{"count": 10, "status":"OK", "data":[{"pols": "[X^4, -3*(3*X+1)*(3*X+2)*(10*X^2+10*X+3), 81*(3*X+1)*(3*X+2)*(3*X+4)*(3*X+5)]", "text": "Hadamard product $B\\ast c$.", "degz": 2, "h3": "18", "sol": "1 18 1350 156240 22141350 3521185668 603258639984 108881071041600 20424293211323430 3946730690210665500", "n_discr_factors": "2", "c3": "-156", "operator": "4 2 0 0 0 0 1 -18 -141 -411 -540 -270 3240 18954 35721 26244 6561", "new_number": "2.10", "id": 1, "operator_tex": "\\theta^4-3 x(3\\theta+1)(3\\theta+2)(10\\theta^2+10\\theta+3)+3^{4} x^{2}(3\\theta+1)(3\\theta+2)(3\\theta+4)(3\\theta+5)", "superseek": "27 18089", "discriminant": "2 1 -270 6561", "aesz": "70", "n_sing_complex": "0", "inst_int": "", "c2h": "72", "hash": "3d2adae6eaf26a56c76b8b67d92cc5df", "dim_h": "9", "inst": " 27 432 18089 997785 68438142 5372412653 462553061328 42629254956495 4139005487642537 418758418475154936", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "A_{n}=\\dbinom{2n}{n}\\dbinom{3n}{n}\\sum_{k=0}^{n}\\dbinom{n}{k}^{2}\\dbinom{2k}{k}", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "(243z-1)(27z-1)", "discr_factors": "6561, z-1/243, z-1/27", "dm_basis": ["-377989751/500000000*I", "6", "1", "1", "-3", "-9", "-1", "0", "0", "18", "0", "0", "-18", "0", "0", "0"], "q": "0 1 -69 2196 -90131 1380525 -161041824 -7106675719 -979853201733 -98506835149437", "yuk": "1 27 3483 488430 63861723 8554767777 1160441624934 158655700035531 21826178601587163 3017335000491897903", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":["1","-1","1/2","-1/6","0","1","-1","1/2","0","0","1","-1","0","0","0","1"],"monodromy_dm":["1","0","0","0","1","1","0","0","0","18","1","0","0","0","1","1"]},{"re":"1/243","im":"0","approx_re":"0.00411522633745","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["1.+.755979502*I","0","26*lambda",".31750278e-1","3","1","1/2","-26*lambda","0","0","1","0","18","0","3","1.-.755979502*I"],"monodromy_dm":["1","-9","-1","-1","0","1","0","0","0","0","1","0","0","0","0","1"]},{"re":"1/27","im":"0","approx_re":"0.037037037037","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["4+468*lambda","-1.-.755979502*I","1/2+78*lambda","-.71415832e-1-52*lambda","9","-2","3/2","-1/2-78*lambda","18","-6","4","-1.-.755979502*I","54","-18","9","-2-468*lambda"],"monodromy_dm":["-5","-36","-4","-3","2","13","1333333/1000000","1","-18","-108","-11","-9","12","72","8","7"]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/3","2/3","4/3","5/3"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -48*(6*X+1)*(6*X+5)*(3*X^2+3*X+1), 4608*(6*X+1)*(6*X+5)*(6*X+7)*(6*X+11)]", "text": "Hadamard product D*d", "degz": 2, "h3": "8", "sol": "1 240 277200 457416960 904864680720 2004880295658240 4800744250465363200 12157214644290912768000 32101389251425947781270800 87536732232366403520671737600", "n_discr_factors": "2", "c3": "-470", "operator": "4 2 0 0 0 0 1 -240 -2448 -7632 -10368 -5184 1774080 15261696 31518720 23887872 5971968", "new_number": "2.16", "id": 7, "operator_tex": "\\theta^4-2^{4} 3 x(6\\theta+1)(6\\theta+5)(3\\theta^2+3\\theta+1)+2^{9} 3^{2} x^{2}(6\\theta+1)(6\\theta+5)(6\\theta+7)(6\\theta+11)", "superseek": "240 19105840", "discriminant": "2 1 -5184 5971968", "aesz": "65", "n_sing_complex": "0", "inst_int": "", "c2h": "92", "hash": "13ba368bcbb10731ac8727b510731ff2", "dim_h": "9", "inst": " 240 57102 19105840 14810143935 10017820614480 9034594808517046 8180523747618348912 8386469469367204264761 8771159613625367710446208 9733175830090381917603283770", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "A_{n}=\\dbinom{3n}{n}\\dbinom{6n}{3n}\\sum_{k=0}^{n}\\dbinom{n}{k}\\dbinom{2k}{k}\\dbinom{2n-2k}{n-k}", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "(3456z-1)(1728z-1)", "discr_factors": "5971968, z-1/3456, z-1/1728", "dm_basis": ["-284703819/125000000*I", "31/6", "1", "1", "-23/6", "-4", "-1", "0", "0", "8", "0", "0", "-8", "0", "0", "0"], "q": "0 1 -1488 1737216 -1936036864 2030351668656 -2106830943512064 2118312344000340992 -2135004674764250185728 2095472552315219510339736", "yuk": "1 240 457056 515857920 947849668896 1252227576810240 1951472479155996672 2805919645433093677056 4293872368316956433226528 6394175358332893061431143552", "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","8","1","0","0","0","1","1"]},{"re":"1/3456","im":"0","approx_re":"0.000289351851852","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["1.+2.277630552*I","0","1.091364639*I",".648450116","23/6","1","529/288","-1.091364639*I","0","0","1","0","8","0","23/6","1.-2.277630552*I"],"monodromy_dm":["1","-9","-1","-1","0","1","0","0","0","0","1","0","0","0","0","1"]},{"re":"1/1728","im":"0","approx_re":"0.000578703703704","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["37/12+940*lambda","-.52083333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333-1.138815272*I",".99826388888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888889+2.182729279*I","1.025632871-1.186265914*I","23/3+1/250000000*I","-11/12+3/1000000000*I","529/144-1/250000000*I","-.99826388888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888889-2.182729279*I","4+1/500000000*I","-1+1/1000000000*I","35/12-1/500000000*I","-25/48-235*lambda","16+9/1000000000*I","-3.999999988+.50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-8*I","23/3-1/125000000*I","-13/12-940*lambda"],"monodromy_dm":["-3","-20","-5/2","-2","1","6","5/8","1/2","-4","-20","-3/2","-2","3","15","15/8","5/2"]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/6","5/6","7/6","11/6"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -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": "[25*X^4, -200-1550*X-4545*X^2-5990*X^3-2035*X^4, -87040-518400*X-1069824*X^2-895872*X^3-269184*X^4, -409600-3932160*X-12619776*X^2-15728640*X^3-5681152*X^4, -2097152*(2*X+1)^4]", "text": "Sporadic Operator. There is a second MUM-point hiding at infinity, corresponding to Operator AESZ225/4.43", "degz": 4, "h3": "20", "sol": "1 8 504 36800 3518200 365275008 41121267264 4856185331712 596136147492600 75323913126862400", "n_discr_factors": "2", "c3": "-128", "operator": "4 4 0 0 0 0 25 -200 -1550 -4545 -5990 -2035 -87040 -518400 -1069824 -895872 -269184 -409600 -3932160 -12619776 -15728640 -5681152 -2097152 -16777216 -50331648 -67108864 -33554432", "new_number": "4.42", "id": 140, "operator_tex": "5^{2} \\theta^4-5 x\\left(407\\theta^4+1198\\theta^3+909\\theta^2+310\\theta+40\\right)-2^{7} x^{2}\\left(2103\\theta^4+6999\\theta^3+8358\\theta^2+4050\\theta+680\\right)-2^{12} x^{3}\\left(1387\\theta^4+3840\\theta^3+3081\\theta^2+960\\theta+100\\right)-2^{21} x^{4}\\left((2\\theta+1)^4\\right)", "superseek": "69/5 29081/5", "discriminant": "4 25 -2035 -269184 -5681152 -33554432", "aesz": "222", "n_sing_complex": "1", "inst_int": "", "c2h": "68", "hash": "aad7a72e711c9c463396d319e0bf7603", "dim_h": "9", "inst": " 69/5 1383/4 29081/5 346080 72023607/5 3784067515/4 281702428686/5 20053762156416/5 1409669129591222/5 85799281232555565/4", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "3", "laurent": null, "discriminant_tex": "-(8192z^2+107z-1)(5+64z)^2", "discr_factors": "-33554432, z^2+107/8192*z-1/8192, (5/64+z)^2", "dm_basis": null, "q": "0 1 -30 -507 15896 -864690 -19722342 -2270250854 -140407232352 -12748761975909", "yuk": "1 69/5 13899/5 785256/5 110759499/5 9002950944/5 1021699028136/5 96623933039367/5 10267526334844491/5 1027648795472786094/5", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-5/64","im":"0","approx_re":"-0.078125","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-107/16384-51/16384*17^(1/2)","im":"0","approx_re":"-0.019365","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":"-107/16384+51/16384*17^(1/2)","im":"0","approx_re":"0.006304","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","1/2","1/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -594*X^4-216*X^3-234*X^2-126*X-24, 137052*X^4+128304*X^3+136728*X^2+60588*X+10224, -15274008*X^4-26453952*X^3-28308528*X^2-14224248*X-2807136, 816293376*X^4+2244806784*X^3+2692634400*X^2+1527715728*X+331304256, -51018336*(3*X+2)*(3*X+4)*(6*X+5)*(6*X+7)]", "text": "This is operator \"5.12\" from ...", "degz": 5, "h3": "72", "sol": "1 24 1152 71520 5101200 396676224 32692889376 2808042450048 248675352512400 22544379039811200", "n_discr_factors": "3", "c3": "450", "operator": "4 5 0 0 0 0 1 -24 -126 -234 -216 -594 10224 60588 136728 128304 137052 -2807136 -14224248 -28308528 -26453952 -15274008 331304256 1527715728 2692634400 2244806784 816293376 -14285134080 -61528113216 -96883820064 -66119763456 -16529940864", "new_number": "5.12", "id": 214, "operator_tex": "\\theta^4-2 3 x\\left(99\\theta^4+36\\theta^3+39\\theta^2+21\\theta+4\\right)+2^{2} 3^{2} x^{2}\\left(3807\\theta^4+3564\\theta^3+3798\\theta^2+1683\\theta+284\\right)-2^{3} 3^{5} x^{3}\\left(7857\\theta^4+13608\\theta^3+14562\\theta^2+7317\\theta+1444\\right)+2^{4} 3^{9} x^{4}\\left(2592\\theta^4+7128\\theta^3+8550\\theta^2+4851\\theta+1052\\right)-2^{5} 3^{13} x^{5}(3\\theta+2)(3\\theta+4)(6\\theta+5)(6\\theta+7)", "superseek": "-30 -14632", "discriminant": "5 1 -594 137052 -15274008 816293376 -16529940864", "aesz": "74", "n_sing_complex": "0", "inst_int": "", "c2h": "-36", "hash": "e668180adb7c88d4e5fbab5eb7ee61c7", "dim_h": "9", "inst": " -30 -516 -14632 -4227807/8 -22139868 -1021798708 -50464650036 -2619966661332 -141334834087546 -7859316901635348", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "-(-1+54z)(162z-1)^2(108z-1)^2", "discr_factors": "-16529940864, (z-1/108)^2, -1/54+z, (z-1/162)^2", "dm_basis": null, "q": "0 1 -30 495 -8236 58839 -2049570 -24155251 -973292856 1233846432", "yuk": "1 -30 -4158 -395094 -33826614 -2767483530 -220708920150 -17309374962378 -1341422964428598 -103033094050216128", "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":"1/162","im":"0","approx_re":"0.00617283950617","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/108","im":"0","approx_re":"0.00925925925926","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"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":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["2/3","5/6","7/6","4/3"],"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": "[529*X^4, -75233*X^4-116794*X^3-89608*X^2-31211*X-4232, 1357863*X^4+999924*X^3-787393*X^2-850862*X-205712, -6206392*X^4+2179848*X^3+1750568*X^2-1413672*X-801872, -980880*X^4+15278304*X^3+35445392*X^2+27267488*X+7128704, -1905152*(4*X+3)*(X+1)^2*(4*X+5)]", "text": "This is operator \"5.51\" from ...", "degz": 5, "h3": "23", "sol": "1 8 324 19304 1388260 111469008 9620458344 873705161232 82410223605732 8003897628341120", "n_discr_factors": "2", "c3": "-74", "operator": "4 5 0 0 0 0 529 -4232 -31211 -89608 -116794 -75233 -205712 -850862 -787393 999924 1357863 -801872 -1413672 1750568 2179848 -6206392 7128704 27267488 35445392 15278304 -980880 -28577280 -118119424 -180989440 -121929728 -30482432", "new_number": "5.51", "id": 262, "operator_tex": "23^{2} \\theta^4-23 x\\left(3271\\theta^4+5078\\theta^3+3896\\theta^2+1357\\theta+184\\right)+x^{2}\\left(1357863\\theta^4+999924\\theta^3-787393\\theta^2-850862\\theta-205712\\right)-2^{3} x^{3}\\left(775799\\theta^4-272481\\theta^3-218821\\theta^2+176709\\theta+100234\\right)-2^{4} 61 x^{4}\\left(1005\\theta^4-15654\\theta^3-36317\\theta^2-27938\\theta-7304\\right)-2^{9} 61^{2} x^{5}(4\\theta+3)(\\theta+1)^2(4\\theta+5)", "superseek": "308/23 70799/23", "discriminant": "5 529 -75233 1357863 -6206392 -980880 -30482432", "aesz": "250", "n_sing_complex": "2", "inst_int": "", "c2h": "62", "hash": "9c19794a84073d1c6dfd11c8a7c9a740", "dim_h": "9", "inst": " 308/23 3526/23 70799/23 2148684/23 81402822/23 3517706942/23 166755728017/23 8463817366930/23 452628943972573/23 25225062363800138/23", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "5", "laurent": null, "discriminant_tex": "-(512z^3+113z^2+121z-1)(-23+244z)^2", "discr_factors": "-30482432, (-23/244+z)^2, z^3+113/512*z^2+121/512*z-1/512", "dm_basis": null, "q": "0 1 -27 31 -1565 -122872 -6002087 -316779981 -17953605095 -1060383625879", "yuk": "1 308/23 28516/23 1911881/23 137544292/23 10175353058/23 759826639561/23 57197214710139/23 4333474629412452/23 329966500157917598/23", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/3072*(33598639+5035776*249^(1/2))^(1/3)+173087/3072/(33598639+5035776*249^(1/2))^(1/3)-113/1536","im":"-1/2*3^(1/2)*(1/1536*(33598639+5035776*249^(1/2))^(1/3)+173087/1536/(33598639+5035776*249^(1/2))^(1/3))","approx_re":"-0.114451","approx_im":"-0.474453","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/3072*(33598639+5035776*249^(1/2))^(1/3)+173087/3072/(33598639+5035776*249^(1/2))^(1/3)-113/1536","im":"1/2*3^(1/2)*(1/1536*(33598639+5035776*249^(1/2))^(1/3)+173087/1536/(33598639+5035776*249^(1/2))^(1/3))","approx_re":"-0.114451","approx_im":"0.474453","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":"1/1536*(33598639+5035776*249^(1/2))^(1/3)-173087/1536/(33598639+5035776*249^(1/2))^(1/3)-113/1536","im":"0","approx_re":"0.008199","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"23/244","im":"0","approx_re":"0.094262295082","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":["3/4","1","1","5/4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[441*X^4, -69069*X^4-128058*X^3-97545*X^2-33516*X-4410, 154240*X^4-923360*X^3-2137700*X^2-1348200*X-272580, 1706176*X^4+7894656*X^3+6723376*X^2+1861776*X+97440, -1280*(2*X+1)*(1916*X^3+2622*X^2+1077*X+91), -102400*(2*X+1)*(X+1)^2*(2*X+3)]", "text": "This is operator \"5.70\" from ...", "degz": 5, "h3": "21", "sol": "1 10 510 38260 3473470 352297260 38418834300 4409395247400 525660485471550 64530507898499500", "n_discr_factors": "2", "c3": "-104", "operator": "4 5 0 0 0 0 441 -4410 -33516 -97545 -128058 -69069 -272580 -1348200 -2137700 -923360 154240 97440 1861776 6723376 7894656 1706176 -116480 -1611520 -6113280 -9164800 -4904960 -307200 -1433600 -2355200 -1638400 -409600", "new_number": "5.70", "id": 283, "operator_tex": "3^{2} 7^{2} \\theta^4-3 7 x\\left(3289\\theta^4+6098\\theta^3+4645\\theta^2+1596\\theta+210\\right)+2^{2} 5 x^{2}\\left(7712\\theta^4-46168\\theta^3-106885\\theta^2-67410\\theta-13629\\right)+2^{4} x^{3}\\left(106636\\theta^4+493416\\theta^3+420211\\theta^2+116361\\theta+6090\\right)-2^{8} 5 x^{4}(2\\theta+1)(1916\\theta^3+2622\\theta^2+1077\\theta+91)-2^{12} 5^{2} x^{5}(2\\theta+1)(\\theta+1)^2(2\\theta+3)", "superseek": "361/21 120472/21", "discriminant": "5 441 -69069 154240 1706176 -4904960 -409600", "aesz": "287", "n_sing_complex": "3", "inst_int": "", "c2h": "66", "hash": "97932196c46a8712f6dcb11165d698be", "dim_h": "9", "inst": " 361/21 4780/21 120472/21 1537864/7 216261320/21 551815860 227115423676/7 42888879100432/21 2844347183044252/21 28081588564888700/3", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "5", "laurent": null, "discriminant_tex": "-(64z^3+800z^2+149z-1)(-21+80z)^2", "discr_factors": "-409600, z^3+25/2*z^2+149/64*z-1/64, (-21/80+z)^2", "dm_basis": null, "q": "0 1 -36 176 -3368 -308928 -16116704 -1091407860 -76859141872 -5629218172992", "yuk": "1 361/21 12867/7 3253105/21 14062309 27032665361/21 834346677435/7 233701770962965/21 21959106394729673/21 2073529096442512813/21", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/48*(-932842+2607*I*237^(1/2))^(1/3)-9553/48/(-932842+2607*I*237^(1/2))^(1/3)-25/6+1/2*I*3^(1/2)*(1/24*(-932842+2607*I*237^(1/2))^(1/3)-9553/24/(-932842+2607*I*237^(1/2))^(1/3))","im":"0","approx_re":"-12.310784","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/48*(-932842+2607*I*237^(1/2))^(1/3)-9553/48/(-932842+2607*I*237^(1/2))^(1/3)-25/6-1/2*I*3^(1/2)*(1/24*(-932842+2607*I*237^(1/2))^(1/3)-9553/24/(-932842+2607*I*237^(1/2))^(1/3))","im":"0","approx_re":"-0.195701","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":"1/24*(-932842+2607*I*237^(1/2))^(1/3)+9553/24/(-932842+2607*I*237^(1/2))^(1/3)-25/6","im":"0","approx_re":"0.006485","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"21/80","im":"0","approx_re":"0.2625","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","1","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[121*X^4, -1210-9075*X-26323*X^2-34496*X^3-16687*X^4, -24266-106953*X-202166*X^2-207620*X^3-90362*X^4, -53130-217437*X-415082*X^2-507996*X^3-245714*X^4, -15226-183269*X-564786*X^2-785972*X^3-407863*X^4, -25160-279826*X-728323*X^2-790148*X^3-434831*X^4, -61152-303576*X-586744*X^2-562248*X^3-290888*X^4, -39040-172960*X-310160*X^2-274400*X^3-104560*X^4, -12800*(X+1)^4]", "text": "This operator has a second MUM-point at infinity corresponding to operator 8.27.", "degz": 8, "h3": "22", "sol": "1 10 466 32392 2727826 256793260 25999151200 2770767256960 306741044897170 34970581120268260", "n_discr_factors": "3", "c3": "-84", "operator": "4 8 0 0 0 0 121 -1210 -9075 -26323 -34496 -16687 -24266 -106953 -202166 -207620 -90362 -53130 -217437 -415082 -507996 -245714 -15226 -183269 -564786 -785972 -407863 -25160 -279826 -728323 -790148 -434831 -61152 -303576 -586744 -562248 -290888 -39040 -172960 -310160 -274400 -104560 -12800 -51200 -76800 -51200 -12800", "new_number": "8.26", "id": 470, "operator_tex": "11^{2} \\theta^4-11 x\\left(1517\\theta^4+3136\\theta^3+2393\\theta^2+825\\theta+110\\right)-x^{2}\\left(24266+106953\\theta+202166\\theta^2+207620\\theta^3+90362\\theta^4\\right)-x^{3}\\left(53130+217437\\theta+415082\\theta^2+507996\\theta^3+245714\\theta^4\\right)-x^{4}\\left(15226+183269\\theta+564786\\theta^2+785972\\theta^3+407863\\theta^4\\right)-x^{5}\\left(25160+279826\\theta+728323\\theta^2+790148\\theta^3+434831\\theta^4\\right)-2^{3} x^{6}\\left(36361\\theta^4+70281\\theta^3+73343\\theta^2+37947\\theta+7644\\right)-2^{4} 5 x^{7}\\left(1307\\theta^4+3430\\theta^3+3877\\theta^2+2162\\theta+488\\right)-2^{9} 5^{2} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "193/11 48570/11", "discriminant": "8 121 -16687 -90362 -245714 -407863 -434831 -290888 -104560 -12800", "aesz": "301", "n_sing_complex": "2", "inst_int": "", "c2h": "64", "hash": "a91db18876a9dfbf42b88f8d64c55d85", "dim_h": "9", "inst": " 193/11 1973/11 48570/11 1689283/11 72444183/11 3550769296/11 190951621547/11 10993183799383/11 666771302469817/11 42142859324558057/11", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "6", "laurent": null, "discriminant_tex": "-(-1+143z+32z^2)(z+1)^2(20z^2+17z+11)^2", "discr_factors": "-12800, (z+1)^2, -1/32+143/32*z+z^2, (z^2+17/20*z+11/20)^2", "dm_basis": null, "q": "0 1 -35 279 -5371 -178284 -10060533 -618825298 -39747432347 -2664472529088", "yuk": "1 193/11 15977/11 1311583/11 108130089/11 9055523068/11 766967495303/11 65496406190814/11 5628510213414185/11 486076279501808176/11", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-143/64-19/64*57^(1/2)","im":"0","approx_re":"-4.475732","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","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"-17/40","im":"-1/40*591^(1/2)","approx_re":"-0.425","approx_im":"-0.607762","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-17/40","im":"1/40*591^(1/2)","approx_re":"-0.425","approx_im":"0.607762","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":"-143/64+19/64*57^(1/2)","im":"0","approx_re":"0.006982","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":[]}]}]}