{"count": 10, "status":"OK", "data":[{"pols": "[X^4, -4*(2*X+1)^2*(3*X^2+3*X+1), -16*(2*X+1)*(4*X+3)*(4*X+5)*(2*X+3)]", "text": "A-Incarnation: (1,1) and (2,2) intersection in $P^3 \\times P^3$", "degz": 2, "h3": "40", "sol": "1 4 108 3280 126700 5355504 243791856 11651694912 578075329260 29514351895600", "n_discr_factors": "2", "c3": "-128", "operator": "4 2 0 0 0 0 1 -4 -28 -76 -96 -48 -720 -3456 -5824 -4096 -1024", "new_number": "2.60", "id": 56, "operator_tex": "\\theta^4-2^{2} x(2\\theta+1)^2(3\\theta^2+3\\theta+1)-2^{4} x^{2}(2\\theta+1)(4\\theta+3)(4\\theta+5)(2\\theta+3)", "superseek": "4 364", "discriminant": "2 1 -48 -1024", "aesz": "18", "n_sing_complex": "0", "inst_int": "", "c2h": "88", "hash": "bb479f8a4185bf4a943dba2d433e13e5", "dim_h": "14", "inst": " 4 39 364 6800 662416/5 3162589 80141644 2204992496 63488383784 9551133342652/5", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "-(16z+1)(64z-1)", "discr_factors": "-1024, z-1/64, z+1/16", "dm_basis": ["-310145437/500000000*I", "31/3", "1", "1", "-11/3", "-20", "-1", "0", "0", "40", "0", "0", "-40", "0", "0", "0"], "q": "0 1 -12 -90 848 -14079 -313608 -8135374 -247756992 -8049920748", "yuk": "1 4 316 9832 435516 16560404 683129368 27488583896 1128956593468 46283031788368", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/16","im":"0","approx_re":"-0.0625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["5.3333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333+1.240581747*I","-2.1666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666667-.620290874*I",".83055555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555556+.237778168*I","-.215484184-.13439635535307517084282460136674259681093394077448747152619589977220956719817767653758542141230068337129840546697038724373576309794988610478359908883826879271070615034168564920273348519362186788154897*I","46/3","-20/3","529/180","-.83055555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555556-.237778168*I","40","-20","26/3","-2.1666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666667-.620290874*I","80","-40","46/3","-10/3-256*lambda"],"monodromy_dm":["-7","-56","-3","-2","4","29","3/2","1","-112","-784","-41","-28","88","616","33","23"]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":["1","-1","1/2","-1/6","0","1","-1","1/2","0","0","1","-1","0","0","0","1"],"monodromy_dm":["1","0","0","0","1","1","0","0","0","40","1","0","0","0","1","1"]},{"re":"1/64","im":"0","approx_re":"0.015625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["1.+.620290874*I","0",".56859997e-1*I",".9619019e-2","11/3","1","121/360","-.56859997e-1*I","0","0","1","0","40","0","11/3","1.-.620290874*I"],"monodromy_dm":["1","-14","-1","-1","0","1","0","0","0","0","1","0","0","0","0","1"]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/2","3/4","5/4","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, 4*(2*X+1)^2*(7*X^2+7*X+3), 48*(2*X+1)*(4*X+3)*(4*X+5)*(2*X+3)]", "text": "This is operator \"2.65\" from ...", "degz": 2, "h3": null, "sol": "1 -12 324 -11280 447300 -19241712 876207024 -41638753728 2046133011780 -103313778625200", "n_discr_factors": "2", "c3": null, "operator": "4 2 0 0 0 0 1 12 76 188 224 112 2160 10368 17472 12288 3072", "new_number": "2.65", "id": 61, "operator_tex": "\\theta^4+2^{2} x(2\\theta+1)^2(7\\theta^2+7\\theta+3)+2^{4} 3 x^{2}(2\\theta+1)(4\\theta+3)(4\\theta+5)(2\\theta+3)", "superseek": "-4 -556/9", "discriminant": "2 1 112 3072", "aesz": "183", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "04a3788c3f9ed53281ae824deb33d833", "dim_h": null, "inst": " -4 8 -556/9 624 -8928 1199704/9 -2132876 35762384 -5668837952/9 11571895488", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "A_{n}=\\binom{2n}{n}\\sum_{j,k=0}^{n}(-4)^{n-j}\\binom{n}{j}\\binom{n}{k}\\binom{j}{k}\\binom{2j}{j}\\binom{2n-3k}{n}", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "(48z+1)(64z+1)", "discr_factors": "3072, z+1/64, z+1/48", "dm_basis": ["-4-310145437/500000000*I", "8", "1/2", "1", "-14", "0", "-1", "0", "-36", "72", "0", "0", "-72", "0", "0", "0"], "q": "0 1 28 558 9520 144885 2085960 28114706 372061120 4641274242", "yuk": "1 -4 60 -1672 39996 -1116004 28791288 -731576472 18310380604 -459175875784", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/48","im":"0","approx_re":"-0.0208333333333","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["3.666666992+1.240581667*I","-.888889273-.413527825*I",".296296213+.137842738*I","-.38694844e-1-.45947515e-1*I","16.000002509-.2845e-5*I","-4.333336913-.1390e-5*I","1.777778225+.1587e-5*I","-.296296073-.137842774*I","48.000008758-.8909e-5*I","-16.000011149-.4045e-5*I","6.333334810+.4721e-5*I","-.888888245-.413528325*I","144.000033661-.28975e-4*I","-48.000035910-.11385e-4*I","16.000005252+.13912e-4*I","-1.666664890-1.240584998*I"],"monodromy_dm":["5","-32000009/1000000-11/1000000*I","-1666667/1000000","-2","666667/1000000","-866667/200000-1/500000*I","-138889/500000","-333333/1000000","-24","96000037/500000+29/500000*I","2200001/200000","3000001/250000-3/1000000*I","17333333/1000000","-866667/6250-21/500000*I","-3611113/500000","-766667/100000+1/500000*I"]},{"re":"-1/64","im":"0","approx_re":"-0.015625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["5.+.620290874*I","-2-64*lambda","7/9+224/9*lambda","-.216878323-.68921208e-1*I","14","-6","49/18","-7/9-224/9*lambda","36","-18","8","-2-64*lambda","72","-36","14","-3.-.620290874*I"],"monodromy_dm":["1","-22","-1","-1","0","1","0","0","0","0","1","0","0","0","0","1"]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":["1","-1","1/2","-1/6","0","1","-1","1/2","0","0","1","-1","0","0","0","1"],"monodromy_dm":["1","0","0","0","1","1","0","0","0","72","1","0","0","0","1","1"]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/2","3/4","5/4","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -1408*X^4-512*X^3-528*X^2-272*X-48, 770048*X^4+720896*X^3+735232*X^2+305152*X+47616, -203423744*X^4-352321536*X^3-362020864*X^2-170655744*X-30670848, 25165824*(2*X+1)*(512*X^3+1152*X^2+1054*X+339), -19327352832*(2*X+1)*(4*X+3)*(4*X+5)*(2*X+3)]", "text": "This is operator \"5.13\" from ...", "degz": 5, "h3": "32", "sol": "1 48 5328 779520 131619600 24257173248 4739368322304 965015828434944 202584554505899280 43534711014765484800", "n_discr_factors": "3", "c3": "360", "operator": "4 5 0 0 0 0 1 -48 -272 -528 -512 -1408 47616 305152 735232 720896 770048 -30670848 -170655744 -362020864 -352321536 -203423744 8531214336 43587207168 82040586240 70866960384 25769803776 -869730877440 -4174708211712 -7035156430848 -4947802324992 -1236950581248", "new_number": "5.13", "id": 220, "operator_tex": "\\theta^4-2^{4} x\\left(88\\theta^4+32\\theta^3+33\\theta^2+17\\theta+3\\right)+2^{9} x^{2}\\left(1504\\theta^4+1408\\theta^3+1436\\theta^2+596\\theta+93\\right)-2^{18} x^{3}\\left(776\\theta^4+1344\\theta^3+1381\\theta^2+651\\theta+117\\right)+2^{23} 3 x^{4}(2\\theta+1)(512\\theta^3+1152\\theta^2+1054\\theta+339)-2^{31} 3^{2} x^{5}(2\\theta+1)(4\\theta+3)(4\\theta+5)(2\\theta+3)", "superseek": "-80 -174096", "discriminant": "5 1 -1408 770048 -203423744 25769803776 -1236950581248", "aesz": "83", "n_sing_complex": "0", "inst_int": "", "c2h": "-16", "hash": "171e1251d8e4f7de878d0d07de6f58ab", "dim_h": "4", "inst": " -80 -2954 -174096 -13270953 -1179175536 -115795446786 -12188186517456 -1349830285576015 -155427513115593600 -18456445525841201614", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "-(128z-1)(384z-1)^2(256z-1)^2", "discr_factors": "-1236950581248, (z-1/384)^2, z-1/128, (z-1/256)^2", "dm_basis": null, "q": "0 1 -80 3840 -181248 5466544 -307951104 46314496 -945821483008 -60856937695080", "yuk": "1 -80 -23712 -4700672 -849364704 -147396942080 -25011821230080 -4180547975487488 -691113107064284384 -113306657061272435072", "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":"1/384","im":"0","approx_re":"0.00260416666667","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/256","im":"0","approx_re":"0.00390625","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"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":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/2","3/4","5/4","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -320*X^4-832*X^3-640*X^2-224*X-32, 13312*X^4+120832*X^3+212992*X^2+125952*X+26368, 917504*X^4+786432*X^3-6291456*X^2-6881280*X-1900544, -262144*(2*X+1)*(56*X^3+468*X^2+646*X+249), -16777216*(2*X+1)*(4*X+3)*(4*X+5)*(2*X+3)]", "text": "This is operator \"5.14\" from ...", "degz": 5, "h3": "16", "sol": "1 32 2448 273920 38525200 6236600832 1103685859584 207343941083136 40648001362459920 8227704225727500800", "n_discr_factors": "3", "c3": "40", "operator": "4 5 0 0 0 0 1 -32 -224 -640 -832 -320 26368 125952 212992 120832 13312 -1900544 -6881280 -6291456 786432 917504 -65273856 -299892736 -461373440 -260046848 -29360128 -754974720 -3623878656 -6106906624 -4294967296 -1073741824", "new_number": "5.14", "id": 221, "operator_tex": "\\theta^4-2^{5} x\\left(10\\theta^4+26\\theta^3+20\\theta^2+7\\theta+1\\right)+2^{8} x^{2}\\left(52\\theta^4+472\\theta^3+832\\theta^2+492\\theta+103\\right)+2^{16} x^{3}\\left(14\\theta^4+12\\theta^3-96\\theta^2-105\\theta-29\\right)-2^{18} x^{4}(2\\theta+1)(56\\theta^3+468\\theta^2+646\\theta+249)-2^{24} x^{5}(2\\theta+1)(4\\theta+3)(4\\theta+5)(2\\theta+3)", "superseek": "64 23360", "discriminant": "5 1 -320 13312 917504 -29360128 -1073741824", "aesz": "116", "n_sing_complex": "0", "inst_int": "", "c2h": "40", "hash": "0b366ad8c78b6697205c5a7fff270f5b", "dim_h": "6", "inst": " 64 12 23360 654490 53956288 3558145052 286700496448 24007522298674 2129883087617536 196912935173735108", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "-(-1+256z)(32z+1)^2(64z-1)^2", "discr_factors": "-1073741824, -1/256+z, (z+1/32)^2, (z-1/64)^2", "dm_basis": null, "q": "0 1 -96 6816 -493568 32166192 -2164343808 130369476096 -8668096954368 469785092535960", "yuk": "1 64 160 630784 41887520 6744536064 768559962112 98338270281728 12291851458808608 1552684770873814528", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/32","im":"0","approx_re":"-0.03125","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","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/64","im":"0","approx_re":"0.015625","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/2","3/4","5/4","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[169*X^4, -2028-14534*X-40859*X^2-52650*X^3-18837*X^4, 281424+1317056*X+1936736*X^2+433792*X^3-364160*X^4, -5001984-16253952*X-8778752*X^2+10223616*X^3+978944*X^4, -196608*(2*X+1)*(40*X^3+684*X^2+1013*X+399), -9437184*(2*X+1)*(4*X+3)*(4*X+5)*(2*X+3)]", "text": "This is operator \"5.44\" from ...", "degz": 5, "h3": "26", "sol": "1 12 468 28560 2135700 179060112 16166559024 1537448717376 151947395002260 15468902712634800", "n_discr_factors": "3", "c3": "-72", "operator": "4 5 0 0 0 0 169 -2028 -14534 -40859 -52650 -18837 281424 1317056 1936736 433792 -364160 -5001984 -16253952 -8778752 10223616 978944 -78446592 -356057088 -532807680 -276824064 -15728640 -424673280 -2038431744 -3435134976 -2415919104 -603979776", "new_number": "5.44", "id": 254, "operator_tex": "13^{2} \\theta^4-13 x\\left(1449\\theta^4+4050\\theta^3+3143\\theta^2+1118\\theta+156\\right)-2^{4} x^{2}\\left(22760\\theta^4-27112\\theta^3-121046\\theta^2-82316\\theta-17589\\right)+2^{8} x^{3}\\left(3824\\theta^4+39936\\theta^3-34292\\theta^2-63492\\theta-19539\\right)-2^{16} 3 x^{4}(2\\theta+1)(40\\theta^3+684\\theta^2+1013\\theta+399)-2^{20} 3^{2} x^{5}(2\\theta+1)(4\\theta+3)(4\\theta+5)(2\\theta+3)", "superseek": "231/13 38037/13", "discriminant": "5 169 -18837 -364160 978944 -15728640 -603979776", "aesz": "240", "n_sing_complex": "2", "inst_int": "", "c2h": "68", "hash": "8f46cd6968b3b676e251a9d8635637fc", "dim_h": "10", "inst": " 231/13 826/13 38037/13 786076/13 32662752/13 1251531252/13 56830429026/13 2686705844700/13 135076469305428/13 7052986465933572/13", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "-(128z-1)(128z^2-13z+1)(13+192z)^2", "discr_factors": "-603979776, z-1/128, (13/192+z)^2, z^2-13/128*z+1/128", "dm_basis": null, "q": "0 1 -38 771 -20752 393365 -14552562 106677773 -15365058336 -334070060625", "yuk": "1 231/13 6839/13 1027230/13 50315703/13 4082844231/13 270331784270/13 19492837156149/13 1375593442802103/13 98470746124684242/13", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-13/192","im":"0","approx_re":"-0.0677083333333","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":"1/128","im":"0","approx_re":"0.0078125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"13/256","im":"-7/256*7^(1/2)","approx_re":"0.05078125","approx_im":"-0.072345","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"13/256","im":"7/256*7^(1/2)","approx_re":"0.05078125","approx_im":"0.072345","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/2","3/4","5/4","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[121*X^4, -19008*X^4-27456*X^3-20988*X^2-7260*X-968, 414208*X^4+151552*X^3-495712*X^2-413248*X-91520, -855040*X^4+9123840*X^3+12730560*X^2+6642240*X+1236400, -51200*(2*X+1)*(4*X+3)*(76*X^2+189*X+125), 2048000*(2*X+1)*(4*X+3)*(4*X+5)*(2*X+3)]", "text": "This is operator \"5.88\" from ...", "degz": 5, "h3": null, "sol": "1 8 360 23120 1796200 155711808 14506352784 1421901486720 144742335103080 15170668907451200", "n_discr_factors": "2", "c3": null, "operator": "4 5 0 0 0 0 121 -968 -7260 -20988 -27456 -19008 -91520 -413248 -495712 151552 414208 1236400 6642240 12730560 9123840 -855040 -19200000 -93030400 -159641600 -116326400 -31129600 92160000 442368000 745472000 524288000 131072000", "new_number": "5.88", "id": 302, "operator_tex": "11^{2} \\theta^4-2^{2} 11 x\\left(432\\theta^4+624\\theta^3+477\\theta^2+165\\theta+22\\right)+2^{5} x^{2}\\left(12944\\theta^4+4736\\theta^3-15491\\theta^2-12914\\theta-2860\\right)-2^{4} 5 x^{3}\\left(10688\\theta^4-114048\\theta^3-159132\\theta^2-83028\\theta-15455\\right)-2^{11} 5^{2} x^{4}(2\\theta+1)(4\\theta+3)(76\\theta^2+189\\theta+125)+2^{14} 5^{3} x^{5}(2\\theta+1)(4\\theta+3)(4\\theta+5)(2\\theta+3)", "superseek": "148/11 44108/11", "discriminant": "5 121 -19008 414208 -855040 -31129600 131072000", "aesz": "324", "n_sing_complex": "3", "inst_int": "", "c2h": null, "hash": "7f84d776cf00ff399b20865542185f87", "dim_h": null, "inst": " 148/11 2044/11 44108/11 1459636/11 60212712/11 2841880156/11 13367497492 740544574348 43226693167388 28924430993344520/11", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "5", "laurent": null, "discriminant_tex": "(5120z^3-512z^2-128z+1)(-11+160z)^2", "discr_factors": "131072000, (-11/160+z)^2, z^3-1/10*z^2-1/40*z+1/5120", "dm_basis": null, "q": "0 1 -28 -46 -720 -186809 -9515448 -549365638 -33949943744 -2188151382601", "yuk": "1 148/11 1500 1191064/11 93433204/11 7526589148/11 613847321112/11 50435568037464/11 4170747136161140/11 346634852510475436/11", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/480*(4922+1110*I*111^(1/2))^(1/3)-17/15/(4922+1110*I*111^(1/2))^(1/3)+1/30+1/16*I*3^(1/2)*(1/30*(4922+1110*I*111^(1/2))^(1/3)-272/15/(4922+1110*I*111^(1/2))^(1/3))","im":"0","approx_re":"-0.120643","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":"-1/480*(4922+1110*I*111^(1/2))^(1/3)-17/15/(4922+1110*I*111^(1/2))^(1/3)+1/30-1/16*I*3^(1/2)*(1/30*(4922+1110*I*111^(1/2))^(1/3)-272/15/(4922+1110*I*111^(1/2))^(1/3))","im":"0","approx_re":"0.007599","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"11/160","im":"0","approx_re":"0.06875","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/240*(4922+1110*I*111^(1/2))^(1/3)+34/15/(4922+1110*I*111^(1/2))^(1/3)+1/30","im":"0","approx_re":"0.213044","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","3/4","5/4","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[9*X^4, 804*X^4+1464*X^3+1200*X^2+468*X+72, 37504*X^4+137536*X^3+186592*X^2+106080*X+21696, 773376*X^4+4073472*X^3+7504384*X^2+5356800*X+1261056, 2048*(2*X+1)*(826*X^3+3543*X^2+4321*X+1594), 65536*(2*X+1)*(4*X+3)*(4*X+5)*(2*X+3)]", "text": "This is operator \"5.92\" from ...", "degz": 5, "h3": null, "sol": "1 -8 72 640 -51800 931392 23595264 -2098077696 59919785640 95968100800", "n_discr_factors": "3", "c3": null, "operator": "4 5 0 0 0 0 9 72 468 1200 1464 804 21696 106080 186592 137536 37504 1261056 5356800 7504384 4073472 773376 3264512 15378432 24954880 16203776 3383296 2949120 14155776 23855104 16777216 4194304", "new_number": "5.92", "id": 307, "operator_tex": "3^{2} \\theta^4+2^{2} 3 x\\left(67\\theta^4+122\\theta^3+100\\theta^2+39\\theta+6\\right)+2^{5} x^{2}\\left(1172\\theta^4+4298\\theta^3+5831\\theta^2+3315\\theta+678\\right)+2^{8} x^{3}\\left(3021\\theta^4+15912\\theta^3+29314\\theta^2+20925\\theta+4926\\right)+2^{11} x^{4}(2\\theta+1)(826\\theta^3+3543\\theta^2+4321\\theta+1594)+2^{16} x^{5}(2\\theta+1)(4\\theta+3)(4\\theta+5)(2\\theta+3)", "superseek": "-16/3 208/3", "discriminant": "5 9 804 37504 773376 3383296 4194304", "aesz": "332", "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "f788b099648b78746af9d38e85874401", "dim_h": null, "inst": " -16/3 -257/6 208/3 10444/3 -116608/3 -3766507/6 16797680 862676923/6 -8221703360 -32108836676/3", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "(32z+1)(2048z^2+52z+1)(8z+3)^2", "discr_factors": "4194304, (z+3/8)^2, z^2+13/512*z+1/2048, z+1/32", "dm_basis": null, "q": "0 1 20 502 10160 177341 3262552 59691418 942027712 13823359702", "yuk": "1 -16/3 -348 5600/3 667372/3 -4858672 -135592728 17284812704/3 220845959660/3 -17980865242720/3", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-3/8","im":"0","approx_re":"-0.375","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","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-13/1024","im":"-7/1024*7^(1/2)","approx_re":"-0.0126953125","approx_im":"-0.018086","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-13/1024","im":"7/1024*7^(1/2)","approx_re":"-0.0126953125","approx_im":"0.018086","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":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/2","3/4","5/4","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -736*X^4-896*X^3-700*X^2-252*X-36, 166656*X^4+463872*X^3+473472*X^2+204672*X+33840, -4460544*X^4-64364544*X^3-99846144*X^2-49600512*X-9061632, -2448949248*X^4-927203328*X^3+8059944960*X^2+6023282688*X+1332412416, 146087608320*X^4+582312001536*X^3-2463105024*X^2-160271695872*X-49304567808, 11529369944064*X^4-10078006542336*X^3-11015685144576*X^2-1638899122176*X+467820085248, -146767085568*(2*X+1)*(1336*X^3+2772*X^2+2234*X+663), -84537841287168*(2*X+1)*(4*X+3)*(4*X+5)*(2*X+3)]", "text": "This is operator \"8.78\" from ...", "degz": 8, "h3": null, "sol": "1 36 3780 555120 95199300 17826144336 3532282505136 728151261963840 154550955916302660 33549072371964349200", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 1 -36 -252 -700 -896 -736 33840 204672 473472 463872 166656 -9061632 -49600512 -99846144 -64364544 -4460544 1332412416 6023282688 8059944960 -927203328 -2448949248 -49304567808 -160271695872 -2463105024 582312001536 146087608320 467820085248 -1638899122176 -11015685144576 -10078006542336 11529369944064 -97306577731584 -522490824622080 -1062593699512320 -1009757548707840 -392161652637696 -3804202857922560 -18260173718028288 -30771774228529152 -21641687369515008 -5410421842378752", "new_number": "8.78", "id": 527, "operator_tex": "\\theta^4-2^{2} x\\left(184\\theta^4+224\\theta^3+175\\theta^2+63\\theta+9\\right)+2^{4} 3 x^{2}\\left(3472\\theta^4+9664\\theta^3+9864\\theta^2+4264\\theta+705\\right)-2^{8} 3^{2} x^{3}\\left(1936\\theta^4+27936\\theta^3+43336\\theta^2+21528\\theta+3933\\right)-2^{16} 3^{3} x^{4}\\left(1384\\theta^4+524\\theta^3-4555\\theta^2-3404\\theta-753\\right)+2^{19} 3^{4} x^{5}\\left(3440\\theta^4+13712\\theta^3-58\\theta^2-3774\\theta-1161\\right)+2^{22} 3^{5} x^{6}\\left(11312\\theta^4-9888\\theta^3-10808\\theta^2-1608\\theta+459\\right)-2^{26} 3^{7} x^{7}(2\\theta+1)(1336\\theta^3+2772\\theta^2+2234\\theta+663)-2^{32} 3^{9} x^{8}(2\\theta+1)(4\\theta+3)(4\\theta+5)(2\\theta+3)", "superseek": "52 48732", "discriminant": "8 1 -736 166656 -4460544 -2448949248 146087608320 11529369944064 -392161652637696 -5410421842378752", "aesz": null, "n_sing_complex": "3", "inst_int": "", "c2h": null, "hash": "2fb524ad6efb19e0117ae7acbd9f67b9", "dim_h": null, "inst": " 52 -399 48732 -992750 98106208 -13164377111/3 346622274844 -20762287104686 1625571068932672 -109698228104560776", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "7", "laurent": null, "discriminant_tex": "-(256z-1)(110592z^3+6912z^2-288z+1)(-1+96z+13824z^2)^2", "discr_factors": "-5410421842378752, z^3+1/16*z^2-1/384*z+1/110592, z-1/256, (-1/13824+1/144*z+z^2)^2", "dm_basis": null, "q": "0 1 -108 7662 -522608 37550709 -2726199720 203058824274 -15495782553792 1207671346097154", "yuk": "1 52 -3140 1315816 -63539140 12263276052 -947833839368 118891440271544 -10630291061138372 1185041309253233704", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/192*(-36+12*I*3^(1/2))^(1/3)-1/16/(-36+12*I*3^(1/2))^(1/3)-1/48+1/96*I*3^(1/2)*(1/2*(-36+12*I*3^(1/2))^(1/3)-6/(-36+12*I*3^(1/2))^(1/3))","im":"0","approx_re":"-0.091906","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/288-1/288*7^(1/2)","im":"0","approx_re":"-0.012659","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":"-1/192*(-36+12*I*3^(1/2))^(1/3)-1/16/(-36+12*I*3^(1/2))^(1/3)-1/48-1/96*I*3^(1/2)*(1/2*(-36+12*I*3^(1/2))^(1/3)-6/(-36+12*I*3^(1/2))^(1/3))","im":"0","approx_re":"0.00385","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","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/288+1/288*7^(1/2)","im":"0","approx_re":"0.005714","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/96*(-36+12*I*3^(1/2))^(1/3)+1/8/(-36+12*I*3^(1/2))^(1/3)-1/48","im":"0","approx_re":"0.025556","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","3/4","5/4","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -256*X^4-512*X^3-448*X^2-192*X-32, 256*(2*X+1)*(4*X+3)*(4*X+5)*(2*X+3)]", "text": "This is operator is equivalent to [2.33]. Transformation:.....", "degz": 2, "h3": null, "sol": "1 32 2160 181760 17021200 1698181632 176677611264 18937576120320 2075622689471760 231465995770380800", "n_discr_factors": "1", "c3": null, "operator": "4 2 0 0 0 0 1 -32 -192 -448 -512 -256 11520 55296 93184 65536 16384", "new_number": "2.71", "id": 614, "operator_tex": "\\theta^4-2^{5} x(2\\theta+1)^2(2\\theta^2+2\\theta+1)+2^{8} x^{2}(2\\theta+1)(4\\theta+3)(4\\theta+5)(2\\theta+3)", "superseek": "0 0", "discriminant": "2 1 -256 16384", "aesz": null, "n_sing_complex": "0", "inst_int": null, "c2h": null, "hash": "757b011780c5986bd45a5bf434c76c28", "dim_h": null, "inst": " 0 -20 0 -865 0 -67460 0 -6821070 0 -800369820", "cleanlist": "False", "n_sing_real": "2", "sol_explicit": null, "n_sing_rational": "2", "n_sing": "2", "laurent": null, "discriminant_tex": "(-1+128z)^2", "discr_factors": "16384, (-1/128+z)^2", "dm_basis": null, "q": "0 1 -64 2912 -110592 3772720 -119642112 3598125568 -103922663424 2907171436184", "yuk": "1 0 -160 0 -55520 0 -14571520 0 -3492443360 0", "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":"1/128","im":"0","approx_re":"0.0078125","approx_im":"0.0","exponents":["0","1/4","3/4","1"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/2","3/4","5/4","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[225*X^4, -3600-28350*X-85965*X^2-115230*X^3-60945*X^4, 299040+1655580*X+3487426*X^2+3302548*X^3+1210456*X^4, -9391920-47583720*X-80265896*X^2-36928992*X^3-489812*X^4, 108531424+457254800*X+559975368*X^2+26995232*X^3-113237888*X^4, -459370368-1440667968*X-188527568*X^2+2703382144*X^3+487624576*X^4, -664307712-5484702912*X-13980708608*X^2-11759384064*X^3+1758486528*X^4, -947968*(2*X+1)*(8454*X^3+5577*X^2-4303*X-3155), 610491392*(2*X+1)*(4*X+3)*(4*X+5)*(2*X+3)]", "text": "This is operator \"8.88\" from ...", "degz": 8, "h3": null, "sol": "1 16 1224 146320 21334600 3485565216 613131550416 113597150382144 21871393240399560 4337630836910800000", "n_discr_factors": "2", "c3": null, "operator": "4 8 0 0 0 0 225 -3600 -28350 -85965 -115230 -60945 299040 1655580 3487426 3302548 1210456 -9391920 -47583720 -80265896 -36928992 -489812 108531424 457254800 559975368 26995232 -113237888 -459370368 -1440667968 -188527568 2703382144 487624576 -664307712 -5484702912 -13980708608 -11759384064 1758486528 2990839040 10060784384 2871395072 -18587756544 -16028242944 27472112640 131866140672 222218866688 156285796352 39071449088", "new_number": "8.88", "id": 615, "operator_tex": "3^{2} 5^{2} \\theta^4-3 5 x\\left(4063\\theta^4+7682\\theta^3+5731\\theta^2+1890\\theta+240\\right)+2 x^{2}\\left(605228\\theta^4+1651274\\theta^3+1743713\\theta^2+827790\\theta+149520\\right)-2^{2} x^{3}\\left(122453\\theta^4+9232248\\theta^3+20066474\\theta^2+11895930\\theta+2347980\\right)-2^{3} x^{4}\\left(14154736\\theta^4-3374404\\theta^3-69996921\\theta^2-57156850\\theta-13566428\\right)+2^{4} x^{5}\\left(30476536\\theta^4+168961384\\theta^3-11782973\\theta^2-90041748\\theta-28710648\\right)+2^{6} 23 x^{6}\\left(1194624\\theta^4-7988712\\theta^3-9497764\\theta^2-3726021\\theta-451296\\right)-2^{8} 7 23^{2} x^{7}(2\\theta+1)(8454\\theta^3+5577\\theta^2-4303\\theta-3155)+2^{10} 7^{2} 23^{3} x^{8}(2\\theta+1)(4\\theta+3)(4\\theta+5)(2\\theta+3)", "superseek": "571/15 394769/15", "discriminant": "8 225 -60945 1210456 -489812 -113237888 487624576 1758486528 -16028242944 39071449088", "aesz": null, "n_sing_complex": "2", "inst_int": null, "c2h": null, "hash": "96ea6b0b71373481f874100af7f89d67", "dim_h": null, "inst": " 571/15 3038/5 394769/15 23541584/15 352406944/3 150234715576/15 14069083470596/15 94040543125688 149022677890363768/15 3281323125192312104/3", "cleanlist": "True", "n_sing_real": "1", "sol_explicit": null, "n_sing_rational": "1", "n_sing": "3", "laurent": null, "discriminant_tex": "(1-261z+2952z^2-12368z^3+23552z^4)(-15+74z+1288z^2)^2", "discr_factors": "39071449088, (-15/1288+37/644*z+z^2)^2, 1/23552-261/23552*z+369/2944*z^2-773/1472*z^3+z^4", "dm_basis": null, "q": "0 1 -62 1091 -42948 -1161275 -172648938 -16995937917 -1934173459304 -225217197298315", "yuk": "1 571/15 73483/15 10659334/15 502244953/5 220254340571/15 32450709296662/15 1608565210138333/5 240743790904006233/5 108637532182085846206/15", "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":"s_1","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"s_3","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"s_2","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"s_5","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"s_4","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"s_6","im":"0","approx_re":"0.0","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":["1/2","3/4","5/4","3/2"],"monodromy":[],"monodromy_dm":[]}]}]}