{"count": 3, "status":"OK", "data":[{"pols": "[25*X^4, -11840*X^4-31360*X^3-28380*X^2-12700*X-2300, 1048576*X^4+8224768*X^3+14445056*X^2+9574400*X+2315760, 109051904*X^4+125829120*X^3-609091584*X^2-813957120*X-271426560, -4294967296*X^4-40802189312*X^3-76403441664*X^2-53485764608*X-12859211776, -67108864*(8*X+5)*(8*X+7)*(8*X+9)*(8*X+11)]", "text": "This is operator \"5.67\" from ...", "degz": 5, "h3": null, "sol": "1 92 14124 2572400 510577900 106698949392 23073900762864 5112820919583168 1153747673591018220 264058057845710757200", "n_discr_factors": "3", "c3": null, "operator": "4 5 0 0 0 0 25 -2300 -12700 -28380 -31360 -11840 2315760 9574400 14445056 8224768 1048576 -271426560 -813957120 -609091584 125829120 109051904 -12859211776 -53485764608 -76403441664 -40802189312 -4294967296 -232532213760 -1013612281856 -1606317768704 -1099511627776 -274877906944", "new_number": "5.67", "id": 279, "operator_tex": "5^{2} \\theta^4-2^{2} 5 x\\left(592\\theta^4+1568\\theta^3+1419\\theta^2+635\\theta+115\\right)+2^{4} x^{2}\\left(65536\\theta^4+514048\\theta^3+902816\\theta^2+598400\\theta+144735\\right)+2^{10} x^{3}\\left(106496\\theta^4+122880\\theta^3-594816\\theta^2-794880\\theta-265065\\right)-2^{19} x^{4}\\left(8192\\theta^4+77824\\theta^3+145728\\theta^2+102016\\theta+24527\\right)-2^{26} x^{5}(8\\theta+5)(8\\theta+7)(8\\theta+9)(8\\theta+11)", "superseek": "116/5 186172/5", "discriminant": "5 25 -11840 1048576 109051904 -4294967296 -274877906944", "aesz": "275", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "f411d346afd4b8ff14b8b4c1836bae77", "dim_h": null, "inst": " 116/5 -5993/5 186172/5 -8039756/5 384321296/5 -4052885815 1165997831068/5 -71146153051852/5 4532878454152584/5 -297595933756401716/5", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "-(-1+64z)(256z+5)^2(256z-1)^2", "discr_factors": "-274877906944, -1/64+z, (z+5/256)^2, (z-1/256)^2", "dm_basis": null, "q": "0 1 -140 15654 -1622960 162641409 -15912329736 1528405518258 -144717142975680 13548270698953236", "yuk": "1 116/5 -47828/5 1005352 -514592212/5 48040162116/5 -4377111701384/5 79987451211288 -36426830877140436/5 3304468393082260496/5", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-5/256","im":"0","approx_re":"-0.01953125","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":"1/256","im":"0","approx_re":"0.00390625","approx_im":"0.0","exponents":["0","0","1","1"],"monodromy":[],"monodromy_dm":[]},{"re":"1/64","im":"0","approx_re":"0.015625","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":["5/8","7/8","9/8","11/8"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[9*X^4, -3*X*(20*X^3+196*X^2+125*X+27), -19127*X^4-69044*X^3-89705*X^2-54504*X-13248, -571598*X^4-2502840*X^3-4285266*X^2-3356496*X-1023120, -8232500*X^4-44760880*X^3-93499500*X^2-86632240*X-30226016, -68565480*X^4-456243648*X^3-1127475304*X^2-1197017168*X-462870080, -344479104*X^4-2763749952*X^3-7959090176*X^2-9534677952*X-4021733504, -1010901888*X^4-9695372544*X^3-32340933760*X^2-43423287040*X-19815752704, -1024*(X+1)*(1454893*X^3+15409953*X^2+50286726*X+48898444), -2048*(X+1)*(X+2)*(227963*X^2+3375435*X+10342960), 16384*(X+3)*(X+2)*(X+1)*(48476*X+271867), -146964480*(X+1)*(X+2)*(X+3)*(X+4)]", "text": "This is operator \"11.9\" from ...", "degz": 11, "h3": null, "sol": "1 0 92 2328 91212 3748080 166091960 7711023600 371249016460 18382200113760", "n_discr_factors": "6", "c3": null, "operator": "4 11 0 0 0 0 9 0 -81 -375 -588 -60 -13248 -54504 -89705 -69044 -19127 -1023120 -3356496 -4285266 -2502840 -571598 -30226016 -86632240 -93499500 -44760880 -8232500 -462870080 -1197017168 -1127475304 -456243648 -68565480 -4021733504 -9534677952 -7959090176 -2763749952 -344479104 -19815752704 -43423287040 -32340933760 -9695372544 -1010901888 -50072006656 -101565614080 -67273399296 -17269602304 -1489810432 -42364764160 -77372928000 -42854791168 -8313495552 -466868224 26725613568 53762342912 35462152192 9219653632 794230784 -3527147520 -7348224000 -5143756800 -1469644800 -146964480", "new_number": "11.9", "id": 346, "operator_tex": "3^{2} \\theta^4-3 x\\theta(20\\theta^3+196\\theta^2+125\\theta+27)-x^{2}\\left(19127\\theta^4+69044\\theta^3+89705\\theta^2+54504\\theta+13248\\right)-2 x^{3}\\left(285799\\theta^4+1251420\\theta^3+2142633\\theta^2+1678248\\theta+511560\\right)-2^{2} x^{4}\\left(2058125\\theta^4+11190220\\theta^3+23374875\\theta^2+21658060\\theta+7556504\\right)-2^{3} x^{5}\\left(8570685\\theta^4+57030456\\theta^3+140934413\\theta^2+149627146\\theta+57858760\\right)-2^{6} x^{6}\\left(5382486\\theta^4+43183593\\theta^3+124360784\\theta^2+148979343\\theta+62839586\\right)-2^{7} x^{7}\\left(7897671\\theta^4+75745098\\theta^3+252663545\\theta^2+339244430\\theta+154810568\\right)-2^{10} x^{8}(\\theta+1)(1454893\\theta^3+15409953\\theta^2+50286726\\theta+48898444)-2^{11} x^{9}(\\theta+1)(\\theta+2)(227963\\theta^2+3375435\\theta+10342960)+2^{14} x^{10}(\\theta+3)(\\theta+2)(\\theta+1)(48476\\theta+271867)-2^{15} 3 5 13 23 x^{11}(\\theta+1)(\\theta+2)(\\theta+3)(\\theta+4)", "superseek": "17/3 4127/9", "discriminant": "11 9 -60 -19127 -571598 -8232500 -68565480 -344479104 -1010901888 -1489810432 -466868224 794230784 -146964480", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "fa7c260e6f07cef5d727e6af380a6373", "dim_h": null, "inst": " 17/3 257/6 4127/9 23827/3 496999/3 71729629/18 104658718 2945771458 785847748280/9 16183383951883/6", "cleanlist": "True", "n_sing_real": "9", "sol_explicit": "", "n_sing_rational": "5", "n_sing": "9", "laurent": null, "discriminant_tex": "-(5z+1)(13z+1)(6z+1)(368z^2+56z-1)(4z+1)^2(8z^2-26z-3)^2", "discr_factors": "-146964480, (z^2-13/4*z-3/8)^2, z+1/5, z+1/13, z^2+7/46*z-1/368, (z+1/4)^2, z+1/6", "dm_basis": null, "q": "0 1 -9 -142 -143 -2414 -370278 -12215191 -354806113 -11395061876", "yuk": "1 17/3 1045/3 37160/3 1525973/3 62124892/3 2582304832/3 107693820839/3 4524706485461/3 190961002869200/3", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/4","im":"0","approx_re":"-0.25","approx_im":"0.0","exponents":["0","0","1","1"],"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":"-7/92-3/46*2^(1/2)","im":"0","approx_re":"-0.168318","approx_im":"0.0","exponents":["0","1","1","2"],"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":"13/8-1/8*193^(1/2)","im":"0","approx_re":"-0.111555","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/13","im":"0","approx_re":"-0.0769230769231","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":"-7/92+3/46*2^(1/2)","im":"0","approx_re":"0.016144","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"13/8+1/8*193^(1/2)","im":"0","approx_re":"3.361555","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","3","4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[25*X^4, 1460*X^4+2440*X^3+1920*X^2+700*X+100, -2144*X^4-33152*X^3-62784*X^2-42560*X-10320, -45312*X^4-43008*X^3+185472*X^2+240000*X+82240, 112640*X^4+716800*X^3+509952*X^2-57344*X-107520, 249856*X^4-1089536*X^3-2228224*X^2-1527808*X-360448, -1409024*X^4-2752512*X^3-2818048*X^2-1769472*X-507904, 2097152*X^4+7340032*X^3+10354688*X^2+6684672*X+1638400, -1048576*(X+1)^4]", "text": "This is operator \"8.65\" from ...", "degz": 8, "h3": null, "sol": "1 -4 92 -2704 95596 -3755504 158254256 -7009022528 322174768876 -15241307862064", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 25 100 700 1920 2440 1460 -10320 -42560 -62784 -33152 -2144 82240 240000 185472 -43008 -45312 -107520 -57344 509952 716800 112640 -360448 -1527808 -2228224 -1089536 249856 -507904 -1769472 -2818048 -2752512 -1409024 1638400 6684672 10354688 7340032 2097152 -1048576 -4194304 -6291456 -4194304 -1048576", "new_number": "8.65", "id": 513, "operator_tex": "5^{2} \\theta^4+2^{2} 5 x\\left(73\\theta^4+122\\theta^3+96\\theta^2+35\\theta+5\\right)-2^{4} x^{2}\\left(134\\theta^4+2072\\theta^3+3924\\theta^2+2660\\theta+645\\right)-2^{6} x^{3}\\left(708\\theta^4+672\\theta^3-2898\\theta^2-3750\\theta-1285\\right)+2^{10} x^{4}\\left(110\\theta^4+700\\theta^3+498\\theta^2-56\\theta-105\\right)+2^{12} x^{5}\\left(61\\theta^4-266\\theta^3-544\\theta^2-373\\theta-88\\right)-2^{14} x^{6}\\left(86\\theta^4+168\\theta^3+172\\theta^2+108\\theta+31\\right)+2^{16} x^{7}\\left(32\\theta^4+112\\theta^3+158\\theta^2+102\\theta+25\\right)-2^{20} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "-24/5 -1608/5", "discriminant": "8 25 1460 -2144 -45312 112640 249856 -1409024 2097152 -1048576", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "5e457fa5807a784e24220c973aeceba8", "dim_h": null, "inst": " -24/5 329/10 -1608/5 48409/10 -455264/5 19503331/10 -228835848/5 5747617313/5 -152077212208/5 4192795689514/5", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "7", "laurent": null, "discriminant_tex": "-(4z-1)(256z^3-192z^2+56z+1)(-5-16z+32z^2)^2", "discr_factors": "-1048576, z-1/4, (-5/32-1/2*z+z^2)^2, z^3-3/4*z^2+7/32*z+1/256", "dm_basis": null, "q": "0 1 12 -34 -48 -6895 194376 -4884294 135726400 -3970197852", "yuk": "1 -24/5 1292/5 -8688 310076 -56908024/5 2106317624/5 -78490695888/5 2942781614636/5 -110864287743072/5", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"1/4-1/8*14^(1/2)","im":"0","approx_re":"-0.217707","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/24*(189+33*33^(1/2))^(1/3)+1/4/(189+33*33^(1/2))^(1/3)+1/4","im":"0","approx_re":"-0.016861","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":"1/4","im":"0","approx_re":"0.25","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/48*(189+33*33^(1/2))^(1/3)-1/8/(189+33*33^(1/2))^(1/3)+1/4","im":"1/8*3^(1/2)*(-1/6*(189+33*33^(1/2))^(1/3)-1/(189+33*33^(1/2))^(1/3))","approx_re":"0.38343","approx_im":"-0.290965","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/48*(189+33*33^(1/2))^(1/3)-1/8/(189+33*33^(1/2))^(1/3)+1/4","im":"-1/8*3^(1/2)*(-1/6*(189+33*33^(1/2))^(1/3)-1/(189+33*33^(1/2))^(1/3))","approx_re":"0.38343","approx_im":"0.290965","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/4+1/8*14^(1/2)","im":"0","approx_re":"0.717707","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","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}]}