{"count": 15, "status":"OK", "data":[{"pols": "[X^4, -32768*X^4-65536*X^3-76800*X^2-44032*X-9584, 16777216*(4*X+3)*(X+1)^2*(4*X+5)]", "text": "Operator equivalent to $\\hat{10}$", "degz": 2, "h3": null, "sol": "1 9584 121274640 1675847866112 24182028281658640 358036114521815971584 5392260049649786475192576 82203046445619132492175994880 1264588295405567142252592792739088 19591686068092839793724643760547997440", "n_discr_factors": "1", "c3": null, "operator": "4 2 0 0 0 0 1 -9584 -44032 -76800 -65536 -32768 251658240 1040187392 1593835520 1073741824 268435456", "new_number": "2.47", "id": 41, "operator_tex": "\\theta^4-2^{4} x\\left(2048\\theta^4+4096\\theta^3+4800\\theta^2+2752\\theta+599\\right)+2^{24} x^{2}(4\\theta+3)(\\theta+1)^2(4\\theta+5)", "superseek": "-3488 -1142687008", "discriminant": "2 1 -32768 268435456", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "413005461e43cfa75125577c2d4c2fde", "dim_h": null, "inst": " -3488 -1406056 -1142687008 -1211614451216 -1500013956719584 -2047565632820782664 -2992130498601611248800 -4596931603702373647469584 -7338906778095272756256582400 -12077720378281710305501331440632", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "2", "laurent": null, "discriminant_tex": "(16384z-1)^2", "discr_factors": "268435456, (z-1/16384)^2", "dm_basis": ["cy[DM_basis]"], "q": "0 1 -5696 14731872 -25158641664 33504667231792 -37915203736676352 38163064333720814080 -35396658050856552890368 30499890168434563551328920", "yuk": "1 -3488 -11251936 -30852552704 -77543336129760 -187501744589951488 -442274176720152856576 -1026300761020352658341888 -2353628981095692850840556768 -5350063041231453839341901122304", "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":["1","-1","1/2","-1/6","0","1","-1","1/2","0","0","1","-1","0","0","0","1"],"monodromy_dm":["cy[T_DM][1]"]},{"re":"1/16384","im":"0","approx_re":"6.103515625e-05","approx_im":"0.0","exponents":["0","-1/2","1","3/2"],"monodromy":["11/12","-152*lambda","23/288","0","0","-11/12","0","23/288","2","0","-11/12","152*lambda","0","2","0","11/12"],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["3/4","1","1","5/4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -65*X^4-130*X^3-105*X^2-40*X-6, 4*(4*X+3)*(X+1)^2*(4*X+5)]", "text": "A-incarnation: $X(1, 1, 1, 1, 1, 1) \\subset  Grass(3, 6)$", "degz": 2, "h3": "42", "sol": "1 6 126 3948 149310 6300756 285675516 13625781336 674863457598 34412622769140", "n_discr_factors": "2", "c3": "-96", "operator": "4 2 0 0 0 0 1 -6 -40 -105 -130 -65 60 248 380 256 64", "new_number": "2.62", "id": 58, "operator_tex": "\\theta^4-x\\left(65\\theta^4+130\\theta^3+105\\theta^2+40\\theta+6\\right)+2^{2} x^{2}(4\\theta+3)(\\theta+1)^2(4\\theta+5)", "superseek": "5 312", "discriminant": "2 1 -65 64", "aesz": "28", "n_sing_complex": "0", "inst_int": "", "c2h": "84", "hash": "06dd455cafc5097e4f671d385984c1a2", "dim_h": "14", "inst": " 5 28 312 4808 91048 1965908 325780668/7 1178954560 31456810796 874502186004", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "(64z-1)(z-1)", "discr_factors": "64, z-1/64, z-1", "dm_basis": ["-96*lambda", "21/2", "1", "1", "-7/2", "-21", "-1", "0", "0", "42", "0", "0", "-42", "0", "0", "0"], "q": "0 1 -16 64 -552 -5632 -165472 -4342772 -123146768 -3627953792", "yuk": "1 5 229 8429 307941 11381005 424644781 15963252737 603625042661 22932015078713", "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":["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","42","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+96*lambda","0","8*lambda",".5153046e-2","7/2","1","7/24","-8*lambda","0","0","1","0","42","0","7/2","1-96*lambda"],"monodromy_dm":["1","-14","-1","-1","0","1","0","0","0","0","1","0","0","0","0","1"]},{"re":"1","im":"0","approx_re":"1.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["16.+8.373926794*I","-5-576*lambda","5/4+144*lambda","-.204864220-.332298682*I","63","-20","21/4","-5/4-144*lambda","252","-84","22","-5-576*lambda","756+1/500000000*I","-252","63","-14.-8.373926794*I"],"monodromy_dm":["-35","-378","-24","-18","12","127","8","6","-252","-2646","-167","-126","156","1638","104","79"]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["3/4","1","1","5/4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -128*X^4-256*X^3-252*X^2-124*X-24, 256*(4*X+3)*(X+1)^2*(4*X+5)]", "text": "This is operator \"2.63\" from ...", "degz": 2, "h3": null, "sol": "1 24 936 43008 2145960 112521024 6098593536 338463166464 19121128195752 1095276775623360", "n_discr_factors": "1", "c3": null, "operator": "4 2 0 0 0 0 1 -24 -124 -252 -256 -128 3840 15872 24320 16384 4096", "new_number": "2.63", "id": 59, "operator_tex": "\\theta^4-2^{2} x\\left(32\\theta^4+64\\theta^3+63\\theta^2+31\\theta+6\\right)+2^{8} x^{2}(4\\theta+3)(\\theta+1)^2(4\\theta+5)", "superseek": "-4 -44", "discriminant": "2 1 -128 4096", "aesz": "84", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "908b978c0c447d3643c3018c40e7f5d1", "dim_h": null, "inst": " -4 -11 -44 -156 -288 3207 55764 578820 4717904 29814248", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "2", "laurent": null, "discriminant_tex": "(64z-1)^2", "discr_factors": "4096, (z-1/64)^2", "dm_basis": ["-96*lambda", "-6", "1", "1", "-2", "24", "-1", "0", "0", "-48", "0", "0", "48", "0", "0", "0"], "q": "0 1 -28 478 -6064 64813 -610696 5253394 -42301888 320357638", "yuk": "1 -4 -92 -1192 -10076 -36004 691432 19127048 296345764 3439350824", "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":["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","-48","1","0","0","0","1","1"]},{"re":"1/64","im":"0","approx_re":"0.015625","approx_im":"0.0","exponents":["0","0","1","1"],"monodromy":["1+96*lambda","1/4","-4*lambda",".5907751e-2","2","1","-1/12","4*lambda","0","6","1","1/4","-48","0","2","1-96*lambda"],"monodromy_dm":["1","4","-1","-1","0","-2","1/8","0","0","-72","4","0","0","60","-5/2","1"]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["3/4","1","1","5/4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -70*X^4-86*X^3-77*X^2-34*X-6, 2025*X^4+4806*X^3+5799*X^2+3390*X+774, -29268*X^4-95904*X^3-135972*X^2-89748*X-22356, 206064*X^4+785376*X^3+1155708*X^2+751356*X+180792, -34992*(4*X+3)*(X+1)^2*(4*X+5)]", "text": "This is operator \"5.102\" from ...", "degz": 5, "h3": "288", "sol": "1 6 54 492 3510 756 -656964 -17079336 -299659338 -3854724060", "n_discr_factors": "3", "c3": "-216", "operator": "4 5 0 0 0 0 1 -6 -34 -77 -86 -70 774 3390 5799 4806 2025 -22356 -89748 -135972 -95904 -29268 180792 751356 1155708 785376 206064 -524880 -2169504 -3324240 -2239488 -559872", "new_number": "5.102", "id": 184, "operator_tex": "\\theta^4-x\\left(70\\theta^4+86\\theta^3+77\\theta^2+34\\theta+6\\right)+3 x^{2}\\left(675\\theta^4+1602\\theta^3+1933\\theta^2+1130\\theta+258\\right)-2^{2} 3^{3} x^{3}\\left(271\\theta^4+888\\theta^3+1259\\theta^2+831\\theta+207\\right)+2^{2} 3^{5} x^{4}\\left(212\\theta^4+808\\theta^3+1189\\theta^2+773\\theta+186\\right)-2^{4} 3^{7} x^{5}(4\\theta+3)(\\theta+1)^2(4\\theta+5)", "superseek": "1 -12", "discriminant": "5 1 -70 2025 -29268 206064 -559872", "aesz": "352", "n_sing_complex": "2", "inst_int": "", "c2h": "216", "hash": "fc8b141522720827b1dd2cd28a232c1b", "dim_h": "66", "inst": " 1 -7/8 -12 -131/4 90 3513/2 10694 -1111/2 -639429 -23067635/4", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "-(16z-1)(432z^2-36z+1)(-1+9z)^2", "discr_factors": "-559872, (-1/9+z)^2, z^2-1/12*z+1/432, z-1/16", "dm_basis": null, "q": "0 1 -10 87 -564 3295 -18198 81229 -391496 2030976", "yuk": "1 1 -6 -323 -2102 11251 379074 3668043 -286518 -466144064", "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":"1/24","im":"-1/72*3^(1/2)","approx_re":"0.0416666666667","approx_im":"-0.024056","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/24","im":"1/72*3^(1/2)","approx_re":"0.0416666666667","approx_im":"0.024056","exponents":["0","1","1","2"],"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":"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":["3/4","1","1","5/4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -4*X*(22*X^3+8*X^2+5*X+1), 1088*X^4-4864*X^3-8480*X^2-5216*X-1152, 36352*X^4+153600*X^3+85760*X^2-9984*X-13824, -417792*X^4+344064*X^3+1812480*X^2+1603584*X+442368, -294912*(4*X+3)*(X+1)^2*(4*X+5)]", "text": "This is operator \"5.112\" from ...", "degz": 5, "h3": null, "sol": "1 0 72 1728 72360 3024000 138700800 6638284800 330006738600 16870582713600", "n_discr_factors": "4", "c3": null, "operator": "4 5 0 0 0 0 1 0 -4 -20 -32 -88 -1152 -5216 -8480 -4864 1088 -13824 -9984 85760 153600 36352 442368 1603584 1812480 344064 -417792 -4423680 -18284544 -28016640 -18874368 -4718592", "new_number": "5.112", "id": 195, "operator_tex": "\\theta^4-2^{2} x\\theta(22\\theta^3+8\\theta^2+5\\theta+1)+2^{5} x^{2}\\left(34\\theta^4-152\\theta^3-265\\theta^2-163\\theta-36\\right)+2^{8} x^{3}\\left(142\\theta^4+600\\theta^3+335\\theta^2-39\\theta-54\\right)-2^{11} 3 x^{4}\\left(68\\theta^4-56\\theta^3-295\\theta^2-261\\theta-72\\right)-2^{15} 3^{2} x^{5}(4\\theta+3)(\\theta+1)^2(4\\theta+5)", "superseek": "4 940", "discriminant": "5 1 -88 1088 36352 -417792 -4718592", "aesz": "395", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "2d13c01eaf16983977dfb0325c5f376e", "dim_h": null, "inst": " 4 60 940 19091 463904 12973348 400305324 13268626837 464051654448 16924201942912", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "A_{n}=\\sum_{j,k=0}^{n}(-4)^{n-k}\\dbinom{n}{j}\\dbinom{n}{k}\\dbinom{2j}{j}\\dbinom{j}{k}\\dbinom{n+j}{n}\\dbinom{2n-2k}{n}", "n_sing_rational": "5", "n_sing": "5", "laurent": null, "discriminant_tex": "-(16z+1)(8z+1)(64z-1)(-1+24z)^2", "discr_factors": "-4718592, z+1/16, (-1/24+z)^2, z+1/8, z-1/64", "dm_basis": null, "q": "0 1 -4 -194 -2768 -45843 -1241656 -43214286 -1607604288 -61898933306", "yuk": "1 4 484 25384 1222308 57988004 2802269032 137304726136 6793538162852 338293656117976", "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":"-1/16","im":"0","approx_re":"-0.0625","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":"1/64","im":"0","approx_re":"0.015625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/24","im":"0","approx_re":"0.0416666666667","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":[]}]}, {"pols": "[9*X^4, -318*X^4-438*X^3-345*X^2-126*X-18, -4511*X^4-24314*X^3-37829*X^2-23598*X-5286, 41828*X^4+128736*X^3+97796*X^2+14508*X-5268, -70224*X^4-89760*X^3+4444*X^2+47740*X+16984, -1936*(4*X+3)*(X+1)^2*(4*X+5)]", "text": "This is operator \"5.49\" from ...", "degz": 5, "h3": "48", "sol": "1 2 54 1028 29110 840252 26776764 886326408 30553518006 1082050391180", "n_discr_factors": "3", "c3": "-92", "operator": "4 5 0 0 0 0 9 -18 -126 -345 -438 -318 -5286 -23598 -37829 -24314 -4511 -5268 14508 97796 128736 41828 16984 47740 4444 -89760 -70224 -29040 -120032 -183920 -123904 -30976", "new_number": "5.49", "id": 259, "operator_tex": "3^{2} \\theta^4-3 x\\left(106\\theta^4+146\\theta^3+115\\theta^2+42\\theta+6\\right)-x^{2}\\left(4511\\theta^4+24314\\theta^3+37829\\theta^2+23598\\theta+5286\\right)+2^{2} x^{3}\\left(10457\\theta^4+32184\\theta^3+24449\\theta^2+3627\\theta-1317\\right)-2^{2} 11 x^{4}\\left(1596\\theta^4+2040\\theta^3-101\\theta^2-1085\\theta-386\\right)-2^{4} 11^{2} x^{5}(4\\theta+3)(\\theta+1)^2(4\\theta+5)", "superseek": "7/3 148", "discriminant": "5 9 -318 -4511 41828 -70224 -30976", "aesz": "248", "n_sing_complex": "0", "inst_int": "", "c2h": "84", "hash": "0c9ccff1cb4f5096e455a9026799ed5a", "dim_h": "15", "inst": " 7/3 551/24 148 8241/4 86854/3 3122483/6 9677518 1187963639/6 12624388525/3 1126077833419/12", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "-(16z+1)(16z^2+44z-1)(-3+11z)^2", "discr_factors": "-30976, z+1/16, (-3/11+z)^2, z^2+11/4*z-1/16", "dm_basis": null, "q": "0 1 -6 -89 116 -1681 -75674 -1706035 -35395000 -846481600", "yuk": "1 7/3 186 11995/3 132042 3618919 112413570 9958166029/3 304119087710/3 9203179246720/3", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"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":"-1/16","im":"0","approx_re":"-0.0625","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":"-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":"3/11","im":"0","approx_re":"0.272727272727","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":[]}]}, {"pols": "[529*X^4, -75233*X^4-116794*X^3-89608*X^2-31211*X-4232, 1357863*X^4+999924*X^3-787393*X^2-850862*X-205712, -6206392*X^4+2179848*X^3+1750568*X^2-1413672*X-801872, -980880*X^4+15278304*X^3+35445392*X^2+27267488*X+7128704, -1905152*(4*X+3)*(X+1)^2*(4*X+5)]", "text": "This is operator \"5.51\" from ...", "degz": 5, "h3": "23", "sol": "1 8 324 19304 1388260 111469008 9620458344 873705161232 82410223605732 8003897628341120", "n_discr_factors": "2", "c3": "-74", "operator": "4 5 0 0 0 0 529 -4232 -31211 -89608 -116794 -75233 -205712 -850862 -787393 999924 1357863 -801872 -1413672 1750568 2179848 -6206392 7128704 27267488 35445392 15278304 -980880 -28577280 -118119424 -180989440 -121929728 -30482432", "new_number": "5.51", "id": 262, "operator_tex": "23^{2} \\theta^4-23 x\\left(3271\\theta^4+5078\\theta^3+3896\\theta^2+1357\\theta+184\\right)+x^{2}\\left(1357863\\theta^4+999924\\theta^3-787393\\theta^2-850862\\theta-205712\\right)-2^{3} x^{3}\\left(775799\\theta^4-272481\\theta^3-218821\\theta^2+176709\\theta+100234\\right)-2^{4} 61 x^{4}\\left(1005\\theta^4-15654\\theta^3-36317\\theta^2-27938\\theta-7304\\right)-2^{9} 61^{2} x^{5}(4\\theta+3)(\\theta+1)^2(4\\theta+5)", "superseek": "308/23 70799/23", "discriminant": "5 529 -75233 1357863 -6206392 -980880 -30482432", "aesz": "250", "n_sing_complex": "2", "inst_int": "", "c2h": "62", "hash": "9c19794a84073d1c6dfd11c8a7c9a740", "dim_h": "9", "inst": " 308/23 3526/23 70799/23 2148684/23 81402822/23 3517706942/23 166755728017/23 8463817366930/23 452628943972573/23 25225062363800138/23", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "5", "laurent": null, "discriminant_tex": "-(512z^3+113z^2+121z-1)(-23+244z)^2", "discr_factors": "-30482432, (-23/244+z)^2, z^3+113/512*z^2+121/512*z-1/512", "dm_basis": null, "q": "0 1 -27 31 -1565 -122872 -6002087 -316779981 -17953605095 -1060383625879", "yuk": "1 308/23 28516/23 1911881/23 137544292/23 10175353058/23 759826639561/23 57197214710139/23 4333474629412452/23 329966500157917598/23", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/3072*(33598639+5035776*249^(1/2))^(1/3)+173087/3072/(33598639+5035776*249^(1/2))^(1/3)-113/1536","im":"-1/2*3^(1/2)*(1/1536*(33598639+5035776*249^(1/2))^(1/3)+173087/1536/(33598639+5035776*249^(1/2))^(1/3))","approx_re":"-0.114451","approx_im":"-0.474453","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/3072*(33598639+5035776*249^(1/2))^(1/3)+173087/3072/(33598639+5035776*249^(1/2))^(1/3)-113/1536","im":"1/2*3^(1/2)*(1/1536*(33598639+5035776*249^(1/2))^(1/3)+173087/1536/(33598639+5035776*249^(1/2))^(1/3))","approx_re":"-0.114451","approx_im":"0.474453","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":"1/1536*(33598639+5035776*249^(1/2))^(1/3)-173087/1536/(33598639+5035776*249^(1/2))^(1/3)-113/1536","im":"0","approx_re":"0.008199","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"23/244","im":"0","approx_re":"0.094262295082","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":[]}]}, {"pols": "[121*X^4, -18403*X^4-33506*X^3-25707*X^2-8954*X-1210, 192470*X^4+282980*X^3+132850*X^2+34540*X+6600, -669988*X^4-983928*X^3-909804*X^2-461736*X-91872, 815800*X^4+2054000*X^3+2285400*X^2+1245200*X+268000, -20000*(4*X+3)*(X+1)^2*(4*X+5)]", "text": "This is operator \"5.79\" from ...", "degz": 5, "h3": "132", "sol": "1 10 450 30772 2551810 236608260 23596946100 2477211489000 270152941907970 30340326488101300", "n_discr_factors": "3", "c3": "-516", "operator": "4 5 0 0 0 0 121 -1210 -8954 -25707 -33506 -18403 6600 34540 132850 282980 192470 -91872 -461736 -909804 -983928 -669988 268000 1245200 2285400 2054000 815800 -300000 -1240000 -1900000 -1280000 -320000", "new_number": "5.79", "id": 292, "operator_tex": "11^{2} \\theta^4-11 x\\left(1673\\theta^4+3046\\theta^3+2337\\theta^2+814\\theta+110\\right)+2 5 x^{2}\\left(19247\\theta^4+28298\\theta^3+13285\\theta^2+3454\\theta+660\\right)-2^{2} x^{3}\\left(167497\\theta^4+245982\\theta^3+227451\\theta^2+115434\\theta+22968\\right)+2^{3} 5^{2} x^{4}\\left(4079\\theta^4+10270\\theta^3+11427\\theta^2+6226\\theta+1340\\right)-2^{5} 5^{4} x^{5}(4\\theta+3)(\\theta+1)^2(4\\theta+5)", "superseek": "181/11 47171/11", "discriminant": "5 121 -18403 192470 -669988 815800 -320000", "aesz": "310", "n_sing_complex": "0", "inst_int": "", "c2h": "-48", "hash": "2b9b103b1c8f0d3175cd1fb9ef5aacc2", "dim_h": "18", "inst": " 181/11 2018/11 47171/11 3261479/22 69313270/11 3365244834/11 179297422954/11 10226880863781/11 614573261709111/11 38486025659517390/11", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "-(z-1)(128z^2-142z+1)(-11+50z)^2", "discr_factors": "-320000, z^2-71/64*z+1/128, z-1, (-11/50+z)^2", "dm_basis": null, "q": "0 1 -34 239 -4824 -174473 -9827854 -593163269 -37812392672 -2510447352650", "yuk": "1 181/11 16325/11 1273798/11 9489423 8664158931/11 726894174086/11 61499016073403/11 5236163106639525/11 448023907787215717/11", "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":"71/128-17/128*17^(1/2)","im":"0","approx_re":"0.007088","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"11/50","im":"0","approx_re":"0.22","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1","im":"0","approx_re":"1.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"71/128+17/128*17^(1/2)","im":"0","approx_re":"1.102287","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":["3/4","1","1","5/4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[169*X^4, -15418*X^4-22100*X^3-17810*X^2-6760*X-1014, 37908+209248*X+487096*X^2+580712*X^3+324908*X^4, -3180153*X^4-8754414*X^3-11733109*X^2-7260552*X-1687608, 18242234*X^4+77647504*X^3+123871092*X^2+83490832*X+20385528, -58945060*X^4-325439824*X^3-608035160*X^2-450086684*X-116707308, 43928784*X^4+439619832*X^3+1126215684*X^2+965430000*X+271755432, 162182412*X^4+532716840*X^3+227690748*X^2-179503416*X-105854472, -184700952*X^4-842442768*X^3-578731176*X^2+133833168*X+143181216, -109737072*X^4-172159776*X^3-152362512*X^2-88569504*X-23302080, 126241632*X^4+247008960*X^3+171442656*X^2+48109248*X+4333824, 418176*(4*X+3)*(X+1)^2*(4*X+5)]", "text": "This is operator \"11.13\" from ...", "degz": 11, "h3": null, "sol": "1 6 126 4092 160110 6981156 326953116 16106882616 823919474862 43390556965140", "n_discr_factors": "3", "c3": null, "operator": "4 11 0 0 0 0 169 -1014 -6760 -17810 -22100 -15418 37908 209248 487096 580712 324908 -1687608 -7260552 -11733109 -8754414 -3180153 20385528 83490832 123871092 77647504 18242234 -116707308 -450086684 -608035160 -325439824 -58945060 271755432 965430000 1126215684 439619832 43928784 -105854472 -179503416 227690748 532716840 162182412 143181216 133833168 -578731176 -842442768 -184700952 -23302080 -88569504 -152362512 -172159776 -109737072 4333824 48109248 171442656 247008960 126241632 6272640 25926912 39726720 26763264 6690816", "new_number": "11.13", "id": 329, "operator_tex": "13^{2} \\theta^4-2 13 x\\left(593\\theta^4+850\\theta^3+685\\theta^2+260\\theta+39\\right)+2^{2} x^{2}\\left(81227\\theta^4+145178\\theta^3+121774\\theta^2+52312\\theta+9477\\right)-x^{3}\\left(3180153\\theta^4+8754414\\theta^3+11733109\\theta^2+7260552\\theta+1687608\\right)+2 x^{4}\\left(9121117\\theta^4+38823752\\theta^3+61935546\\theta^2+41745416\\theta+10192764\\right)-2^{2} x^{5}\\left(14736265\\theta^4+81359956\\theta^3+152008790\\theta^2+112521671\\theta+29176827\\right)+2^{2} 3^{2} x^{6}\\left(1220244\\theta^4+12211662\\theta^3+31283769\\theta^2+26817500\\theta+7548762\\right)+2^{2} 3^{2} x^{7}\\left(4505067\\theta^4+14797690\\theta^3+6324743\\theta^2-4986206\\theta-2940402\\right)-2^{3} 3^{3} x^{8}\\left(855097\\theta^4+3900198\\theta^3+2679311\\theta^2-619598\\theta-662876\\right)-2^{4} 3^{3} x^{9}\\left(254021\\theta^4+398518\\theta^3+352691\\theta^2+205022\\theta+53940\\right)+2^{5} 3^{3} 11 x^{10}\\left(13283\\theta^4+25990\\theta^3+18039\\theta^2+5062\\theta+456\\right)+2^{7} 3^{3} 11^{2} x^{11}(4\\theta+3)(\\theta+1)^2(4\\theta+5)", "superseek": "70/13 15323/39", "discriminant": "11 169 -15418 324908 -3180153 18242234 -58945060 43928784 162182412 -184700952 -109737072 126241632 6690816", "aesz": null, "n_sing_complex": "5", "inst_int": "", "c2h": null, "hash": "89df09ff1ec0d5dfcae0791579c9095e", "dim_h": null, "inst": " 70/13 420/13 15323/39 78225/13 1564284/13 106611124/39 882780787/13 23479011382/13 1973556192430/39 19205237477692/13", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "9", "laurent": null, "discriminant_tex": "(192z^2-69z+1)(2z^3+39z^2-5z+1)(13-112z-18z^2+132z^3)^2", "discr_factors": "6690816, z^3+39/2*z^2-5/2*z+1/2, (13/132-28/33*z-3/22*z^2+z^3)^2, z^2-23/64*z+1/192", "dm_basis": null, "q": "0 1 -16 58 -792 -3613 -250588 -5973466 -182013880 -5605185911", "yuk": "1 70/13 3430/13 137977/13 5009830/13 195535570/13 7676142265/13 302793810011/13 12021258837414/13 479574154898467/13", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/6*(61128+177*177^(1/2))^(1/3)-517/2/(61128+177*177^(1/2))^(1/3)-13/2","im":"0","approx_re":"-19.628663","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/132*(-8586+55*I*607445^(1/2))^(1/3)-1241/132/(-8586+55*I*607445^(1/2))^(1/3)+1/22+1/2*I*3^(1/2)*(1/66*(-8586+55*I*607445^(1/2))^(1/3)-1241/66/(-8586+55*I*607445^(1/2))^(1/3))","im":"0","approx_re":"-0.912176","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":"23/128-11/384*33^(1/2)","im":"0","approx_re":"0.01513","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/12*(61128+177*177^(1/2))^(1/3)+517/4/(61128+177*177^(1/2))^(1/3)-13/2","im":"1/2*3^(1/2)*(-1/6*(61128+177*177^(1/2))^(1/3)+517/2/(61128+177*177^(1/2))^(1/3))","approx_re":"0.064331","approx_im":"-0.146063","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/12*(61128+177*177^(1/2))^(1/3)+517/4/(61128+177*177^(1/2))^(1/3)-13/2","im":"-1/2*3^(1/2)*(-1/6*(61128+177*177^(1/2))^(1/3)+517/2/(61128+177*177^(1/2))^(1/3))","approx_re":"0.064331","approx_im":"0.146063","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/132*(-8586+55*I*607445^(1/2))^(1/3)-1241/132/(-8586+55*I*607445^(1/2))^(1/3)+1/22-1/2*I*3^(1/2)*(1/66*(-8586+55*I*607445^(1/2))^(1/3)-1241/66/(-8586+55*I*607445^(1/2))^(1/3))","im":"0","approx_re":"0.115746","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"23/128+11/384*33^(1/2)","im":"0","approx_re":"0.344245","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/66*(-8586+55*I*607445^(1/2))^(1/3)+1241/66/(-8586+55*I*607445^(1/2))^(1/3)+1/22","im":"0","approx_re":"0.932793","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":[]}]}, {"pols": "[X^4, 6+38*X+96*X^2+116*X^3+91*X^4, 1218+5950*X+11076*X^2+9388*X^3+3649*X^4, 32814+148542*X+258070*X^2+203832*X^3+63585*X^4, 452634+1866098*X+2834854*X^2+1876864*X^3+489086*X^4, 2613816+10006152*X+13629172*X^2+7635136*X^3+1497628*X^4, 3996360+13915740*X+16585980*X^2+8235072*X^3+1566360*X^4, -9795600-30045624*X-25554680*X^2-743296*X^3+2211712*X^4, -2330112+3517808*X+25230064*X^2+25837056*X^3+5467392*X^4, 104256-5010336*X-15655264*X^2-13188096*X^3-958976*X^4, 523008+3215616*X+8458752*X^2+10444800*X^3+4890624*X^4, -18432*(4*X+3)*(X+1)^2*(4*X+5)]", "text": "This is operator \"11.1\" from ...", "degz": 11, "h3": null, "sol": "1 -6 54 12 -26010 1057644 -27064044 361271016 7490403558 -724620112260", "n_discr_factors": "4", "c3": null, "operator": "4 11 0 0 0 0 1 6 38 96 116 91 1218 5950 11076 9388 3649 32814 148542 258070 203832 63585 452634 1866098 2834854 1876864 489086 2613816 10006152 13629172 7635136 1497628 3996360 13915740 16585980 8235072 1566360 -9795600 -30045624 -25554680 -743296 2211712 -2330112 3517808 25230064 25837056 5467392 104256 -5010336 -15655264 -13188096 -958976 523008 3215616 8458752 10444800 4890624 -276480 -1142784 -1751040 -1179648 -294912", "new_number": "11.1", "id": 336, "operator_tex": "\\theta^4+x\\left(6+38\\theta+96\\theta^2+116\\theta^3+91\\theta^4\\right)+x^{2}\\left(1218+5950\\theta+11076\\theta^2+9388\\theta^3+3649\\theta^4\\right)+x^{3}\\left(32814+148542\\theta+258070\\theta^2+203832\\theta^3+63585\\theta^4\\right)+2 x^{4}\\left(244543\\theta^4+938432\\theta^3+1417427\\theta^2+933049\\theta+226317\\right)+2^{2} x^{5}\\left(374407\\theta^4+1908784\\theta^3+3407293\\theta^2+2501538\\theta+653454\\right)+2^{2} 3 x^{6}\\left(130530\\theta^4+686256\\theta^3+1382165\\theta^2+1159645\\theta+333030\\right)+2^{3} x^{7}\\left(276464\\theta^4-92912\\theta^3-3194335\\theta^2-3755703\\theta-1224450\\right)+2^{4} x^{8}\\left(341712\\theta^4+1614816\\theta^3+1576879\\theta^2+219863\\theta-145632\\right)-2^{5} x^{9}\\left(29968\\theta^4+412128\\theta^3+489227\\theta^2+156573\\theta-3258\\right)+2^{8} 3 x^{10}\\left(6368\\theta^4+13600\\theta^3+11014\\theta^2+4187\\theta+681\\right)-2^{11} 3^{2} x^{11}(4\\theta+3)(\\theta+1)^2(4\\theta+5)", "superseek": "-4 550/3", "discriminant": "11 1 91 3649 63585 489086 1497628 1566360 2211712 5467392 -958976 4890624 -294912", "aesz": null, "n_sing_complex": "4", "inst_int": "", "c2h": null, "hash": "9e36d74a520997fe52f0cbbfafae6aaf", "dim_h": null, "inst": " -4 -11 550/3 -2965/2 -3316 8541260/27 -5027678 12718958 34467542200/27 -31586765315", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "9", "laurent": null, "discriminant_tex": "-(4z+1)(3z+1)(96z^3-1576z^2-62z-1)(1+11z-6z^2+16z^3)^2", "discr_factors": "-294912, z+1/3, (1/16+11/16*z-3/8*z^2+z^3)^2, z^3-197/12*z^2-31/48*z-1/96, z+1/4", "dm_basis": null, "q": "0 1 14 201 1368 15052 153726 -69260 17297272 225976842", "yuk": "1 -4 -92 4946 -94972 -414504 68334938 -1724493558 6512011524 930623644346", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/3","im":"0","approx_re":"-0.333333333333","approx_im":"0.0","exponents":["0","1","1","2"],"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":"-1/24*(999+6*79413^(1/2))^(1/3)+41/8/(999+6*79413^(1/2))^(1/3)+1/8","im":"0","approx_re":"-0.085955","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/144*(61824484+15012*417^(1/2))^(1/3)-9772/9/(61824484+15012*417^(1/2))^(1/3)+197/36","im":"-1/4*3^(1/2)*(1/36*(61824484+15012*417^(1/2))^(1/3)-39088/9/(61824484+15012*417^(1/2))^(1/3))","approx_re":"-0.019642","approx_im":"-0.015722","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/144*(61824484+15012*417^(1/2))^(1/3)-9772/9/(61824484+15012*417^(1/2))^(1/3)+197/36","im":"1/4*3^(1/2)*(1/36*(61824484+15012*417^(1/2))^(1/3)-39088/9/(61824484+15012*417^(1/2))^(1/3))","approx_re":"-0.019642","approx_im":"0.015722","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":"1/48*(999+6*79413^(1/2))^(1/3)-41/16/(999+6*79413^(1/2))^(1/3)+1/8","im":"1/2*3^(1/2)*(-1/24*(999+6*79413^(1/2))^(1/3)-41/8/(999+6*79413^(1/2))^(1/3))","approx_re":"0.230478","approx_im":"-0.820976","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/48*(999+6*79413^(1/2))^(1/3)-41/16/(999+6*79413^(1/2))^(1/3)+1/8","im":"-1/2*3^(1/2)*(-1/24*(999+6*79413^(1/2))^(1/3)-41/8/(999+6*79413^(1/2))^(1/3))","approx_re":"0.230478","approx_im":"0.820976","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/72*(61824484+15012*417^(1/2))^(1/3)+19544/9/(61824484+15012*417^(1/2))^(1/3)+197/36","im":"0","approx_re":"16.455951","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":["3/4","1","1","5/4"],"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":[]}]}, {"pols": "[289*X^4, -1734-12138*X-33218*X^2-42160*X^3-21998*X^4, -81600-368492*X-590936*X^2-359008*X^3-57748*X^4, -209304-673812*X-503748*X^2+308160*X^3+258456*X^4, -634896-1736136*X-665192*X^2+1331072*X^3+415360*X^4, 167808+1054320*X+2103024*X^2+1285632*X^3-449280*X^4, 42048+516960*X+1011360*X^2+9216*X^3-975360*X^4, -338688-1476864*X-2492928*X^2-1990656*X^3-663552*X^4, -18432*(4*X+3)*(X+1)^2*(4*X+5)]", "text": "", "degz": 8, "h3": "34", "sol": "1 6 162 6252 290610 15057756 837966276 49048143192 2980860478002 186501421576140", "n_discr_factors": "3", "c3": "-90", "operator": "4 8 0 0 0 0 289 -1734 -12138 -33218 -42160 -21998 -81600 -368492 -590936 -359008 -57748 -209304 -673812 -503748 308160 258456 -634896 -1736136 -665192 1331072 415360 167808 1054320 2103024 1285632 -449280 42048 516960 1011360 9216 -975360 -338688 -1476864 -2492928 -1990656 -663552 -276480 -1142784 -1751040 -1179648 -294912", "new_number": "8.20", "id": 464, "operator_tex": "17^{2} \\theta^4-2 17 x\\left(647\\theta^4+1240\\theta^3+977\\theta^2+357\\theta+51\\right)-2^{2} x^{2}\\left(14437\\theta^4+89752\\theta^3+147734\\theta^2+92123\\theta+20400\\right)+2^{2} 3 x^{3}\\left(21538\\theta^4+25680\\theta^3-41979\\theta^2-56151\\theta-17442\\right)+2^{3} x^{4}\\left(51920\\theta^4+166384\\theta^3-83149\\theta^2-217017\\theta-79362\\right)-2^{4} 3 x^{5}\\left(9360\\theta^4-26784\\theta^3-43813\\theta^2-21965\\theta-3496\\right)-2^{5} 3 x^{6}\\left(10160\\theta^4-96\\theta^3-10535\\theta^2-5385\\theta-438\\right)-2^{8} 3^{2} x^{7}\\left(288\\theta^4+864\\theta^3+1082\\theta^2+641\\theta+147\\right)-2^{11} 3^{2} x^{8}(4\\theta+3)(\\theta+1)^2(4\\theta+5)", "superseek": "118/17 672", "discriminant": "8 289 -21998 -57748 258456 415360 -449280 -975360 -663552 -294912", "aesz": "213", "n_sing_complex": "2", "inst_int": "", "c2h": "76", "hash": "d430b37f4ca641af0b82cbef83547c51", "dim_h": "12", "inst": " 118/17 873/17 672 447987/34 5358846/17 146392320/17 4385052354/17 140593718677/17 4748423946666/17 167107094317077/17", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "7", "laurent": null, "discriminant_tex": "-(4z+1)(32z^3+40z^2+78z-1)(-17+18z+48z^2)^2", "discr_factors": "-294912, (-17/48+3/8*z+z^2)^2, z+1/4, z^3+5/4*z^2+39/16*z-1/32", "dm_basis": null, "q": "0 1 -18 25 -216 -21452 -562194 -19145004 -687292104 -25629759794", "yuk": "1 118/17 7102/17 308566/17 14342686/17 669855868/17 31621056670/17 1504072957540/17 71983998305310/17 3461601057428080/17", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-3/16-1/48*897^(1/2)","im":"0","approx_re":"-0.811457","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/48*(6236+708*177^(1/2))^(1/3)+23/3/(6236+708*177^(1/2))^(1/3)-5/12","im":"-1/4*3^(1/2)*(1/12*(6236+708*177^(1/2))^(1/3)+92/3/(6236+708*177^(1/2))^(1/3))","approx_re":"-0.631368","approx_im":"-1.433512","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/48*(6236+708*177^(1/2))^(1/3)+23/3/(6236+708*177^(1/2))^(1/3)-5/12","im":"1/4*3^(1/2)*(1/12*(6236+708*177^(1/2))^(1/3)+92/3/(6236+708*177^(1/2))^(1/3))","approx_re":"-0.631368","approx_im":"1.433512","exponents":["0","1","1","2"],"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":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/24*(6236+708*177^(1/2))^(1/3)-46/3/(6236+708*177^(1/2))^(1/3)-5/12","im":"0","approx_re":"0.012736","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-3/16+1/48*897^(1/2)","im":"0","approx_re":"0.436457","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":[]}]}, {"pols": "[9*X^4, -36-234*X-603*X^2-738*X^3-342*X^4, -2556-12510*X-22605*X^2-17106*X^3-6135*X^4, 36288+134568*X+190200*X^2+142200*X^3+52992*X^4, -683616-2151888*X-1727864*X^2+450992*X^3+482296*X^4, -129664-3273952*X-9657264*X^2-9689728*X^3-3290416*X^4, 8114944+39123072*X+64345600*X^2+34978176*X^3-6580992*X^4, 15837184+80152064*X+166659840*X^2+171651584*X^3+74914048*X^4, -11214848*(4*X+3)*(X+1)^2*(4*X+5)]", "text": "This is operator \"8.24\" from ...", "degz": 8, "h3": "48", "sol": "1 4 72 1696 49960 1617504 56399616 2065102848 78509001384 3071712566560", "n_discr_factors": "2", "c3": "-86", "operator": "4 8 0 0 0 0 9 -36 -234 -603 -738 -342 -2556 -12510 -22605 -17106 -6135 36288 134568 190200 142200 52992 -683616 -2151888 -1727864 450992 482296 -129664 -3273952 -9657264 -9689728 -3290416 8114944 39123072 64345600 34978176 -6580992 15837184 80152064 166659840 171651584 74914048 -168222720 -695320576 -1065410560 -717750272 -179437568", "new_number": "8.24", "id": 468, "operator_tex": "3^{2} \\theta^4-3^{2} x\\left(38\\theta^4+82\\theta^3+67\\theta^2+26\\theta+4\\right)-3 x^{2}\\left(2045\\theta^4+5702\\theta^3+7535\\theta^2+4170\\theta+852\\right)+2^{3} 3 x^{3}\\left(2208\\theta^4+5925\\theta^3+7925\\theta^2+5607\\theta+1512\\right)+2^{3} x^{4}\\left(60287\\theta^4+56374\\theta^3-215983\\theta^2-268986\\theta-85452\\right)-2^{4} x^{5}\\left(205651\\theta^4+605608\\theta^3+603579\\theta^2+204622\\theta+8104\\right)-2^{7} x^{6}\\left(51414\\theta^4-273267\\theta^3-502700\\theta^2-305649\\theta-63398\\right)+2^{8} 37 x^{7}\\left(7909\\theta^4+18122\\theta^3+17595\\theta^2+8462\\theta+1672\\right)-2^{13} 37^{2} x^{8}(4\\theta+3)(\\theta+1)^2(4\\theta+5)", "superseek": "3 437/3", "discriminant": "8 9 -342 -6135 52992 482296 -3290416 -6580992 74914048 -179437568", "aesz": "286", "n_sing_complex": "2", "inst_int": "", "c2h": "84", "hash": "94afcd38a40c3a3e54fc3c57b4b85459", "dim_h": "15", "inst": " 3 539/24 437/3 18531/8 90274/3 14180887/24 10711739 2751585605/12 4879799322 1342664492735/12", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "7", "laurent": null, "discriminant_tex": "-(-1+40z+504z^2-3088z^3+8192z^4)(-3-3z+148z^2)^2", "discr_factors": "-179437568, (-3/148-3/148*z+z^2)^2, -1/8192+5/1024*z+63/1024*z^2-193/512*z^3+z^4", "dm_basis": null, "q": "0 1 -10 -28 272 -7113 -29692 -1859356 -29643712 -862582466", "yuk": "1 3 548/3 3936 445292/3 11284259/3 382896296/3 3674126480 117401134244 3557373709674", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"3/296-1/296*1785^(1/2)","im":"0","approx_re":"-0.132599","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/2*RootOf(512*_Z^4-386*_Z^3+126*_Z^2+20*_Z-1,index = 3)","im":"0","approx_re":"-0.070843","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":"1/2*RootOf(512*_Z^4-386*_Z^3+126*_Z^2+20*_Z-1,index = 1)","im":"0","approx_re":"0.020383","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"3/296+1/296*1785^(1/2)","im":"0","approx_re":"0.152869","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/2*RootOf(512*_Z^4-386*_Z^3+126*_Z^2+20*_Z-1,index = 2)","im":"0","approx_re":"0.213707","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/2*RootOf(512*_Z^4-386*_Z^3+126*_Z^2+20*_Z-1,index = 4)","im":"0","approx_re":"0.213707","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":["3/4","1","1","5/4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[25*X^4, 150+900*X+2160*X^2+2520*X^3+1530*X^4, 21960+97320*X+162744*X^2+122832*X^3+39564*X^4, 388800+1550340*X+2282796*X^2+1521504*X^3+417528*X^4, 1048464+5228280*X+9858456*X^2+8379072*X^3+2522880*X^4, 839808+11551248*X+32173200*X^2+32037120*X^3+10202112*X^4, 6858432+37348128*X+75730464*X^2+68677632*X^3+25256448*X^4, 14276736+65225088*X+119812608*X^2+107495424*X^3+40310784*X^4, 1119744*(4*X+3)*(X+1)^2*(4*X+5)]", "text": "This is operator \"8.39\" from ...", "degz": 8, "h3": null, "sol": "1 -6 54 -348 -3690 226044 -6054804 112970376 -1231916202 -10937222340", "n_discr_factors": "2", "c3": null, "operator": "4 8 0 0 0 0 25 150 900 2160 2520 1530 21960 97320 162744 122832 39564 388800 1550340 2282796 1521504 417528 1048464 5228280 9858456 8379072 2522880 839808 11551248 32173200 32037120 10202112 6858432 37348128 75730464 68677632 25256448 14276736 65225088 119812608 107495424 40310784 16796160 69424128 106375680 71663616 17915904", "new_number": "8.39", "id": 484, "operator_tex": "5^{2} \\theta^4+2 3 5 x\\left(51\\theta^4+84\\theta^3+72\\theta^2+30\\theta+5\\right)+2^{2} 3 x^{2}\\left(3297\\theta^4+10236\\theta^3+13562\\theta^2+8110\\theta+1830\\right)+2^{2} 3^{3} x^{3}\\left(3866\\theta^4+14088\\theta^3+21137\\theta^2+14355\\theta+3600\\right)+2^{3} 3^{3} x^{4}\\left(11680\\theta^4+38792\\theta^3+45641\\theta^2+24205\\theta+4854\\right)+2^{4} 3^{5} x^{5}\\left(2624\\theta^4+8240\\theta^3+8275\\theta^2+2971\\theta+216\\right)+2^{5} 3^{5} x^{6}\\left(3248\\theta^4+8832\\theta^3+9739\\theta^2+4803\\theta+882\\right)+2^{7} 3^{7} x^{7}\\left(144\\theta^4+384\\theta^3+428\\theta^2+233\\theta+51\\right)+2^{9} 3^{7} x^{8}(4\\theta+3)(\\theta+1)^2(4\\theta+5)", "superseek": "-12/5 136/3", "discriminant": "8 25 1530 39564 417528 2522880 10202112 25256448 40310784 17915904", "aesz": null, "n_sing_complex": "4", "inst_int": "", "c2h": null, "hash": "c1330764e09752f7bb8e86b15541c588", "dim_h": null, "inst": " -12/5 -21/5 136/3 -1743/10 -1056/5 109891/5 -1058496/5 925917/5 123214344/5 -1875209418/5", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "7", "laurent": null, "discriminant_tex": "(1+54z+1152z^2+6048z^3+3456z^4)(5+18z+72z^2)^2", "discr_factors": "17915904, (5/72+1/4*z+z^2)^2, 1/3456+1/64*z+1/3*z^2+7/4*z^3+z^4", "dm_basis": null, "q": "0 1 12 138 1060 8403 60408 267468 1875936 12749085", "yuk": "1 -12/5 -36 6108/5 -55956/5 -132012/5 23742396/5 -72612828 474013548/5 89823262884/5", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"1/2*RootOf(216*_Z^4+756*_Z^3+288*_Z^2+27*_Z+1,index = 3)","im":"0","approx_re":"-1.540068","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/2*RootOf(216*_Z^4+756*_Z^3+288*_Z^2+27*_Z+1,index = 2)","im":"0","approx_re":"-0.152177","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/8","im":"-1/24*31^(1/2)","approx_re":"-0.125","approx_im":"-0.23199","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/8","im":"1/24*31^(1/2)","approx_re":"-0.125","approx_im":"0.23199","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/2*RootOf(216*_Z^4+756*_Z^3+288*_Z^2+27*_Z+1,index = 1)","im":"0","approx_re":"-0.028878","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/2*RootOf(216*_Z^4+756*_Z^3+288*_Z^2+27*_Z+1,index = 4)","im":"0","approx_re":"-0.028878","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":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["3/4","1","1","5/4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[9*X^4, 7104*X^4+11904*X^3+10956*X^2+5004*X+936, 2301952*X^4+6307840*X^3+8641024*X^2+5549568*X+1359744, 441450496*X^4+1277165568*X^3+1851326464*X^2+1393754112*X+379748352, 61337501696*X^4+166161547264*X^3+171387650048*X^2+91477770240*X+18041798656, 6184752906240*X^4+17111149707264*X^3+17944373362688*X^2+5589899935744*X-132070244352, 439804651110400*X^4+1108307720798208*X^3+1459051930058752*X^2+829581523156992*X+173585398235136, 22517998136852480*X^4+58546795155816448*X^3+65583669573582848*X^2+35888059530608640*X+7881299347898368, 36028797018963968*(4*X+3)*(X+1)^2*(4*X+5)]", "text": "This is operator \"8.75\" from ...", "degz": 8, "h3": null, "sol": "1 -104 16488 -3037568 605558440 -126766739904 27432378844416 -6080200735260672 1372174011174250152 -314057497740075256640", "n_discr_factors": "4", "c3": null, "operator": "4 8 0 0 0 0 9 936 5004 10956 11904 7104 1359744 5549568 8641024 6307840 2301952 379748352 1393754112 1851326464 1277165568 441450496 18041798656 91477770240 171387650048 166161547264 61337501696 -132070244352 5589899935744 17944373362688 17111149707264 6184752906240 173585398235136 829581523156992 1459051930058752 1108307720798208 439804651110400 7881299347898368 35888059530608640 65583669573582848 58546795155816448 22517998136852480 540431955284459520 2233785415175766016 3422735716801576960 2305843009213693952 576460752303423488", "new_number": "8.75", "id": 524, "operator_tex": "3^{2} \\theta^4+2^{2} 3 x\\left(592\\theta^4+992\\theta^3+913\\theta^2+417\\theta+78\\right)+2^{7} x^{2}\\left(17984\\theta^4+49280\\theta^3+67508\\theta^2+43356\\theta+10623\\right)+2^{15} x^{3}\\left(13472\\theta^4+38976\\theta^3+56498\\theta^2+42534\\theta+11589\\right)+2^{21} x^{4}\\left(29248\\theta^4+79232\\theta^3+81724\\theta^2+43620\\theta+8603\\right)+2^{30} x^{5}\\left(5760\\theta^4+15936\\theta^3+16712\\theta^2+5206\\theta-123\\right)+2^{37} x^{6}\\left(3200\\theta^4+8064\\theta^3+10616\\theta^2+6036\\theta+1263\\right)+2^{47} x^{7}\\left(160\\theta^4+416\\theta^3+466\\theta^2+255\\theta+56\\right)+2^{55} x^{8}(4\\theta+3)(\\theta+1)^2(4\\theta+5)", "superseek": "-100/3 66364", "discriminant": "8 9 7104 2301952 441450496 61337501696 6184752906240 439804651110400 22517998136852480 576460752303423488", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "76a0af78cc3434c7a78f3edc406baa61", "dim_h": null, "inst": " -100/3 538/3 66364 9836374/3 67135456/3 -32724671906/3 -966495408836 -25876882055654 9140866616260304/3 1274200874423817680/3", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "6", "laurent": null, "discriminant_tex": "(64z+1)(128z+1)(256z+1)^2(32768z^2+128z+3)^2", "discr_factors": "576460752303423488, z+1/64, (z^2+1/256*z+3/32768)^2, (z+1/256)^2, z+1/128", "dm_basis": null, "q": "0 1 140 14814 1293680 92922669 5226525096 199702434578 2302853700800 -208306231537914", "yuk": "1 -100/3 4204/3 5375384/3 629532140/3 8391931900/3 -7068523752008/3 -994523775692344/3 -39746890207952404/3 6663691763259137000/3", "gv2": null, "gv0": null, "gv1": null, 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