{"count": 5, "status":"OK", "data":[{"pols": "[X^4, -12*(3*X+1)*(3*X+2)*(8*X^2+8*X+3), 2304*(3*X+1)*(3*X+2)*(3*X+4)*(3*X+5)]", "text": "", "degz": 2, "h3": null, "sol": "1 72 14760 3951360 1198751400 391176257472 133901221918464 47411323466158080 17215474536402765480 6374166727892926248000", "n_discr_factors": "1", "c3": null, "operator": "4 2 0 0 0 0 1 -72 -516 -1380 -1728 -864 92160 539136 1016064 746496 186624", "new_number": "2.18", "id": 9, "operator_tex": "\\theta^4-2^{2} 3 x(3\\theta+1)(3\\theta+2)(8\\theta^2+8\\theta+3)+2^{8} 3^{2} x^{2}(3\\theta+1)(3\\theta+2)(3\\theta+4)(3\\theta+5)", "superseek": "36 8076", "discriminant": "2 1 -864 186624", "aesz": "110", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "5060b638cac581d5f0f9dd7f40d90e6c", "dim_h": null, "inst": " 36 -144 8076 -57996 6960672 -12143856 10041274764 98875091268 19944340019760 482716439753472", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": 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-64108077643407798000", "n_discr_factors": "1", "c3": null, "operator": "4 2 0 0 0 0 1 -36 -300 -876 -1152 -576 45360 304128 594432 442368 110592", "new_number": "2.22", "id": 14, "operator_tex": "\\theta^4-2^{2} 3 x(4\\theta+1)(4\\theta+3)(3\\theta^2+3\\theta+1)+2^{4} 3^{3} x^{2}(4\\theta+1)(4\\theta+3)(4\\theta+5)(4\\theta+7)", "superseek": "36 -206716/3", "discriminant": "2 1 -576 110592", "aesz": "135", "n_sing_complex": "2", "inst_int": "Hadamard product $C \\ast f$.", "c2h": null, "hash": "85e55291bd94bb32087b43f104c60645", "dim_h": null, "inst": " 36 -477 -206716/3 -4431924 -27005472 113639010155/3 5461011241452 275264717743692 -42134583877440448 -11379150026239273560", "cleanlist": "True", "n_sing_real": "1", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "3", "laurent": null, "discriminant_tex": "1-576z+110592z^2", "discr_factors": "110592, 1/110592-1/192*z+z^2", "dm_basis": 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{"pols": "[X^4, -6*(2*X+1)^2*(9*X^2+9*X+5), 2916*(2*X+1)*(X+1)^2*(2*X+3)]", "text": "Hadamard product $I \\ast \\iota$", "degz": 2, "h3": null, "sol": "1 30 1782 129900 10463670 894351780 79506157500 7268449719960 678536243277750 64381774028157300", "n_discr_factors": "1", "c3": null, "operator": "4 2 0 0 0 0 1 -30 -174 -390 -432 -216 8748 40824 67068 46656 11664", "new_number": "2.58", "id": 53, "operator_tex": "\\theta^4-2 3 x(2\\theta+1)^2(9\\theta^2+9\\theta+5)+2^{2} 3^{6} x^{2}(2\\theta+1)(\\theta+1)^2(2\\theta+3)", "superseek": "-6 -104", "discriminant": "2 1 -216 11664", "aesz": "46", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "2226ec115674e71c483ba2c0350e8adf", "dim_h": null, "inst": " -6 -6 -104 36 -4812 37984 -444900 7911900 -81187538 1584490908", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "2", "laurent": null, "discriminant_tex": "(108z-1)^2", "discr_factors": "11664, (z-1/108)^2", "dm_basis": ["1/2-36*lambda", "-3", "5/6", "1", "0", "12", "-1", "0", "6", "-36", "0", "0", "36", "0", "0", "0"], "q": "0 1 -54 2079 -67356 1981287 -54730890 1447035885 -37047063960 925398152064", "yuk": "1 -6 -54 -2814 2250 -601506 8201682 -152600706 4050895050 -59185718016", "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","-36","1","0","0","0","1","1"]},{"re":"1/108","im":"0","approx_re":"0.00925925925926","approx_im":"0.0","exponents":["0","1/6","5/6","1"],"monodromy":["1/2+36*lambda","1/4+6*lambda","0",".19987912e-1","0","1","0","0","-6","3","1","1/4-6*lambda","-36","-6","0","1/2-36*lambda"],"monodromy_dm":["0","1","-666667/1000000","-1","-333333/1000000","-333333/1000000","111111/1000000","0","-4","-16","2333333/1000000","0","3333333/1000000","13333333/1000000","-1111111/1000000","1"]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/2","1","1","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -3*(3*X+1)*(3*X+2)*(11*X^2+11*X+3), -9*(3*X+1)*(3*X+2)*(3*X+4)*(3*X+5)]", "text": "Hadamard product B*b\nRelated to (:case 7.19), (:case 8.18)\nThis operator corresponds to $(Grass(2,5)\\vert 1,1,3)_{-150}$ from arXiv:0802.2908", "degz": 2, "h3": "15", "sol": "1 18 1710 246960 43347150 8515775268 1800376001424 400791767238720 92704190534597070 22085208822810919500", "n_discr_factors": "1", "c3": "-150", "operator": "4 2 0 0 0 0 1 -18 -147 -444 -594 -297 -360 -2106 -3969 -2916 -729", "new_number": "2.6", "id": 66, "operator_tex": "\\theta^4-3 x(3\\theta+1)(3\\theta+2)(11\\theta^2+11\\theta+3)-3^{2} x^{2}(3\\theta+1)(3\\theta+2)(3\\theta+4)(3\\theta+5)", "superseek": "36 41421", "discriminant": "2 1 -297 -729", "aesz": "24", "n_sing_complex": "0", "inst_int": "", "c2h": "66", "hash": "5e8f8f32b5e99693a2956e1240b9fdff", "dim_h": "8", "inst": " 36 837 41421 2992851 266362506 27112272624 3028463890677 362170461839895 45632464971618513 5991507998411065245", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "A_{n}=\\dbinom{2n}{n}\\dbinom{3n}{n}\\sum_{k=0}^{n}\\dbinom{n}{k}^2\\dbinom{n+k}{n}", "n_sing_rational": "1", "n_sing": "3", "laurent": null, "discriminant_tex": "1-297z-729z^2", "discr_factors": "-729, -1/729+11/27*z+z^2", "dm_basis": ["-150*lambda", "21/4", "1", "1", "-11/4", "-15/2", "-1", "0", "0", "15", "0", "0", "-15", "0", "0", "0"], "q": "0 1 -75 1539 -60073 -2978346 -380743659 -48420276097 -6463392140319 -900815105135718", "yuk": "1 36 6732 1118403 191549196 33295313286 5856252011883 1038763114502247 185431276653575436 33266066964311014380", "gv2": null, "gv0": "540 12555 621315 44892765 3995437590 406684089360 45426958360155 5432556927598425 684486974574277695 89872619976165978675", "gv1": "0 0 -1 13095 17230617 6648808835 1831575868830 433375127634753 94416986839804040 19571240651198871015 3928385495739192861123 771467376541495393981885 149185114850267499674332737 28527921575954705632251978558 5410017459416672999118331855100 1019499107689707626552267048965731 191190228044755566196801759890402648 35719045727096113630007361726280466678 6653312019338283509139215063697202862643", "spectrum":[{"re":"-11/54-5/54*5^(1/2)","im":"0","approx_re":"-0.410747","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["11/2+600*lambda","-9/4-300*lambda","21/20+140*lambda","-.196596398-90*lambda","14","-6","49/15","-21/20-140*lambda","30","-15","8","-9/4-300*lambda","60","-30","14","-7/2-600*lambda"],"monodromy_dm":["-9","-50","-6","-4","5","26","3","2","-45","-225","-26","-18","30","150","18","13"]},{"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","15","1","0","0","0","1","1"]},{"re":"-11/54+5/54*5^(1/2)","im":"0","approx_re":"0.00334","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["1+150*lambda","0","55/2*lambda",".35225900e-1","11/4","1","121/240","-55/2*lambda","0","0","1","0","15","0","11/4","1-150*lambda"],"monodromy_dm":["1","-8","-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":["1/3","2/3","4/3","5/3"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -16-98*X-235*X^2-274*X^3-145*X^4, 8*(2*X+1)*(4*X+5)*(97*X^2+190*X+120), -1296*(4*X+5)*(2*X+3)*(2*X+1)*(4*X+9)]", "text": "This is operator \"3.29\" from ...", "degz": 3, "h3": null, "sol": "1 16 468 17520 774060 38648736 2112034176 123284386368 7552913142060 479729676849280", "n_discr_factors": "2", "c3": null, "operator": "4 3 0 0 0 0 1 -16 -98 -235 -274 -145 4800 21040 32840 23024 6208 -174960 -684288 -876096 -456192 -82944", "new_number": "3.29", "id": 91, "operator_tex": "\\theta^4-x\\left(16+98\\theta+235\\theta^2+274\\theta^3+145\\theta^4\\right)+2^{3} x^{2}(2\\theta+1)(4\\theta+5)(97\\theta^2+190\\theta+120)-2^{4} 3^{4} x^{3}(4\\theta+5)(2\\theta+3)(2\\theta+1)(4\\theta+9)", "superseek": "3 237", "discriminant": "3 1 -145 6208 -82944", "aesz": "411", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "767c4e8d5a7bc53fbbd0d49797e65358", "dim_h": null, "inst": " 3 36 237 4638 72330 1663524 250626066/7 906864822 22842286617 620661630876", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "-(81z-1)(-1+32z)^2", "discr_factors": "-82944, z-1/81, (-1/32+z)^2", "dm_basis": null, "q": "0 1 -34 927 -25016 636071 -16172766 397813539 -9879941312 238196736342", "yuk": "1 3 291 6402 297123 9041253 359327874 12280677237 464315085987 16652026950195", "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":"1/81","im":"0","approx_re":"0.0123456790123","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/32","im":"0","approx_re":"0.03125","approx_im":"0.0","exponents":["0","1/4","1","5/4"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/2","5/4","3/2","9/4"],"monodromy":[],"monodromy_dm":[]}]}]}