{"count": 6, "status":"OK", "data":[{"pols": "[X^4, -16*(2*X+1)^2*(3*X^2+3*X+1), 512*(2*X+1)^2*(2*X+3)^2]", "text": "A*d", "degz": 2, "h3": "32", "sol": "1 16 720 44800 3312400 273321216 24329200896 2287879925760 224190869245200 22677180755257600", "n_discr_factors": "2", "c3": "-88", "operator": "4 2 0 0 0 0 1 -16 -112 -304 -384 -192 4608 24576 45056 32768 8192", "new_number": "2.13", "id": 4, "operator_tex": "\\theta^4-2^{4} x(2\\theta+1)^2(3\\theta^2+3\\theta+1)+2^{9} x^{2}(2\\theta+1)^2(2\\theta+3)^2", "superseek": "16 1232", "discriminant": "2 1 -192 8192", "aesz": "36", "n_sing_complex": "0", "inst_int": "", "c2h": "80", "hash": "dea6fdf568a5907a24ba30fef2caf124", "dim_h": "12", "inst": " 16 42 1232 32159 990128 34017058 1281309072 51913355161 2217439126912 98646336990894", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "A_{n}=\\dbinom{2n}{n}^2\\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": "(128z-1)(64z-1)", "discr_factors": "8192, z-1/128, z-1/64", "dm_basis": ["-88*lambda", "26/3", "1", "1", "-10/3", "-16", "-1", "0", "0", "32", "0", "0", "-32", "0", "0", "0"], "q": "0 1 -48 1536 -44032 1041840 -25188864 473850880 -12342362112 111270160536", "yuk": "1 16 352 33280 2058528 123766016 7347718144 439489011712 26579639900960 1616513123552128", "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","32","1","0","0","0","1","1"]},{"re":"1/128","im":"0","approx_re":"0.0078125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["1+88*lambda","0","55/6*lambda",".5683112e-2","10/3","1","25/72","-55/6*lambda","0","0","1","0","32","0","10/3","1-88*lambda"],"monodromy_dm":["1","-12","-1","-1","0","1","0","0","0","0","1","0","0","0","0","1"]},{"re":"1/64","im":"0","approx_re":"0.015625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["10/3+176*lambda","-7/12-44*lambda","35/144+55/3*lambda","-.73703221e-1-77/6*lambda","20/3+1/500000000*I","-2/3+1/1000000000*I","25/36","-35/144-55/3*lambda","16+1/200000000*I","-4+1/500000000*I","8/3-1/500000000*I","-7/12-44*lambda","64.+.23e-7*I","-15.999999981+.90000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-8*I","20/3-1/125000000*I","-4/3-176*lambda"],"monodromy_dm":["-3","-32","-5/2","-2","1","9","5/8","1/2","-16","-128","-9","-8","12","96","15/2","7"]},{"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, -48*(6*X+1)*(6*X+5)*(8*X^2+8*X+3), 36864*(6*X+1)*(6*X+5)*(6*X+7)*(6*X+11)]", "text": "", "degz": 2, "h3": null, "sol": "1 720 2273040 9605756160 46308725583120 240786868817214720 1315120893663838060800 7435757049324458453913600 43135804200964730778389552400 255247151546465636305978354924800", "n_discr_factors": "1", "c3": null, "operator": "4 2 0 0 0 0 1 -720 -7104 -20928 -27648 -13824 14192640 122093568 252149760 191102976 47775744", "new_number": "2.19", "id": 10, "operator_tex": "\\theta^4-2^{4} 3 x(6\\theta+1)(6\\theta+5)(8\\theta^2+8\\theta+3)+2^{12} 3^{2} x^{2}(6\\theta+1)(6\\theta+5)(6\\theta+7)(6\\theta+11)", "superseek": "-288 -96055968", "discriminant": "2 1 -13824 47775744", "aesz": "112", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "9a988f0cb0ca922885043cdadf98dd79", "dim_h": null, "inst": " -288 162504 -96055968 106571782296 -135291308081760 202640200069218600 -331236087493837278240 582773446380820280519448 -1081357063366546927831256832 2094880412576670910662188706840", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "A_{n}=\\dbinom{3n}{n}\\dbinom{6n}{3n}\\sum_{k=0}^{n}4^{n-k}\\dbinom{2k}{k}^2\\dbinom{2n-2k}{n-k}", "n_sing_rational": "2", "n_sing": "2", "laurent": null, "discriminant_tex": "(6912z-1)^2", "discr_factors": "47775744, (z-1/6912)^2", "dm_basis": ["7/6+96920449/100000000*I", "-4/3", "1/2", "1", "5/3", "0", "-1", "0", "2", "-4", "0", "0", "4", "0", "0", "0"], "q": "0 1 -4224 15018336 -49622038528 157618249425456 -488487774278467584 1488716329019728343552 -4482147177792048362422272 13370796738913860479184841368", "yuk": "1 -288 1299744 -2593511424 6820595366688 -16911413510220288 43770283212359006208 -113613978010386186436608 298380004546986804221324064 -788309299194212710391579741952", "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","-4","1","0","0","0","1","1"]},{"re":"1/6912","im":"0","approx_re":"0.000144675925926","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":["-.16666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666667-.969204490*I","-100*lambda","-35/72-250/3*lambda","-.234839336","-5/3","1/6","-25/36","-35/72+250/3*lambda","-2","0","1/6","100*lambda","-4","-2","-5/3","-.16666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666667+.969204490*I"],"monodromy_dm":["-3","3","0","-1","-1","1","1/4","0","0","0","1","0","1","0","-1/4","1"]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/6","5/6","7/6","11/6"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, 168*X^4+336*X^3+240*X^2+72*X+8, -64*(X+1)^2*(96*X^2+192*X+77), 12800*(X+1)*(X+2)*(2*X+1)*(2*X+5)]", "text": "Operator equivalent to AESZ 328", "degz": 3, "h3": null, "sol": "1 -8 720 -68480 8123920 -1070471808 151600990464 -22585925007360 3494359788725520 -556633716248804480", "n_discr_factors": "2", "c3": null, "operator": "4 3 0 0 0 0 1 8 72 240 336 168 -4928 -22144 -35648 -24576 -6144 128000 499200 627200 307200 51200", "new_number": "3.15", "id": 75, "operator_tex": "\\theta^4+2^{3} x\\left(21\\theta^4+42\\theta^3+30\\theta^2+9\\theta+1\\right)-2^{6} x^{2}(\\theta+1)^2(96\\theta^2+192\\theta+77)+2^{9} 5^{2} x^{3}(\\theta+1)(\\theta+2)(2\\theta+1)(2\\theta+5)", "superseek": "-32 -16288", "discriminant": "3 1 168 -6144 51200", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "e21c92d8f9a2222be40fdc71ea51ee35", "dim_h": null, "inst": " -32 468 -16288 1681645/2 -53608288 3907375492 -312636871456 53569620608583/2 -2417943264831744 227473709385640668", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "(200z+1)(-1+16z)^2", "discr_factors": "51200, (-1/16+z)^2, z+1/200", "dm_basis": ["-17/12-58*lambda", "17/6", "1/2", "1", "-25/6", "0", "-1", "0", "-8", "16", "0", "0", "-16", "0", "0", "0"], "q": "0 1 40 -400 -5888 -1120272 92443392 -7633773824 738647261184 -73820785132648", "yuk": "1 -32 3712 -439808 53816352 -6701036032 843992670208 -107234446909440 13713822929613600 -1762680640062781184", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/200","im":"0","approx_re":"-0.005","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/16","im":"0","approx_re":"0.0625","approx_im":"0.0","exponents":["0","1/6","5/6","1"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/2","1","2","5/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -396*X^4-312*X^3-260*X^2-104*X-16, 60032*X^4+88448*X^3+81216*X^2+35456*X+5888, -4271104*X^4-8945664*X^3-8898560*X^2-4042752*X-696320, 163840*(2*X+1)*(418*X^3+951*X^2+846*X+260), -39321600*(2*X+1)*(3*X+2)*(3*X+4)*(2*X+3)]", "text": "This is operator \"5.108\" from ...", "degz": 5, "h3": "64", "sol": "1 16 720 44800 3245200 256386816 21423257856 1861674946560 166539035005200 15234386035897600", "n_discr_factors": "3", "c3": "-36", "operator": "4 5 0 0 0 0 1 -16 -104 -260 -312 -396 5888 35456 81216 88448 60032 -696320 -4042752 -8898560 -8945664 -4271104 42598400 223805440 433029120 380108800 136970240 -943718400 -4639948800 -7982284800 -5662310400 -1415577600", "new_number": "5.108", "id": 190, "operator_tex": "\\theta^4-2^{2} x\\left(99\\theta^4+78\\theta^3+65\\theta^2+26\\theta+4\\right)+2^{6} x^{2}\\left(938\\theta^4+1382\\theta^3+1269\\theta^2+554\\theta+92\\right)-2^{10} x^{3}\\left(4171\\theta^4+8736\\theta^3+8690\\theta^2+3948\\theta+680\\right)+2^{15} 5 x^{4}(2\\theta+1)(418\\theta^3+951\\theta^2+846\\theta+260)-2^{19} 3 5^{2} x^{5}(2\\theta+1)(3\\theta+2)(3\\theta+4)(2\\theta+3)", "superseek": "4 1268", "discriminant": "5 1 -396 60032 -4271104 136970240 -1415577600", "aesz": "365", "n_sing_complex": "0", "inst_int": "", "c2h": "112", "hash": "f84624e83cd4eb2cc90693bd5627efcf", "dim_h": "20", "inst": " 4 107/2 1268 89439/4 396908 15177407/2 157176420 14114736207/4 86763346976 4638040656201/2", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "-(108z-1)(2048z^2-128z+1)(-1+80z)^2", "discr_factors": "-1415577600, (-1/80+z)^2, z-1/108, z^2-1/16*z+1/2048", "dm_basis": null, "q": "0 1 -40 832 -14592 262032 -3793664 56464896 -757760000 10626762520", "yuk": "1 4 432 34240 1431456 49613504 1639194624 53911512064 1806687665952 63250479979744", "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":"1/32-1/64*2^(1/2)","im":"0","approx_re":"0.009153","approx_im":"0.0","exponents":["0","1","1","2"],"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":"1/80","im":"0","approx_re":"0.0125","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/32+1/64*2^(1/2)","im":"0","approx_re":"0.053347","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","4/3","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[49*X^4, 7*X*(-14-73*X-118*X^2+13*X^3), -56448-267792*X-452856*X^2-322704*X^3-81072*X^4, -2325456-9761472*X-13680576*X^2-7741440*X^3-1567296*X^4, -6912*(2*X+1)*(572*X^3+2370*X^2+2896*X+1095), -82944*(2*X+1)*(6*X+5)*(6*X+7)*(2*X+3)]", "text": "This is operator \"5.34\" from ...", "degz": 5, "h3": "42", "sol": "1 0 72 720 37800 907200 36867600 1210809600 47562114600 1773634262400", "n_discr_factors": "4", "c3": "-112", "operator": "4 5 0 0 0 0 49 0 -98 -511 -826 91 -56448 -267792 -452856 -322704 -81072 -2325456 -9761472 -13680576 -7741440 -1567296 -7568640 -35154432 -56415744 -36716544 -7907328 -8709120 -41140224 -68345856 -47775744 -11943936", "new_number": "5.34", "id": 243, "operator_tex": "7^{2} \\theta^4+7 x\\theta(-14-73\\theta-118\\theta^2+13\\theta^3)-2^{3} 3 x^{2}\\left(3378\\theta^4+13446\\theta^3+18869\\theta^2+11158\\theta+2352\\right)-2^{4} 3^{3} x^{3}\\left(3628\\theta^4+17920\\theta^3+31668\\theta^2+22596\\theta+5383\\right)-2^{8} 3^{3} x^{4}(2\\theta+1)(572\\theta^3+2370\\theta^2+2896\\theta+1095)-2^{10} 3^{4} x^{5}(2\\theta+1)(6\\theta+5)(6\\theta+7)(2\\theta+3)", "superseek": "17/7 5095/21", "discriminant": "5 49 91 -81072 -1567296 -7907328 -11943936", "aesz": "217", "n_sing_complex": "0", "inst_int": "", "c2h": "84", "hash": "e8743aeac19deca699ff90aaef6b8ea7", "dim_h": "14", "inst": " 17/7 254/7 5095/21 29600/7 491991/7 4555616/3 232427670/7 5701763664/7 143522855316/7 3818318314434/7", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "5", "n_sing": "5", "laurent": null, "discriminant_tex": "-(16z+1)(27z+1)(48z-1)(7+24z)^2", "discr_factors": "-11943936, (7/24+z)^2, z+1/27, z+1/16, z-1/48", "dm_basis": null, "q": "0 1 -2 -195 -904 6482 -107274 -6762194 -156595136 -4062227319", "yuk": "1 17/7 2049/7 45872/7 1896449/7 8785556 2296078368/7 79722690827/7 2919304892417/7 104628161571236/7", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-7/24","im":"0","approx_re":"-0.291666666667","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":"-1/27","im":"0","approx_re":"-0.037037037037","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":"1/48","im":"0","approx_re":"0.0208333333333","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": "[X^4, -48*(6*X+1)*(4*X+1)*(4*X+3)*(6*X+5)]", "text": "A-incarnation: X(3,4) in P^5(1,1,1,1,1,2)", "degz": 1, "h3": "2", "sol": "1 720 5821200 75473798400 1205906199498000 21687788871739710720 420947933228872374124800 8617212693271828524003840000 183473821651629217228869993930000 4026236119819439554462540885178400000", "n_discr_factors": "1", "c3": "-156", "operator": "4 1 0 0 0 0 1 -720 -9024 -36672 -55296 -27648", "new_number": "1.12", "id": 552, "operator_tex": "\\theta^4-2^{4} 3 x(6\\theta+1)(4\\theta+1)(4\\theta+3)(6\\theta+5)", "superseek": "7776 66942277344", "discriminant": "1 1 -27648", "aesz": "12", "n_sing_complex": "0", "inst_int": null, "c2h": "32", "hash": "ad7e2e881b3939396323eb746eb17a58", "dim_h": "3", "inst": " 7776 13952088 66942277344 475338414733416 4184555647748620320 42202437596672324405112 467469360560566398889166688 5545773258571693336885436523240 69328598617366670810510410649326848 903213185732777407964502721219416834120", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": null, "n_sing_rational": "2", "n_sing": "2", "laurent": null, "discriminant_tex": "1-27648z", "discr_factors": "-27648, -1/27648+z", "dm_basis": null, "q": "0 1 -6144 6866784 -48364795904 -347475565045200 -4187620294286266368 -52283888489592435338752 -692070099523170842638811136 -9551942712179834224174131115368", "yuk": "1 7776 111624480 1807441496064 30421658654563104 523069455968577547776 9115726520883029624616960 160341990672274274818984181760 2839435908388707018907002154461984 50540548392060303020862091170800768256", "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":"1/27648","im":"0","approx_re":"3.61689814815e-05","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":["1/6","1/4","3/4","5/6"],"monodromy":[],"monodromy_dm":[]}]}]}