{"count": 2, "status":"OK", "data":[{"pols": "[X^4, -9*(3*X+1)*(3*X+2)*(18*X^2+18*X+7), 6561*(3*X+1)*(3*X+2)*(3*X+4)*(3*X+5)]", "text": "Hadamard product $A \\ast$", "degz": 2, "h3": null, "sol": "1 126 44550 20447280 10600093350 5898285669276 3437708031693936 2070249438202545600 1277465155274881042470 803250121997487963298500", "n_discr_factors": "1", "c3": null, "operator": "4 2 0 0 0 0 1 -126 -891 -2349 -2916 -1458 262440 1535274 2893401 2125764 531441", "new_number": "2.29", "id": 21, "operator_tex": "\\theta^4-3^{2} x(3\\theta+1)(3\\theta+2)(18\\theta^2+18\\theta+7)+3^{8} x^{2}(3\\theta+1)(3\\theta+2)(3\\theta+4)(3\\theta+5)", "superseek": "45 27735", "discriminant": "2 1 -1458 531441", "aesz": "142", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "85c2c2d8111a859d4cc03e8892c56af9", "dim_h": null, "inst": " 45 -3465/4 27735 -1156005 55721970 -11805992355/4 167012393760 -9923605211925 612225582446895 -77826861839635245/2", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "2", "laurent": null, "discriminant_tex": "(729z-1)^2", "discr_factors": "531441, (z-1/729)^2", "dm_basis": ["21/16-90*lambda", "3/8", "1/2", "1", "3/8", "0", "-1", "0", "9/2", "-9", "0", "0", "9", "0", "0", "0"], "q": "0 1 -387 112428 -28226469 6500333565 -1412664854688 294446127670425 -59463198577641411 11714577880155593931", "yuk": "1 45 -6885 748890 -73991205 6965246295 -637522845210 57285251059725 -5080885942496805 446312449604535345", "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","-9","1","0","0","0","1","1"]},{"re":"1/729","im":"0","approx_re":"0.00137174211248","approx_im":"0.0","exponents":["0","1/3","2/3","1"],"monodromy":["-5/16+90*lambda","7/32+45*lambda","-7/128+15/4*lambda",".42666543e-1","-3/8","13/16","-1/64","-7/128-15/4*lambda","-9/2","3/4","13/16","7/32-45*lambda","-9","-9/2","-3/8","-5/16-90*lambda"],"monodromy_dm":["-2","0","0","-1","-1","1","333333/1000000","0","0","0","1","0","3","0","-1","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, -(X+1)*(285*X^3+321*X^2+128*X+18), -3280*X^4-2644*X^3+2674*X^2+2356*X+480, -7668*X^4+9216*X^3+10296*X^2+2880*X+180, 216*(2*X+1)*(22*X^3+37*X^2+24*X+6), 432*(2*X+1)*(X+1)^2*(2*X+3)]", "text": "This is operator \"5.82\" from ...", "degz": 5, "h3": "14", "sol": "1 18 1662 236340 40943070 7945789068 1660174030284 365333722192296 83543805631567710 19678956052342595580", "n_discr_factors": "3", "c3": "-96", "operator": "4 5 0 0 0 0 1 -18 -146 -449 -606 -285 480 2356 2674 -2644 -3280 180 2880 10296 9216 -7668 1296 7776 18360 20736 9504 1296 6048 9936 6912 1728", "new_number": "5.82", "id": 296, "operator_tex": "\\theta^4-x(\\theta+1)(285\\theta^3+321\\theta^2+128\\theta+18)-2 x^{2}\\left(1640\\theta^4+1322\\theta^3-1337\\theta^2-1178\\theta-240\\right)-2^{2} 3^{2} x^{3}\\left(213\\theta^4-256\\theta^3-286\\theta^2-80\\theta-5\\right)+2^{3} 3^{3} x^{4}(2\\theta+1)(22\\theta^3+37\\theta^2+24\\theta+6)+2^{4} 3^{3} x^{5}(2\\theta+1)(\\theta+1)^2(2\\theta+3)", "superseek": "45 43531", "discriminant": "5 1 -285 -3280 -7668 9504 1728", "aesz": "313", "n_sing_complex": "0", "inst_int": "", "c2h": "56", "hash": "f8bfe82988e14680bdb775a3ce956216", "dim_h": "7", "inst": " 45 845 43531 3091112 273471538 27632280740 3065139414900 364034045136592 45554291158936325 5940634529870887198", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "(z-1)(48z^2+296z-1)(6z+1)^2", "discr_factors": "1728, (z+1/6)^2, z^2+37/6*z-1/48, z-1", "dm_basis": null, "q": "0 1 -74 1559 -67652 -2528789 -386350534 -46810486807 -6250760414504 -864098531880686", "yuk": "1 45 6805 1175382 197837973 34183942295 5968573821982 1051342819310745 186385431307773077 33209078254865756307", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-37/12-7/6*7^(1/2)","im":"0","approx_re":"-6.170043","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/6","im":"0","approx_re":"-0.166666666667","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":"-37/12+7/6*7^(1/2)","im":"0","approx_re":"0.003377","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":[]}]}]}