{"count": 8, "status":"OK", "data":[{"pols": "[X^4, -4*(4*X+1)*(4*X+3)*(10*X^2+10*X+3), 144*(4*X+1)*(4*X+3)*(4*X+5)*(4*X+7)]", "text": "Hadamard product $C\\ast c$", "degz": 2, "h3": "12", "sol": "1 36 6300 1718640 575675100 216636756336 87874675224336 37563969509352000 16692217815436148700 7642084994921759382000", "n_discr_factors": "2", "c3": "-224", "operator": "4 2 0 0 0 0 1 -36 -312 -952 -1280 -640 15120 101376 198144 147456 36864", "new_number": "2.11", "id": 2, "operator_tex": "\\theta^4-2^{2} x(4\\theta+1)(4\\theta+3)(10\\theta^2+10\\theta+3)+2^{4} 3^{2} x^{2}(4\\theta+1)(4\\theta+3)(4\\theta+5)(4\\theta+7)", "superseek": "64 246848", "discriminant": "2 1 -640 36864", "aesz": "69", "n_sing_complex": "0", "inst_int": "", "c2h": "72", "hash": "729adc350de26d9415643078ed8d3867", "dim_h": "8", "inst": " 64 2616 246848 32024824 5160268864 951777326520 192563937712192 41708381444805880 9517654613752418368 2263204057578067144632", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "A_n=\\dbinom{2n}{n}\\dbinom{4n}{2n}\\sum_{k=0}^{n}\\dbinom{n}{k}^2\\dbinom{2k}{k}", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "(576z-1)(64z-1)", "discr_factors": "36864, z-1/576, z-1/64", "dm_basis": ["-224*lambda", "5", "1", "1", "-3", "-6", "-1", "0", "0", "12", "0", "0", "-12", "0", "0", "0"], "q": "0 1 -168 14124 -1462208 78268110 -14975497440 -813107957064 -407022651161088 -86618851756321563", "yuk": "1 64 20992 6664960 2049609728 645033608064 205583909214208 66049430635281920 21354691301790220288 6938370213425519655232", "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","12","1","0","0","0","1","1"]},{"re":"1/576","im":"0","approx_re":"0.00173611111111","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["1+224*lambda","0","56*lambda",".98194154e-1","3","1","3/4","-56*lambda","0","0","1","0","12","0","3","1-224*lambda"],"monodromy_dm":["1","-8","-1","-1","0","1","0","0","0","0","1","0","0","0","0","1"]},{"re":"1/64","im":"0","approx_re":"0.015625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["4.+3.256527087*I","-1-224*lambda","3/4+168*lambda",".44582463e-1-112*lambda","9","-2","9/4","-3/4-168*lambda","12","-4","4","-1-224*lambda","36","-12","9","-2.-3.256527087*I"],"monodromy_dm":["-5","-30","-4","-3","2","11","1333333/1000000","1","-12","-60","-7","-6","8","40","5333333/1000000","5"]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/4","3/4","5/4","7/4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -16*(4*X+1)*(4*X+3)*(3*X^2+3*X+1), 512*(4*X+1)*(4*X+3)*(4*X+5)*(4*X+7)]", "text": "Hadamard product $C\\ast d$", "degz": 2, "h3": "16", "sol": "1 48 8400 2069760 609008400 200387835648 71201249543424 26742996453888000 10470608789459504400 4232794808237739744000", "n_discr_factors": "2", "c3": "-268", "operator": "4 2 0 0 0 0 1 -48 -400 -1168 -1536 -768 53760 360448 704512 524288 131072", "new_number": "2.15", "id": 6, "operator_tex": "\\theta^4-2^{4} x(4\\theta+1)(4\\theta+3)(3\\theta^2+3\\theta+1)+2^{9} x^{2}(4\\theta+1)(4\\theta+3)(4\\theta+5)(4\\theta+7)", "superseek": "48 73328", "discriminant": "2 1 -768 131072", "aesz": "38", "n_sing_complex": "0", "inst_int": "", "c2h": "88", "hash": "9ce26bb7405c3b98d8aeae5b1102c611", "dim_h": "10", "inst": " 48 998 73328 7388135 857248528 112063100078 16141925788848 2496124778774145 406647185987371136 68996526934808894722", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "A_{n}=\\dbinom{2n}{n}\\dbinom{4n}{2n}\\sum_{k=0}^{n}\\dbinom{n}{k}\\dbinom{2k}{k}\\dbinom{2n-2k}{n-k}", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "(512z-1)(256z-1)", "discr_factors": "131072, z-1/256, z-1/512", "dm_basis": ["-268*lambda", "19/3", "1", "1", "-11/3", "-8", "-1", "0", "0", "16", "0", "0", "-16", "0", "0", "0"], "q": "0 1 -208 32000 -4613120 605381040 -78889707008 9643425928192 -1213793065402368 140184861197932696", "yuk": "1 48 8032 1979904 472848672 107156066048 24205631604736 5536680545574912 1278015887205210912 296445798584795538048", "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","16","1","0","0","0","1","1"]},{"re":"1/512","im":"0","approx_re":"0.001953125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["1+268*lambda","0","I*arctan(173/564)",".105419378","11/3","1","121/144","-I*arctan(173/564)","0","0","1","0","16","0","11/3","1-268*lambda"],"monodromy_dm":["1","-10","-1","-1","0","1","0","0","0","0","1","0","0","0","0","1"]},{"re":"1/256","im":"0","approx_re":"0.00390625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["19/6+4*I*ln(2)^(6/5)*Zeta(5)^(2/9)","-13/24-134*lambda",".49652777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777778+.595253091*I",".64137367e-1-.351740463*I","22/3+3/1000000000*I","-5/6+1/500000000*I","121/72-1/500000000*I","-.49652777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777778-.595253091*I","8+3/1000000000*I","-2+1/500000000*I","17/6-1/500000000*I","-13/24-134*lambda","32+7/500000000*I","-8+7/1000000000*I","22/3-7/1000000000*I","-7/6-4*I*ln(2)^(6/5)*Zeta(5)^(2/9)"],"monodromy_dm":["-3","-24","-5/2","-2","1","7","5/8","1/2","-8","-48","-4","-4","6","36","15/4","4"]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/4","3/4","5/4","7/4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -12*(4*X+1)*(4*X+3)*(3*X^2+3*X+1), 432*(4*X+1)*(4*X+3)*(4*X+5)*(4*X+7)]", "text": "", "degz": 2, "h3": null, "sol": "1 36 3780 388080 8108100 -13827878064 -6049207788624 -1780617654129600 -405415553383655100 -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": ["19/24-1162393719353719131361189363784404603456366390101814206736549803033200099854000208071729302850101578/768799759549186043811713254203741173211443985818991590275710787225120378790852066470688698366857287*I", "8750000003/1000000000+113/6000000000*I", "378000000701999998397/324000000648000002005+1707000001584/324000000648000002005*I", "1", "-17/4-9/1000000000*I", "-12000000009/1000000000-53/2000000000*I", "-324000000647999998643/324000000648000002005-1476000001476/324000000648000002005*I", "0", "3+3/500000000*I", "9000000009/500000000+41/1000000000*I", "0", "0", "-9000000009/500000000-41/1000000000*I", "0", "0", "0"], "q": "0 1 -156 22446 -2570800 297228021 -32847734088 3343576302482 -362209122322368 37293313471891074", "yuk": "1 36 -3780 -1860408 -283646916 -3375683964 8182006866936 1873126855818072 140935535201123388 -30716111646655947000", "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","18","1","0","0","0","1","1"]},{"re":"1/384","im":"-1/1152*3^(1/2)","approx_re":"0.00260416666667","approx_im":"-0.001504","exponents":["0","1","1","2"],"monodromy":["5/24+I*tan(801/812)","-19/144+52*lambda","-323/1728+221/3*lambda",".92182440e-1+247/9*lambda","17/4+9/1000000000*I","41/24-3/1000000000*I","289/288-1/250000000*I","323/1728-221/3*lambda","-3-3/500000000*I","-1/2+1/500000000*I","7/24+3/1000000000*I","-19/144+52*lambda","18.000000018+.41e-7*I","3.000000039-.12000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-7*I","17/4-9/500000000*I","43/24-I*tan(801/812)"],"monodromy_dm":["1","-11","-1","-1","0","1","0","0","0","0","1","0","0","0","0","1"]},{"re":"1/384","im":"1/1152*3^(1/2)","approx_re":"0.00260416666667","approx_im":"0.001504","exponents":["0","1","1","2"],"monodromy":["43/24+I*tan(801/812)","-19/144-52*lambda","323/1728+221/3*lambda",".92182440e-1-247/9*lambda","17/4","7/24","289/288","-323/1728-221/3*lambda","3","-1/2","41/24","-19/144-52*lambda","18","-3","17/4","5/24-I*tan(801/812)"],"monodromy_dm":["-2","-15","-1333333/1000000","-1","1","6","111111/250000","333333/1000000","-12","-60","-4333333/1000000","-4","10","50","1111111/250000","4333333/1000000"]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/4","3/4","5/4","7/4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -4*(4*X+1)*(4*X+3)*(17*X^2+17*X+6), 1152*(4*X+1)*(4*X+3)*(4*X+5)*(4*X+7)]", "text": "Hadamard product $C \\ast g$", "degz": 2, "h3": "24", "sol": "1 72 17640 5765760 2156754600 873251451072 372637196515584 165110467068518400 75269439109043922600 35089980080429298024000", "n_discr_factors": "2", "c3": "-344", "operator": "4 2 0 0 0 0 1 -72 -588 -1676 -2176 -1088 120960 811008 1585152 1179648 294912", "new_number": "2.26", "id": 18, "operator_tex": "\\theta^4-2^{2} x(4\\theta+1)(4\\theta+3)(17\\theta^2+17\\theta+6)+2^{7} 3^{2} x^{2}(4\\theta+1)(4\\theta+3)(4\\theta+5)(4\\theta+7)", "superseek": "44 22500", "discriminant": "2 1 -1088 294912", "aesz": "139", "n_sing_complex": "0", "inst_int": "", "c2h": "120", "hash": "f5d9215987323abcff6ed8709927af5d", "dim_h": "14", "inst": " 44 607 22500 1444678 128626784 13469917781 1522820820452 179595469620910 21853624667881360 2736519633179452216", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "(576z-1)(512z-1)", "discr_factors": "294912, z-1/512, z-1/576", "dm_basis": ["-344*lambda", "9", "1", "1", "-5", "-12", "-1", "0", "0", "24", "0", "0", "-24", "0", "0", "0"], "q": "0 1 -300 70878 -15057904 3009908013 -579157118568 108444942299154 -19911945230728896 3600324639279134982", "yuk": "1 44 4900 607544 92464292 16078348044 2909502853096 522327541415080 91952880538370212 15931292382886118984", "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","24","1","0","0","0","1","1"]},{"re":"1/576","im":"0","approx_re":"0.00173611111111","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["1+344*lambda","0","215/3*lambda",".115791449","5","1","25/24","-215/3*lambda","0","0","1","0","24","0","5","1-344*lambda"],"monodromy_dm":["1","-14","-1","-1","0","1","0","0","0","0","1","0","0","0","0","1"]},{"re":"1/512","im":"0","approx_re":"0.001953125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["-1.363320470+.333408287*I","-2.378556075+1/4*I*2^(1/4)*Pi^(3/2)/ln(2)^(7/4)","1.952097134+1.450430332*I",".352541506-.730455452*I","-2.231842169+5.463251200*I","4.752377305+8.996899861*I","5.529765042-2.362775601*I","-1.121053097-1.662936757*I","-1.857729799+3.694349576*I","2.129374012+I*7^(7/8)/ln(2)^(1/2)/ln(3)^(1/6)","4.991998028-1.348211717*I","-.692201690-1.222934527*I","-10.712842412+26.223605760*I","18.011411066+43.185119335*I","26.542872203-11.341322886*I","-4.381054863-7.982096432*I"],"monodromy_dm":["-30627/12500+270693/1000000*I","-13519851/1000000+2310003/100000*I","299211/250000+70673/100000*I","13949/31250-21853/20000*I","50519/100000-99/1000000*I","1615331/500000-16039/5000*I","-166129/1000000-116483/1000000*I","-15481/200000+153931/1000000*I","-1515571/250000+1187/1000000*I","-6691987/250000+9623401/250000*I","187097/62500+279559/200000*I","185773/200000-73887/40000*I","78936/15625-989/1000000*I","22306623/1000000-8019501/250000*I","-1661293/1000000-1164829/1000000*I","112973/500000+96207/62500*I"]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/4","3/4","5/4","7/4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -16*(4*X+1)*(4*X+3)*(32*X^2+32*X+13), 65536*(4*X+1)*(4*X+3)*(4*X+5)*(4*X+7)]", "text": "This is operator \"2.33\" from ...", "degz": 2, "h3": null, "sol": "1 624 1251600 3268151040 9627237219600 30398161990420224 100419276330270433536 342443246991563367936000 1195637852398571585356438800 4251196450644173123348263008000", "n_discr_factors": "1", "c3": null, "operator": "4 2 0 0 0 0 1 -624 -4864 -13056 -16384 -8192 6881280 46137344 90177536 67108864 16777216", "new_number": "2.33", "id": 26, "operator_tex": "\\theta^4-2^{4} x(4\\theta+1)(4\\theta+3)(32\\theta^2+32\\theta+13)+2^{16} x^{2}(4\\theta+1)(4\\theta+3)(4\\theta+5)(4\\theta+7)", "superseek": "-160 -539680", "discriminant": "2 1 -8192 16777216", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "83a66e92381baa083f87a13e02375bc9", "dim_h": null, "inst": " -160 -6920 -539680 -54568560 -6402958560 -826859298920 -114164994441120 -16560193073405040 -2494945705036829440 -387347549189406370520", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "2", "laurent": null, "discriminant_tex": "(4096z-1)^2", "discr_factors": "16777216, (z-1/4096)^2", "dm_basis": ["11/12-80*lambda", "1/6", "1/2", "1", "1/6", "0", "-1", "0", "2", "-4", "0", "0", "4", "0", "0", "0"], "q": "0 1 -2368 4490848 -7667378176 12339033298480 -19115196671346688 28835535209979429376 -42653444750743181590528 62148392907302732450544280", "yuk": "1 -160 -55520 -14571520 -3492443360 -800369820160 -178601623193600 -39158593093304320 -8478818857075823840 -1818815418971863233280", "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","-4","1","0","0","0","1","1"]},{"re":"1/4096","im":"0","approx_re":"0.000244140625","approx_im":"0.0","exponents":["0","1/4","3/4","1"],"monodromy":["1/12+80*lambda","11/24+40*lambda","-11/288+10/3*lambda",".172495151","-1/6","11/12","-1/144","-11/288-10/3*lambda","-2","1","11/12","11/24-40*lambda","-4","-2","-1/6","1/12-80*lambda"],"monodromy_dm":["-1","0","0","-1","-1","1","1/2","0","0","0","1","0","2","0","-1","1"]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/4","3/4","5/4","7/4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -48*(4*X+1)*(4*X+3)*(72*X^2+72*X+31), 2985984*(4*X+1)*(4*X+3)*(4*X+5)*(4*X+7)]", "text": "Hadamard product $B\\ast c$.", "degz": 2, "h3": null, "sol": "1 4464 62430480 1125574813440 22774986122288400 492361192240067614464 11111529228523281353892096 258444435717705729553874841600 6147075992318968275557995422358800 148748353261886238984942174731767392000", "n_discr_factors": "1", "c3": null, "operator": "4 2 0 0 0 0 1 -4464 -34176 -89472 -110592 -55296 313528320 2102132736 4108713984 3057647616 764411904", "new_number": "2.37", "id": 30, "operator_tex": "\\theta^4-2^{4} 3 x(4\\theta+1)(4\\theta+3)(72\\theta^2+72\\theta+31)+2^{12} 3^{6} x^{2}(4\\theta+1)(4\\theta+3)(4\\theta+5)(4\\theta+7)", "superseek": "-2592 81451104", "discriminant": "2 1 -55296 764411904", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "fb56d2f39692cfb98f66d467355b3c99", "dim_h": null, "inst": " -2592 -307800 81451104 144135316512 98667659422368 19581239950274184 -50326512821418175776 -85029037092133222396896 -75883565825205328055854848 -32231159942230127887254932040", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "2", "laurent": null, "discriminant_tex": "(27648z-1)^2", "discr_factors": "764411904, (z-1/27648)^2", "dm_basis": ["17/24-885/878*I", "7/12", "1/2", "1", "-5/12", "0", "-1", "0", "1", "-2", "0", "0", "2", "0", "0", "0"], "q": "0 1 -16320 214994016 -2554845915136 28636292333415984 -309097701850392262656 3249537123451988136468992 -33503034725538371882466017280 340280437793834402088855557741208", "yuk": "1 -2592 -2464992 2199177216 9224657791776 12333457427793408 4229547831455938560 -17261993897746434293760 -43534866991162985209418976 -55319119486574684150519006976", "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","-2","1","0","0","0","1","1"]},{"re":"1/27648","im":"0","approx_re":"3.61689814815e-05","approx_im":"0.0","exponents":["0","1/6","5/6","1"],"monodromy":["7/24+885/878*I","17/16+104*lambda","85/576-130/3*lambda",".244599715","5/12","29/24","-25/288","85/576+130/3*lambda","-1","3/2","29/24","17/16-104*lambda","-2","-1","5/12","7/24-885/878*I"],"monodromy_dm":["0","-1","0","-1","-1","1","1","0","0","0","1","0","2","0","-2","1"]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/4","3/4","5/4","7/4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -4*(4*X+1)*(4*X+3)*(7*X^2+7*X+2), -128*(4*X+1)*(4*X+3)*(4*X+5)*(4*X+7)]", "text": "C*a", "degz": 2, "h3": "12", "sol": "1 24 4200 1034880 311711400 104849769024 37939351946496 14450910769152000 5718086730211026600 2330121882579042552000", "n_discr_factors": "2", "c3": "-228", "operator": "4 2 0 0 0 0 1 -24 -212 -660 -896 -448 -13440 -90112 -176128 -131072 -32768", "new_number": "2.3", "id": 33, "operator_tex": "\\theta^4-2^{2} x(4\\theta+1)(4\\theta+3)(7\\theta^2+7\\theta+2)-2^{7} x^{2}(4\\theta+1)(4\\theta+3)(4\\theta+5)(4\\theta+7)", "superseek": "52 220220", "discriminant": "2 1 -448 -32768", "aesz": "68", "n_sing_complex": "0", "inst_int": "", "c2h": "72", "hash": "13a48045ff0a42a9fcfbdb710baf1997", "dim_h": "8", "inst": " 52 2814 220220 29135058 4512922272 813434977450 159977765979708 33749653506239610 7496689709059170544 1735643559203414845168", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "A_{n}=\\dbinom{2n}{n}\\dbinom{4n}{2n}\\sum_{k=0}^{n}\\dbinom{n}{k}^3", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "-(64z+1)(512z-1)", "discr_factors": "-32768, z-1/512, z+1/64", "dm_basis": ["-1104893119/1000000000*I", "5", "1", "1", "-3", "-6", "-1", "0", "0", "12", "0", "0", "-12", "0", "0", "0"], "q": "0 1 -116 478 113008 -56372435 -6168706136 -1532666623214 -363738855142208 -89086162864734458", "yuk": "1 52 22564 5945992 1864666276 564115284052 175701961097704 54872373731039896 17279822597059346596 5465086797904141272568", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/64","im":"0","approx_re":"-0.015625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["4.+2.209786237*I","-1.5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000-1.104893119*I","1+152*lambda","-.171535199-114*lambda","8","-3","8/3","-1-152*lambda","12","-6","5","-1.5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000-1.104893119*I","24","-12","8","-2.-2.209786237*I"],"monodromy_dm":["-5","-24","-3","-2","3","13","3/2","1","-24","-96","-11","-8","18","72","9","7"]},{"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","12","1","0","0","0","1","1"]},{"re":"1/512","im":"0","approx_re":"0.001953125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["1.+1.104893119*I","0","57*lambda","276/2713","3","1","3/4","-57*lambda","0","0","1","0","12","0","3","1.-1.104893119*I"],"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":["1/4","3/4","5/4","7/4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -4*(4*X+1)*(4*X+3)*(11*X^2+11*X+3), -16*(4*X+1)*(4*X+3)*(4*X+5)*(4*X+7)]", "text": "Hadamard product C*b\nRelated to (:case 8.139)\nA-Incarnation: double cover of $B_5$.\n\nA:Incarnation: double cover of B", "degz": 2, "h3": "10", "sol": "1 36 7980 2716560 1127025900 523922935536 262254770874096 138273159697358400 75764606627820696300 42763759729830497358000", "n_discr_factors": "1", "c3": "-200", "operator": "4 2 0 0 0 0 1 -36 -324 -1028 -1408 -704 -1680 -11264 -22016 -16384 -4096", "new_number": "2.7", "id": 68, "operator_tex": "\\theta^4-2^{2} x(4\\theta+1)(4\\theta+3)(11\\theta^2+11\\theta+3)-2^{4} x^{2}(4\\theta+1)(4\\theta+3)(4\\theta+5)(4\\theta+7)", "superseek": "92 585396", "discriminant": "2 1 -704 -4096", "aesz": "51", "n_sing_complex": "0", "inst_int": "", "c2h": "64", "hash": "e09b9b149b6845daa8d5ef03df33f22d", "dim_h": "7", "inst": " 92 5052 585396 99982012 21054159152 5072639293460 1341406276920276 379798413120428604 113300338464448477848 35222259453038284682544", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "A_{n}=\\dbinom{2n}{n}\\dbinom{4n}{2n}\\sum_{k=0}^{n}\\dbinom{n}{k}^2\\dbinom{n+k}{n}", "n_sing_rational": "1", "n_sing": "3", "laurent": null, "discriminant_tex": "1-704z-4096z^2", "discr_factors": "-4096, -1/4096+11/64*z+z^2", "dm_basis": ["-96920449/100000000*I", "13/3", "1", "1", "-8/3", "-5", "-1", "0", "0", "10", "0", "0", "-10", "0", "0", "0"], "q": "0 1 -180 9766 -918864 -84667391 -28201300344 -8416763367758 -2661445469478720 -878785166425741292", "yuk": "1 92 40508 15805784 6398889276 2631769894092 1095690103233560 460102352983654760 194456787524058334524 82595946740582956156976", "gv2": null, "gv0": "920 50520 5853960 999820120 210541591520 50726392934600 13414062769202760 3797984131204286040 1133003384644484778480 352222594530382846825440", "gv1": "0 3 -1840 340009 1947267584 1647668876313 1015529214081408 546679951529049217 273876590223518607136 131454144000215093321340 61386446901999188135302512 28140489285817383735441804571 12733882267471101410430994977184 5708617617857487682966717948168761 2541598077099050548073520825079700192 1125727757478747039096578273505284757857 496643774701201827963718706948444720097344 218440805792652989950697635117637496847455342 95850094966095309354494328888252686569873586448", "spectrum":[{"re":"-11/128-5/128*5^(1/2)","im":"0","approx_re":"-0.173284","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["5.6666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666667+3.876817960*I","-2.3333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333-1.938408980*I","133/90+760/3*lambda","-.168701507-.904590857*I","38/3","-16/3","361/90","-133/90-760/3*lambda","20","-10","22/3","-2.3333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333-1.938408980*I","40","-20","38/3","-3.6666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666667-3.876817960*I"],"monodromy_dm":["-9","-40","-6","-4","5","21","3","2","-30","-120","-17","-12","20","80","12","9"]},{"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","10","1","0","0","0","1","1"]},{"re":"-11/128+5/128*5^(1/2)","im":"0","approx_re":"0.001409","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["1.+.969204490*I","0","160/3*lambda",".93935734e-1","8/3","1","32/45","-160/3*lambda","0","0","1","0","10","0","8/3","1.-.969204490*I"],"monodromy_dm":["1","-7","-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":["1/4","3/4","5/4","7/4"],"monodromy":[],"monodromy_dm":[]}]}]}