{"count": 6, "status":"OK", "data":[{"pols": "[X^4, -2*(2*X+1)^2*(7*X^2+7*X+3), 324*(2*X+1)*(X+1)^2*(2*X+3)]", "text": "Hadamard product $I \\ast \\delta$", "degz": 2, "h3": null, "sol": "1 6 54 60 -19530 -755244 -17954244 -226007496 3762274230 350186668260", "n_discr_factors": "1", "c3": null, "operator": "4 2 0 0 0 0 1 -6 -38 -94 -112 -56 972 4536 7452 5184 1296", "new_number": "2.54", "id": 49, "operator_tex": "\\theta^4-2 x(2\\theta+1)^2(7\\theta^2+7\\theta+3)+2^{2} 3^{4} x^{2}(2\\theta+1)(\\theta+1)^2(2\\theta+3)", "superseek": "2 -104", "discriminant": "2 1 -56 1296", "aesz": "41", "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "a9ddeed4299f59fb9ac9f6f248383b8f", "dim_h": null, "inst": " 2 -7 -104 -588 3300 128384 1336396 -5019718 -393656474 -5619028410", "cleanlist": "True", "n_sing_real": "1", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "3", "laurent": null, "discriminant_tex": "1-56z+1296z^2", "discr_factors": "1296, 1/1296-7/162*z+z^2", "dm_basis": ["1-872284041/1000000000*I", "24", "7/6", "1", "-6", "-48", "-1", "0", "12", "72", "0", "0", "-72", "0", "0", "0"], "q": "0 1 -14 207 -1868 19671 -198834 1196141 -14261624 194353344", "yuk": "1 2 -54 -2806 -37686 412502 27728082 458383830 -2570133302 -286975572352", "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","72","1","0","0","0","1","1"]},{"re":"7/324","im":"-1/81*2^(1/2)","approx_re":"0.0216049382716","approx_im":"-0.017459","exponents":["0","1","1","2"],"monodromy":[".872284041*I","-1/6+30*lambda","-1/12+15*lambda","-1/243*3^(1/2)*ln(2)^2/(-8*I*lambda*Pi^3)^(1/6)+5*lambda","6","2","1/2","1/12-15*lambda","-12","-2","0","-1/6+30*lambda","72","12","6","2.-.872284041*I"],"monodromy_dm":["1","-22","-1","-1","0","1","0","0","0","0","1","0","0","0","0","1"]},{"re":"7/324","im":"1/81*2^(1/2)","approx_re":"0.0216049382716","approx_im":"0.017459","exponents":["0","1","1","2"],"monodromy":["2.+.872284041*I","-1/6-30*lambda","1/12+15*lambda","-1/243*3^(1/2)*ln(2)^2/(-8*I*lambda*Pi^3)^(1/6)-5*lambda","6","0","1/2","-1/12-15*lambda","12","-2","2","-1/6-30*lambda","72","-12","6","-.872284041*I"],"monodromy_dm":["-3","-38","-1333333/1000000","-1","1333333/1000000","13666667/1000000","111111/250000","333333/1000000","-64","-608","-20333333/1000000","-16","50666667/1000000","481333333/1000000","16888889/1000000","13666667/1000000"]},{"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, -12*(6*X+1)*(6*X+5)*(2*X^2+2*X+1), 144*(6*X+1)*(6*X+5)*(6*X+7)*(6*X+11)]", "text": "This is operator \"2.66\" from ...", "degz": 2, "h3": null, "sol": "1 60 13860 4084080 1338557220 465817912560 168470811709200 62588625639883200 23717177328413240100 9124964373613212524400", "n_discr_factors": "1", "c3": null, "operator": "4 2 0 0 0 0 1 -60 -552 -1416 -1728 -864 55440 476928 984960 746496 186624", "new_number": "2.66", "id": 62, "operator_tex": "\\theta^4-2^{2} 3 x(6\\theta+1)(6\\theta+5)(2\\theta^2+2\\theta+1)+2^{4} 3^{2} x^{2}(6\\theta+1)(6\\theta+5)(6\\theta+7)(6\\theta+11)", "superseek": "-192 -229568", "discriminant": "2 1 -864 186624", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "0fb32be57a9fcd1b243f9e1341b39d45", "dim_h": null, "inst": " -192 4182 -229568 19136058 -2006581440 243300073558 -32605941989568 4701237108506682 -716718972661760192 114174194786921304150", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "2", "laurent": null, "discriminant_tex": "(432z-1)^2", "discr_factors": "186624, (z-1/432)^2", "dm_basis": ["cy[DM_basis]"], "q": "0 1 -312 87084 -23067968 5930898126 -1495818530208 372227721831608 -91714975889456640 22426994284202015973", "yuk": "1 -192 33264 -6198528 1224740976 -250822680192 52552809723456 -11183838102422016 2407033400780162160 -522488131070429378496", "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":["cy[T_DM][1]"]},{"re":"1/432","im":"0","approx_re":"0.00231481481481","approx_im":"0.0","exponents":["0","0","1","1"],"monodromy":["1","0","58*lambda","0","1","1","5/6","-58*lambda","0","0","1","0","0","0","1","1"],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/6","5/6","7/6","11/6"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -60-460*X-1565*X^2-2210*X^3+623*X^4, -158400*X^4-796032*X^3+1031328*X^2+630720*X+132192, -44872704*X^4+371755008*X^3+276099840*X^2+75582720*X+2612736, 107495424*(2*X+1)*(148*X^3+114*X^2-35*X-41), -557256278016*(2*X+1)*(X+1)^2*(2*X+3)]", "text": "B-Incarnation as fibre product 62211- x 326--1\n", "degz": 5, "h3": null, "sol": "1 60 5508 362400 -34621020 -21200311440 -5254667510400 -808807983160320 -27742344502801500 31345755523549724400", "n_discr_factors": "3", "c3": null, "operator": "4 5 0 0 0 0 1 -60 -460 -1565 -2210 623 132192 630720 1031328 -796032 -158400 2612736 75582720 276099840 371755008 -44872704 -4407312384 -12576964608 4729798656 40418279424 31818645504 -1671768834048 -7801587892224 -12816894394368 -8916100448256 -2229025112064", "new_number": "5.131", "id": 216, "operator_tex": "\\theta^4-x\\left(60+460\\theta+1565\\theta^2+2210\\theta^3-623\\theta^4\\right)-2^{5} 3^{2} x^{2}\\left(550\\theta^4+2764\\theta^3-3581\\theta^2-2190\\theta-459\\right)-2^{8} 3^{4} x^{3}\\left(2164\\theta^4-17928\\theta^3-13315\\theta^2-3645\\theta-126\\right)+2^{14} 3^{8} x^{4}(2\\theta+1)(148\\theta^3+114\\theta^2-35\\theta-41)-2^{20} 3^{12} x^{5}(2\\theta+1)(\\theta+1)^2(2\\theta+3)", "superseek": "325 9106834/3", "discriminant": "5 1 623 -158400 -44872704 31818645504 -2229025112064", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "79657f8be76c1fed5fd1a658989ca15a", "dim_h": null, "inst": " 325 -24254 9106834/3 -514805406 102077718255 -22223178463738 5174048773552737 -1266528111971928142 966257487248084589571/3 -84415770319509012764960", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "-(81z-1)(82944z^2-448z+1)(1+576z)^2", "discr_factors": "-2229025112064, z-1/81, (1/576+z)^2, z^2-7/1296*z+1/82944", "dm_basis": null, "q": "0 1 -220 56766 -15109000 4164405285 -1179786954264 341186437353174 -100284077430244272 29869701184530421506", "yuk": "1 325 -193707 81961831 -32947739691 12759714782200 -4800206466399609 1774698729328589116 -648462393362574948395 234800569401284637227584", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/576","im":"0","approx_re":"-0.00173611111111","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":"7/2592","im":"-1/648*2^(1/2)","approx_re":"0.00270061728395","approx_im":"-0.002182","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"7/2592","im":"1/648*2^(1/2)","approx_re":"0.00270061728395","approx_im":"0.002182","exponents":["0","1","1","2"],"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":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/2","1","1","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, 6+27*X+47*X^2+40*X^3+20*X^4, -(143*X^2+286*X+120)*(X+1)^2, -18*(X+2)*(X+1)*(291*X^2+873*X+766), -540*(X+3)*(X+1)*(41*X^2+164*X+196), 5400*(X+4)*(X+1)*(29*X^2+145*X+150), 972000*(X+5)*(X+4)*(X+2)*(X+1)]", "text": "This is operator \"6.21\" from ...", "degz": 6, "h3": null, "sol": "1 -6 60 -480 5040 -42336 468456 -3906720 46352160 -367896000", "n_discr_factors": "5", "c3": null, "operator": "4 6 0 0 0 0 1 6 27 47 40 20 -120 -526 -835 -572 -143 -27576 -72792 -71406 -31428 -5238 -317520 -689040 -526500 -177120 -22140 3240000 7182000 5351400 1566000 156600 38880000 75816000 47628000 11664000 972000", "new_number": "6.21", "id": 405, "operator_tex": "\\theta^4+x\\left(6+27\\theta+47\\theta^2+40\\theta^3+20\\theta^4\\right)-x^{2}(143\\theta^2+286\\theta+120)(\\theta+1)^2-2 3^{2} x^{3}(\\theta+2)(\\theta+1)(291\\theta^2+873\\theta+766)-2^{2} 3^{3} 5 x^{4}(\\theta+3)(\\theta+1)(41\\theta^2+164\\theta+196)+2^{3} 3^{3} 5^{2} x^{5}(\\theta+4)(\\theta+1)(29\\theta^2+145\\theta+150)+2^{5} 3^{5} 5^{3} x^{6}(\\theta+5)(\\theta+4)(\\theta+2)(\\theta+1)", "superseek": "1 11", "discriminant": "6 1 20 -143 -5238 -22140 156600 972000", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "319d6b2f1541de5252840442cc6f8dcd", "dim_h": null, "inst": " 1 13/4 11 50 1674/5 11339/4 25332 231810 2188747 214734129/10", "cleanlist": "True", "n_sing_real": "6", "sol_explicit": "", "n_sing_rational": "6", "n_sing": "6", "laurent": null, "discriminant_tex": "(6z-1)(15z-1)(9z+1)(12z+1)(10z+1)^2", "discr_factors": "972000, z+1/12, z+1/9, z-1/6, (z+1/10)^2, z-1/15", "dm_basis": null, "q": "0 1 3 -28 -339 -995 8208 79253 -114261 -6614045", "yuk": "1 1 27 298 3227 41851 612630 8688877 118689947 1595596861", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/9","im":"0","approx_re":"-0.111111111111","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/10","im":"0","approx_re":"-0.1","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/12","im":"0","approx_re":"-0.0833333333333","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":"1/15","im":"0","approx_re":"0.0666666666667","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/6","im":"0","approx_re":"0.166666666667","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","4","5"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -76*X^4-80*X^3-73*X^2-33*X-6, 2209*X^4+4228*X^3+4745*X^2+2726*X+648, -31230*X^4-83628*X^3-109782*X^2-73296*X-20232, 225180*X^4+797904*X^3+1263060*X^2+987120*X+307152, -216*(X+1)*(3707*X^3+14055*X^2+20242*X+10704), 15552*(X+1)*(X+2)*(86*X^2+285*X+262), -839808*(X+1)*(X+2)^2*(X+3)]", "text": "This is operator \"7.10\" from ...", "degz": 7, "h3": null, "sol": "1 6 60 816 13104 232416 4408296 87822720 1816916256 38731107264", "n_discr_factors": "5", "c3": null, "operator": "4 7 0 0 0 0 1 -6 -33 -73 -80 -76 648 2726 4745 4228 2209 -20232 -73296 -109782 -83628 -31230 307152 987120 1263060 797904 225180 -2312064 -6684336 -7408152 -3836592 -800712 8149248 21088512 20046528 8444736 1337472 -10077696 -23514624 -19315584 -6718464 -839808", "new_number": "7.10", "id": 432, "operator_tex": "\\theta^4-x\\left(76\\theta^4+80\\theta^3+73\\theta^2+33\\theta+6\\right)+x^{2}\\left(2209\\theta^4+4228\\theta^3+4745\\theta^2+2726\\theta+648\\right)-2 3^{2} x^{3}\\left(1735\\theta^4+4646\\theta^3+6099\\theta^2+4072\\theta+1124\\right)+2^{2} 3^{3} x^{4}\\left(2085\\theta^4+7388\\theta^3+11695\\theta^2+9140\\theta+2844\\right)-2^{3} 3^{3} x^{5}(\\theta+1)(3707\\theta^3+14055\\theta^2+20242\\theta+10704)+2^{6} 3^{5} x^{6}(\\theta+1)(\\theta+2)(86\\theta^2+285\\theta+262)-2^{7} 3^{8} x^{7}(\\theta+1)(\\theta+2)^2(\\theta+3)", "superseek": "1 11", "discriminant": "7 1 -76 2209 -31230 225180 -800712 1337472 -839808", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "b1c277f62ba740f9f7e0371ba53e4194", "dim_h": null, "inst": " 1 13/4 11 50 1674/5 11339/4 25332 231810 2188747 214734129/10", "cleanlist": "True", "n_sing_real": "6", "sol_explicit": "", "n_sing_rational": "6", "n_sing": "6", "laurent": null, "discriminant_tex": "-(3z-1)(18z-1)(27z-1)(12z-1)^2(-1+2z)^2", "discr_factors": "-839808, z-1/18, z-1/27, (-1/2+z)^2, (z-1/12)^2, z-1/3", "dm_basis": null, "q": "0 1 -9 44 -207 949 -5616 15965 -166089 -97109", "yuk": "1 1 27 298 3227 41851 612630 8688877 118689947 1595596861", "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":"1/27","im":"0","approx_re":"0.037037037037","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/18","im":"0","approx_re":"0.0555555555556","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/12","im":"0","approx_re":"0.0833333333333","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/3","im":"0","approx_re":"0.333333333333","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/2","im":"0","approx_re":"0.5","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":["1","2","2","3"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[25*X^4, -10*X*(15+71*X+112*X^2+38*X^3), -24000-77440*X-98716*X^2-63488*X^3-17456*X^4, 118800+126720*X-74160*X^2-161280*X^3-66240*X^4, 8475840+20583936*X+17368704*X^2+6045696*X^3+707328*X^4, 41472*(X+1)*(38*X^3+74*X^2-304*X-495), -82944*(2*X+13)*(2*X+3)*(17*X+39)*(X+1), -2985984*(X+1)*(2*X+5)*(2*X+3)*(X+3)]", "text": "This is operator \"7.16\" from ...", "degz": 7, "h3": null, "sol": "1 0 60 480 16524 332640 9211920 241315200 6825804300 195543163200", "n_discr_factors": "4", "c3": null, "operator": "4 7 0 0 0 0 25 0 -150 -710 -1120 -380 -24000 -77440 -98716 -63488 -17456 118800 126720 -74160 -161280 -66240 8475840 20583936 17368704 6045696 707328 -20528640 -33136128 -9538560 4644864 1575936 -126157824 -284663808 -216566784 -63700992 -5640192 -134369280 -322486272 -271724544 -95551488 -11943936", "new_number": "7.16", "id": 438, "operator_tex": "5^{2} \\theta^4-2 5 x\\theta(15+71\\theta+112\\theta^2+38\\theta^3)-2^{2} x^{2}\\left(4364\\theta^4+15872\\theta^3+24679\\theta^2+19360\\theta+6000\\right)-2^{4} 3^{2} 5 x^{3}\\left(92\\theta^4+224\\theta^3+103\\theta^2-176\\theta-165\\right)+2^{6} 3^{2} x^{4}\\left(1228\\theta^4+10496\\theta^3+30154\\theta^2+35736\\theta+14715\\right)+2^{9} 3^{4} x^{5}(\\theta+1)(38\\theta^3+74\\theta^2-304\\theta-495)-2^{10} 3^{4} x^{6}(2\\theta+13)(2\\theta+3)(17\\theta+39)(\\theta+1)-2^{12} 3^{6} x^{7}(\\theta+1)(2\\theta+5)(2\\theta+3)(\\theta+3)", "superseek": "22/5 68", "discriminant": "7 25 -380 -17456 -66240 707328 1575936 -5640192 -11943936", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "660211ce6175f36772066594bfc33cbb", "dim_h": null, "inst": " 22/5 8 68 3292/5 38826/5 1517408/15 7418706/5 115188852/5 1132445042/3 32217796776/5", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "5", "n_sing": "5", "laurent": null, "discriminant_tex": "-(-1+36z)(12z+5)^2(12z+1)^2(4z-1)^2", "discr_factors": "-11943936, (z+5/12)^2, (z-1/4)^2, (z+1/12)^2, -1/36+z", "dm_basis": null, "q": "0 1 -6 -55 444 -2012 -40662 -48142 -5216472 -98264672", "yuk": "1 22/5 342/5 9202/5 42206 4853272/5 109262898/5 508923236 58976903254/5 1375920735232/5", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-5/12","im":"0","approx_re":"-0.416666666667","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/12","im":"0","approx_re":"-0.0833333333333","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":"1/36","im":"0","approx_re":"0.0277777777778","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","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","3/2","5/2","3"],"monodromy":[],"monodromy_dm":[]}]}]}