{"count": 4, "status":"OK", "data":[{"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, -640*(X+1/2)^4-584*(X+1/2)^2-18, 135168*(X+1)^4+118272*(X+1)^2+10128, -131072*(X+3/2)^2*(80*(X+3/2)^2+63), 67108864*(X+2)^2*(2*X+3)*(2*X+5)]", "text": "YY-Operator equivalent to AESZ 39=$A \\ast \\alpha$.", "degz": 4, "h3": null, "sol": "1 204 41820 9022160 2025179100 466941326544 109640857502736 26078280865871040 6262163022415481820 1514784810773910635600", "n_discr_factors": "2", "c3": null, "operator": "4 4 0 0 0 0 1 -204 -904 -1544 -1280 -640 263568 777216 929280 540672 135168 -71663616 -166330368 -149815296 -62914560 -10485760 4026531840 8321499136 6375342080 2147483648 268435456", "new_number": "4.1", "id": 115, "operator_tex": "\\theta^4-2^{2} x\\left(160\\theta^4+320\\theta^3+386\\theta^2+226\\theta+51\\right)+2^{4} 3 x^{2}\\left(2816\\theta^4+11264\\theta^3+19360\\theta^2+16192\\theta+5491\\right)-2^{15} x^{3}(80\\theta^2+240\\theta+243)(2\\theta+3)^2+2^{26} x^{4}(\\theta+2)^2(2\\theta+3)(2\\theta+5)", "superseek": "-32 -8736", "discriminant": "4 1 -640 135168 -10485760 268435456", "aesz": "~39", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "462066f711fc3742db1ea9befa2fe01b", "dim_h": null, "inst": " -32 -284 -8736 -283900 -10041888 -1152289940/3 -15976746016 -698105875068 -31627354130464 -1474104208483292", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "(256z-1)^2(64z-1)^2", "discr_factors": "268435456, (z-1/64)^2, (z-1/256)^2", "dm_basis": null, "q": "0 1 -88 4140 -203840 8154830 -320933664 11741625528 -434327971328 14542126994661", "yuk": "1 -32 -2304 -235904 -18171904 -1255236032 -82965113856 -5480023883520 -357430226206720 -23056341161344160", "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":"1/256","im":"0","approx_re":"0.00390625","approx_im":"0.0","exponents":["0","-1/2","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/64","im":"0","approx_re":"0.015625","approx_im":"0.0","exponents":["0","-1/2","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["3/2","2","2","5/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -16*X*(7*X^3-10*X^2-6*X-1), 5888*X^4+17408*X^3+38656*X^2+14848*X+1792, -1236992*X^4-5799936*X^3-7593984*X^2-4694016*X-1130496, 102236160*X^4+445906944*X^3+837681152*X^2+555352064*X+135135232, -2067791872*X^4-14675869696*X^3-28311552000*X^2-22389194752*X-6199181312, 35366371328*X^4+44291850240*X^3-78248935424*X^2-26373783552*X+1275068416, -2524367028224*X^4-5209795330048*X^3+11462193971200*X^2+14978698444800*X+4946728583168, 29669634080768*X^4+200420353900544*X^3+227994043940864*X^2+51745765982208*X-11424613007360, -99505802313728*X^4+2388139255529472*X^3+2103915499749376*X^2+356241767399424*X-131391639519232, 17328303253749760*X^4+32545544182169600*X^3+21726349764853760*X^2+5453577673768960*X+263882790666240, -14073748835532800*(X+1)^4]", "text": "This is operator \"11.5\" from ...", "degz": 11, "h3": null, "sol": "1 0 -112 13824 -136944 -42624000 3262265600 33086054400 -21000227586800 1156137025075200", "n_discr_factors": "3", "c3": null, "operator": "4 11 0 0 0 0 1 0 16 96 160 -112 1792 14848 38656 17408 5888 -1130496 -4694016 -7593984 -5799936 -1236992 135135232 555352064 837681152 445906944 102236160 -6199181312 -22389194752 -28311552000 -14675869696 -2067791872 1275068416 -26373783552 -78248935424 44291850240 35366371328 4946728583168 14978698444800 11462193971200 -5209795330048 -2524367028224 -11424613007360 51745765982208 227994043940864 200420353900544 29669634080768 -131391639519232 356241767399424 2103915499749376 2388139255529472 -99505802313728 263882790666240 5453577673768960 21726349764853760 32545544182169600 17328303253749760 -14073748835532800 -56294995342131200 -84442493013196800 -56294995342131200 -14073748835532800", "new_number": "11.5", "id": 342, "operator_tex": "\\theta^4-2^{4} x\\theta(7\\theta^3-10\\theta^2-6\\theta-1)+2^{8} x^{2}\\left(23\\theta^4+68\\theta^3+151\\theta^2+58\\theta+7\\right)-2^{13} x^{3}\\left(151\\theta^4+708\\theta^3+927\\theta^2+573\\theta+138\\right)+2^{17} x^{4}\\left(780\\theta^4+3402\\theta^3+6391\\theta^2+4237\\theta+1031\\right)-2^{22} x^{5}\\left(493\\theta^4+3499\\theta^3+6750\\theta^2+5338\\theta+1478\\right)+2^{26} x^{6}\\left(527\\theta^4+660\\theta^3-1166\\theta^2-393\\theta+19\\right)-2^{30} x^{7}\\left(2351\\theta^4+4852\\theta^3-10675\\theta^2-13950\\theta-4607\\right)+2^{34} x^{8}\\left(1727\\theta^4+11666\\theta^3+13271\\theta^2+3012\\theta-665\\right)-2^{39} x^{9}\\left(181\\theta^4-4344\\theta^3-3827\\theta^2-648\\theta+239\\right)+2^{44} 5 x^{10}\\left(197\\theta^4+370\\theta^3+247\\theta^2+62\\theta+3\\right)-2^{49} 5^{2} x^{11}\\left((\\theta+1)^4\\right)", "superseek": "-32 608", "discriminant": "11 1 -112 5888 -1236992 102236160 -2067791872 35366371328 -2524367028224 29669634080768 -99505802313728 17328303253749760 -14073748835532800", "aesz": null, "n_sing_complex": "4", "inst_int": "", "c2h": null, "hash": "f5f2274632f5544ebf559c6c512159d1", "dim_h": null, "inst": " -32 -616 608 -21270 -15181664 -157477192 14725008608 -891823196878 -50522477326080 2876556822580744", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "8", "laurent": null, "discriminant_tex": "-(-1-80z-9984z^2+8192z^3)(32z-1)^2(40960z^3+1024z^2+64z-1)^2", "discr_factors": "-14073748835532800, (z-1/32)^2, -1/8192-5/512*z-39/32*z^2+z^3, (z^3+1/40*z^2+1/640*z-1/40960)^2", "dm_basis": null, "q": "0 1 16 928 -5120 -413392 15455744 235988480 -68586143744 1647378282136", "yuk": "1 -32 -4960 16384 -1366240 -1897708032 -34015062016 5050677952512 -456613478167776 -36830885970695936", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/960*(2006+30*5721^(1/2))^(1/3)+13/120/(2006+30*5721^(1/2))^(1/3)-1/120","im":"-1/32*3^(1/2)*(1/30*(2006+30*5721^(1/2))^(1/3)+52/15/(2006+30*5721^(1/2))^(1/3))","approx_re":"-0.018565","approx_im":"-0.040844","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/960*(2006+30*5721^(1/2))^(1/3)+13/120/(2006+30*5721^(1/2))^(1/3)-1/120","im":"1/32*3^(1/2)*(1/30*(2006+30*5721^(1/2))^(1/3)+52/15/(2006+30*5721^(1/2))^(1/3))","approx_re":"-0.018565","approx_im":"0.040844","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/192*(61128+177*177^(1/2))^(1/3)-517/64/(61128+177*177^(1/2))^(1/3)+13/32","im":"-1/32*3^(1/2)*(1/6*(61128+177*177^(1/2))^(1/3)-517/2/(61128+177*177^(1/2))^(1/3))","approx_re":"-0.004021","approx_im":"-0.009129","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/192*(61128+177*177^(1/2))^(1/3)-517/64/(61128+177*177^(1/2))^(1/3)+13/32","im":"1/32*3^(1/2)*(1/6*(61128+177*177^(1/2))^(1/3)-517/2/(61128+177*177^(1/2))^(1/3))","approx_re":"-0.004021","approx_im":"0.009129","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":"1/480*(2006+30*5721^(1/2))^(1/3)-13/60/(2006+30*5721^(1/2))^(1/3)-1/120","im":"0","approx_re":"0.012129","approx_im":"0.0","exponents":["0","1","3","4"],"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":"1/96*(61128+177*177^(1/2))^(1/3)+517/32/(61128+177*177^(1/2))^(1/3)+13/32","im":"0","approx_re":"1.226791","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, 80+448*X+1024*X^2+1152*X^3+704*X^4, 104448+466944*X+860160*X^2+671744*X^3+122880*X^4, 47448064+173801472*X+231997440*X^2+85983232*X^3-13631488*X^4, 6677331968+18756927488*X+13522436096*X^2-11542724608*X^3-4966055936*X^4, 51539607552-631360192512*X-2229088026624*X^2-2336462209024*X^3-103079215104*X^4, -25288767438848-87411174408192*X-80814104641536*X^2+17592186044416*X^3+43980465111040*X^4, 140737488355328*(4*X+3)*(X+1)^2*(4*X+5)]", "text": "This is operator \"7.13\" from ...", "degz": 7, "h3": null, "sol": "1 -80 10512 -1703168 309951760 -60610663680 12432852230400 -2637659225640960 573662029814177040 -127162085544458835200", "n_discr_factors": "4", "c3": null, "operator": "4 7 0 0 0 0 1 80 448 1024 1152 704 104448 466944 860160 671744 122880 47448064 173801472 231997440 85983232 -13631488 6677331968 18756927488 13522436096 -11542724608 -4966055936 51539607552 -631360192512 -2229088026624 -2336462209024 -103079215104 -25288767438848 -87411174408192 -80814104641536 17592186044416 43980465111040 2111062325329920 8725724278030336 13370061393756160 9007199254740992 2251799813685248", "new_number": "7.13", "id": 435, "operator_tex": "\\theta^4+2^{4} x\\left(44\\theta^4+72\\theta^3+64\\theta^2+28\\theta+5\\right)+2^{11} x^{2}\\left(60\\theta^4+328\\theta^3+420\\theta^2+228\\theta+51\\right)-2^{18} x^{3}\\left(52\\theta^4-328\\theta^3-885\\theta^2-663\\theta-181\\right)-2^{25} x^{4}\\left(148\\theta^4+344\\theta^3-403\\theta^2-559\\theta-199\\right)-2^{32} x^{5}\\left(24\\theta^4+544\\theta^3+519\\theta^2+147\\theta-12\\right)+2^{39} x^{6}\\left(80\\theta^4+32\\theta^3-147\\theta^2-159\\theta-46\\right)+2^{47} x^{7}(4\\theta+3)(\\theta+1)^2(4\\theta+5)", "superseek": "-32 -107936", "discriminant": "7 1 704 122880 -13631488 -4966055936 -103079215104 43980465111040 2251799813685248", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "80eaab6a34199e98f88d8472c115c4df", "dim_h": null, "inst": " -32 -2840 -107936 -7514224 -575948640 -47096636216 -4228240749344 -393935384419440 -38232842173773568 -3823247114829110920", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "5", "n_sing": "5", "laurent": null, "discriminant_tex": "(64z+1)(128z+1)(128z-1)^2(256z+1)^3", "discr_factors": "2251799813685248, z+1/64, (z+1/256)^3, (z-1/128)^2, z+1/128", "dm_basis": null, "q": "0 1 128 13920 1558528 175396400 19923050496 2287495987712 264657733681152 30859009975433880", "yuk": "1 -32 -22752 -2914304 -480933088 -71993580032 -10172876359680 -1450286577025024 -201694917303686368 -27871741944683845376", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/64","im":"0","approx_re":"-0.015625","approx_im":"0.0","exponents":["0","1","1","2"],"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":"-1/256","im":"0","approx_re":"-0.00390625","approx_im":"0.0","exponents":["0","1/4","7/4","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":"1/128","im":"0","approx_re":"0.0078125","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":[]}]}]}