{"count": 34, "status":"OK", "data":[{"pols": "[X^4, -12*(2*X+1)^2*(3*X^2+3*X+1), 432*(2*X+1)^2*(2*X+3)^2]", "text": "Hadamard product A*f\nExplicit solution not yet verified", "degz": 2, "h3": null, "sol": "1 12 324 8400 44100 -18860688 -2066991696 -152332944192 -8680533018300 -343458761989200", "n_discr_factors": "1", "c3": null, "operator": "4 2 0 0 0 0 1 -12 -84 -228 -288 -144 3888 20736 38016 27648 6912", "new_number": "2.20", "id": 12, "operator_tex": "\\theta^4-2^{2} 3 x(2\\theta+1)^2(3\\theta^2+3\\theta+1)+2^{4} 3^{3} x^{2}(2\\theta+1)^2(2\\theta+3)^2", "superseek": "12 -3284/3", "discriminant": "2 1 -144 6912", "aesz": "133", "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "4c9628f7dd48f4e9e6ec75303e557389", "dim_h": null, "inst": " 12 -42 -3284/3 -20538 -103776 28249414/3 427369380 8149884534 -318803512000/3 -13871427417456", "cleanlist": "True", "n_sing_real": "1", "sol_explicit": "A_{n}=\\dbinom{2n}{n}^2\\sum_{k=0}^{n}(-1)^{k}3^{n-3k}\\dbinom{n}{3k}\\frac{(3k)!}{k!^3}", "n_sing_rational": "1", "n_sing": "3", "laurent": null, "discriminant_tex": "1-144z+6912z^2", "discr_factors": "6912, 1/6912-1/48*z+z^2", "dm_basis": ["5/6-120*lambda", "78000000031/6000000000+71/3000000000*I", "302400000483599999147/259200000446400001090+1124400000899/259200000446400001090*I", "1", "-4-7/1000000000*I", "-48000000031/2000000000-89/2000000000*I", "-648000001115999998236/648000001116000002725-2412000002077/648000001116000002725*I", "0", "6+11/1000000000*I", "36000000031/1000000000+67/1000000000*I", "0", "0", "-36000000031/1000000000-67/1000000000*I", "0", "0", "0"], "q": "0 1 -36 1134 -24912 564597 -11502648 173126610 -4303513152 65913697026", "yuk": "1 12 -324 -29544 -1314756 -12971988 2033927928 146587697352 4172739566652 -77469253445544", "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":"1/96","im":"-1/288*3^(1/2)","approx_re":"0.0104166666667","approx_im":"-0.006014","exponents":["0","1","1","2"],"monodromy":["1/6+120*lambda","-5/36+20*lambda","-5/54+40/3*lambda","-.9896550e-2+50/9*lambda","4+7/1000000000*I","5/3-1/500000000*I","4/9-1/500000000*I","5/54-40/3*lambda","-6.-.11e-7*I","-1+3/1000000000*I","1/3+3/1000000000*I","-5/36+20*lambda","36.000000031+.67e-7*I","-24*I*3^(19/41)*lambda*Pi^3-1/62500000*I","4-9/500000000*I","11/6-120*lambda"],"monodromy_dm":["1","-13","-1","-1","0","1","0","0","0","0","1","0","0","0","0","1"]},{"re":"1/96","im":"1/288*3^(1/2)","approx_re":"0.0104166666667","approx_im":"0.006014","exponents":["0","1","1","2"],"monodromy":["11/6+120*lambda","-5/36-20*lambda","5/54+40/3*lambda","-.9896550e-2-50/9*lambda","4","1/3","4/9","-5/54-40/3*lambda","6","-1","5/3","-5/36-20*lambda","36","-6","4","1/6-120*lambda"],"monodromy_dm":["-2","-21","-1333333/1000000","-1","1","8","111111/250000","333333/1000000","-24","-168","-9666667/1000000","-8","20","140","8888889/1000000","7666667/1000000"]},{"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*(2*X+1)^2*(11*X^2+11*X+3), -16*(2*X+1)^2*(2*X+3)^2]", "text": "Hadamard product $A\\ast b$\n\nA-incarnation: X(1,2,2) in G(2,5)", "degz": 2, "h3": "20", "sol": "1 12 684 58800 6129900 714610512 89611475184 11829354533568 1622229744177900 229106666659213200", "n_discr_factors": "1", "c3": "-120", "operator": "4 2 0 0 0 0 1 -12 -92 -268 -352 -176 -144 -768 -1408 -1024 -256", "new_number": "2.5", "id": 55, "operator_tex": "\\theta^4-2^{2} x(2\\theta+1)^2(11\\theta^2+11\\theta+3)-2^{4} x^{2}(2\\theta+1)^2(2\\theta+3)^2", "superseek": "20 8220", "discriminant": "2 1 -176 -256", "aesz": "25", "n_sing_complex": "0", "inst_int": "", "c2h": "68", "hash": "93279abcbeeade30c29508de7784e582", "dim_h": "9", "inst": " 20 277 8220 352994 18651536 1126617687 74667602300 5297682428242 395996602125000 30845267770384740", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "A_{n}=\\dbinom{2n}{n}^2\\sum_{k=0}^{n}\\dbinom{n}{k}^2\\dbinom{n+k}{n}", "n_sing_rational": "1", "n_sing": "3", "laurent": null, "discriminant_tex": "1-176z-256z^2", "discr_factors": "-256, -1/256+11/16*z+z^2", "dm_basis": ["-120*lambda", "37/6", "1", "1", "-17/6", "-10", "-1", "0", "0", "20", "0", "0", "-20", "0", "0", "0"], "q": "0 1 -44 486 -11184 -390527 -28173000 -2131044622 -168764951744 -13946975993196", "yuk": "1 20 2236 221960 22593852 2331442020 243349644568 25610987588920 2712413425853756 288681522949346960", "gv2": null, "gv0": "400 5540 164400 7059880 373030720 22532353740 1493352046000 105953648564840 7919932042500000 616905355407694800", "gv1": "0 0 0 1537 882496 214941640 37001766880 5388182343297 715201587952800 89732472170109248 10853707837547302400 1280463172653164106787 148416320937642960627520 16982448267723313699121648 1924600069649944296621370400 216520674412430601976469772097 24221257332526265388744193723840 2697512504678650518375575027208704 299363543965147494551366272473595840", "spectrum":[{"re":"-11/32-5/32*5^(1/2)","im":"0","approx_re":"-0.693136","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["16/3+480*lambda","-13/6-240*lambda","299/360+92*lambda","-.167088493-52*lambda","46/3","-20/3","529/180","-299/360-92*lambda","40","-20","26/3","-13/6-240*lambda","80","-40","46/3","-10/3-480*lambda"],"monodromy_dm":["-9","-60","-6","-4","5","31","3","2","-60","-360","-35","-24","40","240","24","17"]},{"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","20","1","0","0","0","1","1"]},{"re":"-11/32+5/32*5^(1/2)","im":"0","approx_re":"0.005636","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["1+120*lambda","0","17*lambda",".16908432e-1","17/6","1","289/720","-17*lambda","0","0","1","0","20","0","17/6","1-120*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":["1/2","1/2","3/2","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, -460*X^4-992*X^3-646*X^2-150*X-12, -12*(6*X+5)*(1866*X^3+5341*X^2+4760*X+1084), -24336*(6*X+5)*(6*X+11)*(3*X+1)*(3*X+7)]", "text": "This is operator \"3.22\" from ...", "degz": 3, "h3": "7", "sol": "1 12 5760 1664544 681014880 301062617856 144001775971872 72412616435777280 37833106664287101024 20355129524032767235200", "n_discr_factors": "2", "c3": "-36", "operator": "4 3 0 0 0 0 1 -12 -150 -646 -992 -460 -65040 -363648 -663180 -496512 -134352 -9369360 -48477312 -74249136 -42052608 -7884864", "new_number": "3.22", "id": 81, "operator_tex": "\\theta^4-2 x\\left(230\\theta^4+496\\theta^3+323\\theta^2+75\\theta+6\\right)-2^{2} 3 x^{2}(6\\theta+5)(1866\\theta^3+5341\\theta^2+4760\\theta+1084)-2^{4} 3^{2} 13^{2} x^{3}(6\\theta+5)(6\\theta+11)(3\\theta+1)(3\\theta+7)", "superseek": "166 1016100", "discriminant": "3 1 -460 -134352 -7884864", "aesz": "392", "n_sing_complex": "0", "inst_int": "", "c2h": "34", "hash": "5862be5cc4d3ec1686e6b9a6ec08f7e7", "dim_h": "4", "inst": " 166 8076 1016100 189329096 43879949258 11641348524744 23747294280862622/7 1058922686246549520 348334789616884018134 119425507449141363609236", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "-(676z-1)(1+108z)^2", "discr_factors": "-7884864, z-1/676, (1/108+z)^2", "dm_basis": ["-36*lambda", "31/12", "1", "1", "-17/12", "-7/2", "-1", "0", "0", "7", "0", "0", "-7", "0", "0", "0"], "q": "0 1 -102 -13479 -20644 -146630244 -70456962006 -21654760723062 -7360483846618200 -2679511387128156252", "yuk": "1 166 64774 27434866 12117126918 5484993657416 2514531308844178 1163617419762268644 542168415370350481158 253936061630708476654552", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/108","im":"0","approx_re":"-0.00925925925926","approx_im":"0.0","exponents":["0","1/3","1","4/3"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/676","im":"0","approx_re":"0.00147928994083","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":["1/3","5/6","11/6","7/3"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -145*X^4-242*X^3-199*X^2-78*X-12, 8*(2*X+1)*(4*X+3)*(97*X^2+182*X+114), -1296*(2*X+1)*(2*X+3)*(4*X+3)*(4*X+7)]", "text": "This is operator \"3.28\" from ...", "degz": 3, "h3": null, "sol": "1 12 336 12880 592200 30657312 1721304144 102371211072 6350998029480 406844209480800", "n_discr_factors": "2", "c3": null, "operator": "4 3 0 0 0 0 1 -12 -78 -199 -242 -145 2736 13488 24184 19408 6208 -81648 -373248 -585792 -373248 -82944", "new_number": "3.28", "id": 90, "operator_tex": "\\theta^4-x\\left(145\\theta^4+242\\theta^3+199\\theta^2+78\\theta+12\\right)+2^{3} x^{2}(2\\theta+1)(4\\theta+3)(97\\theta^2+182\\theta+114)-2^{4} 3^{4} x^{3}(2\\theta+1)(2\\theta+3)(4\\theta+3)(4\\theta+7)", "superseek": "7 1057/3", "discriminant": "3 1 -145 6208 -82944", "aesz": "410", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "accbbff67291992dfbc89e78f5a3c897", "dim_h": null, "inst": " 7 22 1057/3 5460 108241 7234048/3 59236506 1556441700 129191275684/3 1241287839338", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "-(81z-1)(-1+32z)^2", "discr_factors": "-82944, z-1/81, (-1/32+z)^2", "dm_basis": null, "q": "0 1 -30 621 -12304 207042 -3623670 52073342 -951016416 9610016985", "yuk": "1 7 183 9520 349623 13530132 520861152 20318121565 796898500023 31393480000732", "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":"1/81","im":"0","approx_re":"0.0123456790123","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","3/4","1","7/4"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/2","3/4","3/2","7/4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[25*X^4, -26960*X^4-15040*X^3-10420*X^2-2900*X-300, 7382016*X^4-2322432*X^3-9465984*X^2-4847040*X-758160, -134369280*X^4+2418647040*X^3+1941636096*X^2+604661760*X+67184640, -6530347008*(2*X+1)^4]", "text": "Sporadic Operator. There is a second MUM-point hiding at infinity,corresponding to the Operator AESZ 283/4.59", "degz": 4, "h3": null, "sol": "1 12 3564 1081200 418200300 179605378512 83081624727024 40457677635131328 20469840205440869100 10666939181821718624400", "n_discr_factors": "2", "c3": null, "operator": "4 4 0 0 0 0 25 -300 -2900 -10420 -15040 -26960 -758160 -4847040 -9465984 -2322432 7382016 67184640 604661760 1941636096 2418647040 -134369280 -6530347008 -52242776064 -156728328192 -208971104256 -104485552128", "new_number": "4.58", "id": 157, "operator_tex": "5^{2} \\theta^4-2^{2} 5 x\\left(1348\\theta^4+752\\theta^3+521\\theta^2+145\\theta+15\\right)+2^{4} 3^{4} x^{2}\\left(5696\\theta^4-1792\\theta^3-7304\\theta^2-3740\\theta-585\\right)-2^{10} 3^{8} x^{3}\\left(20\\theta^4-360\\theta^3-289\\theta^2-90\\theta-10\\right)-2^{12} 3^{13} x^{4}\\left((2\\theta+1)^4\\right)", "superseek": "364/5 1264916", "discriminant": "4 25 -26960 7382016 -134369280 -104485552128", "aesz": "282", "n_sing_complex": "1", "inst_int": "", "c2h": null, "hash": "582c9abe0a0b8176a2a06ec6c223bef4", "dim_h": null, "inst": " 364/5 43384/5 1264916 1297643028/5 323354425968/5 18440179245448 28857052915378692/5 9671474245508827972/5 3415046183767896342328/5 1256493105328411899065696/5", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "3", "laurent": null, "discriminant_tex": "-(62208z^2+560z-1)(-5+1296z)^2", "discr_factors": "-104485552128, z^2+35/3888*z-1/62208, (-5/1296+z)^2", "dm_basis": null, "q": "0 1 -68 -11994 -1583120 -386690559 -120243104472 -41467710508110 -15241609913408064 -5869609473593985516", "yuk": "1 364/5 347436/5 170764024/5 83049501228/5 40419303246364/5 19915393756194936/5 1979593829994978344 4951794813783569422892/5 2489568667966796604321136/5", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-35/7776-13/7776*13^(1/2)","im":"0","approx_re":"-0.010529","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":"s_1","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"s_2","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-35/7776+13/7776*13^(1/2)","im":"0","approx_re":"0.001527","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"5/1296","im":"0","approx_re":"0.00385802469136","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":["1/2","1/2","1/2","1/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -12-68*X-148*X^2-160*X^3-208*X^4, 1968+11008*X+24192*X^2+24576*X^3+15360*X^4, -152832-720896*X-1327104*X^2-1179648*X^3-458752*X^4, 16384*(4*X+5)^2*(4*X+3)^2]", "text": "Sporadic Operator, reducible to 3.33, so not a primary operator.", "degz": 4, "h3": null, "sol": "1 12 324 11856 504900 23475312 1155060144 59120134848 3115322063172 167873343726000", "n_discr_factors": "2", "c3": null, "operator": "4 4 0 0 0 0 1 -12 -68 -148 -160 -208 1968 11008 24192 24576 15360 -152832 -720896 -1327104 -1179648 -458752 3686400 15728640 24641536 16777216 4194304", "new_number": "4.71", "id": 172, "operator_tex": "\\theta^4-2^{2} x\\left(52\\theta^4+40\\theta^3+37\\theta^2+17\\theta+3\\right)+2^{4} x^{2}\\left(960\\theta^4+1536\\theta^3+1512\\theta^2+688\\theta+123\\right)-2^{8} x^{3}\\left(1792\\theta^4+4608\\theta^3+5184\\theta^2+2816\\theta+597\\right)+2^{14} x^{4}(4\\theta+5)^2(4\\theta+3)^2", "superseek": "-4 -1580/9", "discriminant": "4 1 -208 15360 -458752 4194304", "aesz": "353", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "33845d8200fe810109063e352fbfc8b1", "dim_h": null, "inst": " -4 -24 -1580/9 -1580 -17120 -621272/3 -2660236 -35601596 -493759552 -7061891648", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "(16z-1)(64z-1)^3", "discr_factors": "4194304, z-1/16, (z-1/64)^3", "dm_basis": null, "q": "0 1 -20 174 -1808 10485 -97368 267922 -6478144 -38096766", "yuk": "1 -4 -196 -4744 -101316 -2140004 -44736520 -912460952 -18228118468 -359950718152", "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":"1/64","im":"0","approx_re":"0.015625","approx_im":"0.0","exponents":["0","1/2","3/2","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":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["3/4","3/4","5/4","5/4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -12-92*X-268*X^2-352*X^3-320*X^4, 7344+46656*X+104448*X^2+99840*X^3+44544*X^4, -165888-1492992*X-4709376*X^2-5971968*X^3-2506752*X^4, 2985984*(2*X+1)^4]", "text": "Sporadic Operator. There is a second MUM-point hiding at infinity, corresponding to Operator AESZ 362/4.73", "degz": 4, "h3": null, "sol": "1 12 324 -6000 -2778300 -361782288 -30344052816 -1087320117312 175645509682500 45289843467726000", "n_discr_factors": "2", "c3": null, "operator": "4 4 0 0 0 0 1 -12 -92 -268 -352 -320 7344 46656 104448 99840 44544 -165888 -1492992 -4709376 -5971968 -2506752 2985984 23887872 71663616 95551488 47775744", "new_number": "4.72", "id": 173, "operator_tex": "\\theta^4-2^{2} x\\left(80\\theta^4+88\\theta^3+67\\theta^2+23\\theta+3\\right)+2^{4} 3 x^{2}\\left(928\\theta^4+2080\\theta^3+2176\\theta^2+972\\theta+153\\right)-2^{10} 3^{2} x^{3}\\left(272\\theta^4+648\\theta^3+511\\theta^2+162\\theta+18\\right)+2^{12} 3^{6} x^{4}\\left((2\\theta+1)^4\\right)", "superseek": "20 -119332/9", "discriminant": "4 1 -320 44544 -2506752 47775744", "aesz": "361", "n_sing_complex": "1", "inst_int": "", "c2h": null, "hash": "f55eaa640956f064f5230c04d8173d60", "dim_h": null, "inst": " 20 -139 -119332/9 -462222 -2113440 9744926503/9 86597298876 2523690015938 -1608859520322496/9 -27901291082883368", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "3", "laurent": null, "discriminant_tex": "(20736z^2-224z+1)(-1+48z)^2", "discr_factors": "47775744, z^2-7/648*z+1/20736, (-1/48+z)^2", "dm_basis": null, "q": "0 1 -44 1902 -14192 942453 -28814376 -3593659182 -207641592000 1037108780802", "yuk": "1 20 -1092 -357976 -29583300 -264179980 233877876984 29702873514488 1292129258576956 -130317621146480152", "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":"s_1","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"s_2","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"7/1296","im":"-1/324*2^(1/2)","approx_re":"0.0054012345679","approx_im":"-0.004365","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"7/1296","im":"1/324*2^(1/2)","approx_re":"0.0054012345679","approx_im":"0.004365","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/48","im":"0","approx_re":"0.0208333333333","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":["1/2","1/2","1/2","1/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[49*X^4, -588-4410*X-12726*X^2-16632*X^3-8064*X^4, 29232+145824*X+245172*X^2+140832*X^3+14256*X^4, -111888-413532*X-373140*X^2+54432*X^3+57456*X^4, -1296*(2*X+1)*(36*X^3+306*X^2+421*X+156), -5184*(2*X+1)*(3*X+2)*(3*X+4)*(2*X+3)]", "text": "This is operator \"5.35\" from ...", "degz": 5, "h3": "21", "sol": "1 12 612 48000 4580100 489171312 56221460064 6803598694464 855427705575300 110773656896588400", "n_discr_factors": "2", "c3": "-100", "operator": "4 5 0 0 0 0 49 -588 -4410 -12726 -16632 -8064 29232 145824 245172 140832 14256 -111888 -413532 -373140 54432 57456 -202176 -949968 -1487808 -839808 -93312 -124416 -611712 -1052352 -746496 -186624", "new_number": "5.35", "id": 244, "operator_tex": "7^{2} \\theta^4-2 3 7 x\\left(192\\theta^4+396\\theta^3+303\\theta^2+105\\theta+14\\right)+2^{2} 3 x^{2}\\left(1188\\theta^4+11736\\theta^3+20431\\theta^2+12152\\theta+2436\\right)+2^{2} 3^{3} x^{3}\\left(532\\theta^4+504\\theta^3-3455\\theta^2-3829\\theta-1036\\right)-2^{4} 3^{4} x^{4}(2\\theta+1)(36\\theta^3+306\\theta^2+421\\theta+156)-2^{6} 3^{4} x^{5}(2\\theta+1)(3\\theta+2)(3\\theta+4)(2\\theta+3)", "superseek": "138/7 42984/7", "discriminant": "5 49 -8064 14256 57456 -93312 -186624", "aesz": "218", "n_sing_complex": "2", "inst_int": "", "c2h": "66", "hash": "a76111af659715caf2c4344eedd9d678", "dim_h": "9", "inst": " 138/7 1506/7 42984/7 235596 78950334/7 4311467320/7 258386346378/7 16576489470036/7 3361119367433372/21 78908087793620790/7", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "5", "laurent": null, "discriminant_tex": "-(1296z^3-864z^2+168z-1)(7+12z)^2", "discr_factors": "-186624, (7/12+z)^2, z^3-2/3*z^2+7/54*z-1/1296", "dm_basis": null, "q": "0 1 -42 573 -13784 -136254 -18358578 -1105132514 -81272201832 -6045671622591", "yuk": "1 138/7 12186/7 1160706/7 105559194/7 9868791888/7 931278113874/7 88626516807792/7 8487162714217626/7 816752006287470102/7", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-7/12","im":"0","approx_re":"-0.583333333333","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":"-1/36*(142+34*17^(1/2))^(1/3)-2/9/(142+34*17^(1/2))^(1/3)+2/9","im":"0","approx_re":"0.006145","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/72*(142+34*17^(1/2))^(1/3)+1/9/(142+34*17^(1/2))^(1/3)+2/9","im":"1/12*3^(1/2)*(-1/6*(142+34*17^(1/2))^(1/3)+4/3/(142+34*17^(1/2))^(1/3))","approx_re":"0.330261","approx_im":"-0.128447","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/72*(142+34*17^(1/2))^(1/3)+1/9/(142+34*17^(1/2))^(1/3)+2/9","im":"-1/12*3^(1/2)*(-1/6*(142+34*17^(1/2))^(1/3)+4/3/(142+34*17^(1/2))^(1/3))","approx_re":"0.330261","approx_im":"0.128447","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/2","2/3","4/3","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[25*X^4, -300-2450*X-7630*X^2-10360*X^3-4640*X^4, -84240-475200*X-961164*X^2-808992*X^3-254304*X^4, -2682720-13821840*X-24344064*X^2-17262720*X^3-4458240*X^4, -419904*(19*X^2+59*X+45)*(2*X+1)^2, -5038848*(2*X+1)^2*(2*X+3)^2]", "text": "This is operator \"5.36\" from ...", "degz": 5, "h3": "15", "sol": "1 12 972 109200 14949900 2286334512 376061860944 65109771739584 11710361039820300 2169000021258642000", "n_discr_factors": "3", "c3": "-80", "operator": "4 5 0 0 0 0 25 -300 -2450 -7630 -10360 -4640 -84240 -475200 -961164 -808992 -254304 -2682720 -13821840 -24344064 -17262720 -4458240 -18895680 -100357056 -182658240 -131010048 -31912704 -45349632 -241864704 -443418624 -322486272 -80621568", "new_number": "5.36", "id": 245, "operator_tex": "5^{2} \\theta^4-2 5 x\\left(464\\theta^4+1036\\theta^3+763\\theta^2+245\\theta+30\\right)-2^{2} 3^{2} x^{2}\\left(7064\\theta^4+22472\\theta^3+26699\\theta^2+13200\\theta+2340\\right)-2^{4} 3^{4} x^{3}\\left(3440\\theta^4+13320\\theta^3+18784\\theta^2+10665\\theta+2070\\right)-2^{6} 3^{8} x^{4}(19\\theta^2+59\\theta+45)(2\\theta+1)^2-2^{8} 3^{9} x^{5}(2\\theta+1)^2(2\\theta+3)^2", "superseek": "166/5 360988/15", "discriminant": "5 25 -4640 -254304 -4458240 -31912704 -80621568", "aesz": "219", "n_sing_complex": "0", "inst_int": "", "c2h": "54", "hash": "b7068bb339f61ebd7c591b7be3fe5893", "dim_h": "7", "inst": " 166/5 638 360988/15 7222128/5 524377242/5 131193711836/15 4000277954562/5 391889229956368/5 121356236706820138/15 4351629319618625834/5", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "-(16z+1)(3888z^2+216z-1)(5+36z)^2", "discr_factors": "-80621568, z^2+1/18*z-1/3888, (5/36+z)^2, z+1/16", "dm_basis": null, "q": "0 1 -50 -87 -236 -2064444 -160470498 -16533089262 -1821805810632 -207459102118464", "yuk": "1 166/5 25686/5 3249058/5 462241878/5 65547155416/5 1889190105354 1372095338414932/5 200647286199902294/5 29489565519760542592/5", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-5/36","im":"0","approx_re":"-0.138888888889","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":"-1/36-1/54*3^(1/2)","im":"0","approx_re":"-0.059853","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":"-1/36+1/54*3^(1/2)","im":"0","approx_re":"0.004297","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","3/2","3/2"],"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": "[169*X^4, -2028-14534*X-40859*X^2-52650*X^3-18837*X^4, 281424+1317056*X+1936736*X^2+433792*X^3-364160*X^4, -5001984-16253952*X-8778752*X^2+10223616*X^3+978944*X^4, -196608*(2*X+1)*(40*X^3+684*X^2+1013*X+399), -9437184*(2*X+1)*(4*X+3)*(4*X+5)*(2*X+3)]", "text": "This is operator \"5.44\" from ...", "degz": 5, "h3": "26", "sol": "1 12 468 28560 2135700 179060112 16166559024 1537448717376 151947395002260 15468902712634800", "n_discr_factors": "3", "c3": "-72", "operator": "4 5 0 0 0 0 169 -2028 -14534 -40859 -52650 -18837 281424 1317056 1936736 433792 -364160 -5001984 -16253952 -8778752 10223616 978944 -78446592 -356057088 -532807680 -276824064 -15728640 -424673280 -2038431744 -3435134976 -2415919104 -603979776", "new_number": "5.44", "id": 254, "operator_tex": "13^{2} \\theta^4-13 x\\left(1449\\theta^4+4050\\theta^3+3143\\theta^2+1118\\theta+156\\right)-2^{4} x^{2}\\left(22760\\theta^4-27112\\theta^3-121046\\theta^2-82316\\theta-17589\\right)+2^{8} x^{3}\\left(3824\\theta^4+39936\\theta^3-34292\\theta^2-63492\\theta-19539\\right)-2^{16} 3 x^{4}(2\\theta+1)(40\\theta^3+684\\theta^2+1013\\theta+399)-2^{20} 3^{2} x^{5}(2\\theta+1)(4\\theta+3)(4\\theta+5)(2\\theta+3)", "superseek": "231/13 38037/13", "discriminant": "5 169 -18837 -364160 978944 -15728640 -603979776", "aesz": "240", "n_sing_complex": "2", "inst_int": "", "c2h": "68", "hash": "8f46cd6968b3b676e251a9d8635637fc", "dim_h": "10", "inst": " 231/13 826/13 38037/13 786076/13 32662752/13 1251531252/13 56830429026/13 2686705844700/13 135076469305428/13 7052986465933572/13", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "-(128z-1)(128z^2-13z+1)(13+192z)^2", "discr_factors": "-603979776, z-1/128, (13/192+z)^2, z^2-13/128*z+1/128", "dm_basis": null, "q": "0 1 -38 771 -20752 393365 -14552562 106677773 -15365058336 -334070060625", "yuk": "1 231/13 6839/13 1027230/13 50315703/13 4082844231/13 270331784270/13 19492837156149/13 1375593442802103/13 98470746124684242/13", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-13/192","im":"0","approx_re":"-0.0677083333333","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":"1/128","im":"0","approx_re":"0.0078125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"13/256","im":"-7/256*7^(1/2)","approx_re":"0.05078125","approx_im":"-0.072345","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"13/256","im":"7/256*7^(1/2)","approx_re":"0.05078125","approx_im":"0.072345","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/2","3/4","5/4","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[25*X^4, -3785*X^4-6490*X^3-5245*X^2-2000*X-300, 196416*X^4+629928*X^3+796356*X^2+429840*X+84240, -4901472*X^4-22044960*X^3-36343404*X^2-23925780*X-5307120, 104976*(2*X+1)*(216*X^3+864*X^2+1015*X+356), -3779136*(2*X+1)*(3*X+2)*(3*X+4)*(2*X+3)]", "text": "This is operator \"5.66\" from ...", "degz": 5, "h3": null, "sol": "1 12 324 12000 548100 28767312 1645769664 99394371648 6230457476100 401731786513200", "n_discr_factors": "3", "c3": null, "operator": "4 5 0 0 0 0 25 -300 -2000 -5245 -6490 -3785 84240 429840 796356 629928 196416 -5307120 -23925780 -36343404 -22044960 -4901472 37371456 181293552 303800544 204073344 45349632 -90699264 -445938048 -767164608 -544195584 -136048896", "new_number": "5.66", "id": 278, "operator_tex": "5^{2} \\theta^4-5 x\\left(757\\theta^4+1298\\theta^3+1049\\theta^2+400\\theta+60\\right)+2^{2} 3^{2} x^{2}\\left(5456\\theta^4+17498\\theta^3+22121\\theta^2+11940\\theta+2340\\right)-2^{2} 3^{4} x^{3}\\left(15128\\theta^4+68040\\theta^3+112171\\theta^2+73845\\theta+16380\\right)+2^{4} 3^{8} x^{4}(2\\theta+1)(216\\theta^3+864\\theta^2+1015\\theta+356)-2^{6} 3^{10} x^{5}(2\\theta+1)(3\\theta+2)(3\\theta+4)(2\\theta+3)", "superseek": "49/5 6032/15", "discriminant": "5 25 -3785 196416 -4901472 45349632 -136048896", "aesz": "274", "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "729d44a3b7b561b49603f26a25d26069", "dim_h": null, "inst": " 49/5 -68/5 6032/15 36276/5 350082/5 26161264/15 274004448/5 6603998596/5 97583032357/3 4784860673996/5", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "-(81z-1)(1296z^2-56z+1)(-5+36z)^2", "discr_factors": "-136048896, z-1/81, z^2-7/162*z+1/1296, (-5/36+z)^2", "dm_basis": null, "q": "0 1 -32 804 -20180 436314 -9036624 170450550 -3377965032 57874309731", "yuk": "1 49/5 -99 54337/5 2321169/5 43760299/5 1883664801/5 93983525713/5 3381249602321/5 118563384368092/5", "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":"1/81","im":"0","approx_re":"0.0123456790123","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"7/324","im":"-1/81*2^(1/2)","approx_re":"0.0216049382716","approx_im":"-0.017459","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"7/324","im":"1/81*2^(1/2)","approx_re":"0.0216049382716","approx_im":"0.017459","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"5/36","im":"0","approx_re":"0.138888888889","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":["1/2","2/3","4/3","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[81*X^4, -17937*X^4-28962*X^3-21933*X^2-7452*X-972, 559552*X^4+805888*X^3+391648*X^2+89280*X+9504, -6046720*X^4-8902656*X^3-7399680*X^2-3186432*X-539136, 32768*(2*X+1)*(340*X^3+618*X^2+455*X+129), -4194304*(2*X+1)*(X+1)^2*(2*X+3)]", "text": "This is operator \"5.75\" from ...", "degz": 5, "h3": "18", "sol": "1 12 708 63840 6989220 855982512 112786041984 15645580194816 2254801269803940 334669706566543920", "n_discr_factors": "3", "c3": "-92", "operator": "4 5 0 0 0 0 81 -972 -7452 -21933 -28962 -17937 9504 89280 391648 805888 559552 -539136 -3186432 -7399680 -8902656 -6046720 4227072 23363584 50069504 51642368 22282240 -12582912 -58720256 -96468992 -67108864 -16777216", "new_number": "5.75", "id": 288, "operator_tex": "3^{4} \\theta^4-3^{2} x\\left(1993\\theta^4+3218\\theta^3+2437\\theta^2+828\\theta+108\\right)+2^{5} x^{2}\\left(17486\\theta^4+25184\\theta^3+12239\\theta^2+2790\\theta+297\\right)-2^{8} x^{3}\\left(23620\\theta^4+34776\\theta^3+28905\\theta^2+12447\\theta+2106\\right)+2^{15} x^{4}(2\\theta+1)(340\\theta^3+618\\theta^2+455\\theta+129)-2^{22} x^{5}(2\\theta+1)(\\theta+1)^2(2\\theta+3)", "superseek": "205/9 97622/9", "discriminant": "5 81 -17937 559552 -6046720 22282240 -16777216", "aesz": "298", "n_sing_complex": "0", "inst_int": "", "c2h": "12", "hash": "e52d50673ec5c795512e2bc3e1017b12", "dim_h": "4", "inst": " 205/9 3206/9 97622/9 496806 254037095/9 16476340418/9 1172722066057/9 9930597861190 7176881517850505/9 200193418895368288/3", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "-(z-1)(1024z^2-192z+1)(-9+128z)^2", "discr_factors": "-16777216, (-9/128+z)^2, z^2-3/16*z+1/1024, z-1", "dm_basis": null, "q": "0 1 -44 350 -10696 -567579 -43127416 -3457085002 -294469950256 -26124408525758", "yuk": "1 205/9 25853/9 2635999/9 286186109/9 31754637080/9 3558892191935/9 402243668657756/9 45760195230549629/9 5231946626515654144/9", "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":"3/32-1/16*2^(1/2)","im":"0","approx_re":"0.005362","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"9/128","im":"0","approx_re":"0.0703125","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"3/32+1/16*2^(1/2)","im":"0","approx_re":"0.182138","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":[]}]}, {"pols": "[9*X^4, -1776*X^4-3300*X^3-2487*X^2-837*X-108, 13801*X^4+6652*X^3-18041*X^2-14904*X-3312, -2*X*(8461*X^3-29160*X^2-28365*X-7236), -43092*X^4-72576*X^3-40908*X^2-5376*X+1344, -1176*(X+1)^2*(3*X+2)*(3*X+4)]", "text": "This is operator \"5.76\" from ...", "degz": 5, "h3": "18", "sol": "1 12 732 67080 7456140 926920512 123962745144 17452988516304 2552819496885900 384553561286809200", "n_discr_factors": "3", "c3": "-90", "operator": "4 5 0 0 0 0 9 -108 -837 -2487 -3300 -1776 -3312 -14904 -18041 6652 13801 0 14472 56730 58320 -16922 1344 -5376 -40908 -72576 -43092 -9408 -39984 -62328 -42336 -10584", "new_number": "5.76", "id": 289, "operator_tex": "3^{2} \\theta^4-3 x\\left(592\\theta^4+1100\\theta^3+829\\theta^2+279\\theta+36\\right)+x^{2}\\left(13801\\theta^4+6652\\theta^3-18041\\theta^2-14904\\theta-3312\\right)-2 x^{3}\\theta(8461\\theta^3-29160\\theta^2-28365\\theta-7236)-2^{2} 3 7 x^{4}\\left(513\\theta^4+864\\theta^3+487\\theta^2+64\\theta-16\\right)-2^{3} 3 7^{2} x^{5}(\\theta+1)^2(3\\theta+2)(3\\theta+4)", "superseek": "73/3 11119", "discriminant": "5 9 -1776 13801 -16922 -43092 -10584", "aesz": "306", "n_sing_complex": "0", "inst_int": "", "c2h": "60", "hash": "d14307aa38b16c728ee31e5936937c44", "dim_h": "8", "inst": " 73/3 2131/6 11119 518671 29749701 3901038259/2 140360129678 10814052859404 877844110264408 445563524466054257/6", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "-(z+1)(54z^2+189z-1)(-3+14z)^2", "discr_factors": "-10584, z+1, (-3/14+z)^2, z^2+7/2*z-1/54", "dm_basis": null, "q": "0 1 -45 378 -10275 -622278 -44377758 -3650207751 -314202691197 -28179105875892", "yuk": "1 73/3 8597/3 900712/3 99593429/3 11156137948/3 1263937305152/3 144430573438735/3 16610385291637973/3 1919845069149161008/3", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-7/4-11/36*33^(1/2)","im":"0","approx_re":"-3.505283","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":"-7/4+11/36*33^(1/2)","im":"0","approx_re":"0.005283","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"3/14","im":"0","approx_re":"0.214285714286","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": "[X^4, 6+38*X+96*X^2+116*X^3+91*X^4, 1218+5950*X+11076*X^2+9388*X^3+3649*X^4, 32814+148542*X+258070*X^2+203832*X^3+63585*X^4, 452634+1866098*X+2834854*X^2+1876864*X^3+489086*X^4, 2613816+10006152*X+13629172*X^2+7635136*X^3+1497628*X^4, 3996360+13915740*X+16585980*X^2+8235072*X^3+1566360*X^4, -9795600-30045624*X-25554680*X^2-743296*X^3+2211712*X^4, -2330112+3517808*X+25230064*X^2+25837056*X^3+5467392*X^4, 104256-5010336*X-15655264*X^2-13188096*X^3-958976*X^4, 523008+3215616*X+8458752*X^2+10444800*X^3+4890624*X^4, -18432*(4*X+3)*(X+1)^2*(4*X+5)]", "text": "This is operator \"11.1\" from ...", "degz": 11, "h3": null, "sol": "1 -6 54 12 -26010 1057644 -27064044 361271016 7490403558 -724620112260", "n_discr_factors": "4", "c3": null, "operator": "4 11 0 0 0 0 1 6 38 96 116 91 1218 5950 11076 9388 3649 32814 148542 258070 203832 63585 452634 1866098 2834854 1876864 489086 2613816 10006152 13629172 7635136 1497628 3996360 13915740 16585980 8235072 1566360 -9795600 -30045624 -25554680 -743296 2211712 -2330112 3517808 25230064 25837056 5467392 104256 -5010336 -15655264 -13188096 -958976 523008 3215616 8458752 10444800 4890624 -276480 -1142784 -1751040 -1179648 -294912", "new_number": "11.1", "id": 336, "operator_tex": "\\theta^4+x\\left(6+38\\theta+96\\theta^2+116\\theta^3+91\\theta^4\\right)+x^{2}\\left(1218+5950\\theta+11076\\theta^2+9388\\theta^3+3649\\theta^4\\right)+x^{3}\\left(32814+148542\\theta+258070\\theta^2+203832\\theta^3+63585\\theta^4\\right)+2 x^{4}\\left(244543\\theta^4+938432\\theta^3+1417427\\theta^2+933049\\theta+226317\\right)+2^{2} x^{5}\\left(374407\\theta^4+1908784\\theta^3+3407293\\theta^2+2501538\\theta+653454\\right)+2^{2} 3 x^{6}\\left(130530\\theta^4+686256\\theta^3+1382165\\theta^2+1159645\\theta+333030\\right)+2^{3} x^{7}\\left(276464\\theta^4-92912\\theta^3-3194335\\theta^2-3755703\\theta-1224450\\right)+2^{4} x^{8}\\left(341712\\theta^4+1614816\\theta^3+1576879\\theta^2+219863\\theta-145632\\right)-2^{5} x^{9}\\left(29968\\theta^4+412128\\theta^3+489227\\theta^2+156573\\theta-3258\\right)+2^{8} 3 x^{10}\\left(6368\\theta^4+13600\\theta^3+11014\\theta^2+4187\\theta+681\\right)-2^{11} 3^{2} x^{11}(4\\theta+3)(\\theta+1)^2(4\\theta+5)", "superseek": "-4 550/3", "discriminant": "11 1 91 3649 63585 489086 1497628 1566360 2211712 5467392 -958976 4890624 -294912", "aesz": null, "n_sing_complex": "4", "inst_int": "", "c2h": null, "hash": "9e36d74a520997fe52f0cbbfafae6aaf", "dim_h": null, "inst": " -4 -11 550/3 -2965/2 -3316 8541260/27 -5027678 12718958 34467542200/27 -31586765315", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "9", "laurent": null, "discriminant_tex": "-(4z+1)(3z+1)(96z^3-1576z^2-62z-1)(1+11z-6z^2+16z^3)^2", "discr_factors": "-294912, z+1/3, (1/16+11/16*z-3/8*z^2+z^3)^2, z^3-197/12*z^2-31/48*z-1/96, z+1/4", "dm_basis": null, "q": "0 1 14 201 1368 15052 153726 -69260 17297272 225976842", "yuk": "1 -4 -92 4946 -94972 -414504 68334938 -1724493558 6512011524 930623644346", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/3","im":"0","approx_re":"-0.333333333333","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":"-1/24*(999+6*79413^(1/2))^(1/3)+41/8/(999+6*79413^(1/2))^(1/3)+1/8","im":"0","approx_re":"-0.085955","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/144*(61824484+15012*417^(1/2))^(1/3)-9772/9/(61824484+15012*417^(1/2))^(1/3)+197/36","im":"-1/4*3^(1/2)*(1/36*(61824484+15012*417^(1/2))^(1/3)-39088/9/(61824484+15012*417^(1/2))^(1/3))","approx_re":"-0.019642","approx_im":"-0.015722","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/144*(61824484+15012*417^(1/2))^(1/3)-9772/9/(61824484+15012*417^(1/2))^(1/3)+197/36","im":"1/4*3^(1/2)*(1/36*(61824484+15012*417^(1/2))^(1/3)-39088/9/(61824484+15012*417^(1/2))^(1/3))","approx_re":"-0.019642","approx_im":"0.015722","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":"1/48*(999+6*79413^(1/2))^(1/3)-41/16/(999+6*79413^(1/2))^(1/3)+1/8","im":"1/2*3^(1/2)*(-1/24*(999+6*79413^(1/2))^(1/3)-41/8/(999+6*79413^(1/2))^(1/3))","approx_re":"0.230478","approx_im":"-0.820976","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/48*(999+6*79413^(1/2))^(1/3)-41/16/(999+6*79413^(1/2))^(1/3)+1/8","im":"-1/2*3^(1/2)*(-1/24*(999+6*79413^(1/2))^(1/3)-41/8/(999+6*79413^(1/2))^(1/3))","approx_re":"0.230478","approx_im":"0.820976","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/72*(61824484+15012*417^(1/2))^(1/3)+19544/9/(61824484+15012*417^(1/2))^(1/3)+197/36","im":"0","approx_re":"16.455951","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":["3/4","1","1","5/4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[25*X^4, -3940*X^4-8360*X^3-6380*X^2-2200*X-300, 2896*X^4+81088*X^3+164656*X^2+108000*X+25360, -110528*X^4+304512*X^3+727360*X^2+291840*X+22080, 1203712*X^4+2330624*X^3-5696000*X^2-6426624*X-1962496, -2158592*X^4-5931008*X^3-65536*X^2+7417856*X+3633152, 16154624*X^4-50036736*X^3-25853952*X^2-11894784*X-3801088, -102236160*X^4+36962304*X^3-113377280*X^2-191234048*X-73793536, 158334976*X^4-109051904*X^3-305135616*X^2-250609664*X-68157440, -96468992*X^4-100663296*X^3-356515840*X^2-553648128*X-230686720, 33554432*(X+1)*(7*X^3+31*X^2+35*X+12), -268435456*(X+1)^4]", "text": "This is operator \"11.4\" from ...", "degz": 11, "h3": null, "sol": "1 12 572 42960 3944556 405927312 44976624944 5248589511744 636470775893740 79500376972668432", "n_discr_factors": "3", "c3": null, "operator": "4 11 0 0 0 0 25 -300 -2200 -6380 -8360 -3940 25360 108000 164656 81088 2896 22080 291840 727360 304512 -110528 -1962496 -6426624 -5696000 2330624 1203712 3633152 7417856 -65536 -5931008 -2158592 -3801088 -11894784 -25853952 -50036736 16154624 -73793536 -191234048 -113377280 36962304 -102236160 -68157440 -250609664 -305135616 -109051904 158334976 -230686720 -553648128 -356515840 -100663296 -96468992 402653184 1577058304 2214592512 1275068416 234881024 -268435456 -1073741824 -1610612736 -1073741824 -268435456", "new_number": "11.4", "id": 341, "operator_tex": "5^{2} \\theta^4-2^{2} 5 x\\left(197\\theta^4+418\\theta^3+319\\theta^2+110\\theta+15\\right)+2^{4} x^{2}\\left(181\\theta^4+5068\\theta^3+10291\\theta^2+6750\\theta+1585\\right)-2^{6} x^{3}\\left(1727\\theta^4-4758\\theta^3-11365\\theta^2-4560\\theta-345\\right)+2^{9} x^{4}\\left(2351\\theta^4+4552\\theta^3-11125\\theta^2-12552\\theta-3833\\right)-2^{12} x^{5}\\left(527\\theta^4+1448\\theta^3+16\\theta^2-1811\\theta-887\\right)+2^{15} x^{6}\\left(493\\theta^4-1527\\theta^3-789\\theta^2-363\\theta-116\\right)-2^{17} x^{7}\\left(780\\theta^4-282\\theta^3+865\\theta^2+1459\\theta+563\\right)+2^{20} x^{8}\\left(151\\theta^4-104\\theta^3-291\\theta^2-239\\theta-65\\right)-2^{22} x^{9}\\left(23\\theta^4+24\\theta^3+85\\theta^2+132\\theta+55\\right)+2^{25} x^{10}(\\theta+1)(7\\theta^3+31\\theta^2+35\\theta+12)-2^{28} x^{11}\\left((\\theta+1)^4\\right)", "superseek": "116/5 29628/5", "discriminant": "11 25 -3940 2896 -110528 1203712 -2158592 16154624 -102236160 158334976 -96468992 234881024 -268435456", "aesz": null, "n_sing_complex": "4", "inst_int": "", "c2h": null, "hash": "4222cdacde3dbaf06ed32adadb70f0d6", "dim_h": null, "inst": " 116/5 1059/5 29628/5 2227181/10 51562768/5 2740127457/5 159563395868/5 19902142099427/10 130761042201704 44764725674950396/5", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "8", "laurent": null, "discriminant_tex": "-(-1+156z+160z^2+256z^3)(4z-1)^2(256z^3-128z^2-16z-5)^2", "discr_factors": "-268435456, (z^3-1/2*z^2-1/16*z-5/256)^2, -1/256+39/64*z+5/8*z^2+z^3, (z-1/4)^2", "dm_basis": null, "q": "0 1 -40 502 -12096 -142623 -15843632 -963478046 -67896513280 -4927396898828", "yuk": "1 116/5 8588/5 800072/5 14255676 6445346116/5 591868339256/5 10946048956568 5094948448731692/5 476623998826011152/5", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/96*(6236+708*177^(1/2))^(1/3)+23/6/(6236+708*177^(1/2))^(1/3)-5/24","im":"-1/8*3^(1/2)*(1/12*(6236+708*177^(1/2))^(1/3)+92/3/(6236+708*177^(1/2))^(1/3))","approx_re":"-0.315684","approx_im":"-0.716756","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/96*(6236+708*177^(1/2))^(1/3)+23/6/(6236+708*177^(1/2))^(1/3)-5/24","im":"1/8*3^(1/2)*(1/12*(6236+708*177^(1/2))^(1/3)+92/3/(6236+708*177^(1/2))^(1/3))","approx_re":"-0.315684","approx_im":"0.716756","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/48*(271+3*5721^(1/2))^(1/3)-7/12/(271+3*5721^(1/2))^(1/3)+1/6","im":"-1/8*3^(1/2)*(1/6*(271+3*5721^(1/2))^(1/3)-14/3/(271+3*5721^(1/2))^(1/3))","approx_re":"-0.072055","approx_im":"-0.158527","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/48*(271+3*5721^(1/2))^(1/3)-7/12/(271+3*5721^(1/2))^(1/3)+1/6","im":"1/8*3^(1/2)*(1/6*(271+3*5721^(1/2))^(1/3)-14/3/(271+3*5721^(1/2))^(1/3))","approx_re":"-0.072055","approx_im":"0.158527","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":"1/48*(6236+708*177^(1/2))^(1/3)-23/3/(6236+708*177^(1/2))^(1/3)-5/24","im":"0","approx_re":"0.006368","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","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"1/24*(271+3*5721^(1/2))^(1/3)+7/6/(271+3*5721^(1/2))^(1/3)+1/6","im":"0","approx_re":"0.64411","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": "[25*X^4, -1600*X^4-3200*X^3-3100*X^2-1500*X-300, 58880*X^4+189440*X^3+307840*X^2+236800*X+73200, -1556480*X^4-6021120*X^3-11965440*X^2-11842560*X-4561920, 32047104*X^4+131334144*X^3+266059776*X^2+289751040*X+122204160, -547356672*X^4-2283798528*X^3-4288413696*X^2-4403232768*X-1807024128, 7751073792*X^4+32916897792*X^3+58711867392*X^2+50130321408*X+16666066944, -91804925952*X^4-396210733056*X^3-746519003136*X^2-601563856896*X-168812347392, 901943132160*X^4+3917010173952*X^3+8024072650752*X^2+7528003928064*X+2663953465344, -7146825580544*X^4-30923764531200*X^3-58806692216832*X^2-51488067944448*X-16969415786496, 45079976738816*X^4+228698418577408*X^3+481311215058944*X^2+475813656920064*X+182244052303872, -175921860444160*X^4-1020346790576128*X^3-2278188092751872*X^2-2278188092751872*X-854320534781952, 17592186044416*(2*X+3)^4]", "text": "This is operator \"12.4\" from ...", "degz": 12, "h3": null, "sol": "1 12 108 688 3564 61776 1778160 33990336 430282476 3627238288", "n_discr_factors": "3", "c3": null, "operator": "4 12 0 0 0 0 25 -300 -1500 -3100 -3200 -1600 73200 236800 307840 189440 58880 -4561920 -11842560 -11965440 -6021120 -1556480 122204160 289751040 266059776 131334144 32047104 -1807024128 -4403232768 -4288413696 -2283798528 -547356672 16666066944 50130321408 58711867392 32916897792 7751073792 -168812347392 -601563856896 -746519003136 -396210733056 -91804925952 2663953465344 7528003928064 8024072650752 3917010173952 901943132160 -16969415786496 -51488067944448 -58806692216832 -30923764531200 -7146825580544 182244052303872 475813656920064 481311215058944 228698418577408 45079976738816 -854320534781952 -2278188092751872 -2278188092751872 -1020346790576128 -175921860444160 1424967069597696 3799912185593856 3799912185593856 1688849860263936 281474976710656", "new_number": "12.4", "id": 348, "operator_tex": "5^{2} \\theta^4-2^{2} 5^{2} x\\left(16\\theta^4+32\\theta^3+31\\theta^2+15\\theta+3\\right)+2^{4} 5 x^{2}\\left(736\\theta^4+2368\\theta^3+3848\\theta^2+2960\\theta+915\\right)-2^{10} 5 x^{3}\\left(304\\theta^4+1176\\theta^3+2337\\theta^2+2313\\theta+891\\right)+2^{12} 3 x^{4}\\left(2608\\theta^4+10688\\theta^3+21652\\theta^2+23580\\theta+9945\\right)-2^{16} 3 x^{5}\\left(2784\\theta^4+11616\\theta^3+21812\\theta^2+22396\\theta+9191\\right)+2^{21} 3 x^{6}\\left(1232\\theta^4+5232\\theta^3+9332\\theta^2+7968\\theta+2649\\right)-2^{25} 3^{2} x^{7}\\left(304\\theta^4+1312\\theta^3+2472\\theta^2+1992\\theta+559\\right)+2^{30} 3 x^{8}\\left(280\\theta^4+1216\\theta^3+2491\\theta^2+2337\\theta+827\\right)-2^{32} x^{9}\\left(1664\\theta^4+7200\\theta^3+13692\\theta^2+11988\\theta+3951\\right)+2^{38} x^{10}\\left(164\\theta^4+832\\theta^3+1751\\theta^2+1731\\theta+663\\right)-2^{40} x^{11}\\left(160\\theta^4+928\\theta^3+2072\\theta^2+2072\\theta+777\\right)+2^{44} x^{12}\\left((2\\theta+3)^4\\right)", "superseek": "4 -228/5", "discriminant": "12 25 -1600 58880 -1556480 32047104 -547356672 7751073792 -91804925952 901943132160 -7146825580544 45079976738816 -175921860444160 281474976710656", "aesz": null, "n_sing_complex": "4", "inst_int": "", "c2h": null, "hash": "c24070a1d4a449404cd7b46398fa6d6e", "dim_h": null, "inst": " 4 -29/5 -228/5 3724/5 -31856/5 144561/5 727676/5 -24745444/5 302409672/5 -397179636", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "7", "laurent": null, "discriminant_tex": "(16z-1)^2(256z^2-16z+1)^2(4096z^3-768z^2-5)^2", "discr_factors": "281474976710656, (z-1/16)^2, (z^2-1/16*z+1/256)^2, (z^3-3/16*z^2-5/4096)^2", "dm_basis": null, "q": "0 1 -12 166 -2224 26881 -293128 2837554 -23554240 156388628", "yuk": "1 4 -212/5 -6136/5 238124/5 -796396 31218808/5 249592888/5 -12669429204/5 220456644752/5", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/64*(28+12*5^(1/2))^(1/3)-1/16/(28+12*5^(1/2))^(1/3)+1/16","im":"-1/32*3^(1/2)*(1/2*(28+12*5^(1/2))^(1/3)-2/(28+12*5^(1/2))^(1/3))","approx_re":"-0.013312","approx_im":"-0.074322","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/64*(28+12*5^(1/2))^(1/3)-1/16/(28+12*5^(1/2))^(1/3)+1/16","im":"1/32*3^(1/2)*(1/2*(28+12*5^(1/2))^(1/3)-2/(28+12*5^(1/2))^(1/3))","approx_re":"-0.013312","approx_im":"0.074322","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":"1/32","im":"-1/32*3^(1/2)","approx_re":"0.03125","approx_im":"-0.054127","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"1/32","im":"1/32*3^(1/2)","approx_re":"0.03125","approx_im":"0.054127","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"1/16","im":"0","approx_re":"0.0625","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"1/32*(28+12*5^(1/2))^(1/3)+1/8/(28+12*5^(1/2))^(1/3)+1/16","im":"0","approx_re":"0.214124","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":["3/2","3/2","3/2","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -140*X^4-152*X^3-140*X^2-64*X-12, 8736*X^4+17088*X^3+20592*X^2+12640*X+3216, -315392*X^4-824832*X^3-1141056*X^2-811072*X-236352, 7199488*X^4+22632448*X^3+33786112*X^2+25145856*X+7554816, -104279040*X^4-378722304*X^3-599851008*X^2-439520256*X-124710912, 860700672*X^4+3588636672*X^3+5853929472*X^2+3884212224*X+863797248, -1825210368*X^4-9822339072*X^3-9894887424*X^2+8154611712*X+9521528832, -34791358464*X^4-172884492288*X^3-449399881728*X^2-605350526976*X-289478541312, 286399660032*X^4+1812675428352*X^3+4617302704128*X^2+5673210347520*X+2552626151424, 12230590464*(X+1)*(X^3-105*X^2-277*X-267), -73383542784*(X+1)*(X+2)*(93*X^2+441*X+607), 7925422620672*(X+3)*(X+2)*(X+1)*(X+6), 63403380965376*(X+1)*(X+2)*(X+3)*(X+4)]", "text": "This is operator \"13.10\" from ...", "degz": 13, "h3": null, "sol": "1 12 180 2928 47556 674352 5050224 -159433920 -10791594684 -419663644368", "n_discr_factors": "5", "c3": null, "operator": "4 13 0 0 0 0 1 -12 -64 -140 -152 -140 3216 12640 20592 17088 8736 -236352 -811072 -1141056 -824832 -315392 7554816 25145856 33786112 22632448 7199488 -124710912 -439520256 -599851008 -378722304 -104279040 863797248 3884212224 5853929472 3588636672 860700672 9521528832 8154611712 -9894887424 -9822339072 -1825210368 -289478541312 -605350526976 -449399881728 -172884492288 -34791358464 2552626151424 5673210347520 4617302704128 1812675428352 286399660032 -3265567653888 -6653441212416 -4672085557248 -1271981408256 12230590464 -89087620939776 -198355716145152 -155279576530944 -52836150804480 -6824669478912 285315214344192 570630428688384 372494863171584 95105071448064 7925422620672 1521681143169024 3170169048268800 2219118333788160 634033809653760 63403380965376", "new_number": "13.10", "id": 362, "operator_tex": "\\theta^4-2^{2} x\\left(35\\theta^4+38\\theta^3+35\\theta^2+16\\theta+3\\right)+2^{4} x^{2}\\left(546\\theta^4+1068\\theta^3+1287\\theta^2+790\\theta+201\\right)-2^{6} x^{3}\\left(4928\\theta^4+12888\\theta^3+17829\\theta^2+12673\\theta+3693\\right)+2^{8} x^{4}\\left(28123\\theta^4+88408\\theta^3+131977\\theta^2+98226\\theta+29511\\right)-2^{10} 3^{2} x^{5}\\left(11315\\theta^4+41094\\theta^3+65088\\theta^2+47691\\theta+13532\\right)+2^{13} 3^{2} x^{6}\\left(11674\\theta^4+48674\\theta^3+79399\\theta^2+52683\\theta+11716\\right)-2^{15} 3^{3} x^{7}\\left(2063\\theta^4+11102\\theta^3+11184\\theta^2-9217\\theta-10762\\right)-2^{17} 3^{4} x^{8}\\left(3277\\theta^4+16284\\theta^3+42329\\theta^2+57018\\theta+27266\\right)+2^{20} 3^{5} x^{9}\\left(1124\\theta^4+7114\\theta^3+18121\\theta^2+22265\\theta+10018\\right)+2^{24} 3^{6} x^{10}(\\theta+1)(\\theta^3-105\\theta^2-277\\theta-267)-2^{25} 3^{7} x^{11}(\\theta+1)(\\theta+2)(93\\theta^2+441\\theta+607)+2^{27} 3^{10} x^{12}(\\theta+3)(\\theta+2)(\\theta+1)(\\theta+6)+2^{30} 3^{10} x^{13}(\\theta+1)(\\theta+2)(\\theta+3)(\\theta+4)", "superseek": "4 -628/9", "discriminant": "13 1 -140 8736 -315392 7199488 -104279040 860700672 -1825210368 -34791358464 286399660032 12230590464 -6824669478912 7925422620672 63403380965376", "aesz": null, "n_sing_complex": "4", "inst_int": "", "c2h": null, "hash": "2a9fda379889eb2fd218bd01f2520f7a", "dim_h": null, "inst": " 4 5 -628/9 -2823/4 672 133867/9 207788 15579985/4 94033312/3 -299026336", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "6", "n_sing": "9", "laurent": null, "discriminant_tex": "(8z-1)(10368z^3-1728z^2+72z-1)(12z-1)^2(288z^2-24z+1)^2(4z+1)^3", "discr_factors": "63403380965376, z-1/8, z^3-1/6*z^2+1/144*z-1/10368, (z-1/12)^2, (z+1/4)^3, (z^2-1/12*z+1/288)^2", "dm_basis": null, "q": "0 1 -16 198 -1760 13349 -57888 -559014 17566336 -323621262", "yuk": "1 4 44 -1880 -45124 84004 3210968 71271288 1994192956 22850092936", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/4","im":"0","approx_re":"-0.25","approx_im":"0.0","exponents":["0","1/2","3/2","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":"-1/72*2^(1/3)-1/144*2^(2/3)+1/18","im":"-1/24*3^(1/2)*(1/3*2^(1/3)-1/6*2^(2/3))","approx_re":"0.027033","approx_im":"-0.011216","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/72*2^(1/3)-1/144*2^(2/3)+1/18","im":"1/24*3^(1/2)*(1/3*2^(1/3)-1/6*2^(2/3))","approx_re":"0.027033","approx_im":"0.011216","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/24","im":"-1/24","approx_re":"0.0416666666667","approx_im":"-0.0416666666667","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/24","im":"1/24","approx_re":"0.0416666666667","approx_im":"0.0416666666667","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/12","im":"0","approx_re":"0.0833333333333","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"1/36*2^(1/3)+1/72*2^(2/3)+1/18","im":"0","approx_re":"0.112601","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","2","3","4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[25*X^4, -300-1100*X-1660*X^2-1120*X^3-10480*X^4, 680960*X+1964544*X^4+632832*X^3+969344*X^2+158320, -37018880-144348160*X-209849344*X^2-139444224*X^3-217964544*X^4, 15973089280*X^4+17656250368*X+5061877760+16775118848*X^3+25085739008*X^2, -450117763072-1433513492480*X-1922996109312*X^2-1260052807680*X^3-817352409088*X^4, 101136447045632*X^2+63277149192192*X^3+81033617735680*X+30113106231296*X^4+27403069947904, -1172226564947968-3250626939060224*X-3763978341711872*X^2-2205773333528576*X^3-811916054233088*X^4, 54428574353981440*X^3+16123384538595328*X^4+93195756621529088*X+100329190494044160*X^2+35629414452559872, -769799426687369216-1907350033615814656*X-1916083179597332480*X^2-957108379304591360*X^3-235396918291726336*X^4, 2501498904353177600*X^4+11941558294763536384*X^3+27594548875410538496*X+25978776955975106560*X^2+11710476134977110016, -122831035499414552576-276522424495432007680*X-245184900544560365568*X^2-104031884754863259648*X^3-18970780111600615424*X^4, 1852920498288670539776*X+856593656325123080192+613444312443390001152*X^3+99284105585196269568*X^4+1556901146581421522944*X^2, -3736042135678487625728-7821275372064774029312*X-6275928210327371513856*X^2-2315642842002852151296*X^3-338526576790185443328*X^4, 14379237005456595484672*X^2+673306158690398633984*X^4+18603541398336082804736*X+5017514388048998039552*X^3+9112691572412518498304, -590295810358705651712*(X+2)^4]", "text": "This is operator \"15.4\" from ...", "degz": 15, "h3": null, "sol": "1 12 44 -3792 -207124 -8325552 -309616912 -11277235008 -410187134228 -15004164993648", "n_discr_factors": "5", "c3": null, "operator": "4 15 0 0 0 0 25 -300 -1100 -1660 -1120 -10480 158320 680960 969344 632832 1964544 -37018880 -144348160 -209849344 -139444224 -217964544 5061877760 17656250368 25085739008 16775118848 15973089280 -450117763072 -1433513492480 -1922996109312 -1260052807680 -817352409088 27403069947904 81033617735680 101136447045632 63277149192192 30113106231296 -1172226564947968 -3250626939060224 -3763978341711872 -2205773333528576 -811916054233088 35629414452559872 93195756621529088 100329190494044160 54428574353981440 16123384538595328 -769799426687369216 -1907350033615814656 -1916083179597332480 -957108379304591360 -235396918291726336 11710476134977110016 27594548875410538496 25978776955975106560 11941558294763536384 2501498904353177600 -122831035499414552576 -276522424495432007680 -245184900544560365568 -104031884754863259648 -18970780111600615424 856593656325123080192 1852920498288670539776 1556901146581421522944 613444312443390001152 99284105585196269568 -3736042135678487625728 -7821275372064774029312 -6275928210327371513856 -2315642842002852151296 -338526576790185443328 9112691572412518498304 18603541398336082804736 14379237005456595484672 5017514388048998039552 673306158690398633984 -9444732965739290427392 -18889465931478580854784 -14167099448608935641088 -4722366482869645213696 -590295810358705651712", "new_number": "15.4", "id": 392, "operator_tex": "5^{2} \\theta^4-2^{2} 5 x\\left(524\\theta^4+56\\theta^3+83\\theta^2+55\\theta+15\\right)+2^{4} x^{2}\\left(122784\\theta^4+39552\\theta^3+60584\\theta^2+42560\\theta+9895\\right)-2^{8} x^{3}\\left(851424\\theta^4+544704\\theta^3+819724\\theta^2+563860\\theta+144605\\right)+2^{13} x^{4}\\left(1949840\\theta^4+2047744\\theta^3+3062224\\theta^2+2155304\\theta+617905\\right)-2^{18} x^{5}\\left(3117952\\theta^4+4806720\\theta^3+7335648\\theta^2+5468420\\theta+1717063\\right)+2^{22} x^{6}\\left(7179524\\theta^4+15086448\\theta^3+24112808\\theta^2+19319920\\theta+6533401\\right)-2^{26} x^{7}\\left(12098492\\theta^4+32868584\\theta^3+56087648\\theta^2+48438116\\theta+17467537\\right)+2^{31} x^{8}\\left(7508036\\theta^4+25345280\\theta^3+46719420\\theta^2+43397656\\theta+16591239\\right)-2^{38} x^{9}\\left(856369\\theta^4+3481940\\theta^3+6970670\\theta^2+6938899\\theta+2800514\\right)+2^{42} x^{10}\\left(568775\\theta^4+2715196\\theta^3+5906890\\theta^2+6274274\\theta+2662654\\right)-2^{46} x^{11}\\left(269591\\theta^4+1478382\\theta^3+3484287\\theta^2+3929620\\theta+1745534\\right)+2^{51} x^{12}\\left(44091\\theta^4+272424\\theta^3+691403\\theta^2+822862\\theta+380404\\right)-2^{57} x^{13}\\left(2349\\theta^4+16068\\theta^3+43548\\theta^2+54271\\theta+25924\\right)+2^{63} x^{14}\\left(73\\theta^4+544\\theta^3+1559\\theta^2+2017\\theta+988\\right)-2^{69} x^{15}\\left((\\theta+2)^4\\right)", "superseek": "52/5 13436/5", "discriminant": "15 25 -10480 1964544 -217964544 15973089280 -817352409088 30113106231296 -811916054233088 16123384538595328 -235396918291726336 2501498904353177600 -18970780111600615424 99284105585196269568 -338526576790185443328 673306158690398633984 -590295810358705651712", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "2306e85a3af0a97d616dedf03cc93f69", "dim_h": null, "inst": " 52/5 115 13436/5 89632 18465296/5 871619621/5 45240257244/5 503650715312 147905271435016/5 9063969995240684/5", "cleanlist": "True", "n_sing_real": "8", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "8", "laurent": null, "discriminant_tex": "-(-1+32z)(256z^2-48z+1)^2(512z^2-128z+5)^2(64z-1)^3(16z-1)^3", "discr_factors": "-590295810358705651712, (z-1/16)^3, (z^2-1/4*z+5/512)^2, -1/32+z, (z-1/64)^3, (z^2-3/16*z+1/256)^2", "dm_basis": null, "q": "0 1 4 422 23056 1452289 97060696 6773971762 487971107392 36012102833428", "yuk": "1 52/5 4652/5 362824/5 28686892/5 2308162052/5 37654041112 15517408234744/5 1289345859885612/5 107822942876489488/5", "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":"1/64","im":"0","approx_re":"0.015625","approx_im":"0.0","exponents":["0","2","3","5"],"monodromy":[],"monodromy_dm":[]},{"re":"3/32-1/32*5^(1/2)","im":"0","approx_re":"0.023873","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"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":"1/8-1/32*6^(1/2)","im":"0","approx_re":"0.048453","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","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"3/32+1/32*5^(1/2)","im":"0","approx_re":"0.163627","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"1/8+1/32*6^(1/2)","im":"0","approx_re":"0.201547","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","2","2","2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[361*X^4, -82327*X^4-118028*X^3-90782*X^2-31768*X-4332, 4307495*X^4+7600484*X^3+6216406*X^2+2802424*X+530556, -93729369*X^4-213316800*X^3-236037196*X^2-125748612*X-25260804, 963255200*X^4+3114116800*X^3+4165791036*X^2+2527211236*X+554043972, -1636*(X+1)*(2851324*X^3+10035516*X^2+11221241*X+3481470), 2173983876*(X+1)*(X+2)*(2*X+1)*(2*X+5)]", "text": "This is operator \"6.4\" from ...", "degz": 6, "h3": null, "sol": "1 12 588 46200 4446540 479645712 55701589944 6812461820736 865769606945100 113329467477866640", "n_discr_factors": "3", "c3": null, "operator": "4 6 0 0 0 0 361 -4332 -31768 -90782 -118028 -82327 530556 2802424 6216406 7600484 4307495 -25260804 -125748612 -236037196 -213316800 -93729369 554043972 2527211236 4165791036 3114116800 963255200 -5695684920 -24053635196 -34776054452 -21082870240 -4664766064 21739838760 84785371164 106525209924 52175613024 8695935504", "new_number": "6.4", "id": 426, "operator_tex": "19^{2} \\theta^4-19 x\\left(4333\\theta^4+6212\\theta^3+4778\\theta^2+1672\\theta+228\\right)+x^{2}\\left(4307495\\theta^4+7600484\\theta^3+6216406\\theta^2+2802424\\theta+530556\\right)-x^{3}\\left(93729369\\theta^4+213316800\\theta^3+236037196\\theta^2+125748612\\theta+25260804\\right)+2^{2} x^{4}\\left(240813800\\theta^4+778529200\\theta^3+1041447759\\theta^2+631802809\\theta+138510993\\right)-2^{2} 409 x^{5}(\\theta+1)(2851324\\theta^3+10035516\\theta^2+11221241\\theta+3481470)+2^{2} 3^{2} 19^{2} 409^{2} x^{6}(\\theta+1)(\\theta+2)(2\\theta+1)(2\\theta+5)", "superseek": "370/19 140636/19", "discriminant": "6 361 -82327 4307495 -93729369 963255200 -4664766064 8695935504", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "0f3ddf420018e2870561a3e9fd2551cc", "dim_h": null, "inst": " 370/19 276 140636/19 5568700/19 277119292/19 15745336064/19 981366492904/19 3447094749868 4605736683107190/19 337534917416943468/19", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "6", "laurent": null, "discriminant_tex": "(9z-1)(5776z^3-1920z^2+176z-1)(-19+409z)^2", "discr_factors": "8695935504, z-1/9, (-19/409+z)^2, z^3-120/361*z^2+11/361*z-1/5776", "dm_basis": null, "q": "0 1 -40 412 -12524 -223434 -23485456 -1525491926 -115480412576 -8944553556143", "yuk": "1 370/19 42322/19 3797542/19 356439122/19 34639911870/19 3400996429318/19 336608707066442/19 33533338083155026/19 3357582041988939052/19", "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":"-1/4332*(19608426+3121206*33^(1/2))^(1/3)-3316/361/(19608426+3121206*33^(1/2))^(1/3)+40/361","im":"0","approx_re":"0.006077","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"19/409","im":"0","approx_re":"0.0464547677262","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":"1/8664*(19608426+3121206*33^(1/2))^(1/3)+1658/361/(19608426+3121206*33^(1/2))^(1/3)+40/361","im":"1/4*3^(1/2)*(-1/2166*(19608426+3121206*33^(1/2))^(1/3)+6632/361/(19608426+3121206*33^(1/2))^(1/3))","approx_re":"0.163166","approx_im":"-0.043179","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/8664*(19608426+3121206*33^(1/2))^(1/3)+1658/361/(19608426+3121206*33^(1/2))^(1/3)+40/361","im":"-1/4*3^(1/2)*(-1/2166*(19608426+3121206*33^(1/2))^(1/3)+6632/361/(19608426+3121206*33^(1/2))^(1/3))","approx_re":"0.163166","approx_im":"0.043179","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, -12-64*X-125*X^2-122*X^3-61*X^4, -576-4176*X-8264*X^2-6176*X^3-1544*X^4, 622080+2414592*X+2823168*X^2+1345536*X^3+224256*X^4, -51609600-174735360*X-164007936*X^2-60162048*X^3-7520256*X^4, 1769472*(16*X^2+80*X+35)*(2*X+5)^2, -42467328*(2*X+11)*(2*X+7)*(2*X+5)*(2*X+1)]", "text": "This is operator \"6.5\" from ...", "degz": 6, "h3": null, "sol": "1 12 324 5760 215460 2549232 200116224 -782825472 277853698980 -7114516952400", "n_discr_factors": "3", "c3": null, "operator": "4 6 0 0 0 0 1 -12 -64 -125 -122 -61 -576 -4176 -8264 -6176 -1544 622080 2414592 2823168 1345536 224256 -51609600 -174735360 -164007936 -60162048 -7520256 1548288000 4777574400 3786670080 1132462080 113246208 -16349921280 -46883930112 -32275169280 -8153726976 -679477248", "new_number": "6.5", "id": 427, "operator_tex": "\\theta^4-x\\left(12+64\\theta+125\\theta^2+122\\theta^3+61\\theta^4\\right)-2^{3} x^{2}\\left(193\\theta^4+772\\theta^3+1033\\theta^2+522\\theta+72\\right)+2^{9} 3 x^{3}\\left(146\\theta^4+876\\theta^3+1838\\theta^2+1572\\theta+405\\right)-2^{12} 3^{2} x^{4}\\left(204\\theta^4+1632\\theta^3+4449\\theta^2+4740\\theta+1400\\right)+2^{16} 3^{3} x^{5}(16\\theta^2+80\\theta+35)(2\\theta+5)^2-2^{19} 3^{4} x^{6}(2\\theta+11)(2\\theta+7)(2\\theta+5)(2\\theta+1)", "superseek": "-11 -3422/3", "discriminant": "6 1 -61 -1544 224256 -7520256 113246208 -679477248", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "6a4aeb5833b7673c962d5598842d3f2c", "dim_h": null, "inst": " -11 68 -3422/3 30735 -1014993 37434552 -1486568559 62556815721 -8291619038429/3 127231570499928", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "6", "laurent": null, "discriminant_tex": "-(24z-1)(27648z^3-1728z^2+27z+1)(-1+32z)^2", "discr_factors": "-679477248, z-1/24, (-1/32+z)^2, z^3-1/16*z^2+1/1024*z+1/27648", "dm_basis": null, "q": "0 1 -16 -114 20776 -936859 27143952 -486221306 1441150448 149478220674", "yuk": "1 -11 533 -30809 1967573 -126874136 8085832967 -509893015748 32029091616725 -2014863426369056", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/96*(17+12*2^(1/2))^(1/3)-1/96/(17+12*2^(1/2))^(1/3)+1/48","im":"0","approx_re":"-0.016119","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":"1/32","im":"0","approx_re":"0.03125","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"1/192*(17+12*2^(1/2))^(1/3)+1/192/(17+12*2^(1/2))^(1/3)+1/48","im":"1/6*3^(1/2)*(-1/32*(17+12*2^(1/2))^(1/3)+1/32/(17+12*2^(1/2))^(1/3))","approx_re":"0.03931","approx_im":"-0.026431","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/192*(17+12*2^(1/2))^(1/3)+1/192/(17+12*2^(1/2))^(1/3)+1/48","im":"-1/6*3^(1/2)*(-1/32*(17+12*2^(1/2))^(1/3)+1/32/(17+12*2^(1/2))^(1/3))","approx_re":"0.03931","approx_im":"0.026431","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/24","im":"0","approx_re":"0.0416666666667","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","5/2","7/2","11/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -12-100*X-305*X^2-410*X^3-205*X^4, -3168-14976*X-23744*X^2-16256*X^3-4064*X^4, -87480-336492*X-391668*X^2-186336*X^3-31056*X^4, -806400-2730240*X-2562624*X^2-940032*X^3-117504*X^4, -3456*(16*X^2+80*X+35)*(2*X+5)^2, -10368*(2*X+11)*(2*X+7)*(2*X+5)*(2*X+1)]", "text": "This is operator \"6.6\" from ...", "degz": 6, "h3": null, "sol": "1 12 972 106200 14027580 2067427152 327459248424 54573068762784 9445628232122940 1683369975662266320", "n_discr_factors": "3", "c3": null, "operator": "4 6 0 0 0 0 1 -12 -100 -305 -410 -205 -3168 -14976 -23744 -16256 -4064 -87480 -336492 -391668 -186336 -31056 -806400 -2730240 -2562624 -940032 -117504 -3024000 -9331200 -7395840 -2211840 -221184 -3991680 -11446272 -7879680 -1990656 -165888", "new_number": "6.6", "id": 428, "operator_tex": "\\theta^4-x\\left(12+100\\theta+305\\theta^2+410\\theta^3+205\\theta^4\\right)-2^{5} x^{2}\\left(127\\theta^4+508\\theta^3+742\\theta^2+468\\theta+99\\right)-2^{2} 3 x^{3}\\left(2588\\theta^4+15528\\theta^3+32639\\theta^2+28041\\theta+7290\\right)-2^{6} 3^{2} x^{4}\\left(204\\theta^4+1632\\theta^3+4449\\theta^2+4740\\theta+1400\\right)-2^{7} 3^{3} x^{5}(16\\theta^2+80\\theta+35)(2\\theta+5)^2-2^{7} 3^{4} x^{6}(2\\theta+11)(2\\theta+7)(2\\theta+5)(2\\theta+1)", "superseek": "25 17452", "discriminant": "6 1 -205 -4064 -31056 -117504 -221184 -165888", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "e97e9b0e87960fe4cffbb22a5e935b4a", "dim_h": null, "inst": " 25 446 17452 958347 65098152 5055483196 430715448330 39283093415433 11323641414587648/3 377927448242942418", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "6", "laurent": null, "discriminant_tex": "-(3z+1)(3456z^3+1728z^2+216z-1)(4z+1)^2", "discr_factors": "-165888, (z+1/4)^2, z^3+1/2*z^2+1/16*z-1/3456, z+1/3", "dm_basis": null, "q": "0 1 -52 264 -860 -1537708 -103113984 -9739921118 -1015028462344 -107590224786822", "yuk": "1 25 3593 471229 61337801 8137269025 1091984845133 147735398777215 20112943890039497 2751644863745269693", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/3","im":"0","approx_re":"-0.333333333333","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/24*2^(1/3)-1/48*2^(2/3)-1/6","im":"-1/24*3^(1/2)*(2^(1/3)-1/2*2^(2/3))","approx_re":"-0.252234","approx_im":"-0.033647","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/24*2^(1/3)-1/48*2^(2/3)-1/6","im":"1/24*3^(1/2)*(2^(1/3)-1/2*2^(2/3))","approx_re":"-0.252234","approx_im":"0.033647","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/4","im":"0","approx_re":"-0.25","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":"1/12*2^(1/3)+1/24*2^(2/3)-1/6","im":"0","approx_re":"0.004468","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","5/2","7/2","11/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[9*X^4, -816*X^4-1020*X^3-1041*X^2-531*X-108, 31273*X^4+76540*X^3+103783*X^2+71112*X+19728, -656438*X^4-2362320*X^3-3955914*X^2-3240072*X-1044576, 8147996*X^4+38411008*X^3+76088452*X^2+70904768*X+25237632, -136*(X+1)*(439669*X^3+2114103*X^2+3708554*X+2306280), 499392*(X+1)*(X+2)*(481*X^2+1875*X+1962), -407503872*(X+1)*(X+2)^2*(X+3)]", "text": "This is operator \"7.8\" from ...", "degz": 7, "h3": null, "sol": "1 12 156 2136 30348 443232 6612024 100296432 1541950092 23968741296", "n_discr_factors": "6", "c3": null, "operator": "4 7 0 0 0 0 9 -108 -531 -1041 -1020 -816 19728 71112 103783 76540 31273 -1044576 -3240072 -3955914 -2362320 -656438 25237632 70904768 76088452 38411008 8147996 -313654080 -818017424 -791881352 -347312992 -59794984 1959614208 4812141312 4269302208 1656982656 240207552 -4890046464 -11410108416 -9372589056 -3260030976 -407503872", "new_number": "7.8", "id": 451, "operator_tex": "3^{2} \\theta^4-3 x\\left(272\\theta^4+340\\theta^3+347\\theta^2+177\\theta+36\\right)+x^{2}\\left(31273\\theta^4+76540\\theta^3+103783\\theta^2+71112\\theta+19728\\right)-2 x^{3}\\left(328219\\theta^4+1181160\\theta^3+1977957\\theta^2+1620036\\theta+522288\\right)+2^{2} x^{4}\\left(2036999\\theta^4+9602752\\theta^3+19022113\\theta^2+17726192\\theta+6309408\\right)-2^{3} 17 x^{5}(\\theta+1)(439669\\theta^3+2114103\\theta^2+3708554\\theta+2306280)+2^{6} 3^{3} 17^{2} x^{6}(\\theta+1)(\\theta+2)(481\\theta^2+1875\\theta+1962)-2^{10} 3^{4} 17^{3} x^{7}(\\theta+1)(\\theta+2)^2(\\theta+3)", "superseek": "-1/3 -5/3", "discriminant": "7 9 -816 31273 -656438 8147996 -59794984 240207552 -407503872", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "d5b8cfd5049e5d8670dac5bb5499d46a", "dim_h": null, "inst": " -1/3 11/12 -5/3 19/3 -29 1691/12 -702 11624/3 -67528/3 544423/4", "cleanlist": "True", "n_sing_real": "7", "sol_explicit": "", "n_sing_rational": "7", "n_sing": "7", "laurent": null, "discriminant_tex": "-(17z-1)(9z-1)(8z-1)(18z-1)(16z-1)(-3+34z)^2", "discr_factors": "-407503872, z-1/18, z-1/8, z-1/9, (-3/34+z)^2, z-1/17, z-1/16", "dm_basis": null, "q": "0 1 -11 106 -981 8906 -79826 709113 -6259755 55003180", "yuk": "1 -1/3 7 -136/3 1237/3 -10876/3 30400 -722359/3 5952725/3 -49228048/3", "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":"1/18","im":"0","approx_re":"0.0555555555556","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/17","im":"0","approx_re":"0.0588235294118","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":"3/34","im":"0","approx_re":"0.0882352941176","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","2","2","3"],"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, -12*(3*X^2+3*X+1)^2, 3024*X^4+22464*X^3+31536*X^2+18144*X+4176, 10368*(3*X^2+3*X+1)*(3*X^2-21*X-35), -6718464*X^4-13436928*X^3+28366848*X^2+35085312*X+12192768, 8957952*(3*X^2+3*X+1)*(3*X^2+27*X-11), 2257403904*X^4-7739670528*X^3-13221937152*X^2-7739670528*X-1397440512, -7739670528*(3*X^2+3*X+1)^2, 557256278016*(X+1)^4]", "text": "Hadamard product $d \\ast f$. This operator has a second MUM-point at infinity with the same instanton numbers. Itg can be reduced to an operator of degree 4 with a single MUM-point defined over $Q(\\sqrt{?})$.", "degz": 8, "h3": null, "sol": "1 12 180 2352 6084 -1278288 -68988816 -2512105920 -70933293756 -1393810859472", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 1 -12 -72 -180 -216 -108 4176 18144 31536 22464 3024 -362880 -1306368 -1710720 -559872 93312 12192768 35085312 28366848 -13436928 -6718464 -98537472 -53747712 456855552 806215680 80621568 -1397440512 -7739670528 -13221937152 -7739670528 2257403904 -7739670528 -46438023168 -116095057920 -139314069504 -69657034752 557256278016 2229025112064 3343537668096 2229025112064 557256278016", "new_number": "8.13", "id": 456, "operator_tex": "\\theta^4-2^{2} 3 x\\left((3\\theta^2+3\\theta+1)^2\\right)+2^{4} 3^{2} x^{2}\\left(21\\theta^4+156\\theta^3+219\\theta^2+126\\theta+29\\right)+2^{7} 3^{4} x^{3}(3\\theta^2+3\\theta+1)(3\\theta^2-21\\theta-35)-2^{10} 3^{5} x^{4}\\left(27\\theta^4+54\\theta^3-114\\theta^2-141\\theta-49\\right)+2^{12} 3^{7} x^{5}(3\\theta^2+3\\theta+1)(3\\theta^2+27\\theta-11)+2^{14} 3^{8} x^{6}\\left(21\\theta^4-72\\theta^3-123\\theta^2-72\\theta-13\\right)-2^{17} 3^{10} x^{7}\\left((3\\theta^2+3\\theta+1)^2\\right)+2^{20} 3^{12} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "12 3020/3", "discriminant": "8 1 -108 3024 93312 -6718464 80621568 2257403904 -69657034752 557256278016", "aesz": "163", "n_sing_complex": "4", "inst_int": "", "c2h": null, "hash": "e21fd830a9dca03305deb8363a26fcf2", "dim_h": null, "inst": " 12 -96 3020/3 -71493/4 319584 -19126516/3 139598148 -12567360273/4 221121122720/3 -1788903000504", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "7", "laurent": null, "discriminant_tex": "(1728z^2-72z+1)(432z^2-36z+1)(-1+864z^2)^2", "discr_factors": "557256278016, (-1/864+z^2)^2, z^2-1/12*z+1/432, z^2-1/24*z+1/1728", "dm_basis": null, "q": "0 1 -24 630 -16064 426309 -11440656 310799594 -8551209216 237533688594", "yuk": "1 12 -756 27192 -1144644 39948012 -1377082728 47882164776 -1608623259588 53732432848152", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/72*6^(1/2)","im":"0","approx_re":"-0.034021","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":"1/48","im":"-1/144*3^(1/2)","approx_re":"0.0208333333333","approx_im":"-0.012028","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/48","im":"1/144*3^(1/2)","approx_re":"0.0208333333333","approx_im":"0.012028","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/72*6^(1/2)","im":"0","approx_re":"0.034021","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/24","im":"-1/72*3^(1/2)","approx_re":"0.0416666666667","approx_im":"-0.024056","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/24","im":"1/72*3^(1/2)","approx_re":"0.0416666666667","approx_im":"0.024056","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": "[169*X^4, -13*X*(56*X^3+178*X^2+115*X+26), -28466*X^4-109442*X^3-165603*X^2-117338*X-32448, -233114*X^4-1257906*X^3-2622815*X^2-2467842*X-872352, -989585*X^4-6852298*X^3-17737939*X^2-19969754*X-8108448, -(X+1)*(2458967*X^3+18007287*X^2+44047582*X+35386584), -9*(X+1)*(X+2)*(393163*X^2+2539029*X+4164444), -297*(X+3)*(X+2)*(X+1)*(8683*X+34604), -722007*(X+1)*(X+2)*(X+3)*(X+4)]", "text": "This opeerator is reducible to 6.25", "degz": 8, "h3": null, "sol": "1 0 12 96 1116 14040 186960 2610720 37725660 560071680", "n_discr_factors": "4", "c3": null, "operator": "4 8 0 0 0 0 169 0 -338 -1495 -2314 -728 -32448 -117338 -165603 -109442 -28466 -872352 -2467842 -2622815 -1257906 -233114 -8108448 -19969754 -17737939 -6852298 -989585 -35386584 -79434166 -62054869 -20466254 -2458967 -74959992 -158142510 -113110713 -33466662 -3538467 -61664328 -128524374 -90031689 -25750494 -2578851 -17328168 -36100350 -25270245 -7220070 -722007", "new_number": "8.35", "id": 480, "operator_tex": "13^{2} \\theta^4-13 x\\theta(56\\theta^3+178\\theta^2+115\\theta+26)-x^{2}\\left(28466\\theta^4+109442\\theta^3+165603\\theta^2+117338\\theta+32448\\right)-x^{3}\\left(233114\\theta^4+1257906\\theta^3+2622815\\theta^2+2467842\\theta+872352\\right)-x^{4}\\left(989585\\theta^4+6852298\\theta^3+17737939\\theta^2+19969754\\theta+8108448\\right)-x^{5}(\\theta+1)(2458967\\theta^3+18007287\\theta^2+44047582\\theta+35386584)-3^{2} x^{6}(\\theta+1)(\\theta+2)(393163\\theta^2+2539029\\theta+4164444)-3^{3} 11 x^{7}(\\theta+3)(\\theta+2)(\\theta+1)(8683\\theta+34604)-3^{3} 11^{2} 13 17 x^{8}(\\theta+1)(\\theta+2)(\\theta+3)(\\theta+4)", "superseek": "11/13 385/39", "discriminant": "8 169 -728 -28466 -233114 -989585 -2458967 -3538467 -2578851 -722007", "aesz": "326", "n_sing_complex": "4", "inst_int": "", "c2h": null, "hash": "946b91838924db64fe0ebdf0d473e621", "dim_h": null, "inst": " 11/13 30/13 385/39 672/13 4437/13 33128/13 270112/13 2353504/13 64766054/39 206251142/13", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "8", "laurent": null, "discriminant_tex": "-(3z+1)(13z^2+5z+1)(153z^3+75z^2+14z-1)(13+11z)^2", "discr_factors": "-722007, (13/11+z)^2, z^2+5/13*z+1/13, z+1/3, z^3+25/51*z^2+14/153*z-1/153", "dm_basis": null, "q": "0 1 -2 -17 -44 7 -368 -10515 -114376 -1076816", "yuk": "1 11/13 251/13 3476/13 43259/13 554636/13 7159364/13 92648427/13 1205037307/13 15738154598/13", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-13/11","im":"0","approx_re":"-1.18181818182","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/3","im":"0","approx_re":"-0.333333333333","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/612*(182836+18972*93^(1/2))^(1/3)+89/153/(182836+18972*93^(1/2))^(1/3)-25/153","im":"-1/2*3^(1/2)*(1/306*(182836+18972*93^(1/2))^(1/3)+178/153/(182836+18972*93^(1/2))^(1/3))","approx_re":"-0.272124","approx_im":"-0.216493","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/612*(182836+18972*93^(1/2))^(1/3)+89/153/(182836+18972*93^(1/2))^(1/3)-25/153","im":"1/2*3^(1/2)*(1/306*(182836+18972*93^(1/2))^(1/3)+178/153/(182836+18972*93^(1/2))^(1/3))","approx_re":"-0.272124","approx_im":"0.216493","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-5/26","im":"-3/26*3^(1/2)","approx_re":"-0.192307692308","approx_im":"-0.199852","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-5/26","im":"3/26*3^(1/2)","approx_re":"-0.192307692308","approx_im":"0.199852","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":"1/306*(182836+18972*93^(1/2))^(1/3)-178/153/(182836+18972*93^(1/2))^(1/3)-25/153","im":"0","approx_re":"0.054052","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","3","4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[169*X^4, -2028-15886*X-47931*X^2-64090*X^3-68237*X^4, 8428848*X^4+9027072*X^3+4331664*X^2+932256*X+74256, -427125120*X^4-483459072*X^3-304285312*X^2-95506944*X-12055680, 8797894656*X^4+12157919232*X^3+7559117824*X^2+2183858176*X+241950720, -63167811584*X^4-75064696832*X^3-28806516736*X^2-3414458368*X+11132928, 197529108480*X^4+363095654400*X^3+511946588160*X^2+348497510400*X+81711857664, -297271296*(X+1)*(2*X+1)*(646*X^2+1715*X+1044), 149824733184*(2*X+1)*(X+1)^2*(2*X+3)]", "text": "This is operator \"8.48\" from ...", "degz": 8, "h3": null, "sol": "1 12 852 94800 12860820 1952938512 319085101104 54888964663104 9809637738743700 1805590407439481520", "n_discr_factors": "2", "c3": null, "operator": "4 8 0 0 0 0 169 -2028 -15886 -47931 -64090 -68237 74256 932256 4331664 9027072 8428848 -12055680 -95506944 -304285312 -483459072 -427125120 241950720 2183858176 7559117824 12157919232 8797894656 11132928 -3414458368 -28806516736 -75064696832 -63167811584 81711857664 348497510400 511946588160 363095654400 197529108480 -310351233024 -1440873971712 -2342200541184 -1595752316928 -384074514432 449474199552 2097546264576 3445968863232 2397195730944 599298932736", "new_number": "8.48", "id": 494, "operator_tex": "13^{2} \\theta^4-13 x\\left(5249\\theta^4+4930\\theta^3+3687\\theta^2+1222\\theta+156\\right)+2^{4} 3 x^{2}\\left(175601\\theta^4+188064\\theta^3+90243\\theta^2+19422\\theta+1547\\right)-2^{7} x^{3}\\left(3336915\\theta^4+3777024\\theta^3+2377229\\theta^2+746148\\theta+94185\\right)+2^{10} x^{4}\\left(8591694\\theta^4+11872968\\theta^3+7381951\\theta^2+2132674\\theta+236280\\right)-2^{12} x^{5}\\left(15421829\\theta^4+18326342\\theta^3+7032841\\theta^2+833608\\theta-2718\\right)+2^{16} 3^{2} x^{6}\\left(334895\\theta^4+615600\\theta^3+867965\\theta^2+590850\\theta+138536\\right)-2^{19} 3^{4} 7 x^{7}(\\theta+1)(2\\theta+1)(646\\theta^2+1715\\theta+1044)+2^{22} 3^{6} 7^{2} x^{8}(2\\theta+1)(\\theta+1)^2(2\\theta+3)", "superseek": "359/13 393749/13", "discriminant": "8 169 -68237 8428848 -427125120 8797894656 -63167811584 197529108480 -384074514432 599298932736", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "de7301c14448dbf584c01cc3722d0e58", "dim_h": null, "inst": " 359/13 9162/13 393749/13 23364200/13 1734245216/13 11451266260 14071806017122/13 1425129757584576/13 11700454830043684 16920857571015804084/13", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "7", "laurent": null, "discriminant_tex": "(1-261z+6896z^2-6656z^3+36864z^4)(13-928z+4032z^2)^2", "discr_factors": "599298932736, (13/4032-29/126*z+z^2)^2, 1/36864-29/4096*z+431/2304*z^2-13/72*z^3+z^4", "dm_basis": null, "q": "0 1 -46 -157 -25568 -2139339 -212325770 -22783984499 -2572827342240 -302553146919569", "yuk": "1 359/13 73655/13 817814 1495382455/13 216780652359/13 32155166362958/13 4826629463873205/13 729666437378685367/13 8529631571102663450", "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":"29/252-1/504*2545^(1/2)","im":"0","approx_re":"0.014984","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"29/252+1/504*2545^(1/2)","im":"0","approx_re":"0.215175","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"#ND","im":"#ND","approx_re":"#ND","approx_im":"#ND","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":[]}]}, {"pols": "[X^4, -33*X^4-98*X^3-105*X^2-56*X-12, 272*X^4+2208*X^3+4872*X^2+4656*X+1728, 528*X^4-8160*X^3-45168*X^2-72960*X-40608, -1152*(2*X^2+6*X+5)*(4*X^2+12*X-31), 8448*X^4+231936*X^3+908544*X^2+1268736*X+557568, 69632*X^4+270336*X^3-79872*X^2-1449984*X-1529856, -135168*X^4-1220608*X^3-4116480*X^2-6111232*X-3342336, 65536*(X+3)^4]", "text": "This is operator \"8.55\" from ...", "degz": 8, "h3": null, "sol": "1 12 120 1216 13080 149664 1801312 22528512 290011032 3816913696", "n_discr_factors": "5", "c3": null, "operator": "4 8 0 0 0 0 1 -12 -56 -105 -98 -33 1728 4656 4872 2208 272 -40608 -72960 -45168 -8160 528 178560 145152 -34560 -55296 -9216 557568 1268736 908544 231936 8448 -1529856 -1449984 -79872 270336 69632 -3342336 -6111232 -4116480 -1220608 -135168 5308416 7077888 3538944 786432 65536", "new_number": "8.55", "id": 502, "operator_tex": "\\theta^4-x\\left(33\\theta^4+98\\theta^3+105\\theta^2+56\\theta+12\\right)+2^{3} x^{2}\\left(34\\theta^4+276\\theta^3+609\\theta^2+582\\theta+216\\right)+2^{4} 3 x^{3}\\left(11\\theta^4-170\\theta^3-941\\theta^2-1520\\theta-846\\right)-2^{7} 3^{2} x^{4}(2\\theta^2+6\\theta+5)(4\\theta^2+12\\theta-31)+2^{8} 3 x^{5}\\left(11\\theta^4+302\\theta^3+1183\\theta^2+1652\\theta+726\\right)+2^{11} x^{6}\\left(34\\theta^4+132\\theta^3-39\\theta^2-708\\theta-747\\right)-2^{12} x^{7}\\left(33\\theta^4+298\\theta^3+1005\\theta^2+1492\\theta+816\\right)+2^{16} x^{8}\\left((\\theta+3)^4\\right)", "superseek": "1 68/9", "discriminant": "8 1 -33 272 528 -9216 8448 69632 -135168 65536", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "39ed8ce7572bc79a333f77c892033bcf", "dim_h": null, "inst": " 1 -2 68/9 -30 150 -778 4374 -25438 463459/3 -960634", "cleanlist": "True", "n_sing_real": "7", "sol_explicit": "", "n_sing_rational": "5", "n_sing": "7", "laurent": null, "discriminant_tex": "(z-1)(16z-1)(16z^2-16z+1)(4z-1)^2(4z+1)^2", "discr_factors": "65536, (z-1/4)^2, (z+1/4)^2, z-1, z-1/16, z^2-z+1/16", "dm_basis": null, "q": "0 1 -8 52 -336 2226 -15040 103280 -719520 5072791", "yuk": "1 1 -15 205 -1935 18751 -167859 1500283 -13026191 112620742", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/4","im":"0","approx_re":"-0.25","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":"1/16","im":"0","approx_re":"0.0625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/2-1/4*3^(1/2)","im":"0","approx_re":"0.066987","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","0","-1","1"],"monodromy":[],"monodromy_dm":[]},{"re":"1/2+1/4*3^(1/2)","im":"0","approx_re":"0.933013","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":["3","3","3","3"],"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":[]}]}, {"pols": "[25*X^4, -3380*X^4-4120*X^3-3710*X^2-1650*X-300, 185584*X^4+413632*X^3+501164*X^2+305480*X+76320, -5544384*X^4-17179008*X^3-25159152*X^2-18009840*X-5113440, 99910656*X^4+385357824*X^3+644136192*X^2+508886784*X+154972224, -1120960512*X^4-5065998336*X^3-9322573824*X^2-7852363776*X-2491250688, 7686586368*X^4+39154876416*X^3+77370163200*X^2+67974266880*X+22084337664, -509607936*(X+1)^2*(58*X^2+208*X+201), 48922361856*(X+1)^2*(X+2)^2]", "text": "This is operator \"8.79\" from ...", "degz": 8, "h3": null, "sol": "1 12 204 4368 112140 3300912 107091024 3718116288 135443387916 5110962695760", "n_discr_factors": "4", "c3": null, "operator": "4 8 0 0 0 0 25 -300 -1650 -3710 -4120 -3380 76320 305480 501164 413632 185584 -5113440 -18009840 -25159152 -17179008 -5544384 154972224 508886784 644136192 385357824 99910656 -2491250688 -7852363776 -9322573824 -5065998336 -1120960512 22084337664 67974266880 77370163200 39154876416 7686586368 -102431195136 -310860840960 -343985356800 -165112971264 -29557260288 195689447424 587068342272 635990704128 293534171136 48922361856", "new_number": "8.79", "id": 528, "operator_tex": "5^{2} \\theta^4-2 5 x\\left(338\\theta^4+412\\theta^3+371\\theta^2+165\\theta+30\\right)+2^{2} x^{2}\\left(46396\\theta^4+103408\\theta^3+125291\\theta^2+76370\\theta+19080\\right)-2^{4} 3 x^{3}\\left(115508\\theta^4+357896\\theta^3+524149\\theta^2+375205\\theta+106530\\right)+2^{6} 3^{2} x^{4}\\left(173456\\theta^4+669024\\theta^3+1118292\\theta^2+883484\\theta+269049\\right)-2^{11} 3^{3} x^{5}\\left(20272\\theta^4+91616\\theta^3+168594\\theta^2+142006\\theta+45053\\right)+2^{14} 3^{4} x^{6}\\left(5792\\theta^4+29504\\theta^3+58300\\theta^2+51220\\theta+16641\\right)-2^{21} 3^{5} x^{7}(\\theta+1)^2(58\\theta^2+208\\theta+201)+2^{26} 3^{6} x^{8}(\\theta+1)^2(\\theta+2)^2", "superseek": "22/5 68", "discriminant": "8 25 -3380 185584 -5544384 99910656 -1120960512 7686586368 -29557260288 48922361856", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "064e5b590dd8b6a4daa1e905fbe693c2", "dim_h": null, "inst": " 22/5 8 68 3292/5 38826/5 1517408/15 7418706/5 115188852/5 1132445042/3 32217796776/5", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "5", "n_sing": "5", "laurent": null, "discriminant_tex": "(-1+48z)(16z-1)^2(48z-5)^2(12z-1)^3", "discr_factors": "48922361856, (z-1/12)^3, (z-1/16)^2, -1/48+z, (z-5/48)^2", "dm_basis": null, "q": "0 1 -18 233 -2988 33412 -382914 3792338 -42902088 352614016", "yuk": "1 22/5 342/5 9202/5 42206 4853272/5 109262898/5 508923236 58976903254/5 1375920735232/5", "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":"1/48","im":"0","approx_re":"0.0208333333333","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","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"1/12","im":"0","approx_re":"0.0833333333333","approx_im":"0.0","exponents":["0","1/2","3/2","2"],"monodromy":[],"monodromy_dm":[]},{"re":"5/48","im":"0","approx_re":"0.104166666667","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","2","2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -4*(3*X^2+3*X+1)*(11*X^2+11*X+3), 3856*X^4+15040*X^3+20848*X^2+11616*X+2320, -4224*X^4+25344*X^3+77696*X^2+58368*X+14976, 244736*X^4+489472*X^3-329728*X^2-574464*X-173056, 135168*X^4+1351680*X^3+757760*X^2-131072*X-151552, 3948544*X^4+393216*X^3-1163264*X^2+393216*X+376832, 131072*(3*X^2+3*X+1)*(11*X^2+11*X+3), 1048576*(X+1)^4]", "text": "Hadamard product $b\\ast d$. 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$Q(\\sqrt{?})$.", "degz": 8, "h3": "40", "sol": "1 12 380 16464 845676 48432912 2990911664 195076591680 13256109819628 929751677079312", "n_discr_factors": "3", "c3": "-30", "operator": "4 8 0 0 0 0 1 -12 -80 -212 -264 -132 2320 11616 20848 15040 3856 14976 58368 77696 25344 -4224 -173056 -574464 -329728 489472 244736 -151552 -131072 757760 1351680 135168 376832 393216 -1163264 393216 3948544 393216 2621440 6946816 8650752 4325376 1048576 4194304 6291456 4194304 1048576", "new_number": "8.7", "id": 529, "operator_tex": "\\theta^4-2^{2} x(3\\theta^2+3\\theta+1)(11\\theta^2+11\\theta+3)+2^{4} x^{2}\\left(241\\theta^4+940\\theta^3+1303\\theta^2+726\\theta+145\\right)-2^{7} x^{3}\\left(33\\theta^4-198\\theta^3-607\\theta^2-456\\theta-117\\right)+2^{10} x^{4}\\left(239\\theta^4+478\\theta^3-322\\theta^2-561\\theta-169\\right)+2^{12} x^{5}\\left(33\\theta^4+330\\theta^3+185\\theta^2-32\\theta-37\\right)+2^{14} x^{6}\\left(241\\theta^4+24\\theta^3-71\\theta^2+24\\theta+23\\right)+2^{17} x^{7}(3\\theta^2+3\\theta+1)(11\\theta^2+11\\theta+3)+2^{20} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "12 356", "discriminant": "8 1 -132 3856 -4224 244736 135168 3948544 4325376 1048576", "aesz": "106", "n_sing_complex": "2", "inst_int": "", "c2h": "76", "hash": "fe1c90929d18b81637eaaa93366409ed", "dim_h": "13", "inst": " 12 20 356 34561/4 161840 4245848 110102724 12708064929/4 95966999384 3019304295592", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "7", "laurent": null, "discriminant_tex": "(64z^2+88z-1)(16z^2+44z-1)(1+32z^2)^2", "discr_factors": "1048576, z^2+11/8*z-1/64, z^2+11/4*z-1/16, (1/32+z^2)^2", "dm_basis": null, "q": "0 1 -32 638 -10784 128433 -1511040 1810202 -116066944 -8653279804", "yuk": "1 12 172 9624 553148 20230012 917112952 37765234344 1626632864060 69959942560560", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-11/8-5/8*5^(1/2)","im":"0","approx_re":"-2.772542","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-11/16-5/16*5^(1/2)","im":"0","approx_re":"-1.386271","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"-1/8*2^(1/2)","approx_re":"0.0","approx_im":"-0.176777","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":"1/8*2^(1/2)","approx_re":"0.0","approx_im":"0.176777","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-11/16+5/16*5^(1/2)","im":"0","approx_re":"0.011271","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-11/8+5/8*5^(1/2)","im":"0","approx_re":"0.022542","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":[]}]}]}