{"count": 9, "status":"OK", "data":[{"pols": "[X^4, 15*X^4+30*X^3+35*X^2+20*X+4, -32*(X+1)^2*(66*X^2+132*X+53), -12544*(X+1)*(X+2)*(2*X+1)*(2*X+5)]", "text": "Operator equivalent to AESZ 100= $ a \\ast a$", "degz": 3, "h3": "36", "sol": "1 -4 132 -1120 72100 -265104 59047296 350118912 63064312740 1096066914800", "n_discr_factors": "2", "c3": "-72", "operator": "4 3 0 0 0 0 1 4 20 35 30 15 -1696 -7616 -12256 -8448 -2112 -125440 -489216 -614656 -301056 -50176", "new_number": "3.8", "id": 103, "operator_tex": "\\theta^4+x\\left(15\\theta^4+30\\theta^3+35\\theta^2+20\\theta+4\\right)-2^{5} x^{2}(\\theta+1)^2(66\\theta^2+132\\theta+53)-2^{8} 7^{2} x^{3}(\\theta+1)(\\theta+2)(2\\theta+1)(2\\theta+5)", "superseek": "5 454", "discriminant": "3 1 15 -2112 -50176", "aesz": "~100", "n_sing_complex": "0", "inst_int": "", "c2h": "72", "hash": "82a1ac6ac6fb9ab2e4d6b5d5790d1d9b", "dim_h": "12", "inst": " 5 42 454 7498 154351 3652254 94572705 2621325434 76541504257 2329054186336", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "-(49z-1)(1+32z)^2", "discr_factors": "-50176, (1/32+z)^2, z-1/49", "dm_basis": null, "q": "0 1 4 -258 -4616 -15963 203304 -9506154 -568626864 -17941215870", "yuk": "1 5 341 12263 480213 19293880 788899463 32438437820 1342119102421 55798756615616", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/32","im":"0","approx_re":"-0.03125","approx_im":"0.0","exponents":["0","1/2","1/2","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":"1/49","im":"0","approx_re":"0.0204081632653","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","2","5/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[49*X^4, 1876*X^4+4004*X^3+3276*X^2+1274*X+196, -7672-32900*X-54004*X^2-41064*X^3-12732*X^4, 20704*X^4+67200*X^3+82048*X^2+45192*X+9520, -8352-34416*X-54768*X^2-40704*X^3-12288*X^4, 2304*(X+1)^4]", "text": "There is a second MUM-point corresponding to Operator AESZ 117 /5.515.", "degz": 5, "h3": null, "sol": "1 -4 64 -1408 37216 -1093504 34467616 -1141889536 39261600352 -1389328714624", "n_discr_factors": "3", "c3": null, "operator": "4 5 0 0 0 0 49 196 1274 3276 4004 1876 -7672 -32900 -54004 -41064 -12732 9520 45192 82048 67200 20704 -8352 -34416 -54768 -40704 -12288 2304 9216 13824 9216 2304", "new_number": "5.31", "id": 240, "operator_tex": "7^{2} \\theta^4+2 7 x\\left(134\\theta^4+286\\theta^3+234\\theta^2+91\\theta+14\\right)-2^{2} x^{2}\\left(3183\\theta^4+10266\\theta^3+13501\\theta^2+8225\\theta+1918\\right)+2^{3} x^{3}\\left(2588\\theta^4+8400\\theta^3+10256\\theta^2+5649\\theta+1190\\right)-2^{4} 3 x^{4}\\left(256\\theta^4+848\\theta^3+1141\\theta^2+717\\theta+174\\right)+2^{8} 3^{2} x^{5}\\left((\\theta+1)^4\\right)", "superseek": "-20/7 -104", "discriminant": "5 49 1876 -12732 20704 -12288 2304", "aesz": "212", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "f72aa947ba945355102b3fef56e0af0f", "dim_h": null, "inst": " -20/7 57/4 -104 16385/14 -110508/7 487971/2 -28874844/7 522536803/7 -9957702452/7 112972467743/4", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "(4z-1)(16z^2-44z-1)(6z-7)^2", "discr_factors": "2304, z^2-11/4*z-1/16, (z-7/6)^2, z-1/4", "dm_basis": null, "q": "0 1 10 1 -20 -2412 31482 -619038 12504648 -262953732", "yuk": "1 -20/7 778/7 -19676/7 75014 -1973360 368887198/7 -9904071512/7 267539368234/7 -7259165107184/7", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"11/8-5/8*5^(1/2)","im":"0","approx_re":"-0.022542","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":"7/6","im":"0","approx_re":"1.16666666667","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"11/8+5/8*5^(1/2)","im":"0","approx_re":"2.772542","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, -24*X^3+84*X^4+4+12*X, -896*X-528-256*X^2-1536*X^3+2016*X^4, -10432-14464*X^2-21504*X^3+5376*X^4-23424*X, 3072000*X^3+239616*X^4+2500608+7127040*X+7557120*X^2, 528994304*X+200302592+512352256*X^2+205283328*X^3+28790784*X^4, 14929625088*X+4824367104*X^3+13212516352*X^2+6033784832+631603200*X^4, 183785619456*X+46446673920*X^3+146370330624*X^2+79572303872+5081923584*X^4, 340338409472+717557334016*X+9616490496*X^4+122922467328*X^3+490150559744*X^2, -8388608*(2*X+3)*(2114*X^3+16713*X^2+37111*X+22497), 5033164800*(X+1)*(2*X+5)*(2*X+3)*(X+3)]", "text": "This is operator \"10.6\" from ...", "degz": 10, "h3": null, "sol": "1 -4 52 -688 2500 -124624 660976 -2006848 504491332 4419175280", "n_discr_factors": "4", "c3": null, "operator": "4 10 0 0 0 0 1 4 12 0 -24 84 -528 -896 -256 -1536 2016 -10432 -23424 -14464 -21504 5376 2500608 7127040 7557120 3072000 239616 200302592 528994304 512352256 205283328 28790784 6033784832 14929625088 13212516352 4824367104 631603200 79572303872 183785619456 146370330624 46446673920 5081923584 340338409472 717557334016 490150559744 122922467328 9616490496 -566155542528 -1311365922816 -1043215679488 -333598162944 -35467034624 226492416000 543581798400 458017996800 161061273600 20132659200", "new_number": "10.6", "id": 322, "operator_tex": "\\theta^4+2^{2} x\\left(21\\theta^4-6\\theta^3+3\\theta+1\\right)+2^{4} x^{2}\\left(126\\theta^4-96\\theta^3-16\\theta^2-56\\theta-33\\right)+2^{6} x^{3}\\left(84\\theta^4-336\\theta^3-226\\theta^2-366\\theta-163\\right)+2^{11} 3 x^{4}\\left(39\\theta^4+500\\theta^3+1230\\theta^2+1160\\theta+407\\right)+2^{12} x^{5}\\left(7029\\theta^4+50118\\theta^3+125086\\theta^2+129149\\theta+48902\\right)+2^{14} x^{6}\\left(38550\\theta^4+294456\\theta^3+806428\\theta^2+911232\\theta+368273\\right)+2^{16} x^{7}\\left(77544\\theta^4+708720\\theta^3+2233434\\theta^2+2804346\\theta+1214177\\right)+2^{20} x^{8}\\left(9171\\theta^4+117228\\theta^3+467444\\theta^2+684316\\theta+324572\\right)-2^{23} x^{9}(2\\theta+3)(2114\\theta^3+16713\\theta^2+37111\\theta+22497)+2^{26} 3 5^{2} x^{10}(\\theta+1)(2\\theta+5)(2\\theta+3)(\\theta+3)", "superseek": "8 2200/9", "discriminant": "10 1 84 2016 5376 239616 28790784 631603200 5081923584 9616490496 -35467034624 20132659200", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "b5aa0abf76ddfbd280ec220a43822aa4", "dim_h": null, "inst": " 8 -75/2 2200/9 -8117/2 47936 -4052675/6 11499480 -175321542 2998366528 -53613060132", "cleanlist": "True", "n_sing_real": "6", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "8", "laurent": null, "discriminant_tex": "(12z+1)(6400z^3+192z^2-24z+1)(16z+1)^2(32z^2-32z-1)^2", "discr_factors": "20132659200, (z+1/16)^2, z+1/12, z^3+3/100*z^2-3/800*z+1/6400, (z^2-z-1/32)^2", "dm_basis": null, "q": "0 1 -4 6 464 3333 -67896 874138 -18622400 293110866", "yuk": "1 8 -292 6608 -260036 5992008 -145889992 3944321648 -89764889540 2185809205520", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-9/200*2^(1/3)-3/200*2^(2/3)-1/100","im":"0","approx_re":"-0.090507","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/12","im":"0","approx_re":"-0.0833333333333","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","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"1/2-3/8*2^(1/2)","im":"0","approx_re":"-0.03033","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":"9/400*2^(1/3)+3/400*2^(2/3)-1/100","im":"1/8*3^(1/2)*(-9/50*2^(1/3)+3/50*2^(2/3))","approx_re":"0.030254","approx_im":"-0.02848","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"9/400*2^(1/3)+3/400*2^(2/3)-1/100","im":"-1/8*3^(1/2)*(-9/50*2^(1/3)+3/50*2^(2/3))","approx_re":"0.030254","approx_im":"0.02848","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/2+3/8*2^(1/2)","im":"0","approx_re":"1.03033","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","3/2","5/2","3"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[25*X^4, 80*X^4+1120*X^3+1060*X^2+500*X+100, -15616*X^4-99328*X^3-144256*X^2-101760*X-31760, 212992*X^4-589824*X^3-2886656*X^2-3271680*X-1406720, 1441792*X^4+38273024*X^3+133070848*X^2+162693120*X+74915840, -119537664*X^4-553648128*X^3-68943872*X^2+451149824*X+378208256, 905969664*X^4+402653184*X^3-8002732032*X^2-20006830080*X-12308185088, 11811160064*X^4+168577466368*X^3+365810417664*X^2+374937223168*X+131650813952, -253403070464*X^4-1168231104512*X^3-4232690270208*X^2-6251324899328*X-3202434990080, 1443109011456*X^4+2886218022912*X^3+4913442586624*X^2+12472585027584*X+9212704849920, 25288767438848*X^4+83562883710976*X^3+89610197663744*X^2-16492674416640*X-47897475284992, -17592186044416*(2*X+3)*(4*X^3+28*X^2+51*X+28), -70368744177664*(2*X+3)^4]", "text": "This is operator \"12.3\" from ...", "degz": 12, "h3": null, "sol": "1 -4 108 -912 21484 -254064 5580272 -82631232 1766989548 -30747656496", "n_discr_factors": "4", "c3": null, "operator": "4 12 0 0 0 0 25 100 500 1060 1120 80 -31760 -101760 -144256 -99328 -15616 -1406720 -3271680 -2886656 -589824 212992 74915840 162693120 133070848 38273024 1441792 378208256 451149824 -68943872 -553648128 -119537664 -12308185088 -20006830080 -8002732032 402653184 905969664 131650813952 374937223168 365810417664 168577466368 11811160064 -3202434990080 -6251324899328 -4232690270208 -1168231104512 -253403070464 9212704849920 12472585027584 4913442586624 2886218022912 1443109011456 -47897475284992 -16492674416640 89610197663744 83562883710976 25288767438848 -1477743627730944 -3676766883282944 -3272146604261376 -1196268651020288 -140737488355328 -5699868278390784 -15199648742375424 -15199648742375424 -6755399441055744 -1125899906842624", "new_number": "12.3", "id": 357, "operator_tex": "5^{2} \\theta^4+2^{2} 5 x\\left(4\\theta^4+56\\theta^3+53\\theta^2+25\\theta+5\\right)-2^{4} x^{2}\\left(976\\theta^4+6208\\theta^3+9016\\theta^2+6360\\theta+1985\\right)+2^{8} x^{3}\\left(832\\theta^4-2304\\theta^3-11276\\theta^2-12780\\theta-5495\\right)+2^{13} x^{4}\\left(176\\theta^4+4672\\theta^3+16244\\theta^2+19860\\theta+9145\\right)-2^{16} x^{5}\\left(1824\\theta^4+8448\\theta^3+1052\\theta^2-6884\\theta-5771\\right)+2^{21} x^{6}\\left(432\\theta^4+192\\theta^3-3816\\theta^2-9540\\theta-5869\\right)+2^{24} x^{7}\\left(704\\theta^4+10048\\theta^3+21804\\theta^2+22348\\theta+7847\\right)-2^{29} x^{8}\\left(472\\theta^4+2176\\theta^3+7884\\theta^2+11644\\theta+5965\\right)+2^{32} x^{9}\\left(336\\theta^4+672\\theta^3+1144\\theta^2+2904\\theta+2145\\right)+2^{36} x^{10}\\left(368\\theta^4+1216\\theta^3+1304\\theta^2-240\\theta-697\\right)-2^{44} x^{11}(2\\theta+3)(4\\theta^3+28\\theta^2+51\\theta+28)-2^{46} x^{12}\\left((2\\theta+3)^4\\right)", "superseek": "-12/5 444/5", "discriminant": "12 25 80 -15616 212992 1441792 -119537664 905969664 11811160064 -253403070464 1443109011456 25288767438848 -140737488355328 -1125899906842624", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "45726409a4c817f929c9e6e49b33a941", "dim_h": null, "inst": " -12/5 103/5 444/5 1148/5 -6704 -282147/5 -102292 6992044 315076744/5 41866252/5", "cleanlist": "True", "n_sing_real": "6", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "8", "laurent": null, "discriminant_tex": "-(-1-16z+256z^2)(16z+1)^2(16z-1)^2(8192z^3+768z^2-32z+5)^2", "discr_factors": "-1125899906842624, -1/256-1/16*z+z^2, (z-1/16)^2, (z+1/16)^2, (z^3+3/32*z^2-1/256*z+5/8192)^2", "dm_basis": null, "q": "0 1 4 -90 -1008 4865 179032 687410 -19539392 -279357676", "yuk": "1 -12/5 812/5 11976/5 74284/5 -4190012/5 -60930952/5 -175430792/5 17899706924/5 229690958352/5", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/96*(351+6*3165^(1/2))^(1/3)-7/32/(351+6*3165^(1/2))^(1/3)-1/32","im":"0","approx_re":"-0.148005","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","1","1"],"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":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/192*(351+6*3165^(1/2))^(1/3)+7/64/(351+6*3165^(1/2))^(1/3)-1/32","im":"1/32*3^(1/2)*(-1/6*(351+6*3165^(1/2))^(1/3)+7/2/(351+6*3165^(1/2))^(1/3))","approx_re":"0.027128","approx_im":"-0.058206","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/192*(351+6*3165^(1/2))^(1/3)+7/64/(351+6*3165^(1/2))^(1/3)-1/32","im":"-1/32*3^(1/2)*(-1/6*(351+6*3165^(1/2))^(1/3)+7/2/(351+6*3165^(1/2))^(1/3))","approx_re":"0.027128","approx_im":"0.058206","exponents":["0","1","3","4"],"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":"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":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["3/2","3/2","3/2","3/2"],"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": "[X^4, -88*X^3+4-71*X^4-42*X^2+2*X, -10462*X-13294*X^2-875*X^4-6848*X^3-3132, 3357*X^4-208620-403812*X-276444*X^2-57240*X^3, 679104*X^3-1214676*X-1229580+262116*X^2+149283*X^4, 22661694*X^2+492075*X^4+7820712+23317794*X+8345592*X^3, -4782969*X^4+73338858*X^2+162620946*X+103453848, -43046721*(X+2)^4]", "text": "This is operator \"7.20\" from ...", "degz": 7, "h3": null, "sol": "1 -4 147 4496 223111 12256428 709357485 43160215488 2720187059895 176274536441396", "n_discr_factors": "3", "c3": null, "operator": "4 7 0 0 0 0 1 4 2 -42 -88 -71 -3132 -10462 -13294 -6848 -875 -208620 -403812 -276444 -57240 3357 -1229580 -1214676 262116 679104 149283 7820712 23317794 22661694 8345592 492075 103453848 162620946 73338858 0 -4782969 -688747536 -1377495072 -1033121304 -344373768 -43046721", "new_number": "7.20", "id": 443, "operator_tex": "\\theta^4-x\\left(88\\theta^3-4+71\\theta^4+42\\theta^2-2\\theta\\right)-x^{2}\\left(10462\\theta+13294\\theta^2+875\\theta^4+6848\\theta^3+3132\\right)+3^{2} x^{3}\\left(373\\theta^4-6360\\theta^3-30716\\theta^2-44868\\theta-23180\\right)+3^{4} x^{4}\\left(1843\\theta^4+8384\\theta^3+3236\\theta^2-14996\\theta-15180\\right)+3^{8} x^{5}\\left(75\\theta^4+1272\\theta^3+3454\\theta^2+3554\\theta+1192\\right)-3^{11} x^{6}\\left(27\\theta^4-414\\theta^2-918\\theta-584\\right)-3^{16} x^{7}\\left((\\theta+2)^4\\right)", "superseek": "10 3394/3", "discriminant": "7 1 -71 -875 3357 149283 492075 -4782969 -43046721", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "9d5791eaabb9d0e9cb4b5cd0b2158b12", "dim_h": null, "inst": " 10 77 3394/3 24029 640402 58912007/3 659800738 23733455789 2698636083688/3 35532268316211", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "-(-1+81z)(9z-1)^2(81z^2+14z+1)^2", "discr_factors": "-43046721, -1/81+z, (z-1/9)^2, (z^2+14/81*z+1/81)^2", "dm_basis": null, "q": "0 1 -14 -135 -458 -22038 -1292652 -48153487 -1891905026 -78912224514", "yuk": "1 10 626 30556 1538482 80050260 4241695676 226311653144 12151530902450 655768568366740", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-7/81","im":"-4/81*2^(1/2)","approx_re":"-0.0864197530864","approx_im":"-0.069838","exponents":["0","-1/2","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"-7/81","im":"4/81*2^(1/2)","approx_re":"-0.0864197530864","approx_im":"0.069838","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":"1/81","im":"0","approx_re":"0.0123456790123","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/9","im":"0","approx_re":"0.111111111111","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":["2","2","2","2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, 82*X^4+98*X^3+77*X^2+28*X+4, -636-2916*X-4463*X^2-1850*X^3+553*X^4, -24348*X^4-90168*X^3-108796*X^2-59664*X-12544, -232704-958176*X-1354432*X^2-728000*X^3-231712*X^4, 963072*X^4+255744*X^3-2946432*X^2-3152256*X-919808, 415744+7217664*X+22600448*X^2+24046080*X^3+5878016*X^4, -20034560*X^4-43583488*X^3-38857728*X^2-17065984*X-3141632, 2768896*(X+1)^4]", "text": "This operator has a second MUM-point at infinity corresponding to operator 8.28", "degz": 8, "h3": null, "sol": "1 -4 112 -3712 155536 -7165504 355277056 -18506272768 1000758296848 -55700350533184", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 1 4 28 77 98 82 -636 -2916 -4463 -1850 553 -12544 -59664 -108796 -90168 -24348 -232704 -958176 -1354432 -728000 -231712 -919808 -3152256 -2946432 255744 963072 415744 7217664 22600448 24046080 5878016 -3141632 -17065984 -38857728 -43583488 -20034560 2768896 11075584 16613376 11075584 2768896", "new_number": "8.29", "id": 473, "operator_tex": "\\theta^4+x\\left(82\\theta^4+98\\theta^3+77\\theta^2+28\\theta+4\\right)-x^{2}\\left(636+2916\\theta+4463\\theta^2+1850\\theta^3-553\\theta^4\\right)-2^{2} x^{3}\\left(6087\\theta^4+22542\\theta^3+27199\\theta^2+14916\\theta+3136\\right)-2^{5} x^{4}\\left(7241\\theta^4+22750\\theta^3+42326\\theta^2+29943\\theta+7272\\right)+2^{7} x^{5}\\left(7524\\theta^4+1998\\theta^3-23019\\theta^2-24627\\theta-7186\\right)+2^{8} x^{6}\\left(22961\\theta^4+93930\\theta^3+88283\\theta^2+28194\\theta+1624\\right)-2^{10} 13 x^{7}\\left(1505\\theta^4+3274\\theta^3+2919\\theta^2+1282\\theta+236\\right)+2^{14} 13^{2} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "-5 -641", "discriminant": "8 1 82 553 -24348 -231712 963072 5878016 -20034560 2768896", "aesz": "304", "n_sing_complex": "3", "inst_int": "", "c2h": null, "hash": "cf055a245b1537ed4f2609fa56cf67aa", "dim_h": null, "inst": " -5 469/8 -641 50173/4 -276231 58913297/8 -211861501 26272904923/4 -213904895800 58141299762679/8", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "7", "laurent": null, "discriminant_tex": "(16z-1)(64z^3-432z^2-76z-1)(-1-11z+52z^2)^2", "discr_factors": "2768896, (-1/52-11/52*z+z^2)^2, z-1/16, z^3-27/4*z^2-19/16*z-1/64", "dm_basis": null, "q": "0 1 12 -112 -192 -20336 562432 -19211008 653916160 -23597083368", "yuk": "1 -5 464 -17312 803232 -34528880 1590642176 -72668494848 3362932633376 -155936669055512", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/24*(22005+111*I*111^(1/2))^(1/3)-131/4/(22005+111*I*111^(1/2))^(1/3)+9/4+1/8*I*3^(1/2)*(1/3*(22005+111*I*111^(1/2))^(1/3)-262/(22005+111*I*111^(1/2))^(1/3))","im":"0","approx_re":"-0.157556","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"11/104-1/104*329^(1/2)","im":"0","approx_re":"-0.068638","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/24*(22005+111*I*111^(1/2))^(1/3)-131/4/(22005+111*I*111^(1/2))^(1/3)+9/4-1/8*I*3^(1/2)*(1/3*(22005+111*I*111^(1/2))^(1/3)-262/(22005+111*I*111^(1/2))^(1/3))","im":"0","approx_re":"-0.014327","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","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"11/104+1/104*329^(1/2)","im":"0","approx_re":"0.280177","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/12*(22005+111*I*111^(1/2))^(1/3)+131/2/(22005+111*I*111^(1/2))^(1/3)+9/4","im":"0","approx_re":"6.921883","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": "[25*X^4, 380*X^4+1720*X^3+1460*X^2+600*X+100, 11344*X^4+68032*X^3+117424*X^2+77280*X+18640, -107520*X^4-29184*X^3+843264*X^2+1013760*X+339200, -971776*X^4-6944768*X^3-11622400*X^2-7904256*X-1934336, 5386240*X^4+17539072*X^3+29487104*X^2+23527424*X+6926336, 10043392*X^4+25559040*X^3+15941632*X^2-3538944*X-4079616, -2883584-10223616*X-10485760*X^2-524288*X^3+2883584*X^4, -1048576*(X+1)^4]", "text": "This is operator \"8.45\" from ...", "degz": 8, "h3": null, "sol": "1 -4 -4 464 -4244 -64304 2188976 -10994624 -630978836 14385797456", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 25 100 600 1460 1720 380 18640 77280 117424 68032 11344 339200 1013760 843264 -29184 -107520 -1934336 -7904256 -11622400 -6944768 -971776 6926336 23527424 29487104 17539072 5386240 -4079616 -3538944 15941632 25559040 10043392 -2883584 -10223616 -10485760 -524288 2883584 -1048576 -4194304 -6291456 -4194304 -1048576", "new_number": "8.45", "id": 491, "operator_tex": "5^{2} \\theta^4+2^{2} 5 x\\left(19\\theta^4+86\\theta^3+73\\theta^2+30\\theta+5\\right)+2^{4} x^{2}\\left(709\\theta^4+4252\\theta^3+7339\\theta^2+4830\\theta+1165\\right)-2^{8} x^{3}\\left(420\\theta^4+114\\theta^3-3294\\theta^2-3960\\theta-1325\\right)-2^{10} x^{4}\\left(949\\theta^4+6782\\theta^3+11350\\theta^2+7719\\theta+1889\\right)+2^{12} x^{5}\\left(1315\\theta^4+4282\\theta^3+7199\\theta^2+5744\\theta+1691\\right)+2^{14} x^{6}\\left(613\\theta^4+1560\\theta^3+973\\theta^2-216\\theta-249\\right)+2^{18} x^{7}\\left(11\\theta^4-2\\theta^3-40\\theta^2-39\\theta-11\\right)-2^{20} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "-12/5 -20", "discriminant": "8 25 380 11344 -107520 -971776 5386240 10043392 2883584 -1048576", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "52e4f6959f297529016ddef66a399c12", "dim_h": null, "inst": " -12/5 -83/5 -20 3941/20 -13872/5 -197789/5 173580 57625509/20 -244692056/5 -480447172", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "7", "laurent": null, "discriminant_tex": "-(8z+1)(128z^3-624z^2-20z-1)(-5+32z+32z^2)^2", "discr_factors": "-1048576, z^3-39/8*z^2-5/32*z-1/128, z+1/8, (-5/32+z+z^2)^2", "dm_basis": null, "q": "0 1 8 126 1280 12209 135664 1558810 14866944 131815364", "yuk": "1 -12/5 -676/5 -2712/5 12476 -1734012/5 -8545160 297689688/5 7376127532/5 -178380511536/5", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/2-1/8*26^(1/2)","im":"0","approx_re":"-1.137377","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":"-1/48*(61128+177*177^(1/2))^(1/3)-517/16/(61128+177*177^(1/2))^(1/3)+13/8","im":"-1/8*3^(1/2)*(1/6*(61128+177*177^(1/2))^(1/3)-517/2/(61128+177*177^(1/2))^(1/3))","approx_re":"-0.016083","approx_im":"-0.036516","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/48*(61128+177*177^(1/2))^(1/3)-517/16/(61128+177*177^(1/2))^(1/3)+13/8","im":"1/8*3^(1/2)*(1/6*(61128+177*177^(1/2))^(1/3)-517/2/(61128+177*177^(1/2))^(1/3))","approx_re":"-0.016083","approx_im":"0.036516","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":"-1/2+1/8*26^(1/2)","im":"0","approx_re":"0.137377","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/24*(61128+177*177^(1/2))^(1/3)+517/8/(61128+177*177^(1/2))^(1/3)+13/8","im":"0","approx_re":"4.907166","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": "[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":[]}]}]}