{"count": 2, "status":"OK", "data":[{"pols": "[X^4, -704*(X+1/2)^4-652*(X+1/2)^2-21, 187904*(X+1)^4+228672*(X+1)^2+19824, -128000*(X+3/2)^2*(176*(X+3/2)^2+141), 256000000*(X+2)^2*(2*X+3)*(2*X+5)]", "text": "YY-operator equivalent to AESZ 121 =$b \\ast e \\tilde A \\ast \\eta$", "degz": 4, "h3": null, "sol": "1 228 44716 8258768 1469227500 253733647728 42642370753264 6970600688094528 1105114457148006124 168933127196275073200", "n_discr_factors": "1", "c3": null, "operator": "4 4 0 0 0 0 1 -228 -1004 -1708 -1408 -704 436400 1208960 1356096 751616 187904 -154656000 -358272000 -322176000 -135168000 -22528000 15360000000 31744000000 24320000000 8192000000 1024000000", "new_number": "4.6", "id": 170, "operator_tex": "\\theta^4-2^{2} x\\left(176\\theta^4+352\\theta^3+427\\theta^2+251\\theta+57\\right)+2^{4} x^{2}\\left(11744\\theta^4+46976\\theta^3+84756\\theta^2+75560\\theta+27275\\right)-2^{8} 5^{3} x^{3}(176\\theta^2+528\\theta+537)(2\\theta+3)^2+2^{14} 5^{6} x^{4}(\\theta+2)^2(2\\theta+3)(2\\theta+5)", "superseek": "-28 1036", "discriminant": "4 1 -704 187904 -22528000 1024000000", "aesz": null, "n_sing_complex": "1", "inst_int": "", "c2h": null, "hash": "e42780ff25b428328423d5eea814a37a", "dim_h": null, "inst": " -28 -21 1036 53976 1260496 31899337 507180268 3964357416 -299161562136 -16443487872164", "cleanlist": "True", "n_sing_real": "1", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "2", "laurent": null, "discriminant_tex": "(1-352z+32000z^2)^2", "discr_factors": "1024000000, (1/32000-11/1000*z+z^2)^2", "dm_basis": null, "q": "0 1 -92 6310 -354928 18451201 -887962344 41276142642 -1847354908608 80878912980756", "yuk": "1 -28 -196 27944 3454268 157561972 6890284568 173962831896 2029754451260 -218088778769200", "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":["-1/2","0","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"s_2","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["-1/2","0","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"11/2000","im":"-1/1000","approx_re":"0.0055","approx_im":"-0.001","exponents":["0","-1/2","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"11/2000","im":"1/1000","approx_re":"0.0055","approx_im":"0.001","exponents":["0","-1/2","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["3/2","2","2","5/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[81*X^4, -9909*X^4-10746*X^3-7965*X^2-2592*X-324, -86400*X^4-898992*X^3-1561248*X^2-867888*X-169344, 13910208*X^4+19715328*X^3-9327168*X^2-14961024*X-4326912, 112509952*X^4+634849280*X^3+57610240*X^2-224283648*X-80093184, -4664246272*X^4+2094891008*X^3+4194140160*X^2+1856798720*X+224215040, -74138910720*X^4-70271631360*X^3-47035842560*X^2-21172322304*X-4385669120, -359250526208*X^4-918267363328*X^3-1016095309824*X^2-545863499776*X-115091701760, -78920024064*(X+1)^2*(3*X+2)*(3*X+4)]", "text": "This is operator \"8.47\" from ...", "degz": 8, "h3": null, "sol": "1 4 228 12640 901540 70455504 5932407936 524802634752 48205904264100 4557901439462800", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 81 -324 -2592 -7965 -10746 -9909 -169344 -867888 -1561248 -898992 -86400 -4326912 -14961024 -9327168 19715328 13910208 -80093184 -224283648 57610240 634849280 112509952 224215040 1856798720 4194140160 2094891008 -4664246272 -4385669120 -21172322304 -47035842560 -70271631360 -74138910720 -115091701760 -545863499776 -1016095309824 -918267363328 -359250526208 -631360192512 -2683280818176 -4182761275392 -2841120866304 -710280216576", "new_number": "8.47", "id": 493, "operator_tex": "3^{4} \\theta^4-3^{3} x\\left(367\\theta^4+398\\theta^3+295\\theta^2+96\\theta+12\\right)-2^{4} 3^{3} x^{2}\\left(200\\theta^4+2081\\theta^3+3614\\theta^2+2009\\theta+392\\right)+2^{6} 3 x^{3}\\left(72449\\theta^4+102684\\theta^3-48579\\theta^2-77922\\theta-22536\\right)+2^{10} x^{4}\\left(109873\\theta^4+619970\\theta^3+56260\\theta^2-219027\\theta-78216\\right)-2^{14} 7 x^{5}\\left(40669\\theta^4-18266\\theta^3-36570\\theta^2-16190\\theta-1955\\right)-2^{17} 7 x^{6}\\left(80805\\theta^4+76590\\theta^3+51265\\theta^2+23076\\theta+4780\\right)-2^{24} 7^{2} x^{7}\\left(437\\theta^4+1117\\theta^3+1236\\theta^2+664\\theta+140\\right)-2^{29} 3 7^{2} x^{8}(\\theta+1)^2(3\\theta+2)(3\\theta+4)", "superseek": "31/3 43174/9", "discriminant": "8 81 -9909 -86400 13910208 112509952 -4664246272 -74138910720 -359250526208 -710280216576", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "b79bf25fcecf028aa40c1a6a8233efe7", "dim_h": null, "inst": " 31/3 1964/9 43174/9 1469755/9 19813517/3 315467008 148386069209/9 925792234621 492778954234601/9 10128857593326760/3", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "7", "laurent": null, "discriminant_tex": "-(27z+1)(2048z^3+768z^2+112z-1)(-9+168z+3584z^2)^2", "discr_factors": "-710280216576, z+1/27, (-9/3584+3/64*z+z^2)^2, z^3+3/8*z^2+7/128*z-1/2048", "dm_basis": null, "q": "0 1 -16 -434 -4696 -227995 -13002992 -803331770 -50035732496 -3256430021246", "yuk": "1 31/3 15805/9 388597/3 94080125/9 2476689656/3 613269045055/9 50896421738780/9 4266050711213693/9 119745285879396640/3", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/96*(189+33*33^(1/2))^(1/3)+1/16/(189+33*33^(1/2))^(1/3)-1/8","im":"-1/16*3^(1/2)*(1/6*(189+33*33^(1/2))^(1/3)+1/(189+33*33^(1/2))^(1/3))","approx_re":"-0.191715","approx_im":"-0.145483","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/96*(189+33*33^(1/2))^(1/3)+1/16/(189+33*33^(1/2))^(1/3)-1/8","im":"1/16*3^(1/2)*(1/6*(189+33*33^(1/2))^(1/3)+1/(189+33*33^(1/2))^(1/3))","approx_re":"-0.191715","approx_im":"0.145483","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-3/128-3/896*273^(1/2)","im":"0","approx_re":"-0.078759","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/27","im":"0","approx_re":"-0.037037037037","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":"1/48*(189+33*33^(1/2))^(1/3)-1/8/(189+33*33^(1/2))^(1/3)-1/8","im":"0","approx_re":"0.00843","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-3/128+3/896*273^(1/2)","im":"0","approx_re":"0.031884","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":["2/3","1","1","4/3"],"monodromy":[],"monodromy_dm":[]}]}]}