{"count": 19, "status":"OK", "data":[{"pols": "[X^4, -3*(3*X+1)*(3*X+2)*(10*X^2+10*X+3), 81*(3*X+1)*(3*X+2)*(3*X+4)*(3*X+5)]", "text": "Hadamard product $B\\ast c$.", "degz": 2, "h3": "18", "sol": "1 18 1350 156240 22141350 3521185668 603258639984 108881071041600 20424293211323430 3946730690210665500", "n_discr_factors": "2", "c3": "-156", "operator": "4 2 0 0 0 0 1 -18 -141 -411 -540 -270 3240 18954 35721 26244 6561", "new_number": "2.10", "id": 1, "operator_tex": "\\theta^4-3 x(3\\theta+1)(3\\theta+2)(10\\theta^2+10\\theta+3)+3^{4} x^{2}(3\\theta+1)(3\\theta+2)(3\\theta+4)(3\\theta+5)", "superseek": "27 18089", "discriminant": "2 1 -270 6561", "aesz": "70", "n_sing_complex": "0", "inst_int": "", "c2h": "72", "hash": "3d2adae6eaf26a56c76b8b67d92cc5df", "dim_h": "9", "inst": " 27 432 18089 997785 68438142 5372412653 462553061328 42629254956495 4139005487642537 418758418475154936", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "A_{n}=\\dbinom{2n}{n}\\dbinom{3n}{n}\\sum_{k=0}^{n}\\dbinom{n}{k}^{2}\\dbinom{2k}{k}", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "(243z-1)(27z-1)", "discr_factors": "6561, z-1/243, z-1/27", "dm_basis": ["-377989751/500000000*I", "6", "1", "1", "-3", "-9", "-1", "0", "0", "18", "0", "0", "-18", "0", "0", "0"], "q": "0 1 -69 2196 -90131 1380525 -161041824 -7106675719 -979853201733 -98506835149437", "yuk": "1 27 3483 488430 63861723 8554767777 1160441624934 158655700035531 21826178601587163 3017335000491897903", "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","18","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","26*lambda",".31750278e-1","3","1","1/2","-26*lambda","0","0","1","0","18","0","3","1.-.755979502*I"],"monodromy_dm":["1","-9","-1","-1","0","1","0","0","0","0","1","0","0","0","0","1"]},{"re":"1/27","im":"0","approx_re":"0.037037037037","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["4+468*lambda","-1.-.755979502*I","1/2+78*lambda","-.71415832e-1-52*lambda","9","-2","3/2","-1/2-78*lambda","18","-6","4","-1.-.755979502*I","54","-18","9","-2-468*lambda"],"monodromy_dm":["-5","-36","-4","-3","2","13","1333333/1000000","1","-18","-108","-11","-9","12","72","8","7"]},{"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, -4*(4*X+1)*(4*X+3)*(10*X^2+10*X+3), 144*(4*X+1)*(4*X+3)*(4*X+5)*(4*X+7)]", "text": "Hadamard product $C\\ast c$", "degz": 2, "h3": "12", "sol": "1 36 6300 1718640 575675100 216636756336 87874675224336 37563969509352000 16692217815436148700 7642084994921759382000", "n_discr_factors": "2", "c3": "-224", "operator": "4 2 0 0 0 0 1 -36 -312 -952 -1280 -640 15120 101376 198144 147456 36864", "new_number": "2.11", "id": 2, "operator_tex": "\\theta^4-2^{2} x(4\\theta+1)(4\\theta+3)(10\\theta^2+10\\theta+3)+2^{4} 3^{2} x^{2}(4\\theta+1)(4\\theta+3)(4\\theta+5)(4\\theta+7)", "superseek": "64 246848", "discriminant": "2 1 -640 36864", "aesz": "69", "n_sing_complex": "0", "inst_int": "", "c2h": "72", "hash": "729adc350de26d9415643078ed8d3867", "dim_h": "8", "inst": " 64 2616 246848 32024824 5160268864 951777326520 192563937712192 41708381444805880 9517654613752418368 2263204057578067144632", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "A_n=\\dbinom{2n}{n}\\dbinom{4n}{2n}\\sum_{k=0}^{n}\\dbinom{n}{k}^2\\dbinom{2k}{k}", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "(576z-1)(64z-1)", "discr_factors": "36864, z-1/576, z-1/64", "dm_basis": ["-224*lambda", "5", "1", "1", "-3", "-6", "-1", "0", "0", "12", "0", "0", "-12", "0", "0", "0"], "q": "0 1 -168 14124 -1462208 78268110 -14975497440 -813107957064 -407022651161088 -86618851756321563", "yuk": "1 64 20992 6664960 2049609728 645033608064 205583909214208 66049430635281920 21354691301790220288 6938370213425519655232", "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":"1/576","im":"0","approx_re":"0.00173611111111","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["1+224*lambda","0","56*lambda",".98194154e-1","3","1","3/4","-56*lambda","0","0","1","0","12","0","3","1-224*lambda"],"monodromy_dm":["1","-8","-1","-1","0","1","0","0","0","0","1","0","0","0","0","1"]},{"re":"1/64","im":"0","approx_re":"0.015625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["4.+3.256527087*I","-1-224*lambda","3/4+168*lambda",".44582463e-1-112*lambda","9","-2","9/4","-3/4-168*lambda","12","-4","4","-1-224*lambda","36","-12","9","-2.-3.256527087*I"],"monodromy_dm":["-5","-30","-4","-3","2","11","1333333/1000000","1","-12","-60","-7","-6","8","40","5333333/1000000","5"]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/4","3/4","5/4","7/4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -12*(6*X+1)*(6*X+5)*(10*X^2+10*X+3), 1296*(6*X+1)*(6*X+5)*(6*X+7)*(6*X+11)]", "text": "Hadamard product $B\\ast c$.", "degz": 2, "h3": "6", "sol": "1 180 207900 379819440 855338063580 2167450747141680 5924949977000854800 17076367676457532872000 51175952834979624544935900 158042895581787941968966522800", "n_discr_factors": "2", "c3": "-364", "operator": "4 2 0 0 0 0 1 -180 -1896 -6216 -8640 -4320 498960 4292352 8864640 6718464 1679616", "new_number": "2.12", "id": 3, "operator_tex": "\\theta^4-2^{2} 3 x(6\\theta+1)(6\\theta+5)(10\\theta^2+10\\theta+3)+2^{4} 3^{4} x^{2}(6\\theta+1)(6\\theta+5)(6\\theta+7)(6\\theta+11)", "superseek": "432 78259376", "discriminant": "2 1 -4320 1679616", "aesz": "64", "n_sing_complex": "0", "inst_int": "", "c2h": "72", "hash": "43991f21e20c16ab91690259b788b4cd", "dim_h": "7", "inst": " 432 130842 78259376 68104755558 73096116588720 89957635345588154 121397410414443262896 175425142979625752223270 267068913422544522425517488 423688098858554692149799695930", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "A_{n}=\\dbinom{3n}{n}\\dbinom{6n}{3n}\\sum_{k=0}^{n}\\dbinom{n}{k}^2\\dbinom{2k}{k}", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "(3888z-1)(432z-1)", "discr_factors": "1679616, z-1/432, z-1/3888", "dm_basis": ["-364*lambda", "4", "1", "1", "-3", "-3", "-1", "0", "0", "6", "0", "0", "-6", "0", "0", "0"], "q": "0 1 -1176 761004 -577776704 287718512334 -296784707487264 8781941004951992 -281956134384797984256 -291062648274107532288795", "yuk": "1 432 1047168 2113003584 4358705402880 9137014573590432 19430849236761091584 41639311772154039173760 89817673205572743843717120 194693237885034956850315252336", "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","6","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+364*lambda","0","182*lambda",".518587877","3","1","3/2","-182*lambda","0","0","1","0","6","0","3","1-364*lambda"],"monodromy_dm":["1","-7","-1","-1","0","1","0","0","0","0","1","0","0","0","0","1"]},{"re":"1/432","im":"0","approx_re":"0.00231481481481","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["4.+5.291856516*I","-1-364*lambda","3/2+546*lambda","1.055763632-364*lambda","9","-2","9/2","-3/2-546*lambda","6","-2","4","-1-364*lambda","18","-6","9","-2.-5.291856516*I"],"monodromy_dm":["-5","-24","-4","-3","2","9","1333333/1000000","1","-6","-24","-3","-3","4","16","2666667/1000000","3"]},{"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, -4*(2*X+1)^2*(7*X^2+7*X+2), -128*(2*X+1)^2*(2*X+3)^2]", "text": "Hadamard product $A \\ast a$, where $A$ is (:case 2.1.1)", "degz": 2, "h3": "24", "sol": "1 8 360 22400 1695400 143011008 12963734784 1236284375040 122432502277800 12483618390900800", "n_discr_factors": "2", "c3": "-120", "operator": "4 2 0 0 0 0 1 -8 -60 -172 -224 -112 -1152 -6144 -11264 -8192 -2048", "new_number": "2.1", "id": 11, "operator_tex": "\\theta^4-2^{2} x(2\\theta+1)^2(7\\theta^2+7\\theta+2)-2^{7} x^{2}(2\\theta+1)^2(2\\theta+3)^2", "superseek": "12 3204", "discriminant": "2 1 -112 -2048", "aesz": "45", "n_sing_complex": "0", "inst_int": "", "c2h": "72", "hash": "cdf289f6febf84eb577a238542a57457", "dim_h": "10", "inst": " 12 163 3204 107582 4203360 190881921 9458941572 502640311894 28123887334416 1640055889524440", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "A_{n}=\\dbinom{2n}{n}^2\\sum_{k=0}^{n}\\dbinom{n}{k}^3", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "-(16z+1)(128z-1)", "discr_factors": "-2048, z+1/16, z-1/128", "dm_basis": ["-120*lambda", "7", "1", "1", "-3", "-12", "-1", "0", "0", "24", "0", "0", "-24", "0", "0", "0"], "q": "0 1 -28 -34 1488 -200915 -6984840 -407799534 -24230964160 -1498995588346", "yuk": "1 12 1316 86520 6886564 525420012 41230582760 3244416959208 257351846576292 20502313866875784", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/16","im":"0","approx_re":"-0.0625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["4+240*lambda","-3/2-120*lambda","5/8+50*lambda","-.159319280-30*lambda","10","-4","25/12","-5/8-50*lambda","24","-12","6","-3/2-120*lambda","48","-24","10","-2-240*lambda"],"monodromy_dm":["-5","-36","-3","-2","3","19","3/2","1","-48","-288","-23","-16","36","216","18","13"]},{"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","24","1","0","0","0","1","1"]},{"re":"1/128","im":"0","approx_re":"0.0078125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["1+120*lambda","0","15*lambda",".14090360e-1","3","1","3/8","-15*lambda","0","0","1","0","24","0","3","1-120*lambda"],"monodromy_dm":["1","-10","-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":["1/2","1/2","3/2","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"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, -4*(4*X+1)*(4*X+3)*(7*X^2+7*X+2), -128*(4*X+1)*(4*X+3)*(4*X+5)*(4*X+7)]", "text": "C*a", "degz": 2, "h3": "12", "sol": "1 24 4200 1034880 311711400 104849769024 37939351946496 14450910769152000 5718086730211026600 2330121882579042552000", "n_discr_factors": "2", "c3": "-228", "operator": "4 2 0 0 0 0 1 -24 -212 -660 -896 -448 -13440 -90112 -176128 -131072 -32768", "new_number": "2.3", "id": 33, "operator_tex": "\\theta^4-2^{2} x(4\\theta+1)(4\\theta+3)(7\\theta^2+7\\theta+2)-2^{7} x^{2}(4\\theta+1)(4\\theta+3)(4\\theta+5)(4\\theta+7)", "superseek": "52 220220", "discriminant": "2 1 -448 -32768", "aesz": "68", "n_sing_complex": "0", "inst_int": "", "c2h": "72", "hash": "13a48045ff0a42a9fcfbdb710baf1997", "dim_h": "8", "inst": " 52 2814 220220 29135058 4512922272 813434977450 159977765979708 33749653506239610 7496689709059170544 1735643559203414845168", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "A_{n}=\\dbinom{2n}{n}\\dbinom{4n}{2n}\\sum_{k=0}^{n}\\dbinom{n}{k}^3", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "-(64z+1)(512z-1)", "discr_factors": "-32768, z-1/512, z+1/64", "dm_basis": ["-1104893119/1000000000*I", "5", "1", "1", "-3", "-6", "-1", "0", "0", "12", "0", "0", "-12", "0", "0", "0"], "q": "0 1 -116 478 113008 -56372435 -6168706136 -1532666623214 -363738855142208 -89086162864734458", "yuk": "1 52 22564 5945992 1864666276 564115284052 175701961097704 54872373731039896 17279822597059346596 5465086797904141272568", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/64","im":"0","approx_re":"-0.015625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["4.+2.209786237*I","-1.5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000-1.104893119*I","1+152*lambda","-.171535199-114*lambda","8","-3","8/3","-1-152*lambda","12","-6","5","-1.5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000-1.104893119*I","24","-12","8","-2.-2.209786237*I"],"monodromy_dm":["-5","-24","-3","-2","3","13","3/2","1","-24","-96","-11","-8","18","72","9","7"]},{"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":"1/512","im":"0","approx_re":"0.001953125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["1.+1.104893119*I","0","57*lambda","276/2713","3","1","3/4","-57*lambda","0","0","1","0","12","0","3","1.-1.104893119*I"],"monodromy_dm":["1","-8","-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":["1/4","3/4","5/4","7/4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -12*(6*X+1)*(6*X+5)*(7*X^2+7*X+2), -1152*(6*X+1)*(6*X+5)*(6*X+7)*(6*X+11)]", "text": "Hadamard product D*a", "degz": 2, "h3": "6", "sol": "1 120 138600 228708480 463140798120 1049021939085120 2558060804992492800 6569302147162140672000 17530836228424587378796200 48188316359473969642904740800", "n_discr_factors": "2", "c3": "-366", "operator": "4 2 0 0 0 0 1 -120 -1284 -4308 -6048 -3024 -443520 -3815424 -7879680 -5971968 -1492992", "new_number": "2.4", "id": 44, "operator_tex": "\\theta^4-2^{2} 3 x(6\\theta+1)(6\\theta+5)(7\\theta^2+7\\theta+2)-2^{7} 3^{2} x^{2}(6\\theta+1)(6\\theta+5)(6\\theta+7)(6\\theta+11)", "superseek": "372 71562236", "discriminant": "2 1 -3024 -1492992", "aesz": "62", "n_sing_complex": "0", "inst_int": "", "c2h": "72", "hash": "07a3fd7577f878056e765831c6820f3d", "dim_h": "7", "inst": " 372 136182 71562236 63364481358 65860679690400 79731159343319570 105274670715264426492 149145928602499979170278 222456686052033401879944688 345847268611005007252536310320", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "A_{n}=\\frac{(6n)!}{(3n)!(2n)!n!}\\sum_{k=0}^{n}\\dbinom{n}{k}^3", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "-(432z+1)(3456z-1)", "discr_factors": "-1492992, z+1/432, z-1/3456", "dm_basis": ["-366*lambda", "4", "1", "1", "-3", "-3", "-1", "0", "0", "6", "0", "0", "-6", "0", "0", "0"], "q": "0 1 -804 60894 33466160 -125049218259 -73798244967672 -137218105849556206 -217758218544315797568 -356855888534213849342202", "yuk": "1 372 1089828 1932180744 4055327896740 8232584961300372 17221930420090297320 36109212055335698287128 76362715444484044663079076 162170924131932349972411858296", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/432","im":"0","approx_re":"-0.00231481481481","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["4.+3.547288434*I","-3/2-366*lambda","1.7500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+2.069251586*I",".298604603-366*lambda","7","-5/2","49/12","-1.7500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000-2.069251586*I","6","-3","9/2","-3/2-366*lambda","12","-6","7","-2.-3.547288434*I"],"monodromy_dm":["-5","-18","-3","-2","3","10","3/2","1","-12","-36","-5","-4","9","27","9/2","4"]},{"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","6","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+366*lambda","0","183*lambda",".524302301","3","1","3/2","-183*lambda","0","0","1","0","6","0","3","1-366*lambda"],"monodromy_dm":["1","-7","-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":["1/6","5/6","7/6","11/6"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -2*(2*X+1)^2*(17*X^2+17*X+5), 4*(2*X+1)*(X+1)^2*(2*X+3)]", "text": "Hadamard product $I \\ast \\gamma$", "degz": 2, "h3": "24", "sol": "1 10 438 28900 2310070 206389260 19829802300 2005342876680 210655032909750 22787749078623100", "n_discr_factors": "1", "c3": "-116", "operator": "4 2 0 0 0 0 1 -10 -74 -210 -272 -136 12 56 92 64 16", "new_number": "2.53", "id": 48, "operator_tex": "\\theta^4-2 x(2\\theta+1)^2(17\\theta^2+17\\theta+5)+2^{2} x^{2}(2\\theta+1)(\\theta+1)^2(2\\theta+3)", "superseek": "14 10424/3", "discriminant": "2 1 -136 16", "aesz": "29", "n_sing_complex": "0", "inst_int": "", "c2h": "72", "hash": "92e8a038051b3fb8e0cc6ad6a52b8bfb", "dim_h": "10", "inst": " 14 303/2 10424/3 113664 4579068 632241922/3 10640861204 575106521678 98235955748510/3 1942800973152771", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "3", "laurent": null, "discriminant_tex": "1-136z+16z^2", "discr_factors": "16, 1/16-17/2*z+z^2", "dm_basis": ["-116*lambda", "7", "1", "1", "-3", "-12", "-1", "0", "0", "24", "0", "0", "-24", "0", "0", "0"], "q": "0 1 -34 303 -5396 -122185 -7247646 -411600019 -24878258760 -1565584028352", "yuk": "1 14 1226 93830 7275722 572383514 45521513426 3649815392986 294454546374858 23871337246981760", "gv2": null, "gv0": "336 3636 83392 2727936 109897632 5057935376 255380668896 13802556520272 785887645988080 46627223355666504", "gv1": "0 0 0 66 121056 29099400 4233172704 496392888006 51960605375840 5085222689866104 476714409804578496 43409205232304770480 3872757884182127506368 340410931084603171622976 29592091293200835428214720 2550862857452554085533481862 218456411713150420229553031392 18613027853364203337165477519080 1579429134513012615638126828947296", "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","24","1","0","0","0","1","1"]},{"re":"17/4-3*2^(1/2)","im":"0","approx_re":"0.007359","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["1+116*lambda","0","29/2*lambda","79/6000","3","1","3/8","-29/2*lambda","0","0","1","0","24","0","3","1-116*lambda"],"monodromy_dm":["1","-10","-1","-1","0","1","0","0","0","0","1","0","0","0","0","1"]},{"re":"17/4+3*2^(1/2)","im":"0","approx_re":"8.492641","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["21.+14.053465106*I","-8.-5.621386042*I","5/2+725/2*lambda","-.337500198-580/3*lambda","75","-29","75/8","-5/2-725/2*lambda","240","-96","31","-8.-5.621386042*I","600+1/1000000000*I","-240","75","-19.-14.053465106*I"],"monodromy_dm":["-49","-370","-35","-25","20","149","14","10","-240","-1776","-167","-120","140","1036","98","71"]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/2","1","1","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -4*(2*X+1)^2*(10*X^2+10*X+3), 144*(2*X+1)^2*(2*X+3)^2]", "text": "Hadamard product A*c", "degz": 2, "h3": "24", "sol": "1 12 540 37200 3131100 295484112 30026448144 3213620879040 357404511707100 40942438891582800", "n_discr_factors": "2", "c3": "-112", "operator": "4 2 0 0 0 0 1 -12 -88 -248 -320 -160 1296 6912 12672 9216 2304", "new_number": "2.9", "id": 70, "operator_tex": "\\theta^4-2^{2} x(2\\theta+1)^2(10\\theta^2+10\\theta+3)+2^{4} 3^{2} x^{2}(2\\theta+1)^2(2\\theta+3)^2", "superseek": "16 11056/3", "discriminant": "2 1 -160 2304", "aesz": "58", "n_sing_complex": "0", "inst_int": "", "c2h": "72", "hash": "1ca6d3d1c4514db0651efce420265f5a", "dim_h": "10", "inst": " 16 142 11056/3 121470 4971792 232972910 11970852368 658336558910 114422902654000/3 2302523619150318", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "A_{n}=\\dbinom{2n}{n}^2\\sum_{k=0}^{n}\\dbinom{n}{k}^2\\dbinom{2k}{k}", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "(144z-1)(16z-1)", "discr_factors": "2304, z-1/144, z-1/16", "dm_basis": ["-112*lambda", "7", "1", "1", "-3", "-12", "-1", "0", "0", "24", "0", "0", "-24", "0", "0", "0"], "q": "0 1 -40 684 -15808 79566 -10214112 -374227528 -26140953088 -1633455293211", "yuk": "1 16 1152 99520 7775232 621474016 50322249216 4106002362240 337068325937152 27804765345021520", "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","24","1","0","0","0","1","1"]},{"re":"1/144","im":"0","approx_re":"0.00694444444444","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["1+112*lambda","0","14*lambda",".12274269e-1","3","1","3/8","-14*lambda","0","0","1","0","24","0","3","1-112*lambda"],"monodromy_dm":["1","-10","-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":["4.+1.628263543*I","-1-112*lambda","3/8+42*lambda","-.88177192e-1-28*lambda","9","-2","9/8","-3/8-42*lambda","24","-8","4","-1-112*lambda","72","-24","9","-2.-1.628263543*I"],"monodromy_dm":["-5","-42","-4","-3","2","15","1333333/1000000","1","-24","-168","-15","-12","16","112","10666667/1000000","9"]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/2","1/2","3/2","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -172*X^4-344*X^3-286*X^2-114*X-18, 36*(X+1)^2*(236*X^2+472*X+187), -32400*(X+1)*(X+2)*(2*X+1)*(2*X+5)]", "text": "Operator equivalent to AESZ 103 =$c \\ast c$.", "degz": 3, "h3": "36", "sol": "1 18 630 28980 1593270 99340668 6771183804 491734025640 37390439327670 2942412630737580", "n_discr_factors": "2", "c3": "-48", "operator": "4 3 0 0 0 0 1 -18 -114 -286 -344 -172 6732 30456 49212 33984 8496 -324000 -1263600 -1587600 -777600 -129600", "new_number": "3.10", "id": 71, "operator_tex": "\\theta^4-2 x\\left(86\\theta^4+172\\theta^3+143\\theta^2+57\\theta+9\\right)+2^{2} 3^{2} x^{2}(\\theta+1)^2(236\\theta^2+472\\theta+187)-2^{4} 3^{4} 5^{2} x^{3}(\\theta+1)(\\theta+2)(2\\theta+1)(2\\theta+5)", "superseek": "10 664", "discriminant": "3 1 -172 8496 -129600", "aesz": "~103", "n_sing_complex": "0", "inst_int": "", "c2h": "72", "hash": "9239615e8ac132ca232c13367a39ae3b", "dim_h": "12", "inst": " 10 24 664 9088 234388 5667648 162977404 4849452496 154029465758 5070777681360", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "-(100z-1)(-1+36z)^2", "discr_factors": "-129600, z-1/100, (-1/36+z)^2", "dm_basis": ["-48*lambda", "9", "1", "1", "-3", "-18", "-1", "0", "0", "36", "0", "0", "-36", "0", "0", "0"], "q": "0 1 -42 1407 -46436 1436487 -44122518 1303343085 -38697997416 1108968963840", "yuk": "1 10 202 17938 581834 29298510 1224230098 55901249582 2482920259786 112287480555520", "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":[],"monodromy_dm":[]},{"re":"1/100","im":"0","approx_re":"0.01","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/36","im":"0","approx_re":"0.0277777777778","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/2","1","2","5/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, 15*X^4+30*X^3+35*X^2+20*X+4, -32*(X+1)^2*(66*X^2+132*X+53), -12544*(X+1)*(X+2)*(2*X+1)*(2*X+5)]", "text": "Operator equivalent to AESZ 100= $ a \\ast a$", "degz": 3, "h3": "36", "sol": "1 -4 132 -1120 72100 -265104 59047296 350118912 63064312740 1096066914800", "n_discr_factors": "2", "c3": "-72", "operator": "4 3 0 0 0 0 1 4 20 35 30 15 -1696 -7616 -12256 -8448 -2112 -125440 -489216 -614656 -301056 -50176", "new_number": "3.8", "id": 103, "operator_tex": "\\theta^4+x\\left(15\\theta^4+30\\theta^3+35\\theta^2+20\\theta+4\\right)-2^{5} x^{2}(\\theta+1)^2(66\\theta^2+132\\theta+53)-2^{8} 7^{2} x^{3}(\\theta+1)(\\theta+2)(2\\theta+1)(2\\theta+5)", "superseek": "5 454", "discriminant": "3 1 15 -2112 -50176", "aesz": "~100", "n_sing_complex": "0", "inst_int": "", "c2h": "72", "hash": "82a1ac6ac6fb9ab2e4d6b5d5790d1d9b", "dim_h": "12", "inst": " 5 42 454 7498 154351 3652254 94572705 2621325434 76541504257 2329054186336", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "-(49z-1)(1+32z)^2", "discr_factors": "-50176, (1/32+z)^2, z-1/49", "dm_basis": null, "q": "0 1 4 -258 -4616 -15963 203304 -9506154 -568626864 -17941215870", "yuk": "1 5 341 12263 480213 19293880 788899463 32438437820 1342119102421 55798756615616", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/32","im":"0","approx_re":"-0.03125","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/49","im":"0","approx_re":"0.0204081632653","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","2","5/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -144*X^4-180*X^3-159*X^2-69*X-12, 7857*X^4+17820*X^3+20871*X^2+12096*X+2736, -205578*X^4-629856*X^3-851958*X^2-542376*X-129600, 2598156*X^4+9447840*X^3+13568148*X^2+8608032*X+2006208, -1417176*(X+1)^2*(3*X+2)*(3*X+4)]", "text": "A-Incarnation: (3,0),(0,3),(1,1) intersection in $P^3 \\times \\P^3$.", "degz": 5, "h3": "54", "sol": "1 12 252 6600 198540 6616512 238795704 9174387024 370128617100 15513158060400", "n_discr_factors": "3", "c3": "-18", "operator": "4 5 0 0 0 0 1 -12 -69 -159 -180 -144 2736 12096 20871 17820 7857 -129600 -542376 -851958 -629856 -205578 2006208 8608032 13568148 9447840 2598156 -11337408 -48183984 -75110328 -51018336 -12754584", "new_number": "5.3", "id": 249, "operator_tex": "\\theta^4-3 x\\left(48\\theta^4+60\\theta^3+53\\theta^2+23\\theta+4\\right)+3^{2} x^{2}\\left(873\\theta^4+1980\\theta^3+2319\\theta^2+1344\\theta+304\\right)-2 3^{4} x^{3}\\left(1269\\theta^4+3888\\theta^3+5259\\theta^2+3348\\theta+800\\right)+2^{2} 3^{6} x^{4}\\left(891\\theta^4+3240\\theta^3+4653\\theta^2+2952\\theta+688\\right)-2^{3} 3^{11} x^{5}(\\theta+1)^2(3\\theta+2)(3\\theta+4)", "superseek": "3 245/3", "discriminant": "5 1 -144 7857 -205578 2598156 -12754584", "aesz": "20", "n_sing_complex": "0", "inst_int": "", "c2h": "72", "hash": "a9a698dc5c79ffda497a7897390408b0", "dim_h": "15", "inst": " 3 33/2 245/3 879 11829 993487/6 2570790 43196640 2285716376/3 27978313311/2", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "-(54z-1)(27z-1)^2(18z-1)^2", "discr_factors": "-12754584, (z-1/18)^2, z-1/54, (z-1/27)^2", "dm_basis": null, "q": "0 1 -21 306 -3931 41658 -433134 3702113 -38458437 216542484", "yuk": "1 3 135 2208 56391 1478628 35767872 881780973 22116736071 555429081576", "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":[],"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","1/3","2/3","1"],"monodromy":[],"monodromy_dm":[]},{"re":"1/18","im":"0","approx_re":"0.0555555555556","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":["2/3","1","1","4/3"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[25*X^4, -300-2050*X-5510*X^2-6920*X^3-3280*X^4, 58320+276240*X+460644*X^2+304992*X^3+64224*X^4, -1136160-4408560*X-5230656*X^2-1952640*X^3-152064*X^4, -1728*(2*X+1)*(586*X^3+3039*X^2+3947*X+1527), -20736*(2*X+1)*(6*X+5)*(6*X+7)*(2*X+3)]", "text": "This is operator \"5.40\" from ...", "degz": 5, "h3": "30", "sol": "1 12 396 19920 1241100 87281712 6628328784 530854264512 44210267063820 3794011978270800", "n_discr_factors": "4", "c3": "-76", "operator": "4 5 0 0 0 0 25 -300 -2050 -5510 -6920 -3280 58320 276240 460644 304992 64224 -1136160 -4408560 -5230656 -1952640 -152064 -2638656 -12097728 -18892224 -11515392 -2025216 -2177280 -10285056 -17086464 -11943936 -2985984", "new_number": "5.40", "id": 250, "operator_tex": "5^{2} \\theta^4-2 5 x\\left(328\\theta^4+692\\theta^3+551\\theta^2+205\\theta+30\\right)+2^{2} 3 x^{2}\\left(5352\\theta^4+25416\\theta^3+38387\\theta^2+23020\\theta+4860\\right)-2^{4} 3^{3} x^{3}\\left(352\\theta^4+4520\\theta^3+12108\\theta^2+10205\\theta+2630\\right)-2^{6} 3^{3} x^{4}(2\\theta+1)(586\\theta^3+3039\\theta^2+3947\\theta+1527)-2^{8} 3^{4} x^{5}(2\\theta+1)(6\\theta+5)(6\\theta+7)(2\\theta+3)", "superseek": "62/5 4060/3", "discriminant": "5 25 -3280 64224 -152064 -2025216 -2985984", "aesz": "226", "n_sing_complex": "0", "inst_int": "", "c2h": "72", "hash": "92f95cd33ac4bf18c2d05ce3040c5203", "dim_h": "11", "inst": " 62/5 55 4060/3 28790 861786 142235826/5 1037839042 202280686482/5 24925623464146/15 71113248663729", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "5", "n_sing": "5", "laurent": null, "discriminant_tex": "-(16z-1)(108z-1)(12z-1)(5+12z)^2", "discr_factors": "-2985984, z-1/108, z-1/16, z-1/12, (5/12+z)^2", "dm_basis": null, "q": "0 1 -34 681 -15884 276164 -7151058 68883986 -4231865736 -52348783680", "yuk": "1 62/5 2262/5 182762/5 9215062/5 538616312/5 30723123378/5 1779893957092/5 103567720693846/5 1211385300394048", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-5/12","im":"0","approx_re":"-0.416666666667","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","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":"1/12","im":"0","approx_re":"0.0833333333333","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","5/6","7/6","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[25*X^4, -2365*X^4-4460*X^3-3480*X^2-1250*X-175, 3946*X^4-9272*X^3-28834*X^2-21790*X-5490, 6174*X^4+34560*X^3+20646*X^2-6210*X-5760, -6723*X^4+8424*X^3+37098*X^2+32886*X+9234, -6561*(X+1)^4]", "text": "There is a second MUM-point at infinity,\ncorresponding to Operator AESZ 319/5.85\nFibre product: 53211- x 632--1(1)\n", "degz": 5, "h3": "30", "sol": "1 7 219 9961 546379 33440757 2199262269 152168119383 10933656369867 808865626688413", "n_discr_factors": "3", "c3": "-86", "operator": "4 5 0 0 0 0 25 -175 -1250 -3480 -4460 -2365 -5490 -21790 -28834 -9272 3946 -5760 -6210 20646 34560 6174 9234 32886 37098 8424 -6723 -6561 -26244 -39366 -26244 -6561", "new_number": "5.84", "id": 298, "operator_tex": "5^{2} \\theta^4-5 x\\left(473\\theta^4+892\\theta^3+696\\theta^2+250\\theta+35\\right)+2 x^{2}\\left(1973\\theta^4-4636\\theta^3-14417\\theta^2-10895\\theta-2745\\right)+2 3^{2} x^{3}\\left(343\\theta^4+1920\\theta^3+1147\\theta^2-345\\theta-320\\right)-3^{4} x^{4}\\left(83\\theta^4-104\\theta^3-458\\theta^2-406\\theta-114\\right)-3^{8} x^{5}\\left((\\theta+1)^4\\right)", "superseek": "46/5 1126", "discriminant": "5 25 -2365 3946 6174 -6723 -6561", "aesz": "318", "n_sing_complex": "0", "inst_int": "", "c2h": "72", "hash": "3fa38f629ecd5f39b585ce0c1bd88463", "dim_h": "11", "inst": " 46/5 717/10 1126 51481/2 3609772/5 693353459/30 4058216342/5 305088059917/10 6040466014836/5 249239441393223/5", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "-(z+1)(81z^2+92z-1)(-5+9z)^2", "discr_factors": "-6561, z+1, (-5/9+z)^2, z^2+92/81*z-1/81", "dm_basis": null, "q": "0 1 -22 75 -874 -37047 -1214304 -48755214 -2049708066 -89619902802", "yuk": "1 46/5 2914/5 152056/5 8239874/5 451221546/5 24960879448/5 1391968205352/5 78102551578626/5 880699944993500", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-46/81-13/81*13^(1/2)","im":"0","approx_re":"-1.14657","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":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"-46/81+13/81*13^(1/2)","im":"0","approx_re":"0.010767","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": "[X^4, -4*(3*X^2+3*X+1)*(10*X^2+10*X+3), 3344*X^4+16832*X^3+23536*X^2+13408*X+2928, 34560*X^4-207360*X^3-634752*X^2-480384*X-127872, -2092032*X^4-4184064*X^3+5068800*X^2+7160832*X+2405376, 9953280*X^4+99532800*X^3+56070144*X^2-8294400*X-11612160, 277364736*X^4-286654464*X^3-571981824*X^2-286654464*X-35831808, -95551488*(3*X^2+3*X+1)*(10*X^2+10*X+3), 6879707136*(X+1)^4]", "text": "Hadamard product $c \\ast d$. This operator has a second MUM-point at infinity with the same instanton numbers. It\ncan be reduced to an operator of degree 4 with a single \nMUM-point defined over $\\Q(\\sqrt{?})$.", "degz": 8, "h3": "48", "sol": "1 12 300 10416 431964 20026512 1002175824 52995470400 2920544068572 166150997604048", "n_discr_factors": "5", "c3": "28", "operator": "4 8 0 0 0 0 1 -12 -76 -196 -240 -120 2928 13408 23536 16832 3344 -127872 -480384 -634752 -207360 34560 2405376 7160832 5068800 -4184064 -2092032 -11612160 -8294400 56070144 99532800 9953280 -35831808 -286654464 -571981824 -286654464 277364736 -286654464 -1815478272 -4682022912 -5733089280 -2866544640 6879707136 27518828544 41278242816 27518828544 6879707136", "new_number": "8.10", "id": 453, "operator_tex": "\\theta^4-2^{2} x(3\\theta^2+3\\theta+1)(10\\theta^2+10\\theta+3)+2^{4} x^{2}\\left(209\\theta^4+1052\\theta^3+1471\\theta^2+838\\theta+183\\right)+2^{7} 3^{2} x^{3}\\left(30\\theta^4-180\\theta^3-551\\theta^2-417\\theta-111\\right)-2^{10} 3^{2} x^{4}\\left(227\\theta^4+454\\theta^3-550\\theta^2-777\\theta-261\\right)+2^{12} 3^{4} x^{5}\\left(30\\theta^4+300\\theta^3+169\\theta^2-25\\theta-35\\right)+2^{14} 3^{4} x^{6}\\left(209\\theta^4-216\\theta^3-431\\theta^2-216\\theta-27\\right)-2^{17} 3^{6} x^{7}(3\\theta^2+3\\theta+1)(10\\theta^2+10\\theta+3)+2^{20} 3^{8} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "12 1828/3", "discriminant": "8 1 -120 3344 34560 -2092032 9953280 277364736 -2866544640 6879707136", "aesz": "123", "n_sing_complex": "0", "inst_int": "", "c2h": "72", "hash": "f0d76ab2b6b8808f4faa4ab8ecadff2c", "dim_h": "14", "inst": " 12 -47/2 1828/3 -10813/4 127948 -1853581/6 39969036 280168449/4 50657172196/3 256398596897/2", "cleanlist": "True", "n_sing_real": "7", "sol_explicit": "", "n_sing_rational": "5", "n_sing": "7", "laurent": null, "discriminant_tex": "(36z-1)(8z-1)(72z-1)(4z-1)(-1+288z^2)^2", "discr_factors": "6879707136, z-1/8, z-1/36, (-1/288+z^2)^2, z-1/4, z-1/72", "dm_basis": null, "q": "0 1 -28 572 -11744 233550 -4947920 102001240 -2228888832 46514995429", "yuk": "1 12 -176 16464 -173184 15993512 -66712640 13709379360 35861388288 12309692860092", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/24*2^(1/2)","im":"0","approx_re":"-0.058926","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":"1/72","im":"0","approx_re":"0.0138888888889","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/36","im":"0","approx_re":"0.0277777777778","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/24*2^(1/2)","im":"0","approx_re":"0.058926","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/8","im":"0","approx_re":"0.125","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":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -(10*X^2+10*X+3)*(17*X^2+17*X+6), 7209*X^4+36612*X^3+51273*X^2+29322*X+6480, 110160*X^4-660960*X^3-2021112*X^2-1537704*X-419904, -10182672*X^4-20365344*X^3+24984288*X^2+35166960*X+11967264, 71383680*X^4+713836800*X^3+403527744*X^2-52488000*X-85660416, 3027087936*X^4-3265173504*X^3-6428310336*X^2-3265173504*X-408146688, -272097792*(10*X^2+10*X+3)*(17*X^2+17*X+6), 176319369216*(X+1)^4]", "text": "Hadamard product $c \\ast g$. This operator has a second MUM-point\nat infinity with the same instanton numbers. It can be reduced to an operator of degree 4 with a single MUM-point defined over $Q(\\sqrt{?})$.", "degz": 8, "h3": "72", "sol": "1 18 630 29016 1529766 87271668 5244963984 327192462720 20994740454438 1377396131965308", "n_discr_factors": "5", "c3": "216", "operator": "4 8 0 0 0 0 1 -18 -111 -281 -340 -170 6480 29322 51273 36612 7209 -419904 -1537704 -2021112 -660960 110160 11967264 35166960 24984288 -20365344 -10182672 -85660416 -52488000 403527744 713836800 71383680 -408146688 -3265173504 -6428310336 -3265173504 3027087936 -4897760256 -30202854912 -76459479552 -92513249280 -46256624640 176319369216 705277476864 1057916215296 705277476864 176319369216", "new_number": "8.12", "id": 455, "operator_tex": "\\theta^4-x(10\\theta^2+10\\theta+3)(17\\theta^2+17\\theta+6)+3^{4} x^{2}\\left(89\\theta^4+452\\theta^3+633\\theta^2+362\\theta+80\\right)+2^{3} 3^{4} x^{3}\\left(170\\theta^4-1020\\theta^3-3119\\theta^2-2373\\theta-648\\right)-2^{4} 3^{8} x^{4}\\left(97\\theta^4+194\\theta^3-238\\theta^2-335\\theta-114\\right)+2^{6} 3^{8} x^{5}\\left(170\\theta^4+1700\\theta^3+961\\theta^2-125\\theta-204\\right)+2^{6} 3^{12} x^{6}\\left(89\\theta^4-96\\theta^3-189\\theta^2-96\\theta-12\\right)-2^{9} 3^{12} x^{7}(10\\theta^2+10\\theta+3)(17\\theta^2+17\\theta+6)+2^{12} 3^{16} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "17 1387", "discriminant": "8 1 -170 7209 110160 -10182672 71383680 3027087936 -46256624640 176319369216", "aesz": "175", "n_sing_complex": "0", "inst_int": "", "c2h": "72", "hash": "f6db11b5e593983f455489d5bb1003c5", "dim_h": "18", "inst": " 17 -299/4 1387 -47623/2 500282 -42126461/4 254375312 -12313756771/2 160380505659 -8361141516655/2", "cleanlist": "True", "n_sing_real": "7", "sol_explicit": "", "n_sing_rational": "5", "n_sing": "7", "laurent": null, "discriminant_tex": "(81z-1)(8z-1)(72z-1)(9z-1)(-1+648z^2)^2", "discr_factors": "176319369216, z-1/9, z-1/8, z-1/72, z-1/81, (-1/648+z^2)^2", "dm_basis": null, "q": "0 1 -39 1164 -32809 938661 -27510480 817408641 -24553710831 744082098363", "yuk": "1 17 -581 37466 -1524517 62535267 -2274792026 87250732033 -3152323257893 116917388662877", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/36*2^(1/2)","im":"0","approx_re":"-0.039284","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":"1/81","im":"0","approx_re":"0.0123456790123","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/72","im":"0","approx_re":"0.0138888888889","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/36*2^(1/2)","im":"0","approx_re":"0.039284","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/9","im":"0","approx_re":"0.111111111111","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/8","im":"0","approx_re":"0.125","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": "[X^4, -(10*X^2+10*X+3)*(7*X^2+7*X+2), -71*X^4-1148*X^3-1591*X^2-886*X-192, -5040*X^4+30240*X^3+92808*X^2+69336*X+17280, -20592*X^4-41184*X^3+163872*X^2+184464*X+59616, 362880*X^4+3628800*X^3+2026944*X^2-388800*X-393984, -368064*X^4+4478976*X^3+7397568*X^2+4478976*X+933120, 373248*(10*X^2+10*X+3)*(7*X^2+7*X+2), 26873856*(X+1)^4]", "text": "Hadamard product $a \\ast c$. This operator has a second MUM-point at infinity with the same instanton point. \nIt is reducible to an operator of degree 4 with a single MUM-point defined over $Q(\\sqrt{-2})$", "degz": 8, "h3": "36", "sol": "1 6 150 5208 221094 10478556 534006096 28636761600 1594933457958 91464881448084", "n_discr_factors": "5", "c3": "-60", "operator": "4 8 0 0 0 0 1 -6 -41 -111 -140 -70 -192 -886 -1591 -1148 -71 17280 69336 92808 30240 -5040 59616 184464 163872 -41184 -20592 -393984 -388800 2026944 3628800 362880 933120 4478976 7397568 4478976 -368064 2239488 15303168 41430528 52254720 26127360 26873856 107495424 161243136 107495424 26873856", "new_number": "8.2", "id": 474, "operator_tex": "\\theta^4-x(10\\theta^2+10\\theta+3)(7\\theta^2+7\\theta+2)-x^{2}\\left(71\\theta^4+1148\\theta^3+1591\\theta^2+886\\theta+192\\right)-2^{3} 3^{2} x^{3}\\left(70\\theta^4-420\\theta^3-1289\\theta^2-963\\theta-240\\right)-2^{4} 3^{2} x^{4}\\left(143\\theta^4+286\\theta^3-1138\\theta^2-1281\\theta-414\\right)+2^{6} 3^{4} x^{5}\\left(70\\theta^4+700\\theta^3+391\\theta^2-75\\theta-76\\right)-2^{6} 3^{4} x^{6}\\left(71\\theta^4-864\\theta^3-1427\\theta^2-864\\theta-180\\right)+2^{9} 3^{6} x^{7}(10\\theta^2+10\\theta+3)(7\\theta^2+7\\theta+2)+2^{12} 3^{8} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "7 1271/3", "discriminant": "8 1 -70 -71 -5040 -20592 362880 -368064 26127360 26873856", "aesz": "104", "n_sing_complex": "2", "inst_int": "", "c2h": "72", "hash": "d6bd0d1524954c8ce0a6421d295e9795", "dim_h": "12", "inst": " 7 93/2 1271/3 18507/2 190710 9428013/2 128027760 7423428159/2 339968018663/3 3607055297185", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "5", "n_sing": "7", "laurent": null, "discriminant_tex": "(9z+1)(8z-1)(72z-1)(z+1)(1+72z^2)^2", "discr_factors": "26873856, z+1/9, z-1/8, z-1/72, z+1, (1/72+z^2)^2", "dm_basis": null, "q": "0 1 -17 28 337 -25739 -225296 -10088399 -338161817 -10983844277", "yuk": "1 7 379 11446 592603 23838757 1018237222 43913521687 1900398201307 82612228546555", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1","im":"0","approx_re":"-1.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/9","im":"0","approx_re":"-0.111111111111","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"-1/12*2^(1/2)","approx_re":"0.0","approx_im":"-0.117851","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":"0","im":"1/12*2^(1/2)","approx_re":"0.0","approx_im":"0.117851","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/72","im":"0","approx_re":"0.0138888888889","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/8","im":"0","approx_re":"0.125","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": "[X^4, -4*(3*X^2+3*X+1)*(7*X^2+7*X+2), 1440*X^4+2688*X^3+3744*X^2+2112*X+384, -21504*X^4+129024*X^3+395264*X^2+297984*X+77824, 606208*X^4+1212416*X^3+819200*X^2+212992*X+98304, 5505024*X^4+55050240*X^3+30932992*X^2-4980736*X-6291456, 94371840*X^4+201326592*X^3+283115520*X^2+201326592*X+50331648, 67108864*(3*X^2+3*X+1)*(7*X^2+7*X+2), 4294967296*(X+1)^4]", "text": "Hadamard product $a \\ast d$. This operator has a second MUM-point at infinity with the same instanton numbers.\nIt can be reduced to an operator of degree 4 with a single MUM-point defined over\n$Q(\\sqrt{-1})$.", "degz": 8, "h3": "48", "sol": "1 8 200 6272 233896 9692608 432683264 20387430400 1000461680296 50660529892928", "n_discr_factors": "5", "c3": "12", "operator": "4 8 0 0 0 0 1 -8 -52 -136 -168 -84 384 2112 3744 2688 1440 77824 297984 395264 129024 -21504 98304 212992 819200 1212416 606208 -6291456 -4980736 30932992 55050240 5505024 50331648 201326592 283115520 201326592 94371840 134217728 872415232 2281701376 2818572288 1409286144 4294967296 17179869184 25769803776 17179869184 4294967296", "new_number": "8.3", "id": 485, "operator_tex": "\\theta^4-2^{2} x(3\\theta^2+3\\theta+1)(7\\theta^2+7\\theta+2)+2^{5} 3 x^{2}\\left(15\\theta^4+28\\theta^3+39\\theta^2+22\\theta+4\\right)-2^{10} x^{3}\\left(21\\theta^4-126\\theta^3-386\\theta^2-291\\theta-76\\right)+2^{14} x^{4}\\left(37\\theta^4+74\\theta^3+50\\theta^2+13\\theta+6\\right)+2^{18} x^{5}\\left(21\\theta^4+210\\theta^3+118\\theta^2-19\\theta-24\\right)+2^{21} 3 x^{6}\\left(15\\theta^4+32\\theta^3+45\\theta^2+32\\theta+8\\right)+2^{26} x^{7}(3\\theta^2+3\\theta+1)(7\\theta^2+7\\theta+2)+2^{32} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "8 -104", "discriminant": "8 1 -84 1440 -21504 606208 5505024 94371840 1409286144 4294967296", "aesz": "105", "n_sing_complex": "2", "inst_int": "", "c2h": "72", "hash": "7b27135451cf2016217211c633b7ab83", "dim_h": "14", "inst": " 8 71/2 -104 4202 50112 1190589/2 19232792 750651197/2 8202541856 213407759180", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "7", "n_sing": "7", "laurent": null, "discriminant_tex": "(8z+1)(64z-1)(4z+1)(32z-1)(1+256z^2)^2", "discr_factors": "4294967296, z-1/32, (1/256+z^2)^2, z+1/8, z+1/4, z-1/64", "dm_basis": null, "q": "0 1 -20 150 912 -51715 530216 -531590 -169210560 1317153558", "yuk": "1 8 292 -2800 269220 6264008 128581096 6596847664 192166975652 5979653010224", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/4","im":"0","approx_re":"-0.25","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/8","im":"0","approx_re":"-0.125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"-1/16","approx_re":"0.0","approx_im":"-0.0625","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":"0","im":"1/16","approx_re":"0.0","approx_im":"0.0625","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/64","im":"0","approx_re":"0.015625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/32","im":"0","approx_re":"0.03125","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": "[X^4, -(7*X^2+7*X+2)*(17*X^2+17*X+6), 3520*X^4+7168*X^3+9920*X^2+5504*X+960, -68544*X^4+411264*X^3+1258560*X^2+953856*X+255744, 3391488*X^4+6782976*X^3+3612672*X^2+221184*X+331776, 39481344*X^4+394813440*X^3+222621696*X^2-31850496*X-46448640, 1167851520*X^4+2293235712*X^3+3163815936*X^2+2293235712*X+573308928, 191102976*(7*X^2+7*X+2)*(17*X^2+17*X+6), 110075314176*(X+1)^4]", "text": "Hadamard product $a \\ast g$. This operator has a second MUM-point at infinity with the same instanton numbers.\nIt can be reduced to an operator of degree 4 with a single MUM-point defined over\n$Q(\\sqrt{?})$.", "degz": 8, "h3": "72", "sol": "1 12 420 17472 828324 42238512 2264481024 125871390720 7191959038884 419977122762288", "n_discr_factors": "5", "c3": "192", "operator": "4 8 0 0 0 0 1 -12 -76 -195 -238 -119 960 5504 9920 7168 3520 255744 953856 1258560 411264 -68544 331776 221184 3612672 6782976 3391488 -46448640 -31850496 222621696 394813440 39481344 573308928 2293235712 3163815936 2293235712 1167851520 2293235712 14523826176 37265080320 45482508288 22741254144 110075314176 440301256704 660451885056 440301256704 110075314176", "new_number": "8.5", "id": 507, "operator_tex": "\\theta^4-x(7\\theta^2+7\\theta+2)(17\\theta^2+17\\theta+6)+2^{6} x^{2}\\left(55\\theta^4+112\\theta^3+155\\theta^2+86\\theta+15\\right)-2^{6} 3^{2} x^{3}\\left(119\\theta^4-714\\theta^3-2185\\theta^2-1656\\theta-444\\right)+2^{12} 3^{2} x^{4}\\left(92\\theta^4+184\\theta^3+98\\theta^2+6\\theta+9\\right)+2^{12} 3^{4} x^{5}\\left(119\\theta^4+1190\\theta^3+671\\theta^2-96\\theta-140\\right)+2^{18} 3^{4} x^{6}\\left(55\\theta^4+108\\theta^3+149\\theta^2+108\\theta+27\\right)+2^{18} 3^{6} x^{7}(7\\theta^2+7\\theta+2)(17\\theta^2+17\\theta+6)+2^{24} 3^{8} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "11 -2434/3", "discriminant": "8 1 -119 3520 -68544 3391488 39481344 1167851520 22741254144 110075314176", "aesz": "173", "n_sing_complex": "2", "inst_int": "", "c2h": "72", "hash": "afa82ed9ee239bb5fcac960f8884db01", "dim_h": "18", "inst": " 11 229/4 -2434/3 7512 54801 -12678391/6 32879631 150774408 -30805117507/3 890194486255/4", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "7", "n_sing": "7", "laurent": null, "discriminant_tex": "(72z-1)(8z+1)(64z-1)(9z+1)(1+576z^2)^2", "discr_factors": "110075314176, z-1/72, z+1/9, z+1/8, (1/576+z^2)^2, z-1/64", "dm_basis": null, "q": "0 1 -28 334 2984 -203003 3367304 9854854 -1734288784 35967438370", "yuk": "1 11 469 -21895 481237 6850136 -456443513 11277713444 77196978133 -7485643576096", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/8","im":"0","approx_re":"-0.125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/9","im":"0","approx_re":"-0.111111111111","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"-1/24","approx_re":"0.0","approx_im":"-0.0416666666667","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":"0","im":"1/24","approx_re":"0.0","approx_im":"0.0416666666667","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/72","im":"0","approx_re":"0.0138888888889","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/64","im":"0","approx_re":"0.015625","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":[]}]}]}