{"count": 2, "status":"OK", "data":[{"pols": "[X^4, -48*(6*X+1)*(6*X+5)*(3*X^2+3*X+1), 4608*(6*X+1)*(6*X+5)*(6*X+7)*(6*X+11)]", "text": "Hadamard product D*d", "degz": 2, "h3": "8", "sol": "1 240 277200 457416960 904864680720 2004880295658240 4800744250465363200 12157214644290912768000 32101389251425947781270800 87536732232366403520671737600", "n_discr_factors": "2", "c3": "-470", "operator": "4 2 0 0 0 0 1 -240 -2448 -7632 -10368 -5184 1774080 15261696 31518720 23887872 5971968", "new_number": "2.16", "id": 7, "operator_tex": "\\theta^4-2^{4} 3 x(6\\theta+1)(6\\theta+5)(3\\theta^2+3\\theta+1)+2^{9} 3^{2} x^{2}(6\\theta+1)(6\\theta+5)(6\\theta+7)(6\\theta+11)", "superseek": "240 19105840", "discriminant": "2 1 -5184 5971968", "aesz": "65", "n_sing_complex": "0", "inst_int": "", "c2h": "92", "hash": "13ba368bcbb10731ac8727b510731ff2", "dim_h": "9", "inst": " 240 57102 19105840 14810143935 10017820614480 9034594808517046 8180523747618348912 8386469469367204264761 8771159613625367710446208 9733175830090381917603283770", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "A_{n}=\\dbinom{3n}{n}\\dbinom{6n}{3n}\\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": "(3456z-1)(1728z-1)", "discr_factors": "5971968, z-1/3456, z-1/1728", "dm_basis": ["-284703819/125000000*I", "31/6", "1", "1", "-23/6", "-4", "-1", "0", "0", "8", "0", "0", "-8", "0", "0", "0"], "q": "0 1 -1488 1737216 -1936036864 2030351668656 -2106830943512064 2118312344000340992 -2135004674764250185728 2095472552315219510339736", "yuk": "1 240 457056 515857920 947849668896 1252227576810240 1951472479155996672 2805919645433093677056 4293872368316956433226528 6394175358332893061431143552", "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","8","1","0","0","0","1","1"]},{"re":"1/3456","im":"0","approx_re":"0.000289351851852","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["1.+2.277630552*I","0","1.091364639*I",".648450116","23/6","1","529/288","-1.091364639*I","0","0","1","0","8","0","23/6","1.-2.277630552*I"],"monodromy_dm":["1","-9","-1","-1","0","1","0","0","0","0","1","0","0","0","0","1"]},{"re":"1/1728","im":"0","approx_re":"0.000578703703704","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["37/12+940*lambda","-.52083333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333-1.138815272*I",".99826388888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888889+2.182729279*I","1.025632871-1.186265914*I","23/3+1/250000000*I","-11/12+3/1000000000*I","529/144-1/250000000*I","-.99826388888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888889-2.182729279*I","4+1/500000000*I","-1+1/1000000000*I","35/12-1/500000000*I","-25/48-235*lambda","16+9/1000000000*I","-3.999999988+.50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-8*I","23/3-1/125000000*I","-13/12-940*lambda"],"monodromy_dm":["-3","-20","-5/2","-2","1","6","5/8","1/2","-4","-20","-3/2","-2","3","15","15/8","5/2"]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/6","5/6","7/6","11/6"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[49*X^4, -3598*X^4-7280*X^3-6090*X^2-2450*X-392, 53988*X^4+222144*X^3+324888*X^2+201348*X+45584, -137608*X^4-919968*X^3-1987728*X^2-1621032*X-443296, -92192*X^4-474688*X^3-770400*X^2-507856*X-118592, -96*(4*X+5)*(3*X+2)*(3*X+4)*(4*X+3)]", "text": "This is operator \"5.10\" from ...", "degz": 5, "h3": "56", "sol": "1 8 144 3680 114400 4007808 151802784 6070154112 252560008800 10831854176000", "n_discr_factors": "4", "c3": "-78", "operator": "4 5 0 0 0 0 49 -392 -2450 -6090 -7280 -3598 45584 201348 324888 222144 53988 -443296 -1621032 -1987728 -919968 -137608 -118592 -507856 -770400 -474688 -92192 -11520 -50496 -80544 -55296 -13824", "new_number": "5.10", "id": 192, "operator_tex": "7^{2} \\theta^4-2 7 x\\left(257\\theta^4+520\\theta^3+435\\theta^2+175\\theta+28\\right)+2^{2} x^{2}\\left(13497\\theta^4+55536\\theta^3+81222\\theta^2+50337\\theta+11396\\right)-2^{3} x^{3}\\left(17201\\theta^4+114996\\theta^3+248466\\theta^2+202629\\theta+55412\\right)-2^{4} x^{4}\\left(5762\\theta^4+29668\\theta^3+48150\\theta^2+31741\\theta+7412\\right)-2^{5} 3 x^{5}(4\\theta+5)(3\\theta+2)(3\\theta+4)(4\\theta+3)", "superseek": "30/7 124", "discriminant": "5 49 -3598 53988 -137608 -92192 -13824", "aesz": "59", "n_sing_complex": "0", "inst_int": "", "c2h": "92", "hash": "f47563daeb0f7328bd675f13cfb84a55", "dim_h": "17", "inst": " 30/7 129/14 124 72129/56 130434/7 2064581/7 36176970/7 1355749161/14 13366726990/7 549282494475/14", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "5", "n_sing": "5", "laurent": null, "discriminant_tex": "-(4z-1)(16z-1)(54z-1)(7+2z)^2", "discr_factors": "-13824, z-1/54, z-1/4, (7/2+z)^2, z-1/16", "dm_basis": null, "q": "0 1 -18 201 -2364 21756 -253410 1628554 -30934248 -60999180", "yuk": "1 30/7 78 23466/7 577578/7 16304280/7 445973478/7 12408700740/7 347072362794/7 9744343999176/7", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-7/2","im":"0","approx_re":"-3.5","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":"1/54","im":"0","approx_re":"0.0185185185185","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":"1/4","im":"0","approx_re":"0.25","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":["2/3","3/4","5/4","4/3"],"monodromy":[],"monodromy_dm":[]}]}]}