{"count": 3, "status":"OK", "data":[{"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, -216*X^4-396*X^3-366*X^2-168*X-30, 36*(3*X+2)^2*(6*X+7)^2]", "text": "This is operator \"2.67\" from ...", "degz": 2, "h3": null, "sol": "1 30 1764 127776 10248750 873280548 77450342760 7067309298912 658756010890548 62425680018101400", "n_discr_factors": "1", "c3": null, "operator": "4 2 0 0 0 0 1 -30 -168 -366 -396 -216 7056 33264 57348 42768 11664", "new_number": "2.67", "id": 63, "operator_tex": "\\theta^4-2 3 x\\left(36\\theta^4+66\\theta^3+61\\theta^2+28\\theta+5\\right)+2^{2} 3^{2} x^{2}(3\\theta+2)^2(6\\theta+7)^2", "superseek": "-6 -170", "discriminant": "2 1 -216 11664", "aesz": "245", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "0ef0bca0dbecbedad92696fd7c0f9e42", "dim_h": null, "inst": " -6 -33 -170 -1029 -3246 39781 1237170 21512571 301031416 3536912187", "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": ["-6521007/125000000-90357723/1000000000*I", "-3+4511615154067544842086723740124334848694351954431101272196462779644508392806538050844596873167533211/2604782223680891931509451724762066519358428478691519147090699072692122550847025398588836869330367971*I", "1/2-3081490456277555159153769728602633601692409347626414678367139999430219011336903561652776870289659281/3558198688874218386798087732443200684026390216561310209643580926168315471826781724716716871248950591*I", "1", "-3/2+1/2*I*3^(1/2)", "27/2-5941739851857534525019677751646036095696294561235787866025785559858797774276172540036416876045407141/762325578427705482137746574067229488156369299800529597635468373844463859062368874404292289563613477*I", "-1/2+3081490456277555159153769728602633601692409347626414678367139999430219011336903561652776870289659281/3558198688874218386798087732443200684026390216561310209643580926168315471826781724716716871248950591*I", "0", "0", "-27+11883479703715069050039355503292072191392589122471575732051571119717595548552345080072833752090814282/762325578427705482137746574067229488156369299800529597635468373844463859062368874404292289563613477*I", "0", "0", "27-11883479703715069050039355503292072191392589122471575732051571119717595548552345080072833752090814282/762325578427705482137746574067229488156369299800529597635468373844463859062368874404292289563613477*I", "0", "0", "0"], "q": "0 1 -48 1440 -32848 637872 -11009952 174295160 -2581422144 36123632856", "yuk": "1 -6 -270 -4596 -66126 -405756 8587836 424349304 11014370226 219451897668", "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","-27-15588457/1000000*I","1","0","0","0","1/2-34641/40000*I","1"]},{"re":"1/108","im":"0","approx_re":"0.00925925925926","approx_im":"0.0","exponents":["0","1/6","1","7/6"],"monodromy":["1.052168056+.90357723e-1*I","1/4-1/12*I*3^(1/2)","-3*3^(1/6)/Pi^(9/2)/Zeta(5)^6-6*lambda",".10688274e-1-1/5*I*5^(4/7)*ln(2)^12","3/2-1/2*I*3^(1/2)","3/4-1/4*I*3^(1/2)","-1/8+1/24*I*3^(1/2)","3*3^(1/6)/Pi^(9/2)/Zeta(5)^6+6*lambda","0","9/2-3/2*I*3^(1/2)","3/4-1/4*I*3^(1/2)","1/4-1/12*I*3^(1/2)","-27+9*I*3^(1/2)","0","3/2-1/2*I*3^(1/2)",".447831944-.956383127*I"],"monodromy_dm":["1/2-34641/40000*I","3/2-34641/40000*I","-1/2+34641/40000*I","-1","0","-3/2+34641/40000*I","83333/1000000-72169/500000*I","0","0","-42","3-1732051/1000000*I","0","0","18-6581793/200000*I","1/2+2309401/1000000*I","1"]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["2/3","2/3","7/6","7/6"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[25*X^4, 5*X^2*(-1-2*X+107*X^2), 4800+20800*X+34276*X^2+23768*X^3+8696*X^4, -190080-604260*X-613836*X^2-152928*X^3+11088*X^4, -2115072-7610544*X-10054080*X^2-5688000*X^3-1016640*X^4, -13379904-41383872*X-44831232*X^2-20601216*X^3-4567104*X^4, -19968768-43390080*X-11736576*X^2+24634368*X^3+12358656*X^4, 39191040+151352064*X+204353280*X^2+106002432*X^3+12690432*X^4, -26873856*(X+1)^4]", "text": "This is operator \"8.84\" from ...", "degz": 8, "h3": null, "sol": "1 0 -12 144 324 -21600 182400 2116800 -59931900 239904000", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 25 0 0 -5 -10 535 4800 20800 34276 23768 8696 -190080 -604260 -613836 -152928 11088 -2115072 -7610544 -10054080 -5688000 -1016640 -13379904 -41383872 -44831232 -20601216 -4567104 -19968768 -43390080 -11736576 24634368 12358656 39191040 151352064 204353280 106002432 12690432 -26873856 -107495424 -161243136 -107495424 -26873856", "new_number": "8.84", "id": 534, "operator_tex": "5^{2} \\theta^4+5 x\\theta^2(-1-2\\theta+107\\theta^2)+2^{2} x^{2}\\left(2174\\theta^4+5942\\theta^3+8569\\theta^2+5200\\theta+1200\\right)+2^{2} 3^{2} x^{3}\\left(308\\theta^4-4248\\theta^3-17051\\theta^2-16785\\theta-5280\\right)-2^{4} 3^{2} x^{4}\\left(7060\\theta^4+39500\\theta^3+69820\\theta^2+52851\\theta+14688\\right)-2^{6} 3^{4} x^{5}\\left(881\\theta^4+3974\\theta^3+8648\\theta^2+7983\\theta+2581\\right)+2^{7} 3^{4} x^{6}\\left(1192\\theta^4+2376\\theta^3-1132\\theta^2-4185\\theta-1926\\right)+2^{8} 3^{6} x^{7}\\left(68\\theta^4+568\\theta^3+1095\\theta^2+811\\theta+210\\right)-2^{12} 3^{8} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "1/5 224/5", "discriminant": "8 25 535 8696 11088 -1016640 -4567104 12358656 12690432 -26873856", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "258fab6f0a4f132fe597fc6f30e54eea", "dim_h": null, "inst": " 1/5 -6 224/5 -448/5 -4334/5 162734/15 4944/5 -5368254/5 52756707/5 93552762/5", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "7", "laurent": null, "discriminant_tex": "-(9z-1)(576z^3+368z^2+16z+1)(-5-36z+72z^2)^2", "discr_factors": "-26873856, z-1/9, (-5/72-1/2*z+z^2)^2, z^3+23/36*z^2+1/36*z+1/576", "dm_basis": null, "q": "0 1 0 28 -324 1306 -6192 2566 -308712 9605779", "yuk": "1 1/5 -239/5 6049/5 -28911/5 -541749/5 11722657/5 1695793/5 -2748574959/5 38459645452/5", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/216*(76276+3348*93^(1/2))^(1/3)-421/54/(76276+3348*93^(1/2))^(1/3)-23/108","im":"0","approx_re":"-0.597246","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/4-1/12*19^(1/2)","im":"0","approx_re":"-0.113242","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/432*(76276+3348*93^(1/2))^(1/3)+421/108/(76276+3348*93^(1/2))^(1/3)-23/108","im":"1/8*3^(1/2)*(-1/54*(76276+3348*93^(1/2))^(1/3)+842/27/(76276+3348*93^(1/2))^(1/3))","approx_re":"-0.020821","approx_im":"-0.049733","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/432*(76276+3348*93^(1/2))^(1/3)+421/108/(76276+3348*93^(1/2))^(1/3)-23/108","im":"-1/8*3^(1/2)*(-1/54*(76276+3348*93^(1/2))^(1/3)+842/27/(76276+3348*93^(1/2))^(1/3))","approx_re":"-0.020821","approx_im":"0.049733","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":"1/9","im":"0","approx_re":"0.111111111111","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/4+1/12*19^(1/2)","im":"0","approx_re":"0.613242","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":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}]}