{"count": 3, "status":"OK", "data":[{"pols": "[X^4, -4*(2*X+1)^2*(11*X^2+11*X+3), -16*(2*X+1)^2*(2*X+3)^2]", "text": "Hadamard product $A\\ast b$\n\nA-incarnation: X(1,2,2) in G(2,5)", "degz": 2, "h3": "20", "sol": "1 12 684 58800 6129900 714610512 89611475184 11829354533568 1622229744177900 229106666659213200", "n_discr_factors": "1", "c3": "-120", "operator": "4 2 0 0 0 0 1 -12 -92 -268 -352 -176 -144 -768 -1408 -1024 -256", "new_number": "2.5", "id": 55, "operator_tex": "\\theta^4-2^{2} x(2\\theta+1)^2(11\\theta^2+11\\theta+3)-2^{4} x^{2}(2\\theta+1)^2(2\\theta+3)^2", "superseek": "20 8220", "discriminant": "2 1 -176 -256", "aesz": "25", "n_sing_complex": "0", "inst_int": "", "c2h": "68", "hash": "93279abcbeeade30c29508de7784e582", "dim_h": "9", "inst": " 20 277 8220 352994 18651536 1126617687 74667602300 5297682428242 395996602125000 30845267770384740", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "A_{n}=\\dbinom{2n}{n}^2\\sum_{k=0}^{n}\\dbinom{n}{k}^2\\dbinom{n+k}{n}", "n_sing_rational": "1", "n_sing": "3", "laurent": null, "discriminant_tex": "1-176z-256z^2", "discr_factors": "-256, -1/256+11/16*z+z^2", "dm_basis": ["-120*lambda", "37/6", "1", "1", "-17/6", "-10", "-1", "0", "0", "20", "0", "0", "-20", "0", "0", "0"], "q": "0 1 -44 486 -11184 -390527 -28173000 -2131044622 -168764951744 -13946975993196", "yuk": "1 20 2236 221960 22593852 2331442020 243349644568 25610987588920 2712413425853756 288681522949346960", "gv2": null, "gv0": "400 5540 164400 7059880 373030720 22532353740 1493352046000 105953648564840 7919932042500000 616905355407694800", "gv1": "0 0 0 1537 882496 214941640 37001766880 5388182343297 715201587952800 89732472170109248 10853707837547302400 1280463172653164106787 148416320937642960627520 16982448267723313699121648 1924600069649944296621370400 216520674412430601976469772097 24221257332526265388744193723840 2697512504678650518375575027208704 299363543965147494551366272473595840", "spectrum":[{"re":"-11/32-5/32*5^(1/2)","im":"0","approx_re":"-0.693136","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["16/3+480*lambda","-13/6-240*lambda","299/360+92*lambda","-.167088493-52*lambda","46/3","-20/3","529/180","-299/360-92*lambda","40","-20","26/3","-13/6-240*lambda","80","-40","46/3","-10/3-480*lambda"],"monodromy_dm":["-9","-60","-6","-4","5","31","3","2","-60","-360","-35","-24","40","240","24","17"]},{"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","20","1","0","0","0","1","1"]},{"re":"-11/32+5/32*5^(1/2)","im":"0","approx_re":"0.005636","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["1+120*lambda","0","17*lambda",".16908432e-1","17/6","1","289/720","-17*lambda","0","0","1","0","20","0","17/6","1-120*lambda"],"monodromy_dm":["1","-9","-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":["1/2","1/2","3/2","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[25*X^4, -200-1550*X-4545*X^2-5990*X^3-2035*X^4, -87040-518400*X-1069824*X^2-895872*X^3-269184*X^4, -409600-3932160*X-12619776*X^2-15728640*X^3-5681152*X^4, -2097152*(2*X+1)^4]", "text": "Sporadic Operator. There is a second MUM-point hiding at infinity, corresponding to Operator AESZ225/4.43", "degz": 4, "h3": "20", "sol": "1 8 504 36800 3518200 365275008 41121267264 4856185331712 596136147492600 75323913126862400", "n_discr_factors": "2", "c3": "-128", "operator": "4 4 0 0 0 0 25 -200 -1550 -4545 -5990 -2035 -87040 -518400 -1069824 -895872 -269184 -409600 -3932160 -12619776 -15728640 -5681152 -2097152 -16777216 -50331648 -67108864 -33554432", "new_number": "4.42", "id": 140, "operator_tex": "5^{2} \\theta^4-5 x\\left(407\\theta^4+1198\\theta^3+909\\theta^2+310\\theta+40\\right)-2^{7} x^{2}\\left(2103\\theta^4+6999\\theta^3+8358\\theta^2+4050\\theta+680\\right)-2^{12} x^{3}\\left(1387\\theta^4+3840\\theta^3+3081\\theta^2+960\\theta+100\\right)-2^{21} x^{4}\\left((2\\theta+1)^4\\right)", "superseek": "69/5 29081/5", "discriminant": "4 25 -2035 -269184 -5681152 -33554432", "aesz": "222", "n_sing_complex": "1", "inst_int": "", "c2h": "68", "hash": "aad7a72e711c9c463396d319e0bf7603", "dim_h": "9", "inst": " 69/5 1383/4 29081/5 346080 72023607/5 3784067515/4 281702428686/5 20053762156416/5 1409669129591222/5 85799281232555565/4", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "3", "laurent": null, "discriminant_tex": "-(8192z^2+107z-1)(5+64z)^2", "discr_factors": "-33554432, z^2+107/8192*z-1/8192, (5/64+z)^2", "dm_basis": null, "q": "0 1 -30 -507 15896 -864690 -19722342 -2270250854 -140407232352 -12748761975909", "yuk": "1 69/5 13899/5 785256/5 110759499/5 9002950944/5 1021699028136/5 96623933039367/5 10267526334844491/5 1027648795472786094/5", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-5/64","im":"0","approx_re":"-0.078125","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-107/16384-51/16384*17^(1/2)","im":"0","approx_re":"-0.019365","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":"s_1","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"s_2","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-107/16384+51/16384*17^(1/2)","im":"0","approx_re":"0.006304","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":["1/2","1/2","1/2","1/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[169*X^4, -2028-14534*X-40859*X^2-52650*X^3-18837*X^4, 281424+1317056*X+1936736*X^2+433792*X^3-364160*X^4, -5001984-16253952*X-8778752*X^2+10223616*X^3+978944*X^4, -196608*(2*X+1)*(40*X^3+684*X^2+1013*X+399), -9437184*(2*X+1)*(4*X+3)*(4*X+5)*(2*X+3)]", "text": "This is operator \"5.44\" from ...", "degz": 5, "h3": "26", "sol": "1 12 468 28560 2135700 179060112 16166559024 1537448717376 151947395002260 15468902712634800", "n_discr_factors": "3", "c3": "-72", "operator": "4 5 0 0 0 0 169 -2028 -14534 -40859 -52650 -18837 281424 1317056 1936736 433792 -364160 -5001984 -16253952 -8778752 10223616 978944 -78446592 -356057088 -532807680 -276824064 -15728640 -424673280 -2038431744 -3435134976 -2415919104 -603979776", "new_number": "5.44", "id": 254, "operator_tex": "13^{2} \\theta^4-13 x\\left(1449\\theta^4+4050\\theta^3+3143\\theta^2+1118\\theta+156\\right)-2^{4} x^{2}\\left(22760\\theta^4-27112\\theta^3-121046\\theta^2-82316\\theta-17589\\right)+2^{8} x^{3}\\left(3824\\theta^4+39936\\theta^3-34292\\theta^2-63492\\theta-19539\\right)-2^{16} 3 x^{4}(2\\theta+1)(40\\theta^3+684\\theta^2+1013\\theta+399)-2^{20} 3^{2} x^{5}(2\\theta+1)(4\\theta+3)(4\\theta+5)(2\\theta+3)", "superseek": "231/13 38037/13", "discriminant": "5 169 -18837 -364160 978944 -15728640 -603979776", "aesz": "240", "n_sing_complex": "2", "inst_int": "", "c2h": "68", "hash": "8f46cd6968b3b676e251a9d8635637fc", "dim_h": "10", "inst": " 231/13 826/13 38037/13 786076/13 32662752/13 1251531252/13 56830429026/13 2686705844700/13 135076469305428/13 7052986465933572/13", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "-(128z-1)(128z^2-13z+1)(13+192z)^2", "discr_factors": "-603979776, z-1/128, (13/192+z)^2, z^2-13/128*z+1/128", "dm_basis": null, "q": "0 1 -38 771 -20752 393365 -14552562 106677773 -15365058336 -334070060625", "yuk": "1 231/13 6839/13 1027230/13 50315703/13 4082844231/13 270331784270/13 19492837156149/13 1375593442802103/13 98470746124684242/13", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-13/192","im":"0","approx_re":"-0.0677083333333","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":"1/128","im":"0","approx_re":"0.0078125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"13/256","im":"-7/256*7^(1/2)","approx_re":"0.05078125","approx_im":"-0.072345","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"13/256","im":"7/256*7^(1/2)","approx_re":"0.05078125","approx_im":"0.072345","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/2","3/4","5/4","3/2"],"monodromy":[],"monodromy_dm":[]}]}]}