{"count": 8, "status":"OK", "data":[{"pols": "[X^4, -12*(6*X+1)*(6*X+5)*(10*X^2+10*X+3), 1296*(6*X+1)*(6*X+5)*(6*X+7)*(6*X+11)]", "text": "Hadamard product $B\\ast c$.", "degz": 2, "h3": "6", "sol": "1 180 207900 379819440 855338063580 2167450747141680 5924949977000854800 17076367676457532872000 51175952834979624544935900 158042895581787941968966522800", "n_discr_factors": "2", "c3": "-364", "operator": "4 2 0 0 0 0 1 -180 -1896 -6216 -8640 -4320 498960 4292352 8864640 6718464 1679616", "new_number": "2.12", "id": 3, "operator_tex": "\\theta^4-2^{2} 3 x(6\\theta+1)(6\\theta+5)(10\\theta^2+10\\theta+3)+2^{4} 3^{4} x^{2}(6\\theta+1)(6\\theta+5)(6\\theta+7)(6\\theta+11)", "superseek": "432 78259376", "discriminant": "2 1 -4320 1679616", "aesz": "64", "n_sing_complex": "0", "inst_int": "", "c2h": "72", "hash": "43991f21e20c16ab91690259b788b4cd", "dim_h": "7", "inst": " 432 130842 78259376 68104755558 73096116588720 89957635345588154 121397410414443262896 175425142979625752223270 267068913422544522425517488 423688098858554692149799695930", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "A_{n}=\\dbinom{3n}{n}\\dbinom{6n}{3n}\\sum_{k=0}^{n}\\dbinom{n}{k}^2\\dbinom{2k}{k}", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "(3888z-1)(432z-1)", "discr_factors": "1679616, z-1/432, z-1/3888", "dm_basis": ["-364*lambda", "4", "1", "1", "-3", "-3", "-1", "0", "0", "6", "0", "0", "-6", "0", "0", "0"], "q": "0 1 -1176 761004 -577776704 287718512334 -296784707487264 8781941004951992 -281956134384797984256 -291062648274107532288795", "yuk": "1 432 1047168 2113003584 4358705402880 9137014573590432 19430849236761091584 41639311772154039173760 89817673205572743843717120 194693237885034956850315252336", "gv2": null, "gv0": null, "gv1": null, 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{"pols": "[X^4, -36*(6*X+1)*(6*X+5)*(3*X^2+3*X+1), 3888*(6*X+1)*(6*X+5)*(6*X+7)*(6*X+11)]", "text": "Hadamard product $D \\ast f$", "degz": 2, "h3": null, "sol": "1 180 124740 85765680 12047014980 -138347920030320 -407867835147973200 -809458695400609425600 -1242946112250152673920700 -1325793448735384487307649200", "n_discr_factors": "1", "c3": null, "operator": "4 2 0 0 0 0 1 -180 -1836 -5724 -7776 -3888 1496880 12877056 26593920 20155392 5038848", "new_number": "2.23", "id": 15, "operator_tex": "\\theta^4-2^{2} 3^{2} x(6\\theta+1)(6\\theta+5)(3\\theta^2+3\\theta+1)+2^{4} 3^{5} x^{2}(6\\theta+1)(6\\theta+5)(6\\theta+7)(6\\theta+11)", "superseek": "180 -21847076", "discriminant": "2 1 -3888 5038848", "aesz": "136", "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "ff626c2fb953cb886f45f717a6a98a20", "dim_h": null, "inst": " 180 -15615 -21847076 -7438074210 255591208800 3524103544056787 2733373264646275740 510493877185227959502 -1362287491078617530018240 -1721607492813490002646127880", "cleanlist": "True", "n_sing_real": "1", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "3", "laurent": null, "discriminant_tex": "1-3888z+5038848z^2", "discr_factors": "5038848, 1/5038848-1/1296*z+z^2", "dm_basis": ["37/48-2587775989/1000000000*I", "53/8+109/6000000000*I", "3779999999999999971/3240000000000000025+837600000/129600000000000001*I", "1", "-35/8-3/250000000*I", "-6-33/2000000000*I", "-129599999999999999/129600000000000001-720000000/129600000000000001*I", "0", "3/2+1/250000000*I", "9+1/40000000*I", "0", "0", "-9-1/40000000*I", "0", "0", "0"], "q": "0 1 -1116 1183086 -1060601520 951553112949 -831445527865032 696322110834525906 -591612438600290367936 495108992295096652536066", "yuk": "1 180 -124740 -589870872 -476036874180 31948901100180 761206364926270200 937547029773672579000 261372865118360678390844 -993107580996312179973167832", "gv2": null, "gv0": null, "gv1": null, 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{"pols": "[X^4, -12*(6*X+1)*(6*X+5)*(11*X^2+11*X+3), -144*(6*X+1)*(6*X+5)*(6*X+7)*(6*X+11)]", "text": "Hadamard product D*b", "degz": 2, "h3": "5", "sol": "1 180 263340 600359760 1674535082220 5241848970037680 17682527926185922800 62858194850514176942400 232283449582150476496229100 884380168260018662188830073200", "n_discr_factors": "1", "c3": "-310", "operator": "4 2 0 0 0 0 1 -180 -1956 -6708 -9504 -4752 -55440 -476928 -984960 -746496 -186624", "new_number": "2.8", "id": 69, "operator_tex": "\\theta^4-2^{2} 3 x(6\\theta+1)(6\\theta+5)(11\\theta^2+11\\theta+3)-2^{4} 3^{2} x^{2}(6\\theta+1)(6\\theta+5)(6\\theta+7)(6\\theta+11)", "superseek": "684 195638820", "discriminant": "2 1 -4752 -186624", "aesz": "63", "n_sing_complex": "0", "inst_int": "", "c2h": "62", "hash": "06c1a4c0aa33f5051126908a9898430d", "dim_h": "6", "inst": " 684 253314 195638820 225040578570 319342448936304 518678194659431382 924742518999240521412 1765350300279949945903098 3550840060459824682540995768 7442817913346821405606737574632", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "A_{n}=\\dbinom{3n}{n}\\dbinom{6n}{3n}\\sum_{k=0}^{n}\\dbinom{n}{k}^2\\dbinom{n+k}{n}", "n_sing_rational": "1", "n_sing": "3", "laurent": null, "discriminant_tex": "1-4752z-186624z^2", "discr_factors": "-186624, -1/186624+11/432*z+z^2", "dm_basis": ["-18778337/12500000*I", "41/12", "1", "1", "-31/12", "-5/2", "-1", "0", "0", "5", "0", "0", "-5", "0", "0", "0"], "q": "0 1 -1236 518886 -341674576 -139917999999 -394931030325048 -772657012856807950 -1652733244361094441792 -3681781681705227994077036", "yuk": "1 684 2027196 5282248824 14402599055676 39917806117038684 112034490051721453848 317186684016739498845000 903859353743348774901441852 2588562404075212193577668163696", "gv2": null, "gv0": "3420 1266570 978194100 1125202892850 1596712244681520 2593390973297156910 4623712594996202607060 8826751501399749729515490 17754200302299123412704978840 37214089566734107028033687873160", "gv1": "1 -611 -3437965 524537945 45789504955348 237013737984797903 922140400732269341707 3194302059028418771226413 10422130250486093277576627602 32835948356762502255457871199012 101197837229894144239785401837134687 307353612113700782742506313245639065747 924111578878985088236416673619227863043666 2758694347598875436399107807565293524221631211 8192783760701900165883854702691298475934825311210 24238246646997852102562442441857224687577031126730717 71504687170135476618498894144695286670786901837784141886 210493121686083905667207826208012300271051389728190355845174 618640193094906782902605489784535343596488530257809790743381583"}, {"pols": "[X^4, -576*(X+1/2)^4-516*(X+1/2)^2-15, 69120*(X+1)^4-43200*(X+1)^2-4176, 82944*(X+3/2)^2*(48*(X+3/2)^2+37), 11943936*(X+2)^2*(2*X+3)*(2*X+5)]", "text": "YY-Operator equivalent to $d \\ast e \\tilde A\\st \\epsilon$", "degz": 4, "h3": null, "sol": "1 180 44676 11798640 3241596996 911927850768 260684645619888 75383026726593600 21988913736501928260 6457716149904879040080", "n_discr_factors": "1", "c3": null, "operator": "4 4 0 0 0 0 1 -180 -804 -1380 -1152 -576 21744 190080 371520 276480 69120 27060480 62954496 56816640 23887872 3981312 716636160 1481048064 1134673920 382205952 47775744", "new_number": "4.5", "id": 159, "operator_tex": "\\theta^4-2^{2} 3 x\\left(48\\theta^4+96\\theta^3+115\\theta^2+67\\theta+15\\right)+2^{4} 3^{2} x^{2}\\left(480\\theta^4+1920\\theta^3+2580\\theta^2+1320\\theta+151\\right)+2^{8} 3^{4} x^{3}(48\\theta^2+144\\theta+145)(2\\theta+3)^2+2^{14} 3^{6} x^{4}(\\theta+2)^2(2\\theta+3)(2\\theta+5)", "superseek": "-36 -62596/3", "discriminant": "4 1 -576 69120 3981312 47775744", "aesz": null, "n_sing_complex": "1", "inst_int": "", "c2h": null, "hash": "f5b4785eb6dd46eea771050179115d33", "dim_h": null, "inst": " -36 -756 -62596/3 -839088 -37432800 -5568714004/3 -97940149740 -5432676734880 -312731103096896 -18548876430404064", "cleanlist": "True", "n_sing_real": "1", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "2", "laurent": null, "discriminant_tex": "(-1+288z+6912z^2)^2", "discr_factors": "47775744, (-1/6912+1/24*z+z^2)^2", "dm_basis": null, "q": "0 1 -84 558 79088 -2506251 -15199704 1128529682 -69405940032 -2821201832574", "yuk": "1 -36 -6084 -563400 -53707716 -4679100036 -400947977736 -33593471360856 -2781530541966276 -227980974158200584", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/48-1/72*3^(1/2)","im":"0","approx_re":"-0.04489","approx_im":"0.0","exponents":["0","-1/2","1","3/2"],"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":["-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":"-1/48+1/72*3^(1/2)","im":"0","approx_re":"0.003223","approx_im":"0.0","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": "[169*X^4, -15821*X^4-19162*X^3-14651*X^2-5070*X-676, -82144*X^4-1343296*X^3-2272384*X^2-1337856*X-265200, 9119488*X^4+36162048*X^3+38695360*X^2+17269824*X+2820480, -10240*(2*X+1)*(4324*X^3+10698*X^2+9903*X+3110), 4915200*(2*X+1)*(3*X+2)*(3*X+4)*(2*X+3)]", "text": "This is operator \"5.98\" from ...", "degz": 5, "h3": null, "sol": "1 4 180 7600 433300 26523504 1760408496 122456917440 8849508138900 658069964266000", "n_discr_factors": "3", "c3": null, "operator": "4 5 0 0 0 0 169 -676 -5070 -14651 -19162 -15821 -265200 -1337856 -2272384 -1343296 -82144 2820480 17269824 38695360 36162048 9119488 -31846400 -165099520 -312360960 -263372800 -88555520 117964800 579993600 997785600 707788800 176947200", "new_number": "5.98", "id": 313, "operator_tex": "13^{2} \\theta^4-13 x\\left(1217\\theta^4+1474\\theta^3+1127\\theta^2+390\\theta+52\\right)-2^{4} x^{2}\\left(5134\\theta^4+83956\\theta^3+142024\\theta^2+83616\\theta+16575\\right)+2^{6} x^{3}\\left(142492\\theta^4+565032\\theta^3+604615\\theta^2+269841\\theta+44070\\right)-2^{11} 5 x^{4}(2\\theta+1)(4324\\theta^3+10698\\theta^2+9903\\theta+3110)+2^{16} 3 5^{2} x^{5}(2\\theta+1)(3\\theta+2)(3\\theta+4)(2\\theta+3)", "superseek": "87/13 21589/13", "discriminant": "5 169 -15821 -82144 9119488 -88555520 176947200", "aesz": "341", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "eed12a307d671fcf681b9d108c5e4c9e", "dim_h": null, "inst": " 87/13 1532/13 21589/13 589110/13 17749920/13 652121660/13 25606888578/13 1088305023982/13 48500571351604/13 2257264405232620/13", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "(27z+1)(256z^2-96z+1)(-13+160z)^2", "discr_factors": "176947200, z+1/27, z^2-3/8*z+1/256, (-13/160+z)^2", "dm_basis": null, "q": "0 1 -14 -301 736 -52635 -3014442 -134862035 -6142738464 -304565522449", "yuk": "1 87/13 12343/13 582990/13 37715383/13 2218740087/13 140858873806/13 8783162782341/13 42862477691859 2719762808915562", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"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":"3/16-1/8*2^(1/2)","im":"0","approx_re":"0.010723","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"13/160","im":"0","approx_re":"0.08125","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"3/16+1/8*2^(1/2)","im":"0","approx_re":"0.364277","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","2/3","4/3","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, 12+56*X+100*X^2+88*X^3+172*X^4, 12048*X^4+14784*X^3+17712*X^2+9952*X+2256, 432256*X^4+923904*X^3+1185408*X^2+737792*X+186240, 7751680*X^4+25311232*X^3+35200000*X^2+22459392*X+5437440, 33214464*X^4+188669952*X^3+212963328*X^2-3096576*X-67424256, -1147650048*X^4-4994629632*X^3-12364333056*X^2-15859777536*X-7297449984, -17323130880*X^4-99635429376*X^3-245132034048*X^2-295728316416*X-130689662976, -3737124864*X^4-44845498368*X^3-20978860032*X^2-20384317440*X-23272095744, 1353518678016*X^4+9702935101440*X^3+28091627864064*X^2+35372906053632*X+15653117362176, 48922361856*(X+1)*(109*X^3+651*X^2+1373*X+933), -1174136684544*(X+1)*(X+2)*(27*X^2+153*X+199), -169075682574336*(X+1)*(X+2)^2*(X+3)]", "text": "This is operator \"12.5\" from ...", "degz": 12, "h3": null, "sol": "1 -12 180 -2736 42948 -691632 11651184 -208526400 3997652292 -81421375536", "n_discr_factors": "5", "c3": null, "operator": "4 12 0 0 0 0 1 12 56 100 88 172 2256 9952 17712 14784 12048 186240 737792 1185408 923904 432256 5437440 22459392 35200000 25311232 7751680 -67424256 -3096576 212963328 188669952 33214464 -7297449984 -15859777536 -12364333056 -4994629632 -1147650048 -130689662976 -295728316416 -245132034048 -99635429376 -17323130880 -23272095744 -20384317440 -20978860032 -44845498368 -3737124864 15653117362176 35372906053632 28091627864064 9702935101440 1353518678016 45644563611648 112814966439936 99018860396544 37180995010560 5332537442304 -467306400448512 -1060245426143232 -835985319395328 -274747984183296 -31701690482688 -2028908190892032 -4734119112081408 -3888740699209728 -1352605460594688 -169075682574336", "new_number": "12.5", "id": 358, "operator_tex": "\\theta^4+2^{2} x\\left(43\\theta^4+22\\theta^3+25\\theta^2+14\\theta+3\\right)+2^{4} x^{2}\\left(753\\theta^4+924\\theta^3+1107\\theta^2+622\\theta+141\\right)+2^{7} x^{3}\\left(3377\\theta^4+7218\\theta^3+9261\\theta^2+5764\\theta+1455\\right)+2^{10} x^{4}\\left(7570\\theta^4+24718\\theta^3+34375\\theta^2+21933\\theta+5310\\right)+2^{12} 3^{2} x^{5}\\left(901\\theta^4+5118\\theta^3+5777\\theta^2-84\\theta-1829\\right)-2^{14} 3^{2} x^{6}\\left(7783\\theta^4+33872\\theta^3+83851\\theta^2+107556\\theta+49489\\right)-2^{17} 3^{3} x^{7}\\left(4895\\theta^4+28154\\theta^3+69267\\theta^2+83564\\theta+36929\\right)-2^{20} 3^{4} x^{8}\\left(44\\theta^4+528\\theta^3+247\\theta^2+240\\theta+274\\right)+2^{23} 3^{5} x^{9}\\left(664\\theta^4+4760\\theta^3+13781\\theta^2+17353\\theta+7679\\right)+2^{26} 3^{6} x^{10}(\\theta+1)(109\\theta^3+651\\theta^2+1373\\theta+933)-2^{29} 3^{7} x^{11}(\\theta+1)(\\theta+2)(27\\theta^2+153\\theta+199)-2^{33} 3^{9} x^{12}(\\theta+1)(\\theta+2)^2(\\theta+3)", "superseek": "4 2252/9", "discriminant": "12 1 172 12048 432256 7751680 33214464 -1147650048 -17323130880 -3737124864 1353518678016 5332537442304 -31701690482688 -169075682574336", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "bb257a283455fdd1fa17fef9649505e3", "dim_h": null, "inst": " 4 -31 2252/9 -11109/4 33312 -4091081/9 6559596 -399687825/4 1577400224 -25647405040", "cleanlist": "True", "n_sing_real": "6", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "8", "laurent": null, "discriminant_tex": "-(16z+1)(432z^2+36z+1)(24z+1)^2(288z^2+48z+1)^2(8z-1)^3", "discr_factors": "-169075682574336, (z^2+1/6*z+1/288)^2, z^2+1/12*z+1/432, (z+1/24)^2, (z-1/8)^3, z+1/16", "dm_basis": null, "q": "0 1 8 54 -128 -2875 -72144 -100310 -7419904 102483090", "yuk": "1 4 -244 6760 -177988 4164004 -98179432 2249941432 -51160219588 1149924770056", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/12-1/24*2^(1/2)","im":"0","approx_re":"-0.142259","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/16","im":"0","approx_re":"-0.0625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/24","im":"-1/72*3^(1/2)","approx_re":"-0.0416666666667","approx_im":"-0.024056","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/24","im":"0","approx_re":"-0.0416666666667","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/24","im":"1/72*3^(1/2)","approx_re":"-0.0416666666667","approx_im":"0.024056","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/12+1/24*2^(1/2)","im":"0","approx_re":"-0.024408","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":"1/8","im":"0","approx_re":"0.125","approx_im":"0.0","exponents":["0","1/2","3/2","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","2","2","3"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -140*X^4-152*X^3-140*X^2-64*X-12, 8736*X^4+17088*X^3+20592*X^2+12640*X+3216, -315392*X^4-824832*X^3-1141056*X^2-811072*X-236352, 7199488*X^4+22632448*X^3+33786112*X^2+25145856*X+7554816, -104279040*X^4-378722304*X^3-599851008*X^2-439520256*X-124710912, 860700672*X^4+3588636672*X^3+5853929472*X^2+3884212224*X+863797248, -1825210368*X^4-9822339072*X^3-9894887424*X^2+8154611712*X+9521528832, -34791358464*X^4-172884492288*X^3-449399881728*X^2-605350526976*X-289478541312, 286399660032*X^4+1812675428352*X^3+4617302704128*X^2+5673210347520*X+2552626151424, 12230590464*(X+1)*(X^3-105*X^2-277*X-267), -73383542784*(X+1)*(X+2)*(93*X^2+441*X+607), 7925422620672*(X+3)*(X+2)*(X+1)*(X+6), 63403380965376*(X+1)*(X+2)*(X+3)*(X+4)]", "text": "This is operator \"13.10\" from ...", "degz": 13, "h3": null, "sol": "1 12 180 2928 47556 674352 5050224 -159433920 -10791594684 -419663644368", "n_discr_factors": "5", "c3": null, "operator": "4 13 0 0 0 0 1 -12 -64 -140 -152 -140 3216 12640 20592 17088 8736 -236352 -811072 -1141056 -824832 -315392 7554816 25145856 33786112 22632448 7199488 -124710912 -439520256 -599851008 -378722304 -104279040 863797248 3884212224 5853929472 3588636672 860700672 9521528832 8154611712 -9894887424 -9822339072 -1825210368 -289478541312 -605350526976 -449399881728 -172884492288 -34791358464 2552626151424 5673210347520 4617302704128 1812675428352 286399660032 -3265567653888 -6653441212416 -4672085557248 -1271981408256 12230590464 -89087620939776 -198355716145152 -155279576530944 -52836150804480 -6824669478912 285315214344192 570630428688384 372494863171584 95105071448064 7925422620672 1521681143169024 3170169048268800 2219118333788160 634033809653760 63403380965376", "new_number": "13.10", "id": 362, "operator_tex": "\\theta^4-2^{2} x\\left(35\\theta^4+38\\theta^3+35\\theta^2+16\\theta+3\\right)+2^{4} x^{2}\\left(546\\theta^4+1068\\theta^3+1287\\theta^2+790\\theta+201\\right)-2^{6} x^{3}\\left(4928\\theta^4+12888\\theta^3+17829\\theta^2+12673\\theta+3693\\right)+2^{8} x^{4}\\left(28123\\theta^4+88408\\theta^3+131977\\theta^2+98226\\theta+29511\\right)-2^{10} 3^{2} x^{5}\\left(11315\\theta^4+41094\\theta^3+65088\\theta^2+47691\\theta+13532\\right)+2^{13} 3^{2} x^{6}\\left(11674\\theta^4+48674\\theta^3+79399\\theta^2+52683\\theta+11716\\right)-2^{15} 3^{3} x^{7}\\left(2063\\theta^4+11102\\theta^3+11184\\theta^2-9217\\theta-10762\\right)-2^{17} 3^{4} x^{8}\\left(3277\\theta^4+16284\\theta^3+42329\\theta^2+57018\\theta+27266\\right)+2^{20} 3^{5} x^{9}\\left(1124\\theta^4+7114\\theta^3+18121\\theta^2+22265\\theta+10018\\right)+2^{24} 3^{6} x^{10}(\\theta+1)(\\theta^3-105\\theta^2-277\\theta-267)-2^{25} 3^{7} x^{11}(\\theta+1)(\\theta+2)(93\\theta^2+441\\theta+607)+2^{27} 3^{10} x^{12}(\\theta+3)(\\theta+2)(\\theta+1)(\\theta+6)+2^{30} 3^{10} x^{13}(\\theta+1)(\\theta+2)(\\theta+3)(\\theta+4)", "superseek": "4 -628/9", "discriminant": "13 1 -140 8736 -315392 7199488 -104279040 860700672 -1825210368 -34791358464 286399660032 12230590464 -6824669478912 7925422620672 63403380965376", "aesz": null, "n_sing_complex": "4", "inst_int": "", "c2h": null, "hash": "2a9fda379889eb2fd218bd01f2520f7a", "dim_h": null, "inst": " 4 5 -628/9 -2823/4 672 133867/9 207788 15579985/4 94033312/3 -299026336", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "6", "n_sing": "9", "laurent": null, "discriminant_tex": "(8z-1)(10368z^3-1728z^2+72z-1)(12z-1)^2(288z^2-24z+1)^2(4z+1)^3", "discr_factors": "63403380965376, z-1/8, z^3-1/6*z^2+1/144*z-1/10368, (z-1/12)^2, (z+1/4)^3, (z^2-1/12*z+1/288)^2", "dm_basis": null, "q": "0 1 -16 198 -1760 13349 -57888 -559014 17566336 -323621262", "yuk": "1 4 44 -1880 -45124 84004 3210968 71271288 1994192956 22850092936", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/4","im":"0","approx_re":"-0.25","approx_im":"0.0","exponents":["0","1/2","3/2","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":"-1/72*2^(1/3)-1/144*2^(2/3)+1/18","im":"-1/24*3^(1/2)*(1/3*2^(1/3)-1/6*2^(2/3))","approx_re":"0.027033","approx_im":"-0.011216","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/72*2^(1/3)-1/144*2^(2/3)+1/18","im":"1/24*3^(1/2)*(1/3*2^(1/3)-1/6*2^(2/3))","approx_re":"0.027033","approx_im":"0.011216","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/24","im":"-1/24","approx_re":"0.0416666666667","approx_im":"-0.0416666666667","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/24","im":"1/24","approx_re":"0.0416666666667","approx_im":"0.0416666666667","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/12","im":"0","approx_re":"0.0833333333333","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"1/36*2^(1/3)+1/72*2^(2/3)+1/18","im":"0","approx_re":"0.112601","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/8","im":"0","approx_re":"0.125","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","3","4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -12*(3*X^2+3*X+1)^2, 3024*X^4+22464*X^3+31536*X^2+18144*X+4176, 10368*(3*X^2+3*X+1)*(3*X^2-21*X-35), -6718464*X^4-13436928*X^3+28366848*X^2+35085312*X+12192768, 8957952*(3*X^2+3*X+1)*(3*X^2+27*X-11), 2257403904*X^4-7739670528*X^3-13221937152*X^2-7739670528*X-1397440512, -7739670528*(3*X^2+3*X+1)^2, 557256278016*(X+1)^4]", "text": "Hadamard product $d \\ast f$. This operator has a second MUM-point at infinity with the same instanton numbers. Itg can be reduced to an operator of degree 4 with a single MUM-point defined over $Q(\\sqrt{?})$.", "degz": 8, "h3": null, "sol": "1 12 180 2352 6084 -1278288 -68988816 -2512105920 -70933293756 -1393810859472", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 1 -12 -72 -180 -216 -108 4176 18144 31536 22464 3024 -362880 -1306368 -1710720 -559872 93312 12192768 35085312 28366848 -13436928 -6718464 -98537472 -53747712 456855552 806215680 80621568 -1397440512 -7739670528 -13221937152 -7739670528 2257403904 -7739670528 -46438023168 -116095057920 -139314069504 -69657034752 557256278016 2229025112064 3343537668096 2229025112064 557256278016", "new_number": "8.13", "id": 456, "operator_tex": "\\theta^4-2^{2} 3 x\\left((3\\theta^2+3\\theta+1)^2\\right)+2^{4} 3^{2} x^{2}\\left(21\\theta^4+156\\theta^3+219\\theta^2+126\\theta+29\\right)+2^{7} 3^{4} x^{3}(3\\theta^2+3\\theta+1)(3\\theta^2-21\\theta-35)-2^{10} 3^{5} x^{4}\\left(27\\theta^4+54\\theta^3-114\\theta^2-141\\theta-49\\right)+2^{12} 3^{7} x^{5}(3\\theta^2+3\\theta+1)(3\\theta^2+27\\theta-11)+2^{14} 3^{8} x^{6}\\left(21\\theta^4-72\\theta^3-123\\theta^2-72\\theta-13\\right)-2^{17} 3^{10} x^{7}\\left((3\\theta^2+3\\theta+1)^2\\right)+2^{20} 3^{12} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "12 3020/3", "discriminant": "8 1 -108 3024 93312 -6718464 80621568 2257403904 -69657034752 557256278016", "aesz": "163", "n_sing_complex": "4", "inst_int": "", "c2h": null, "hash": "e21fd830a9dca03305deb8363a26fcf2", "dim_h": null, "inst": " 12 -96 3020/3 -71493/4 319584 -19126516/3 139598148 -12567360273/4 221121122720/3 -1788903000504", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "7", "laurent": null, "discriminant_tex": "(1728z^2-72z+1)(432z^2-36z+1)(-1+864z^2)^2", "discr_factors": "557256278016, (-1/864+z^2)^2, z^2-1/12*z+1/432, z^2-1/24*z+1/1728", "dm_basis": null, "q": "0 1 -24 630 -16064 426309 -11440656 310799594 -8551209216 237533688594", "yuk": "1 12 -756 27192 -1144644 39948012 -1377082728 47882164776 -1608623259588 53732432848152", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/72*6^(1/2)","im":"0","approx_re":"-0.034021","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":"1/48","im":"-1/144*3^(1/2)","approx_re":"0.0208333333333","approx_im":"-0.012028","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/48","im":"1/144*3^(1/2)","approx_re":"0.0208333333333","approx_im":"0.012028","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/72*6^(1/2)","im":"0","approx_re":"0.034021","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/24","im":"-1/72*3^(1/2)","approx_re":"0.0416666666667","approx_im":"-0.024056","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/24","im":"1/72*3^(1/2)","approx_re":"0.0416666666667","approx_im":"0.024056","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}]}