{"count": 3, "status":"OK", "data":[{"pols": "[X^4, 8+32*X+44*X^2+24*X^3+96*X^4, -160+3344*X^4+32*X^3+368*X^2, 28544*X^4-155904*X^3-284800*X^2-267264*X-99328, -7036928-9865216*X^3-19801088*X^2-18862080*X-1442816*X^4, -53469184*X^4-293748736*X^3-641900544*X^2-642482176*X-249151488, -5247598592-12833783808*X-11946295296*X^2-4941938688*X^3-822607872*X^4, -46409973760*X^3-129895497728*X^2-153933053952*X-67398270976-6129975296*X^4, -1009686413312*X-491354324992-183341416448*X^3-717477642240*X^2-10099884032*X^4, -1469080141824+157840048128*X^4+496068722688*X^3-471372660736*X^2-2145336164352*X, 13258564042752*X^2+10617159155712*X+2638720532480+850403524608*X^4+6390911336448*X^3, 35596688949248*X+15427522527232+6047313952768*X^3+26938034880512*X^2-549755813888*X^4, -549755813888*(2*X+3)^4]", "text": "This is operator \"12.17\" from ...", "degz": 12, "h3": null, "sol": "1 -8 112 -1152 19216 -193664 3997440 -32147456 967568656 -3759626368", "n_discr_factors": "4", "c3": null, "operator": "4 12 0 0 0 0 1 8 32 44 24 96 -160 0 368 32 3344 -99328 -267264 -284800 -155904 28544 -7036928 -18862080 -19801088 -9865216 -1442816 -249151488 -642482176 -641900544 -293748736 -53469184 -5247598592 -12833783808 -11946295296 -4941938688 -822607872 -67398270976 -153933053952 -129895497728 -46409973760 -6129975296 -491354324992 -1009686413312 -717477642240 -183341416448 -10099884032 -1469080141824 -2145336164352 -471372660736 496068722688 157840048128 2638720532480 10617159155712 13258564042752 6390911336448 850403524608 15427522527232 35596688949248 26938034880512 6047313952768 -549755813888 -44530220924928 -118747255799808 -118747255799808 -52776558133248 -8796093022208", "new_number": "12.17", "id": 354, "operator_tex": "\\theta^4+2^{2} x\\left(24\\theta^4+6\\theta^3+11\\theta^2+8\\theta+2\\right)+2^{4} x^{2}\\left(209\\theta^4+2\\theta^3+23\\theta^2-10\\right)+2^{7} x^{3}\\left(223\\theta^4-1218\\theta^3-2225\\theta^2-2088\\theta-776\\right)-2^{10} x^{4}\\left(1409\\theta^4+9634\\theta^3+19337\\theta^2+18420\\theta+6872\\right)-2^{13} x^{5}\\left(6527\\theta^4+35858\\theta^3+78357\\theta^2+78428\\theta+30414\\right)-2^{17} x^{6}\\left(6276\\theta^4+37704\\theta^3+91143\\theta^2+97914\\theta+40036\\right)-2^{21} x^{7}\\left(2923\\theta^4+22130\\theta^3+61939\\theta^2+73401\\theta+32138\\right)-2^{24} x^{8}\\left(602\\theta^4+10928\\theta^3+42765\\theta^2+60182\\theta+29287\\right)+2^{26} x^{9}\\left(2352\\theta^4+7392\\theta^3-7024\\theta^2-31968\\theta-21891\\right)+2^{29} x^{10}\\left(1584\\theta^4+11904\\theta^3+24696\\theta^2+19776\\theta+4915\\right)-2^{35} x^{11}\\left(16\\theta^4-176\\theta^3-784\\theta^2-1036\\theta-449\\right)-2^{39} x^{12}\\left((2\\theta+3)^4\\right)", "superseek": "4 52", "discriminant": "12 1 96 3344 28544 -1442816 -53469184 -822607872 -6129975296 -10099884032 157840048128 850403524608 -549755813888 -8796093022208", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "e65be092d4832d3740d2a3078755f447", "dim_h": null, "inst": " 4 7/2 52 500 2796 108891/2 523876 8014175 112614496 3281174301/2", "cleanlist": "True", "n_sing_real": "6", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "8", "laurent": null, "discriminant_tex": "-(8z+1)(256z^2+16z-1)(1024z^3-160z^2-28z-1)^2(16z+1)^3", "discr_factors": "-8796093022208, (z^3-5/32*z^2-7/256*z-1/1024)^2, (z+1/16)^3, z^2+1/16*z-1/256, z+1/8", "dm_basis": null, "q": "0 1 0 -64 -256 -336 -3584 -161792 -3244032 -45146984", "yuk": "1 4 32 1408 32032 349504 11761664 179689472 4103289632 82095968992", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/8","im":"0","approx_re":"-0.125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/32-1/32*5^(1/2)","im":"0","approx_re":"-0.101127","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/16","im":"0","approx_re":"-0.0625","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/192*(1187+6*3165^(1/2))^(1/3)-109/192/(1187+6*3165^(1/2))^(1/3)+5/96","im":"-1/8*3^(1/2)*(1/24*(1187+6*3165^(1/2))^(1/3)-109/24/(1187+6*3165^(1/2))^(1/3))","approx_re":"-0.057187","approx_im":"-0.018391","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/192*(1187+6*3165^(1/2))^(1/3)-109/192/(1187+6*3165^(1/2))^(1/3)+5/96","im":"1/8*3^(1/2)*(1/24*(1187+6*3165^(1/2))^(1/3)-109/24/(1187+6*3165^(1/2))^(1/3))","approx_re":"-0.057187","approx_im":"0.018391","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":"-1/32+1/32*5^(1/2)","im":"0","approx_re":"0.038627","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/96*(1187+6*3165^(1/2))^(1/3)+109/96/(1187+6*3165^(1/2))^(1/3)+5/96","im":"0","approx_re":"0.270624","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":["3/2","3/2","3/2","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -152*X^4-200*X^3-212*X^2-112*X-24, 9872*X^4+25568*X^3+37776*X^2+28992*X+9376, -364032*X^4-1399808*X^3-2642176*X^2-2539008*X-1014016, 8529920*X^4+43130880*X^3+98770944*X^2+112343040*X+52101120, -135135232*X^4-830013440*X^3-2213789696*X^2-2879913984*X-1501495296, 1517879296*X^4+10569777152*X^3+31405178880*X^2+45223772160*X+25817448448, -12704546816*X^4-93967089664*X^3-293598134272*X^2-446554963968*X-269278511104, 83248545792*X^4+626159255552*X^3+1939722993664*X^2+2903272062976*X+1730242674688, -436207616000*X^4-3331284008960*X^3-10178669838336*X^2-14365726081024*X-7823954018304, 1791001362432*X^4+13958643712000*X^3+44105019162624*X^2+63200443760640*X+33853200662528, -5634997092352*X^4-43843026157568*X^3-140393890971648*X^2-210762635149312*X-122007135977472, 13194139533312*X^4+107752139522048*X^3+340298848796672*X^2+490931941801984*X+272060408397824, -1099511627776*(2*X+5)^4]", "text": "This is operator \"13.3\" from ...", "degz": 13, "h3": null, "sol": "1 24 464 8832 178960 4010368 100357376 2772019200 82738408720 2613822935424", "n_discr_factors": "4", "c3": null, "operator": "4 13 0 0 0 0 1 -24 -112 -212 -200 -152 9376 28992 37776 25568 9872 -1014016 -2539008 -2642176 -1399808 -364032 52101120 112343040 98770944 43130880 8529920 -1501495296 -2879913984 -2213789696 -830013440 -135135232 25817448448 45223772160 31405178880 10569777152 1517879296 -269278511104 -446554963968 -293598134272 -93967089664 -12704546816 1730242674688 2903272062976 1939722993664 626159255552 83248545792 -7823954018304 -14365726081024 -10178669838336 -3331284008960 -436207616000 33853200662528 63200443760640 44105019162624 13958643712000 1791001362432 -122007135977472 -210762635149312 -140393890971648 -43843026157568 -5634997092352 272060408397824 490931941801984 340298848796672 107752139522048 13194139533312 -687194767360000 -1099511627776000 -659706976665600 -175921860444160 -17592186044416", "new_number": "13.3", "id": 371, "operator_tex": "\\theta^4-2^{2} x\\left(38\\theta^4+50\\theta^3+53\\theta^2+28\\theta+6\\right)+2^{4} x^{2}\\left(617\\theta^4+1598\\theta^3+2361\\theta^2+1812\\theta+586\\right)-2^{8} x^{3}\\left(1422\\theta^4+5468\\theta^3+10321\\theta^2+9918\\theta+3961\\right)+2^{11} x^{4}\\left(4165\\theta^4+21060\\theta^3+48228\\theta^2+54855\\theta+25440\\right)-2^{14} x^{5}\\left(8248\\theta^4+50660\\theta^3+135119\\theta^2+175776\\theta+91644\\right)+2^{16} x^{6}\\left(23161\\theta^4+161282\\theta^3+479205\\theta^2+690060\\theta+393943\\right)-2^{20} x^{7}\\left(12116\\theta^4+89614\\theta^3+279997\\theta^2+425868\\theta+256804\\right)+2^{23} x^{8}\\left(9924\\theta^4+74644\\theta^3+231233\\theta^2+346097\\theta+206261\\right)-2^{27} x^{9}\\left(3250\\theta^4+24820\\theta^3+75837\\theta^2+107033\\theta+58293\\right)+2^{28} x^{10}\\left(6672\\theta^4+52000\\theta^3+164304\\theta^2+235440\\theta+126113\\right)-2^{32} x^{11}\\left(1312\\theta^4+10208\\theta^3+32688\\theta^2+49072\\theta+28407\\right)+2^{36} x^{12}\\left(192\\theta^4+1568\\theta^3+4952\\theta^2+7144\\theta+3959\\right)-2^{40} x^{13}\\left((2\\theta+5)^4\\right)", "superseek": "4 52", "discriminant": "13 1 -152 9872 -364032 8529920 -135135232 1517879296 -12704546816 83248545792 -436207616000 1791001362432 -5634997092352 13194139533312 -17592186044416", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "9127ce057848ca38f220a7bb67e245a2", "dim_h": null, "inst": " 4 7/2 52 500 2796 108891/2 523876 8014175 112614496 3281174301/2", "cleanlist": "True", "n_sing_real": "6", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "8", "laurent": null, "discriminant_tex": "-(1-48z+256z^2)(8z-1)^2(512z^3-32z^2+20z-1)^2(16z-1)^3", "discr_factors": "-17592186044416, (z^3-1/16*z^2+5/128*z-1/512)^2, 1/256-3/16*z+z^2, (z-1/8)^2, (z-1/16)^3", "dm_basis": null, "q": "0 1 -16 192 -2304 24240 -254976 2316288 -22216704 157621400", "yuk": "1 4 32 1408 32032 349504 11761664 179689472 4103289632 82095968992", "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":"-1/96*(64+3*3165^(1/2))^(1/3)+29/96/(64+3*3165^(1/2))^(1/3)+1/48","im":"-1/8*3^(1/2)*(1/12*(64+3*3165^(1/2))^(1/3)+29/12/(64+3*3165^(1/2))^(1/3))","approx_re":"0.005863","approx_im":"-0.196043","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/96*(64+3*3165^(1/2))^(1/3)+29/96/(64+3*3165^(1/2))^(1/3)+1/48","im":"1/8*3^(1/2)*(1/12*(64+3*3165^(1/2))^(1/3)+29/12/(64+3*3165^(1/2))^(1/3))","approx_re":"0.005863","approx_im":"0.196043","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"3/32-1/32*5^(1/2)","im":"0","approx_re":"0.023873","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/48*(64+3*3165^(1/2))^(1/3)-29/48/(64+3*3165^(1/2))^(1/3)+1/48","im":"0","approx_re":"0.050774","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","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/8","im":"0","approx_re":"0.125","approx_im":"0.0","exponents":["0","0","-1","1"],"monodromy":[],"monodromy_dm":[]},{"re":"3/32+1/32*5^(1/2)","im":"0","approx_re":"0.163627","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":["5/2","5/2","5/2","5/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -48*X^4+96*X^3+92*X^2+44*X+8, -4096*X^4-50176*X^3-61952*X^2-28544*X-5248, 126976*X^4-122880*X^3-3571712*X^2-3280896*X-888832, -27525120*X^4-11796480*X^3+261881856*X^2+190906368*X+45416448, -809500672*X^4-8346664960*X^3-7846494208*X^2-1582301184*X+278921216, 3087007744*X^4+185623117824*X^3+156564979712*X^2+45097156608*X+1275068416, -2560874250240*X^4-4992899481600*X^3-3741990256640*X^2-1245540515840*X-150323855360, -1717986918400*(X+1)^4]", "text": "This is operator \"8.66\" from ...", "degz": 8, "h3": null, "sol": "1 -8 424 -6272 859816 2204992 2994022144 96187875328 15174775326376 906671921263552", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 1 8 44 92 96 -48 -5248 -28544 -61952 -50176 -4096 -888832 -3280896 -3571712 -122880 126976 45416448 190906368 261881856 -11796480 -27525120 278921216 -1582301184 -7846494208 -8346664960 -809500672 1275068416 45097156608 156564979712 185623117824 3087007744 -150323855360 -1245540515840 -3741990256640 -4992899481600 -2560874250240 -1717986918400 -6871947673600 -10307921510400 -6871947673600 -1717986918400", "new_number": "8.66", "id": 514, "operator_tex": "\\theta^4-2^{2} x\\left(12\\theta^4-24\\theta^3-23\\theta^2-11\\theta-2\\right)-2^{7} x^{2}\\left(32\\theta^4+392\\theta^3+484\\theta^2+223\\theta+41\\right)+2^{12} x^{3}\\left(31\\theta^4-30\\theta^3-872\\theta^2-801\\theta-217\\right)-2^{16} 3 x^{4}\\left(140\\theta^4+60\\theta^3-1332\\theta^2-971\\theta-231\\right)-2^{20} x^{5}\\left(772\\theta^4+7960\\theta^3+7483\\theta^2+1509\\theta-266\\right)+2^{26} x^{6}\\left(46\\theta^4+2766\\theta^3+2333\\theta^2+672\\theta+19\\right)-2^{30} 5 x^{7}\\left(477\\theta^4+930\\theta^3+697\\theta^2+232\\theta+28\\right)-2^{36} 5^{2} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "4 12332", "discriminant": "8 1 -48 -4096 126976 -27525120 -809500672 3087007744 -2560874250240 -1717986918400", "aesz": null, "n_sing_complex": "5", "inst_int": "", "c2h": null, "hash": "d941d8e5d41f2e7285be47b4fbc81023", "dim_h": null, "inst": " 4 500 12332 358180 15491360 885685372 54935795244 3548002584068 239694499238576 16917401503904160", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "7", "laurent": null, "discriminant_tex": "-(64z+1)(4096z^3+6144z^2+48z-1)(1-32z+2560z^2)^2", "discr_factors": "-1717986918400, z+1/64, (1/2560-1/80*z+z^2)^2, z^3+3/2*z^2+3/256*z-1/4096", "dm_basis": null, "q": "0 1 12 -930 -52496 -1340883 -28378200 -2072239982 -209770968384 -17118246818298", "yuk": "1 4 4004 332968 22927524 1936420004 191308377320 18842977768696 1816577345970340 174737289945254872", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-3/64*(-148+4*I*3^(1/2))^(1/3)-21/16/(-148+4*I*3^(1/2))^(1/3)-1/2+1/32*I*3^(1/2)*(3/2*(-148+4*I*3^(1/2))^(1/3)-42/(-148+4*I*3^(1/2))^(1/3))","im":"0","approx_re":"-1.492036","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-3/64*(-148+4*I*3^(1/2))^(1/3)-21/16/(-148+4*I*3^(1/2))^(1/3)-1/2-1/32*I*3^(1/2)*(3/2*(-148+4*I*3^(1/2))^(1/3)-42/(-148+4*I*3^(1/2))^(1/3))","im":"0","approx_re":"-0.017379","approx_im":"0.0","exponents":["0","1","1","2"],"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":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/160","im":"-3/160","approx_re":"0.00625","approx_im":"-0.01875","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/160","im":"3/160","approx_re":"0.00625","approx_im":"0.01875","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"3/32*(-148+4*I*3^(1/2))^(1/3)+21/8/(-148+4*I*3^(1/2))^(1/3)-1/2","im":"0","approx_re":"0.009415","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":[]}]}]}