{"count": 3, "status":"OK", "data":[{"pols": "[X^4, -4928*X-1360-6464*X^2-3072*X^3-1536*X^4, -262144*X-651264+1703936*X^2+1835008*X^3+458752*X^4, 3251634176+3615490048*X^2+5410652160*X+1207959552*X^3+201326592*X^4, -1545382920192-2714419331072*X-1846835937280*X^2-584115552256*X^3-73014444032*X^4, -259759622062080*X^2-474164389478400*X-335625924378624-65970697666560*X^3-6597069766656*X^4, 2533274790395904*(X+3)^4]", "text": "This is operator \"6.33\" from ...", "degz": 6, "h3": null, "sol": "1 1360 1516304 1522167040 1444349938960 1320519296632064 1176435721504129280 1028122237568411488256 885307276490857727434000 753420342756902018230969600", "n_discr_factors": "3", "c3": null, "operator": "4 6 0 0 0 0 1 -1360 -4928 -6464 -3072 -1536 -651264 -262144 1703936 1835008 458752 3251634176 5410652160 3615490048 1207959552 201326592 -1545382920192 -2714419331072 -1846835937280 -584115552256 -73014444032 -335625924378624 -474164389478400 -259759622062080 -65970697666560 -6597069766656 205195258022068224 273593677362757632 136796838681378816 30399297484750848 2533274790395904", "new_number": "6.33", "id": 418, "operator_tex": "\\theta^4-2^{4} x\\left(96\\theta^4+192\\theta^3+404\\theta^2+308\\theta+85\\right)+2^{12} x^{2}\\left(112\\theta^4+448\\theta^3+416\\theta^2-64\\theta-159\\right)+2^{20} x^{3}\\left(192\\theta^4+1152\\theta^3+3448\\theta^2+5160\\theta+3101\\right)-2^{28} x^{4}\\left(272\\theta^4+2176\\theta^3+6880\\theta^2+10112\\theta+5757\\right)-2^{38} 3 x^{5}\\left(8\\theta^4+80\\theta^3+315\\theta^2+575\\theta+407\\right)+2^{48} 3^{2} x^{6}\\left((\\theta+3)^4\\right)", "superseek": "352 26115552", "discriminant": "6 1 -1536 458752 201326592 -73014444032 -6597069766656 2533274790395904", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "0677bb20f37d2fa88bafbc665d5157c1", "dim_h": null, "inst": " 352 60664 26115552 16623590600 13165993300256 11986704764296088 12020218264693813856 12940227600404919292744 14708343012850857454009600 17451325510266418328472861992", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "(256z-1)^2(768z-1)^2(256z+1)^2", "discr_factors": "2533274790395904, (z-1/768)^2, (z-1/256)^2, (z+1/256)^2", "dm_basis": null, "q": "0 1 512 445280 480479232 578735581744 745583606296576 1005278122520203776 1400774260891946319872 2001101029745058591951512", "yuk": "1 352 485664 705120256 1063910284064 1645749162532352 2589128229793560576 4122934864789978152960 6625396531408382588168992 10722382056368275084678118656", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/256","im":"0","approx_re":"-0.00390625","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":"1/768","im":"0","approx_re":"0.00130208333333","approx_im":"0.0","exponents":["0","1","-2","3"],"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":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["3","3","3","3"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[9*X^4, -324*X^2-60-192*X^3-96*X^4-228*X, -17408*X^3-9936-31744*X^2-4352*X^4-28672*X, 793856+882688*X^2+49152*X^4+1320960*X+294912*X^3, 10485760*X+9961472*X^2+458752*X^4+3670016*X^3+3084288, -478412800*X-62914560*X^3-252968960*X^2-6291456*X^4-353173504, 16777216*(X+3)^4]", "text": "This is operator \"6.34\" from ...", "degz": 6, "h3": null, "sol": "1 20/3 332/3 13360/27 966020/81 253744/9 1234573360/729 1826462528/2187 652178380780/2187 -4552695203120/19683", "n_discr_factors": "3", "c3": null, "operator": "4 6 0 0 0 0 9 -60 -228 -324 -192 -96 -9936 -28672 -31744 -17408 -4352 793856 1320960 882688 294912 49152 3084288 10485760 9961472 3670016 458752 -353173504 -478412800 -252968960 -62914560 -6291456 1358954496 1811939328 905969664 201326592 16777216", "new_number": "6.34", "id": 419, "operator_tex": "3^{2} \\theta^4-2^{2} 3 x\\left(8\\theta^4+16\\theta^3+27\\theta^2+19\\theta+5\\right)-2^{4} x^{2}\\left(272\\theta^4+1088\\theta^3+1984\\theta^2+1792\\theta+621\\right)+2^{8} x^{3}\\left(192\\theta^4+1152\\theta^3+3448\\theta^2+5160\\theta+3101\\right)+2^{12} x^{4}\\left(112\\theta^4+896\\theta^3+2432\\theta^2+2560\\theta+753\\right)-2^{16} x^{5}\\left(96\\theta^4+960\\theta^3+3860\\theta^2+7300\\theta+5389\\right)+2^{24} x^{6}\\left((\\theta+3)^4\\right)", "superseek": "4/3 -124/81", "discriminant": "6 9 -96 -4352 49152 458752 -6291456 16777216", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "1153f8807d42d96ede28f7a8d06c144b", "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-3)^2(16z+1)^2", "discr_factors": "16777216, (z-3/16)^2, (z+1/16)^2, (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","1","-2","3"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["3","3","3","3"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -33*X^4-98*X^3-105*X^2-56*X-12, 272*X^4+2208*X^3+4872*X^2+4656*X+1728, 528*X^4-8160*X^3-45168*X^2-72960*X-40608, -1152*(2*X^2+6*X+5)*(4*X^2+12*X-31), 8448*X^4+231936*X^3+908544*X^2+1268736*X+557568, 69632*X^4+270336*X^3-79872*X^2-1449984*X-1529856, -135168*X^4-1220608*X^3-4116480*X^2-6111232*X-3342336, 65536*(X+3)^4]", "text": "This is operator \"8.55\" from ...", "degz": 8, "h3": null, "sol": "1 12 120 1216 13080 149664 1801312 22528512 290011032 3816913696", "n_discr_factors": "5", "c3": null, "operator": "4 8 0 0 0 0 1 -12 -56 -105 -98 -33 1728 4656 4872 2208 272 -40608 -72960 -45168 -8160 528 178560 145152 -34560 -55296 -9216 557568 1268736 908544 231936 8448 -1529856 -1449984 -79872 270336 69632 -3342336 -6111232 -4116480 -1220608 -135168 5308416 7077888 3538944 786432 65536", "new_number": "8.55", "id": 502, "operator_tex": "\\theta^4-x\\left(33\\theta^4+98\\theta^3+105\\theta^2+56\\theta+12\\right)+2^{3} x^{2}\\left(34\\theta^4+276\\theta^3+609\\theta^2+582\\theta+216\\right)+2^{4} 3 x^{3}\\left(11\\theta^4-170\\theta^3-941\\theta^2-1520\\theta-846\\right)-2^{7} 3^{2} x^{4}(2\\theta^2+6\\theta+5)(4\\theta^2+12\\theta-31)+2^{8} 3 x^{5}\\left(11\\theta^4+302\\theta^3+1183\\theta^2+1652\\theta+726\\right)+2^{11} x^{6}\\left(34\\theta^4+132\\theta^3-39\\theta^2-708\\theta-747\\right)-2^{12} x^{7}\\left(33\\theta^4+298\\theta^3+1005\\theta^2+1492\\theta+816\\right)+2^{16} x^{8}\\left((\\theta+3)^4\\right)", "superseek": "1 68/9", "discriminant": "8 1 -33 272 528 -9216 8448 69632 -135168 65536", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "39ed8ce7572bc79a333f77c892033bcf", "dim_h": null, "inst": " 1 -2 68/9 -30 150 -778 4374 -25438 463459/3 -960634", "cleanlist": "True", "n_sing_real": "7", "sol_explicit": "", "n_sing_rational": "5", "n_sing": "7", "laurent": null, "discriminant_tex": "(z-1)(16z-1)(16z^2-16z+1)(4z-1)^2(4z+1)^2", "discr_factors": "65536, (z-1/4)^2, (z+1/4)^2, z-1, z-1/16, z^2-z+1/16", "dm_basis": null, "q": "0 1 -8 52 -336 2226 -15040 103280 -719520 5072791", "yuk": "1 1 -15 205 -1935 18751 -167859 1500283 -13026191 112620742", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/4","im":"0","approx_re":"-0.25","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":"1/16","im":"0","approx_re":"0.0625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/2-1/4*3^(1/2)","im":"0","approx_re":"0.066987","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","0","-1","1"],"monodromy":[],"monodromy_dm":[]},{"re":"1/2+1/4*3^(1/2)","im":"0","approx_re":"0.933013","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1","im":"0","approx_re":"1.0","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":["3","3","3","3"],"monodromy":[],"monodromy_dm":[]}]}]}