{"count": 3, "status":"OK", "data":[{"pols": "[X^4, -3*(3*X+1)*(3*X+2)*(17*X^2+17*X+6), 648*(3*X+1)*(3*X+2)*(3*X+4)*(3*X+5)]", "text": "Hadamard product $B\\ast g$.", "degz": 2, "h3": "36", "sol": "1 36 3780 524160 82952100 14193715536 2558150090496 478581063966720 92098312591711140 18122109528268746000", "n_discr_factors": "2", "c3": "-156", "operator": "4 2 0 0 0 0 1 -36 -264 -723 -918 -459 25920 151632 285768 209952 52488", "new_number": "2.25", "id": 17, "operator_tex": "\\theta^4-3 x(3\\theta+1)(3\\theta+2)(17\\theta^2+17\\theta+6)+2^{3} 3^{4} x^{2}(3\\theta+1)(3\\theta+2)(3\\theta+4)(3\\theta+5)", "superseek": "27 2618", "discriminant": "2 1 -459 52488", "aesz": "138", "n_sing_complex": "0", "inst_int": "", "c2h": "108", "hash": "c524254b716132352b27914640b03c8b", "dim_h": "15", "inst": " 27 189/4 2618 43713 2319057 196286095/2 5214508191 272574896067 14990046252383 3356489455171983/4", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "A_{n}=\\dbinom{2n}{n}\\dbinom{3n}{n}\\sum_{j,k}^{n}(-1)^{j}8^{n-j}\\dbinom{n}{j}\\dbinom{j}{k}^3", "n_sing_rational": "3", "n_sing": "3", "laurent": "None", "discriminant_tex": "(243z-1)(216z-1)", "discr_factors": "52488, z-1/243, z-1/216", "dm_basis": ["-377989751/500000000*I", "21/2", "1", "1", "-9/2", "-18", "-1", "0", "0", "36", "0", "0", "-36", "0", "0", "0"], "q": "0 1 -120 10782 -841288 60234693 -4078954368 264886454966 -16689963727536 1025543560906530", "yuk": "1 27 405 70713 2798037 289882152 21198969351 1788576309540 139558349584341 10927743718057920", "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":"1/243","im":"0","approx_re":"0.00411522633745","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["1.+.755979502*I","0","39/2*lambda",".15875139e-1","9/2","1","9/16","-39/2*lambda","0","0","1","0","36","0","9/2","1.-.755979502*I"],"monodromy_dm":["1","-15","-1","-1","0","1","0","0","0","0","1","0","0","0","0","1"]},{"re":"1/216","im":"0","approx_re":"0.00462962962963","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[".84386396e-1+.881341465*I","-.593907697+1.816219110*I",".987405021+.251865740*I","-.18197034e-1-.280246794*I","-.610146073+4.105015738*I","3.086102688+5.881005017*I","1/ln(2)^(8/3)/ln(3)^(8/5)*Zeta(5)^8-1.317777791*I","-.605925748-.688412508*I","-1.084750363+4.722447485*I","1.891556916+7.035664131*I","4.676916900-1.255046419*I","-.642466556-.856579334*I","-4.881168587+32.840125900*I","16.688821505+47.048040140*I","24.445126799-10.542222328*I","-3.847405984-5.507300063*I"],"monodromy_dm":["-2450927/1000000+271203/1000000*I","-7338521/500000+382623/15625*I","299583/500000+49333/125000*I","33897/250000-456113/500000*I","505191/1000000-1/10000*I","3414753/1000000-1697749/500000*I","-3307/40000-1004/15625*I","-7533/250000+131179/1000000*I","-1136679/125000+28/15625*I","-43465553/1000000+61118963/1000000*I","1244077/500000+18072/15625*I","4339/8000-295153/125000*I","378893/50000-1493/1000000*I","18110647/500000-5093247/100000*I","-19377/15625-3012/3125*I","548021/1000000+983843/500000*I"]},{"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": "[25*X^4, -765*X^4-1260*X^3-1080*X^2-450*X-75, 3186*X^4+4968*X^3+3246*X^2+930*X+90, -22842*X^4-116640*X^3-237546*X^2-204930*X-63180, 67797*X^4+332424*X^3+551610*X^2+385398*X+97686, -59049*(X+1)^4]", "text": "There is a second MUM-point at infinity, \ncorresponding to Operator AESZ 290/5.71\nA-Incarnation: diagonal subfamily 1,1,1-section in $P^2 \\times P^2 \\times P^2$\n", "degz": 5, "h3": "90", "sol": "1 3 27 381 6219 111753 2151549 43497891 912018123 19671397617", "n_discr_factors": "3", "c3": "-90", "operator": "4 5 0 0 0 0 25 -75 -450 -1080 -1260 -765 90 930 3246 4968 3186 -63180 -204930 -237546 -116640 -22842 97686 385398 551610 332424 67797 -59049 -236196 -354294 -236196 -59049", "new_number": "5.1", "id": 227, "operator_tex": "5^{2} \\theta^4-3 5 x\\left(51\\theta^4+84\\theta^3+72\\theta^2+30\\theta+5\\right)+2 3 x^{2}\\left(531\\theta^4+828\\theta^3+541\\theta^2+155\\theta+15\\right)-2 3^{3} x^{3}\\left(423\\theta^4+2160\\theta^3+4399\\theta^2+3795\\theta+1170\\right)+3^{5} x^{4}\\left(279\\theta^4+1368\\theta^3+2270\\theta^2+1586\\theta+402\\right)-3^{10} x^{5}\\left((\\theta+1)^4\\right)", "superseek": "6/5 118/5", "discriminant": "5 25 -765 3186 -22842 67797 -59049", "aesz": "17", "n_sing_complex": "2", "inst_int": "", "c2h": "108", "hash": "370d10edbf5900002f79cf6163e106a5", "dim_h": "24", "inst": " 6/5 39/10 118/5 1443/10 6108/5 117827/10 609006/5 13554147/10 15889556 968968881/5", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "-(27z-1)(27z^2+1)(-5+9z)^2", "discr_factors": "-59049, z^2+1/27, (-5/9+z)^2, z-1/27", "dm_basis": null, "q": "0 1 -6 3 -74 105 -3744 -35310 -429666 -5527026", "yuk": "1 6/5 162/5 3192/5 46338/5 763506/5 12728664/5 208889064/5 693981594 57917434812/5", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"0","im":"-1/9*3^(1/2)","approx_re":"0.0","approx_im":"-0.19245","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":"0","im":"1/9*3^(1/2)","approx_re":"0.0","approx_im":"0.19245","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":"5/9","im":"0","approx_re":"0.555555555556","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[49*X^4, -98-588*X-1407*X^2-1638*X^3-273*X^4, -15512-68656*X-114922*X^2-86444*X^3-24146*X^4, 128128+323904*X+133572*X^2-193704*X^3-115692*X^4, 428896+1641536*X+2163720*X^2+1018160*X^3+37336*X^4, 16224*(X+1)^2*(6*X+5)*(6*X+7)]", "text": "This is operator \"5.81\" from ...", "degz": 5, "h3": "84", "sol": "1 2 30 308 5950 96252 1973244 38397480 823170366 17515057340", "n_discr_factors": "4", "c3": "-108", "operator": "4 5 0 0 0 0 49 -98 -588 -1407 -1638 -273 -15512 -68656 -114922 -86444 -24146 128128 323904 133572 -193704 -115692 428896 1641536 2163720 1018160 37336 567840 2303808 3488160 2336256 584064", "new_number": "5.81", "id": 295, "operator_tex": "7^{2} \\theta^4-7 x\\left(39\\theta^4+234\\theta^3+201\\theta^2+84\\theta+14\\right)-2 x^{2}\\left(12073\\theta^4+43222\\theta^3+57461\\theta^2+34328\\theta+7756\\right)-2^{2} x^{3}\\left(28923\\theta^4+48426\\theta^3-33393\\theta^2-80976\\theta-32032\\right)+2^{3} 13 x^{4}\\left(359\\theta^4+9790\\theta^3+20805\\theta^2+15784\\theta+4124\\right)+2^{5} 3 13^{2} x^{5}(\\theta+1)^2(6\\theta+5)(6\\theta+7)", "superseek": "5/7 48/7", "discriminant": "5 49 -273 -24146 -115692 37336 584064", "aesz": "312", "n_sing_complex": "0", "inst_int": "", "c2h": "108", "hash": "767262575f8b1458839c1e9a8beacf0a", "dim_h": "23", "inst": " 5/7 239/28 48/7 4451/14 5888/7 177307/7 124308 21455179/7 21345700 3274689851/7", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "5", "n_sing": "5", "laurent": null, "discriminant_tex": "(16z+1)(2z-1)(27z-1)(7+26z)^2", "discr_factors": "584064, z-1/2, z-1/27, (7/26+z)^2, z+1/16", "dm_basis": null, "q": "0 1 -4 -40 248 -1488 -864 -90452 -266448 -17360416", "yuk": "1 5/7 69 1301/7 142915/7 736005/7 38300091/7 298463513/7 1569313509 108927108401/7", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-7/26","im":"0","approx_re":"-0.269230769231","approx_im":"0.0","exponents":["0","1","3","4"],"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":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"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":"1/2","im":"0","approx_re":"0.5","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":["5/6","1","1","7/6"],"monodromy":[],"monodromy_dm":[]}]}]}