{"count": 3, "status":"OK", "data":[{"pols": "[X^4, -1808*X^4-3680*X^3-2532*X^2-692*X-68, -16*(4*X+3)*(3808*X^3+10504*X^2+8884*X+1635), -30976*(4*X+1)*(4*X+3)*(4*X+7)*(4*X+9)]", "text": "This is operator Pi = 3.14 (approx.), equivalent to AESZ 238.", "degz": 3, "h3": "5", "sol": "1 68 42220 38866320 43812369900 55414549043568 75528977653335024 108483998232210868800 161980690467592131864300 249190451217633428740094000", "n_discr_factors": "2", "c3": "-100", "operator": "4 3 0 0 0 0 1 -68 -692 -2532 -3680 -1808 -78480 -531072 -1072768 -855040 -243712 -5854464 -37171200 -64430080 -39649280 -7929856", "new_number": "3.14", "id": 74, "operator_tex": "\\theta^4-2^{2} x\\left(452\\theta^4+920\\theta^3+633\\theta^2+173\\theta+17\\right)-2^{4} x^{2}(4\\theta+3)(3808\\theta^3+10504\\theta^2+8884\\theta+1635)-2^{8} 11^{2} x^{3}(4\\theta+1)(4\\theta+3)(4\\theta+7)(4\\theta+9)", "superseek": "444 19050964", "discriminant": "3 1 -1808 -243712 -7929856", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": "38", "hash": "dc96aa2da269d989ee90c49dab6a9c5a", "dim_h": "4", "inst": " 444 57104 19050964 9432910668 5781274591408 4058389108418096 3128917495561043956 2583677026445362637052 2248245582621571943692888 2038917173314965930447657536", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "-(1936z-1)(1+64z)^2", "discr_factors": "-7929856, (1/64+z)^2, z-1/1936", "dm_basis": ["-100*lambda", "29/12", "1", "1", "-19/12", "-5/2", "-1", "0", "0", "5", "0", "0", "-5", "0", "0", "0"], "q": "0 1 -420 11814 -8013968 -9634342911 -6823847203608 -6014006082869582 -5551278928382532672 -5331789302913401246700", "yuk": "1 444 457276 514376472 603706740028 722659323926444 876612047933142040 1073218700977438077352 1322842637540629376910652 1638971029731125947466491824", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/64","im":"0","approx_re":"-0.015625","approx_im":"0.0","exponents":["0","1/2","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/1936","im":"0","approx_re":"0.00051652892562","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":["1/4","3/4","7/4","9/4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[27*X^4, 108-432*X^4+468*X+756*X^2+576*X^3, -99264*X^2-11520*X^4-23472-78528*X-61440*X^3, 501760*X^2-132096-34816*X+606208*X^3+217088*X^4, 16637952+589824*X^4+44793856*X+39354368*X^2+12582912*X^3, -402391040*X^2-26214400*X^4-72351744-302776320*X-188743680*X^3, 1329594368*X^2+240123904+926941184*X+805306368*X^3+150994944*X^4, -268435456*(X+1)^4]", "text": "This is operator \"7.19\" from ...", "degz": 7, "h3": null, "sol": "1 -4 68 -496 9796 -84944 1732016 -16427072 337469764 -3388418704", "n_discr_factors": "3", "c3": null, "operator": "4 7 0 0 0 0 27 108 468 756 576 -432 -23472 -78528 -99264 -61440 -11520 -132096 -34816 501760 606208 217088 16637952 44793856 39354368 12582912 589824 -72351744 -302776320 -402391040 -188743680 -26214400 240123904 926941184 1329594368 805306368 150994944 -268435456 -1073741824 -1610612736 -1073741824 -268435456", "new_number": "7.19", "id": 441, "operator_tex": "3^{3} \\theta^4-2^{2} 3^{2} x\\left(12\\theta^4-16\\theta^3-21\\theta^2-13\\theta-3\\right)-2^{4} 3 x^{2}\\left(240\\theta^4+1280\\theta^3+2068\\theta^2+1636\\theta+489\\right)+2^{10} x^{3}\\left(212\\theta^4+592\\theta^3+490\\theta^2-34\\theta-129\\right)+2^{13} x^{4}\\left(72\\theta^4+1536\\theta^3+4804\\theta^2+5468\\theta+2031\\right)-2^{18} x^{5}\\left(100\\theta^4+720\\theta^3+1535\\theta^2+1155\\theta+276\\right)+2^{20} x^{6}\\left(144\\theta^4+768\\theta^3+1268\\theta^2+884\\theta+229\\right)-2^{28} x^{7}\\left((\\theta+1)^4\\right)", "superseek": "4/3 -124/81", "discriminant": "7 27 -432 -11520 217088 589824 -26214400 150994944 -268435456", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "f7f0f5d883101c38ed22cb74c80c8f5c", "dim_h": null, "inst": " 4/3 -14/9 -124/81 -4498/243 37024/729 165074/243 80629772/19683 122791610/59049 -1576000/9 -7208283828944/4782969", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "-(16z-1)^2(16z+1)^2(16z-3)^3", "discr_factors": "-268435456, (z+1/16)^2, (z-3/16)^3, (z-1/16)^2", "dm_basis": null, "q": "0 1 4/3 -182/3 -24976/81 544783/243 96632/3 559420178/6561 -29268772288/19683 -18960126", "yuk": "1 4/3 -100/9 -40 -290572/243 4628972/729 146680 27656038040/19683 62798695324/59049 -127656040", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/16","im":"0","approx_re":"-0.0625","approx_im":"0.0","exponents":["0","0","1","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":"1/16","im":"0","approx_re":"0.0625","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"3/16","im":"0","approx_re":"0.1875","approx_im":"0.0","exponents":["0","2","3","5"],"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, -676-4394*X-11323*X^2-13858*X^3-6929*X^4, -35152-159536*X-265720*X^2-185952*X^3-48984*X^4, 336960+1175616*X+1495936*X^2+843648*X^3+208832*X^4, -1098240-3208192*X-2512896*X^2+223232*X^3+383488*X^4, 729088+172032*X-3960832*X^2-5201920*X^3-1552384*X^4, 917504+5111808*X+8945664*X^2+5111808*X^3-294912*X^4, 262144+1835008*X+5242880*X^2+6815744*X^3+3407872*X^4, -2097152*(X+1)^4]", "text": "The operator has a second MUM-point at infinity, corresponding to operator 8.19.", "degz": 8, "h3": "52", "sol": "1 4 68 1552 43156 1331504 44101616 1535335232 55477774228 2063217683344", "n_discr_factors": "4", "c3": "-88", "operator": "4 8 0 0 0 0 169 -676 -4394 -11323 -13858 -6929 -35152 -159536 -265720 -185952 -48984 336960 1175616 1495936 843648 208832 -1098240 -3208192 -2512896 223232 383488 729088 172032 -3960832 -5201920 -1552384 917504 5111808 8945664 5111808 -294912 262144 1835008 5242880 6815744 3407872 -2097152 -8388608 -12582912 -8388608 -2097152", "new_number": "8.18", "id": 461, "operator_tex": "13^{2} \\theta^4-13^{2} x\\left(41\\theta^4+82\\theta^3+67\\theta^2+26\\theta+4\\right)-2^{3} 13 x^{2}\\left(471\\theta^4+1788\\theta^3+2555\\theta^2+1534\\theta+338\\right)+2^{6} 13 x^{3}\\left(251\\theta^4+1014\\theta^3+1798\\theta^2+1413\\theta+405\\right)+2^{9} x^{4}\\left(749\\theta^4+436\\theta^3-4908\\theta^2-6266\\theta-2145\\right)-2^{12} x^{5}\\left(379\\theta^4+1270\\theta^3+967\\theta^2-42\\theta-178\\right)-2^{15} x^{6}\\left(9\\theta^4-156\\theta^3-273\\theta^2-156\\theta-28\\right)+2^{18} x^{7}\\left(13\\theta^4+26\\theta^3+20\\theta^2+7\\theta+1\\right)-2^{21} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "3 1621/13", "discriminant": "8 169 -6929 -48984 208832 383488 -1552384 -294912 3407872 -2097152", "aesz": "197", "n_sing_complex": "0", "inst_int": "", "c2h": "-8", "hash": "4cc8bdba73e5fa6cb4089fa5296429de", "dim_h": "8", "inst": " 3 226/13 1621/13 20666/13 289056/13 4823420/13 86575842/13 1674803122/13 34027261716/13 721083596092/13", "cleanlist": "True", "n_sing_real": "7", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "7", "laurent": null, "discriminant_tex": "-(z-1)(8z+1)(64z^2-48z+1)(-13+64z^2)^2", "discr_factors": "-2097152, z-1, (-13/64+z^2)^2, z^2-3/4*z+1/64, z+1/8", "dm_basis": null, "q": "0 1 -10 -13 136 -3931 -40798 -970035 -20224224 -458183025", "yuk": "1 3 1847/13 43806/13 1324471/13 36132039/13 1041904334/13 29695513845/13 857500522935/13 24805873834770/13", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/8*13^(1/2)","im":"0","approx_re":"-0.450694","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":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"3/8-1/4*2^(1/2)","im":"0","approx_re":"0.021447","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/8*13^(1/2)","im":"0","approx_re":"0.450694","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"3/8+1/4*2^(1/2)","im":"0","approx_re":"0.728553","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","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}]}