{"count": 2, "status":"OK", "data":[{"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, -741*X^2-84-702*X^3-189*X^4-390*X, 84564*X^3+57672+195534*X^2+1458*X^4+171396*X, -6088608-6386040*X^2+1180980*X^4-12203460*X+2361960*X^3, -385944264*X-648121824*X^2-29760696*X^4-365631408*X^3-41570496, 16045266672*X-1836660096*X^3+8290479600*X^2-1836660096*X^4+7856823744, 1377495072*(3*X+5)*(3*X+4)*(2*X+3)^2]", "text": "This is operator \"6.35\" from ...", "degz": 6, "h3": null, "sol": "1 84 7452 692688 66448116 6513064848 648237493296 65250781987968 6624881063467092 677185739050601424", "n_discr_factors": "4", "c3": null, "operator": "4 6 0 0 0 0 1 -84 -390 -741 -702 -189 57672 171396 195534 84564 1458 -6088608 -12203460 -6386040 2361960 1180980 -41570496 -385944264 -648121824 -365631408 -29760696 7856823744 16045266672 8290479600 -1836660096 -1836660096 247949112960 665330119776 668085109920 297538935552 49589822592", "new_number": "6.35", "id": 420, "operator_tex": "\\theta^4-3 x\\left(63\\theta^4+234\\theta^3+247\\theta^2+130\\theta+28\\right)+2 3^{4} x^{2}\\left(9\\theta^4+522\\theta^3+1207\\theta^2+1058\\theta+356\\right)+2^{2} 3^{7} x^{3}\\left(135\\theta^4+270\\theta^3-730\\theta^2-1395\\theta-696\\right)-2^{3} 3^{10} x^{4}\\left(63\\theta^4+774\\theta^3+1372\\theta^2+817\\theta+88\\right)-2^{4} 3^{13} x^{5}\\left(72\\theta^4+72\\theta^3-325\\theta^2-629\\theta-308\\right)+2^{5} 3^{16} x^{6}(3\\theta+5)(3\\theta+4)(2\\theta+3)^2", "superseek": null, "discriminant": "6 1 -189 1458 1180980 -29760696 -1836660096 49589822592", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "de26083962cade55a4938b4011d0008e", "dim_h": null, "inst": " 21 -1617/4 7941 -986355/4 8179455 -1227169941/4 12151571244 -1015240586355/2 21975670374150 -3923026912252995/4", "cleanlist": "False", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "5", "n_sing": "5", "laurent": null, "discriminant_tex": "(54z-1)(27z-1)(54z+1)^2(108z-1)^2", "discr_factors": "49589822592, (z+1/54)^2, z-1/54, (z-1/108)^2, z-1/27", "dm_basis": null, "q": "0 1 -54 2565 -125676 6195150 -310093758 15690242988 -802117062504 41365068279705", "yuk": "1 21 -3213 214428 -15784893 1022431896 -66266965620 4167988936713 -259901605891773 16020263702969778", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/54","im":"0","approx_re":"-0.0185185185185","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":"1/108","im":"0","approx_re":"0.00925925925926","approx_im":"0.0","exponents":["0","-1/2","1","3/2"],"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":"1/27","im":"0","approx_re":"0.037037037037","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":["4/3","3/2","3/2","5/3"],"monodromy":[],"monodromy_dm":[]}]}]}