{"count": 4, "status":"OK", "data":[{"pols": "[X^4, -12*(6*X+1)*(6*X+5)*(17*X^2+17*X+6), 10368*(6*X+1)*(6*X+5)*(6*X+7)*(6*X+11)]", "text": "Hadamard product $D \\ast g$", "degz": 2, "h3": "12", "sol": "1 360 582120 1274232960 3204505984680 8736880767975360 25125062975063251200 75058282703368409702400 230765336778536073410668200 725681808237345335937810849600", "n_discr_factors": "2", "c3": "-676", "operator": "4 2 0 0 0 0 1 -360 -3612 -10956 -14688 -7344 3991680 34338816 70917120 53747712 13436928", "new_number": "2.27", "id": 19, "operator_tex": "\\theta^4-2^{2} 3 x(6\\theta+1)(6\\theta+5)(17\\theta^2+17\\theta+6)+2^{7} 3^{4} x^{2}(6\\theta+1)(6\\theta+5)(6\\theta+7)(6\\theta+11)", "superseek": "108 -4945756", "discriminant": "2 1 -7344 13436928", "aesz": "140", "n_sing_complex": "0", "inst_int": "", "c2h": "132", "hash": "74692097f8183c067c2c4b1a5c93387b", "dim_h": "13", "inst": " 108 54135 -4945756 7925523138 -2434666062240 3610413024179357 -1753141171437991260 2473338137905558015002 -1633555754281511059059568 2138880900876687840583380600", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "(3888z-1)(3456z-1)", "discr_factors": "13436928, z-1/3888, z-1/3456", "dm_basis": ["-409488897/125000000*I", "15/2", "1", "1", "-11/2", "-6", "-1", "0", "0", "12", "0", "0", "-12", "0", "0", "0"], "q": "0 1 -2172 3924702 -6580766128 10592280086829 -16628695641496008 25659158141952015890 -39107720971061645226432 59046921778459766741974278", "yuk": "1 108 433188 -133535304 507233914020 -304333257779892 779849213089638888 -601327421803231002072 1266349126608152937595044 -1190862144871221562187960376", "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","12","1","0","0","0","1","1"]},{"re":"1/3888","im":"0","approx_re":"0.000257201646091","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["1.+3.275911176*I","0","1.501459289*I",".894299503","11/2","1","121/48","-1.501459289*I","0","0","1","0","12","0","11/2","1.-3.275911176*I"],"monodromy_dm":["1","-13","-1","-1","0","1","0","0","0","0","1","0","0","0","0","1"]},{"re":"1/3456","im":"0","approx_re":"0.000289351851852","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["-5.088262696-2.403669772*I","-9.231233148+8.267057761*I","6.171205313+7.544982974*I","3.227450678-3.068539845*I","-6.270037138+8.225054977*I","9.605336680+17.587574161*I","14.123297626-6.142790642*I","-3.279565479-6.225556868*I","-2.195545276+2.457029703*I","2.297135143+5.799775915*I","5.638341607-1.600871223*I","-.887292619-2.058764958*I","-13.680081028+17.945574495*I","18.775280028+38.372889078*I","30.814467548-13.402452309*I","-6.155415591-13.583033166*I"],"monodromy_dm":["-38267/15625+13499/50000*I","-12876777/1000000+21372913/1000000*I","2704613/1000000+425569/250000*I","1140007/1000000-299093/200000*I","50519/100000-49/500000*I","1558779/500000-741279/250000*I","-37439/100000-139281/500000*I","-91481/500000+12797/62500*I","-151557/50000+147/250000*I","-12705349/1000000+8895347/500000*I","162317/50000+1671373/1000000*I","1097773/1000000-245703/200000*I","50519/20000-49/100000*I","10587791/1000000-7412789/500000*I","-37439/20000-1392811/1000000*I","85189/1000000+511881/500000*I"]},{"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": "[X^4, -43*X^4-86*X^3-77*X^2-34*X-6, 12*(X+1)^2*(6*X+5)*(6*X+7)]", "text": "This is operator \"2.64\" from ...", "degz": 2, "h3": "132", "sol": "1 6 66 924 14850 261756 4933236 97806456 2017042434 42917560620", "n_discr_factors": "2", "c3": "-96", "operator": "4 2 0 0 0 0 1 -6 -34 -77 -86 -43 420 1704 2580 1728 432", "new_number": "2.64", "id": 60, "operator_tex": "\\theta^4-x\\left(43\\theta^4+86\\theta^3+77\\theta^2+34\\theta+6\\right)+2^{2} 3 x^{2}(\\theta+1)^2(6\\theta+5)(6\\theta+7)", "superseek": "1 7", "discriminant": "2 1 -43 432", "aesz": "182", "n_sing_complex": "0", "inst_int": "", "c2h": "132", "hash": "89ba4729efa82413b33fe6928ff8d2c9", "dim_h": "33", "inst": " 1 7/4 7 40 270 7913/4 15618 131512 1168395 21654889/2", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "(27z-1)(16z-1)", "discr_factors": "432, z-1/16, z-1/27", "dm_basis": ["-96*lambda", "55/2", "1", "1", "-11/2", "-66", "-1", "0", "0", "132", "0", "0", "-132", "0", "0", "0"], "q": "0 1 -10 63 -336 1399 -6150 17483 -103744 -85626", "yuk": "1 1 15 190 2575 33751 427506 5356975 67336719 851760145", "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","132","1","0","0","0","1","1"]},{"re":"1/27","im":"0","approx_re":"0.037037037037","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["1+96*lambda","0","4*lambda",".1639606e-2","11/2","1","11/48","-4*lambda","0","0","1","0","132","0","11/2","1-96*lambda"],"monodromy_dm":["1","-33","-1","-1","0","1","0","0","0","0","1","0","0","0","0","1"]},{"re":"1/16","im":"0","approx_re":"0.0625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["17/4+288*lambda","-13/24-48*lambda","13/96+12*lambda","-.21754163e-1-52/11*lambda","33/2","-7/4","11/16","-13/96-12*lambda","66","-11","15/4","-13/24-48*lambda","396","-66","33/2","-9/4-288*lambda"],"monodromy_dm":["-5","-132","-7/2","-3","1","23","583333/1000000","1/2","-66","-1452","-75/2","-33","45","990","105/4","47/2"]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["5/6","1","1","7/6"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[121*X^4, 847+5929*X+16170*X^2+20482*X^3+10010*X^4, -11198-55253*X-103725*X^2-89990*X^3-32126*X^4, 1716+20625*X+63474*X^2+74184*X^3+28723*X^4, -770-4991*X-13167*X^2-16352*X^3-7945*X^4, 49*(X+1)^4]", "text": "There is a second MUM-point at infinity, corresponding to Operator AESZ 193/5.22", "degz": 5, "h3": "132", "sol": "1 -7 199 -8359 423751 -23973757 1457477659 -93222362023 6192061490503 -423467225669257", "n_discr_factors": "2", "c3": "-408", "operator": "4 5 0 0 0 0 121 847 5929 16170 20482 10010 -11198 -55253 -103725 -89990 -32126 1716 20625 63474 74184 28723 -770 -4991 -13167 -16352 -7945 49 196 294 196 49", "new_number": "5.25", "id": 233, "operator_tex": "11^{2} \\theta^4+7 11 x\\left(130\\theta^4+266\\theta^3+210\\theta^2+77\\theta+11\\right)-x^{2}\\left(11198+55253\\theta+103725\\theta^2+89990\\theta^3+32126\\theta^4\\right)+x^{3}\\left(1716+20625\\theta+63474\\theta^2+74184\\theta^3+28723\\theta^4\\right)-7 x^{4}\\left(1135\\theta^4+2336\\theta^3+1881\\theta^2+713\\theta+110\\right)+7^{2} x^{5}\\left((\\theta+1)^4\\right)", "superseek": "-84/11 -9052/11", "discriminant": "5 121 10010 -32126 28723 -7945 49", "aesz": "198", "n_sing_complex": "3", "inst_int": "", "c2h": "132", "hash": "a1f924763b047c2720d99cfca5ca63db", "dim_h": "33", "inst": " -84/11 639/11 -9052/11 189021/11 -4838013/11 141421066/11 -4533181206/11 155521104120/11 -510941431295 846550286988477/44", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "5", "laurent": null, "discriminant_tex": "(z^3-159z^2+84z+1)(-11+7z)^2", "discr_factors": "49, z^3-159*z^2+84*z+1, (-11/7+z)^2", "dm_basis": null, "q": "0 1 21 93 970 -23541 740418 -27416745 1047984201 -41848595538", "yuk": "1 -84/11 5028/11 -244488/11 12102372/11 -604751709/11 30546710880/11 -1554881153742/11 7238801582892 -4097239337799093/11", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-3/4*(43452+228*I*3^(1/2))^(1/3)-927/(43452+228*I*3^(1/2))^(1/3)+53+1/2*I*3^(1/2)*(3/2*(43452+228*I*3^(1/2))^(1/3)-1854/(43452+228*I*3^(1/2))^(1/3))","im":"0","approx_re":"-0.011648","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":"-3/4*(43452+228*I*3^(1/2))^(1/3)-927/(43452+228*I*3^(1/2))^(1/3)+53-1/2*I*3^(1/2)*(3/2*(43452+228*I*3^(1/2))^(1/3)-1854/(43452+228*I*3^(1/2))^(1/3))","im":"0","approx_re":"0.541757","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"11/7","im":"0","approx_re":"1.57142857143","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"3/2*(43452+228*I*3^(1/2))^(1/3)+1854/(43452+228*I*3^(1/2))^(1/3)+53","im":"0","approx_re":"158.469891","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": "[6561*X^4, -13122-72171*X-159975*X^2-175608*X^3-99954*X^4, -428004-1521180*X-2033921*X^2-1177556*X^3-205589*X^4, 2310517*X^4+12882402*X^3+26939429*X^2+25052328*X+8683524, -32579600-84939800*X-80445300*X^2-33268700*X^3-5152600*X^4, 2500*(X+1)*(1593*X^3+8667*X^2+15104*X+8516), -250000*(X+2)*(X+1)*(2*X+3)^2]", "text": "This is operator \"6.9\" from ...", "degz": 6, "h3": "162", "sol": "1 2 14 104 1030 10852 124424 1489168 18523558 236834780", "n_discr_factors": "3", "c3": "-88", "operator": "4 6 0 0 0 0 6561 -13122 -72171 -159975 -175608 -99954 -428004 -1521180 -2033921 -1177556 -205589 8683524 25052328 26939429 12882402 2310517 -32579600 -84939800 -80445300 -33268700 -5152600 21290000 59050000 59427500 25650000 3982500 -4500000 -12750000 -13250000 -6000000 -1000000", "new_number": "6.9", "id": 431, "operator_tex": "3^{8} \\theta^4-3^{4} x\\left(1234\\theta^4+2168\\theta^3+1975\\theta^2+891\\theta+162\\right)-x^{2}\\left(428004+1521180\\theta+2033921\\theta^2+1177556\\theta^3+205589\\theta^4\\right)+x^{3}\\left(2310517\\theta^4+12882402\\theta^3+26939429\\theta^2+25052328\\theta+8683524\\right)-2^{2} 5^{2} x^{4}\\left(51526\\theta^4+332687\\theta^3+804453\\theta^2+849398\\theta+325796\\right)+2^{2} 5^{4} x^{5}(\\theta+1)(1593\\theta^3+8667\\theta^2+15104\\theta+8516)-2^{4} 5^{6} x^{6}(\\theta+2)(\\theta+1)(2\\theta+3)^2", "superseek": "31/81 29/9", "discriminant": "6 6561 -99954 -205589 2310517 -5152600 3982500 -1000000", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": "132", "hash": "98af5121f39c27098356e3ade277f975", "dim_h": "38", "inst": " 31/81 40/27 29/9 1532/81 6551/81 42442/81 250475/81 588796/27 12225961/81 91935268/81", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "6", "laurent": null, "discriminant_tex": "-(16z-1)(25z^3-17z^2+2z+1)(-81+50z)^2", "discr_factors": "-1000000, z^3-17/25*z^2+2/25*z+1/25, (-81/50+z)^2, z-1/16", "dm_basis": null, "q": "0 1 -3 -7 27 -119 -173 -1634 -13683 -110258", "yuk": "1 31/81 991/81 7078/81 33013/27 818906/81 9175510/81 9545884/9 100498855/9 8912732647/81", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/150*(58796+6900*69^(1/2))^(1/3)-278/75/(58796+6900*69^(1/2))^(1/3)+17/75","im":"0","approx_re":"-0.17455","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":"1/16","im":"0","approx_re":"0.0625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/300*(58796+6900*69^(1/2))^(1/3)+139/75/(58796+6900*69^(1/2))^(1/3)+17/75","im":"1/2*3^(1/2)*(-1/150*(58796+6900*69^(1/2))^(1/3)+278/75/(58796+6900*69^(1/2))^(1/3))","approx_re":"0.427275","approx_im":"-0.215865","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/300*(58796+6900*69^(1/2))^(1/3)+139/75/(58796+6900*69^(1/2))^(1/3)+17/75","im":"-1/2*3^(1/2)*(-1/150*(58796+6900*69^(1/2))^(1/3)+278/75/(58796+6900*69^(1/2))^(1/3))","approx_re":"0.427275","approx_im":"0.215865","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"81/50","im":"0","approx_re":"1.62","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","3/2","3/2","2"],"monodromy":[],"monodromy_dm":[]}]}]}