{"count": 4, "status":"OK", "data":[{"pols": "[9*X^4, -1464*X^4-1776*X^3-1392*X^2-504*X-72, 62128*X^4+85696*X^3+55216*X^2+20448*X+3648, -1032576*X^4-1716480*X^3-1648000*X^2-811008*X-158208, 6766592*X^4+17514496*X^3+19759104*X^2+10780672*X+2293760, -1572864*(X+1)^2*(3*X+2)*(3*X+4)]", "text": "This is operator \"5.110\" from ...", "degz": 5, "h3": null, "sol": "1 8 264 13760 873640 62035008 4737460224 380801236992 31795322783400 2733835498222400", "n_discr_factors": "4", "c3": null, "operator": "4 5 0 0 0 0 9 -72 -504 -1392 -1776 -1464 3648 20448 55216 85696 62128 -158208 -811008 -1648000 -1716480 -1032576 2293760 10780672 19759104 17514496 6766592 -12582912 -53477376 -83361792 -56623104 -14155776", "new_number": "5.110", "id": 193, "operator_tex": "3^{2} \\theta^4-2^{3} 3 x\\left(61\\theta^4+74\\theta^3+58\\theta^2+21\\theta+3\\right)+2^{4} x^{2}\\left(3883\\theta^4+5356\\theta^3+3451\\theta^2+1278\\theta+228\\right)-2^{7} x^{3}\\left(8067\\theta^4+13410\\theta^3+12875\\theta^2+6336\\theta+1236\\right)+2^{14} x^{4}\\left(413\\theta^4+1069\\theta^3+1206\\theta^2+658\\theta+140\\right)-2^{19} 3 x^{5}(\\theta+1)^2(3\\theta+2)(3\\theta+4)", "superseek": "32/3 6752/3", "discriminant": "5 9 -1464 62128 -1032576 6766592 -14155776", "aesz": "377", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "4b8e1b4341fae957e1766a0071de5ba5", "dim_h": null, "inst": " 32/3 731/6 6752/3 355219/6 5936896/3 152130019/2 9620513888/3 434121543602/3 6880335263104 1022806701520268/3", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "5", "n_sing": "5", "laurent": null, "discriminant_tex": "-(4z-1)(108z-1)(8z-1)(-3+64z)^2", "discr_factors": "-14155776, z-1/8, z-1/108, z-1/4, (-3/64+z)^2", "dm_basis": null, "q": "0 1 -24 54 -2336 -68931 -3364560 -160274470 -8059944576 -422609180202", "yuk": "1 32/3 2956/3 182336/3 3789988 742112032/3 49290311416/3 3299836263616/3 222270241694188/3 15047293220590784/3", "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":"1/108","im":"0","approx_re":"0.00925925925926","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"3/64","im":"0","approx_re":"0.046875","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":["2/3","1","1","4/3"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[841*X^4, -6728-47937*X-132733*X^2-169592*X^3-87754*X^4, 5568+57768*X+239159*X^2+424220*X^3+258647*X^4, -76560-336864*X-581647*X^2-532614*X^3-272743*X^4, 75616+332792*X+552228*X^2+421124*X^3+130696*X^4, -3468*(X+1)^2*(3*X+2)*(3*X+4)]", "text": "This is operator \"5.24\" from ...", "degz": 5, "h3": "29", "sol": "1 8 264 13040 778840 51955008 3725735664 281152383072 22035642730200 1778348612268800", "n_discr_factors": "2", "c3": "-100", "operator": "4 5 0 0 0 0 841 -6728 -47937 -132733 -169592 -87754 5568 57768 239159 424220 258647 -76560 -336864 -581647 -532614 -272743 75616 332792 552228 421124 130696 -27744 -117912 -183804 -124848 -31212", "new_number": "5.24", "id": 232, "operator_tex": "29^{2} \\theta^4-29 x\\left(3026\\theta^4+5848\\theta^3+4577\\theta^2+1653\\theta+232\\right)+x^{2}\\left(5568+57768\\theta+239159\\theta^2+424220\\theta^3+258647\\theta^4\\right)-x^{3}\\left(76560+336864\\theta+581647\\theta^2+532614\\theta^3+272743\\theta^4\\right)+2^{2} 17 x^{4}\\left(1922\\theta^4+6193\\theta^3+8121\\theta^2+4894\\theta+1112\\right)-2^{2} 3 17^{2} x^{5}(\\theta+1)^2(3\\theta+2)(3\\theta+4)", "superseek": "285/29 40626/29", "discriminant": "5 841 -87754 258647 -272743 130696 -31212", "aesz": "195", "n_sing_complex": "2", "inst_int": "", "c2h": "74", "hash": "49a600431b3e9aaa9d9d6947f8df7d2b", "dim_h": "11", "inst": " 285/29 2362/29 40626/29 997476/29 30096841/29 1036931650/29 39188167891/29 1585184851720/29 67548466106031/29 2999289959592904/29", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "5", "laurent": null, "discriminant_tex": "-(27z^3-67z^2+102z-1)(-29+34z)^2", "discr_factors": "-31212, z^3-67/27*z^2+34/9*z-1/27, (-29/34+z)^2", "dm_basis": null, "q": "0 1 -25 146 -1925 -41626 -1710492 -73263248 -3311266553 -155893120414", "yuk": "1 285/29 19181/29 1097187/29 63857645/29 3762105410/29 223978352483/29 13441541586898/29 811614707938285/29 49242831792393786/29", "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*(4157812+472068*93^(1/2))^(1/3)+7546/81/(4157812+472068*93^(1/2))^(1/3)+67/81","im":"0","approx_re":"0.009868","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"29/34","im":"0","approx_re":"0.852941176471","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/324*(4157812+472068*93^(1/2))^(1/3)-3773/81/(4157812+472068*93^(1/2))^(1/3)+67/81","im":"1/2*3^(1/2)*(-1/162*(4157812+472068*93^(1/2))^(1/3)-7546/81/(4157812+472068*93^(1/2))^(1/3))","approx_re":"1.235807","approx_im":"-1.492036","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/324*(4157812+472068*93^(1/2))^(1/3)-3773/81/(4157812+472068*93^(1/2))^(1/3)+67/81","im":"-1/2*3^(1/2)*(-1/162*(4157812+472068*93^(1/2))^(1/3)-7546/81/(4157812+472068*93^(1/2))^(1/3))","approx_re":"1.235807","approx_im":"1.492036","exponents":["0","1","1","2"],"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, -13*X^4-14*X^3-16*X^2-9*X-2, 33*X^4-88*X^3-265*X^2-324*X-148, 217*X^4+2362*X^3+6403*X^2+8178*X+4160, -1354*X^4-8268*X^3-16178*X^2-12420*X-720, 1812*X^4-15192*X^3-139320*X^2-347460*X-301320, 7580*X^4+149208*X^3+707964*X^2+1423392*X+1075344, -38540*X^4-356680*X^3-743540*X^2+429576*X+2089856, 47256*X^4-85088*X^3-3329000*X^2-13330608*X-16415360, 94304*X^4+2569088*X^3+16637888*X^2+42511200*X+38564800, -391808*X^4-5430528*X^3-25443520*X^2-46255680*X-22811520, 433728*X^4+2572416*X^3-8937408*X^2-87598848*X-152957952, 1152*(X+4)*(371*X^3+8580*X^2+53325*X+101564), -27648*(X+4)*(X+5)*(51*X^2+519*X+1330), 829440*(X+4)*(X+5)^2*(X+6)]", "text": "This is operator \"14.1\" from ...", "degz": 14, "h3": null, "sol": "1 2 16 48 264 1008 5008 21824 106792 500496", "n_discr_factors": "9", "c3": null, "operator": "4 14 0 0 0 0 1 -2 -9 -16 -14 -13 -148 -324 -265 -88 33 4160 8178 6403 2362 217 -720 -12420 -16178 -8268 -1354 -301320 -347460 -139320 -15192 1812 1075344 1423392 707964 149208 7580 2089856 429576 -743540 -356680 -38540 -16415360 -13330608 -3329000 -85088 47256 38564800 42511200 16637888 2569088 94304 -22811520 -46255680 -25443520 -5430528 -391808 -152957952 -87598848 -8937408 2572416 433728 468006912 362723328 100967040 11593728 427392 -735436800 -617932800 -194116608 -27039744 -1410048 497664000 406425600 123586560 16588800 829440", "new_number": "14.1", "id": 380, "operator_tex": "\\theta^4-x\\left(13\\theta^4+14\\theta^3+16\\theta^2+9\\theta+2\\right)+x^{2}\\left(33\\theta^4-88\\theta^3-265\\theta^2-324\\theta-148\\right)+x^{3}\\left(217\\theta^4+2362\\theta^3+6403\\theta^2+8178\\theta+4160\\right)-2 x^{4}\\left(677\\theta^4+4134\\theta^3+8089\\theta^2+6210\\theta+360\\right)+2^{2} 3 x^{5}\\left(151\\theta^4-1266\\theta^3-11610\\theta^2-28955\\theta-25110\\right)+2^{2} x^{6}\\left(1895\\theta^4+37302\\theta^3+176991\\theta^2+355848\\theta+268836\\right)-2^{2} x^{7}\\left(9635\\theta^4+89170\\theta^3+185885\\theta^2-107394\\theta-522464\\right)+2^{3} x^{8}\\left(5907\\theta^4-10636\\theta^3-416125\\theta^2-1666326\\theta-2051920\\right)+2^{5} x^{9}\\left(2947\\theta^4+80284\\theta^3+519934\\theta^2+1328475\\theta+1205150\\right)-2^{6} x^{10}\\left(6122\\theta^4+84852\\theta^3+397555\\theta^2+722745\\theta+356430\\right)+2^{6} 3 x^{11}\\left(2259\\theta^4+13398\\theta^3-46549\\theta^2-456244\\theta-796656\\right)+2^{7} 3^{2} x^{12}(\\theta+4)(371\\theta^3+8580\\theta^2+53325\\theta+101564)-2^{10} 3^{3} x^{13}(\\theta+4)(\\theta+5)(51\\theta^2+519\\theta+1330)+2^{11} 3^{4} 5 x^{14}(\\theta+4)(\\theta+5)^2(\\theta+6)", "superseek": "0 0", "discriminant": "14 1 -13 33 217 -1354 1812 7580 -38540 47256 94304 -391808 433728 427392 -1410048 829440", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "a8cf56492aecc07971e82c9104785180", "dim_h": null, "inst": " 0 1/4 0 -1/2 0 28/9 0 -14 0 2223/20", "cleanlist": "True", "n_sing_real": "9", "sol_explicit": "", "n_sing_rational": "9", "n_sing": "11", "laurent": null, "discriminant_tex": "(z-1)(6z-1)(4z-1)(3z+1)(4z+1)(5z-1)(2z+1)^2(2z-1)^2(6z^2-2z+1)^2", "discr_factors": "829440, z+1/4, z-1/4, z-1/6, (z-1/2)^2, (z^2-1/3*z+1/6)^2, z-1, (z+1/2)^2, z-1/5, z+1/3", "dm_basis": null, "q": "0 1 -1 -5 11 26 -99 -146 871 717", "yuk": "1 0 2 0 -30 0 674 0 -7198 0", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/2","im":"0","approx_re":"-0.5","approx_im":"0.0","exponents":["0","0","-1","1"],"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":"-1/4","im":"0","approx_re":"-0.25","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":"1/6","im":"-1/6*5^(1/2)","approx_re":"0.166666666667","approx_im":"-0.372678","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/6","im":"0","approx_re":"0.166666666667","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/6","im":"1/6*5^(1/2)","approx_re":"0.166666666667","approx_im":"0.372678","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/5","im":"0","approx_re":"0.2","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":"1/2","im":"0","approx_re":"0.5","approx_im":"0.0","exponents":["0","0","-1","1"],"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":["4","5","5","6"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[9*X^4, -348*X^4-2136*X^3-1608*X^2-540*X-72, -71456*X^4-81152*X^3-19424*X^2-4224*X-384, -1304576*X^4-7603200*X^3-20482048*X^2-13022208*X-2734080, 20799488*X^4-299319296*X^3-432332800*X^2-254951424*X-50724864, 1695547392*X^4+10245636096*X^3+4701814784*X^2-706740224*X-583008256, 38084280320*X^4+143344533504*X^3+115393691648*X^2+28789702656*X+536870912, -6442450944*(2*X+1)*(110*X^3+225*X^2+184*X+57), 1236950581248*(2*X+1)*(X+1)^2*(2*X+3)]", "text": "This is operator \"8.49\" from ...", "degz": 8, "h3": null, "sol": "1 8 264 16640 1130920 85756608 7041264384 606620332032 54248100552360 4995253852297280", "n_discr_factors": "4", "c3": null, "operator": "4 8 0 0 0 0 9 -72 -540 -1608 -2136 -348 -384 -4224 -19424 -81152 -71456 -2734080 -13022208 -20482048 -7603200 -1304576 -50724864 -254951424 -432332800 -299319296 20799488 -583008256 -706740224 4701814784 10245636096 1695547392 536870912 28789702656 115393691648 143344533504 38084280320 -367219703808 -1919850381312 -3820373409792 -3607772528640 -1417339207680 3710851743744 17317308137472 28449863368704 19791209299968 4947802324992", "new_number": "8.49", "id": 495, "operator_tex": "3^{2} \\theta^4-2^{2} 3 x\\left(29\\theta^4+178\\theta^3+134\\theta^2+45\\theta+6\\right)-2^{5} x^{2}\\left(2233\\theta^4+2536\\theta^3+607\\theta^2+132\\theta+12\\right)-2^{10} x^{3}\\left(1274\\theta^4+7425\\theta^3+20002\\theta^2+12717\\theta+2670\\right)+2^{13} x^{4}\\left(2539\\theta^4-36538\\theta^3-52775\\theta^2-31122\\theta-6192\\right)+2^{20} x^{5}\\left(1617\\theta^4+9771\\theta^3+4484\\theta^2-674\\theta-556\\right)+2^{25} x^{6}\\left(1135\\theta^4+4272\\theta^3+3439\\theta^2+858\\theta+16\\right)-2^{31} 3 x^{7}(2\\theta+1)(110\\theta^3+225\\theta^2+184\\theta+57)+2^{37} 3^{2} x^{8}(2\\theta+1)(\\theta+1)^2(2\\theta+3)", "superseek": "56/3 17704/3", "discriminant": "8 9 -348 -71456 -1304576 20799488 1695547392 38084280320 -1417339207680 4947802324992", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "4fa01cbee2fc74e3a62e00386e6fa1c0", "dim_h": null, "inst": " 56/3 -83/6 17704/3 -25024/3 13408832/3 329502271/6 16966193320/3 1129554212443/6 34456919967200/3 1622868038583172/3", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "7", "laurent": null, "discriminant_tex": "(4z-1)(131072z^3+2048z^2+88z-1)(48z+1)^2(64z-3)^2", "discr_factors": "4947802324992, (z+1/48)^2, (z-3/64)^2, z^3+1/64*z^2+11/16384*z-1/131072, z-1/4", "dm_basis": null, "q": "0 1 -28 342 -19536 652669 -31706568 782733242 -46709670976 626920704150", "yuk": "1 56/3 -92 478064/3 -1601812/3 558701352 11862241000 1939801436272 96388625594532 25119094656566864/3", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/48","im":"0","approx_re":"-0.0208333333333","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/768*(307+39*78^(1/2))^(1/3)+29/768/(307+39*78^(1/2))^(1/3)-1/192","im":"-1/16*3^(1/2)*(1/48*(307+39*78^(1/2))^(1/3)+29/48/(307+39*78^(1/2))^(1/3))","approx_re":"-0.01214","approx_im":"-0.027095","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/768*(307+39*78^(1/2))^(1/3)+29/768/(307+39*78^(1/2))^(1/3)-1/192","im":"1/16*3^(1/2)*(1/48*(307+39*78^(1/2))^(1/3)+29/48/(307+39*78^(1/2))^(1/3))","approx_re":"-0.01214","approx_im":"0.027095","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":"1/384*(307+39*78^(1/2))^(1/3)-29/384/(307+39*78^(1/2))^(1/3)-1/192","im":"0","approx_re":"0.008655","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"3/64","im":"0","approx_re":"0.046875","approx_im":"0.0","exponents":["0","1","3","4"],"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":["1/2","1","1","3/2"],"monodromy":[],"monodromy_dm":[]}]}]}