X-16, 2048*X*(37*X^3-137*X^2-10*X-1), -11862016*X^4-29884416*X^3-23134208*X^2-8650752*X-1245184, -1509949440*X^4-2516582400*X^3-1509949440*X^2-251658240*X+41943040, 26843545600*(X+1)^4]", "text": "This is operator \"5.11\" from ...", "degz": 5, "h3": "32", "sol": "1 16 656 40192 3006736 252252416 22788843776 2168291250176 214374731955472 21830665093755136", "n_discr_factors": "4", "c3": "304", "operator": "4 5 0 0 0 0 1 -16 -128 -464 -672 624 0 -2048 -20480 -280576 75776 -1245184 -8650752 -23134208 -29884416 -11862016 41943040 -251658240 -1509949440 -2516582400 -1509949440 26843545600 107374182400 161061273600 107374182400 26843545600", "new_number": "5.11", "id": 203, "operator_tex": "\\theta^4+2^{4} x\\left(39\\theta^4-42\\theta^3-29\\theta^2-8\\theta-1\\right)+2^{11} x^{2}\\theta(37\\theta^3-137\\theta^2-10\\theta-1)-2^{16} x^{3}\\left(181\\theta^4+456\\theta^3+353\\theta^2+132\\theta+19\\right)-2^{23} 5 x^{4}\\left(36\\theta^4+60\\theta^3+36\\theta^2+6\\theta-1\\right)+2^{30} 5^{2} x^{5}\\left((\\theta+1)^4\\right)", "superseek": "112 378800", "discriminant": "5 1 624 75776 -11862016 -1509949440 26843545600", "aesz": "71", "n_sing_complex": "0", "inst_int": "", "c2h": "32", "hash": "cf4de65b0566a4f6294132c167d227eb", "dim_h": "8", "inst": " 112 -4570 378800 -40565898 5098744272 -707870516690 105432934036208 -16535931080941762 2698540270299157632 -454448691741869508414", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "5", "n_sing": "5", "laurent": null, "discriminant_tex": "(16z-1)(128z-1)(128z+1)(1+320z)^2", "discr_factors": "26843545600, z+1/128, z-1/16, z-1/128, (1/320+z)^2", "dm_basis": null, "q": "0 1 -64 5152 -592896 81453872 -12454109184 2036443729408 -348923423752192 61860266815790744", "yuk": "1 112 -36448 10227712 -2596253920 637343034112 -152900021413888 36163496374419456 -8466396716038436064 1967235857048096141440", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/128","im":"0","approx_re":"-0.0078125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/320","im":"0","approx_re":"-0.003125","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":"1/128","im":"0","approx_re":"0.0078125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/16","im":"0","approx_re":"0.0625","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, -1408*X^4-512*X^3-528*X^2-272*X-48, 770048*X^4+720896*X^3+735232*X^2+305152*X+47616, -203423744*X^4-352321536*X^3-362020864*X^2-170655744*X-30670848, 25165824*(2*X+1)*(512*X^3+1152*X^2+1054*X+339), -19327352832*(2*X+1)*(4*X+3)*(4*X+5)*(2*X+3)]", "text": "This is operator \"5.13\" from ...", "degz": 5, "h3": "32", "sol": "1 48 5328 779520 131619600 24257173248 4739368322304 965015828434944 202584554505899280 43534711014765484800", "n_discr_factors": "3", "c3": "360", "operator": "4 5 0 0 0 0 1 -48 -272 -528 -512 -1408 47616 305152 735232 720896 770048 -30670848 -170655744 -362020864 -352321536 -203423744 8531214336 43587207168 82040586240 70866960384 25769803776 -869730877440 -4174708211712 -7035156430848 -4947802324992 -1236950581248", "new_number": "5.13", "id": 220, "operator_tex": "\\theta^4-2^{4} x\\left(88\\theta^4+32\\theta^3+33\\theta^2+17\\theta+3\\right)+2^{9} x^{2}\\left(1504\\theta^4+1408\\theta^3+1436\\theta^2+596\\theta+93\\right)-2^{18} x^{3}\\left(776\\theta^4+1344\\theta^3+1381\\theta^2+651\\theta+117\\right)+2^{23} 3 x^{4}(2\\theta+1)(512\\theta^3+1152\\theta^2+1054\\theta+339)-2^{31} 3^{2} x^{5}(2\\theta+1)(4\\theta+3)(4\\theta+5)(2\\theta+3)", "superseek": "-80 -174096", "discriminant": "5 1 -1408 770048 -203423744 25769803776 -1236950581248", "aesz": "83", "n_sing_complex": "0", "inst_int": "", "c2h": "-16", "hash": "171e1251d8e4f7de878d0d07de6f58ab", "dim_h": "4", "inst": " -80 -2954 -174096 -13270953 -1179175536 -115795446786 -12188186517456 -1349830285576015 -155427513115593600 -18456445525841201614", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "-(128z-1)(384z-1)^2(256z-1)^2", "discr_factors": "-1236950581248, (z-1/384)^2, z-1/128, (z-1/256)^2", "dm_basis": null, "q": "0 1 -80 3840 -181248 5466544 -307951104 46314496 -945821483008 -60856937695080", "yuk": "1 -80 -23712 -4700672 -849364704 -147396942080 -25011821230080 -4180547975487488 -691113107064284384 -113306657061272435072", "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":"1/384","im":"0","approx_re":"0.00260416666667","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/256","im":"0","approx_re":"0.00390625","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"1/128","im":"0","approx_re":"0.0078125","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","3/4","5/4","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -16-112*X-320*X^2-416*X^3-208*X^4, 5120+29184*X+63744*X^2+49152*X^3+2304*X^4, -245760-1302528*X-2330624*X^2+1007616*X^3+1552384*X^4, 31064064+122028032*X+112852992*X^2-167772160*X^3-49086464*X^4, -368050176-1976565760*X-3571449856*X^2+136314880*X^3-3421503488*X^4, 9160359936+20937965568*X+3707764736*X^2+20937965568*X^3+102726893568*X^4, 181462368256+1179505393664*X+3039494668288*X^2+3719978549248*X^3+1859989274624*X^4, -5806795784192*(X+1)^4]", "text": "This operator has a second MUM-point, corresponding to operator 8.18", "degz": 8, "h3": "32", "sol": "1 16 752 49408 3805456 322370816 29129674496 2759377375232 271039591709968 27401384461854976", "n_discr_factors": "4", "c3": "80", "operator": "4 8 0 0 0 0 1 -16 -112 -320 -416 -208 5120 29184 63744 49152 2304 -245760 -1302528 -2330624 1007616 1552384 31064064 122028032 112852992 -167772160 -49086464 -368050176 -1976565760 -3571449856 136314880 -3421503488 9160359936 20937965568 3707764736 20937965568 102726893568 181462368256 1179505393664 3039494668288 3719978549248 1859989274624 -5806795784192 -23227183136768 -34840774705152 -23227183136768 -5806795784192", "new_number": "8.19", "id": 462, "operator_tex": "\\theta^4-2^{4} x\\left(13\\theta^4+26\\theta^3+20\\theta^2+7\\theta+1\\right)+2^{8} x^{2}\\left(9\\theta^4+192\\theta^3+249\\theta^2+114\\theta+20\\right)+2^{12} x^{3}\\left(379\\theta^4+246\\theta^3-569\\theta^2-318\\theta-60\\right)-2^{16} x^{4}\\left(749\\theta^4+2560\\theta^3-1722\\theta^2-1862\\theta-474\\right)-2^{20} 13 x^{5}\\left(251\\theta^4-10\\theta^3+262\\theta^2+145\\theta+27\\right)+2^{24} 13 x^{6}\\left(471\\theta^4+96\\theta^3+17\\theta^2+96\\theta+42\\right)+2^{28} 13^{2} x^{7}\\left(41\\theta^4+82\\theta^3+67\\theta^2+26\\theta+4\\right)-2^{35} 13^{2} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "32 7584", "discriminant": "8 1 -208 2304 1552384 -49086464 -3421503488 102726893568 1859989274624 -5806795784192", "aesz": "201", "n_sing_complex": "0", "inst_int": "", "c2h": "56", "hash": "d21570c07bca6887061716b2d727fa75", "dim_h": "10", "inst": " 32 -152 7584 -160593 7055200 -213557688 10843665184 -373079787214 20257075760896 -766662378340104", "cleanlist": "True", "n_sing_real": "7", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "7", "laurent": null, "discriminant_tex": "-(128z-1)(16z+1)(256z^2-96z+1)(-1+3328z^2)^2", "discr_factors": "-5806795784192, z-1/128, z^2-3/8*z+1/256, z+1/16, (-1/3328+z^2)^2", "dm_basis": null, "q": "0 1 -48 1504 -48128 1753392 -73966080 3182293504 -149641527296 7014952908440", "yuk": "1 32 -1184 204800 -10279136 881900032 -46128257024 3719377158144 -191016861332704 14767408229897984", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/16","im":"0","approx_re":"-0.0625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/208*13^(1/2)","im":"0","approx_re":"-0.017334","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":"1/128","im":"0","approx_re":"0.0078125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"3/16-1/8*2^(1/2)","im":"0","approx_re":"0.010723","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/208*13^(1/2)","im":"0","approx_re":"0.017334","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"3/16+1/8*2^(1/2)","im":"0","approx_re":"0.364277","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":[]}]}]}