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{"pols": "[X^4, -16*(2*X+1)^2*(8*X^2+8*X+3), 4096*(2*X+1)^2*(2*X+3)^2]", "text": "B-Incarnations:\nFibre product 81111- x 18--21, 4*11-- x 53211, \nDouble Octics: D.O.8, D.O.36, D.O.73, D.O.249, D.O.258,D.O.265\n", "degz": 2, "h3": null, "sol": "1 48 5904 940800 169520400 32825979648 6664766701824 1399343499620352 301253424381795600 66124078946867884800", "n_discr_factors": "1", "c3": null, "operator": "4 2 0 0 0 0 1 -48 -320 -832 -1024 -512 36864 196608 360448 262144 65536", "new_number": "2.17", "id": 8, "operator_tex": "\\theta^4-2^{4} x(2\\theta+1)^2(8\\theta^2+8\\theta+3)+2^{12} x^{2}(2\\theta+1)^2(2\\theta+3)^2", "superseek": "32 1440", "discriminant": "2 1 -512 65536", "aesz": "111", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "d8535e0f3d0bfd4ebcc9c042df43c218", "dim_h": null, "inst": " 32 -96 1440 19704 -14496 15837984 163296032 7479253880 329193772800 7032903948768", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": 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"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":"1/256","im":"0","approx_re":"0.00390625","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":["-2/3+96*lambda","48*lambda","-5/72+4*lambda","-.13526746e-1","-2/3","2/3","-1/36","-5/72-4*lambda","-8","0","2/3","-48*lambda","-16","-8","-2/3","-2/3-96*lambda"],"monodromy_dm":["-3","0","0","-1","-1","1","1/4","0","0","0","1","0","4","0","-1","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": "[X^4, -12*(3*X+1)*(3*X+2)*(8*X^2+8*X+3), 2304*(3*X+1)*(3*X+2)*(3*X+4)*(3*X+5)]", "text": "", "degz": 2, "h3": null, "sol": "1 72 14760 3951360 1198751400 391176257472 133901221918464 47411323466158080 17215474536402765480 6374166727892926248000", "n_discr_factors": "1", "c3": null, "operator": "4 2 0 0 0 0 1 -72 -516 -1380 -1728 -864 92160 539136 1016064 746496 186624", "new_number": "2.18", "id": 9, "operator_tex": "\\theta^4-2^{2} 3 x(3\\theta+1)(3\\theta+2)(8\\theta^2+8\\theta+3)+2^{8} 3^{2} x^{2}(3\\theta+1)(3\\theta+2)(3\\theta+4)(3\\theta+5)", "superseek": "36 8076", "discriminant": "2 1 -864 186624", "aesz": "110", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "5060b638cac581d5f0f9dd7f40d90e6c", "dim_h": null, "inst": " 36 -144 8076 -57996 6960672 -12143856 10041274764 98875091268 19944340019760 482716439753472", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "A_{n}=\\dbinom{2n}{n}\\dbinom{3n}{n}\\sum_{k=0}^{n}4^{n-k}\\dbinom{2k}{k}^2\\dbinom{2n-2k}{n-k}", "n_sing_rational": "2", "n_sing": "2", "laurent": null, "discriminant_tex": "(432z-1)^2", "discr_factors": "186624, (z-1/432)^2", "dm_basis": ["3/2-24*lambda", "0", "1/2", "1", "1", "0", "-1", "0", "6", "-12", "0", "0", "12", "0", "0", "0"], "q": "0 1 -228 39006 -5773648 784430637 -100616704632 12381829002386 -1476632870320704 171818463840250374", "yuk": "1 36 -1116 218088 -3712860 870084036 -2622855960 3444157244088 50624043016356 14539423874623128", "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":"1/432","im":"0","approx_re":"0.00231481481481","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":["-1/2+24*lambda","12*lambda","-1/8+2*lambda","-.1127229e-2","-1","1/2","-1/12","-1/8-2*lambda","-6","0","1/2","-12*lambda","-12","-6","-1","-1/2-24*lambda"],"monodromy_dm":["-3","1","0","-1","-1","1","1/4","0","0","0","1","0","3","0","-3/4","1"]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/3","2/3","4/3","5/3"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -48*(6*X+1)*(6*X+5)*(8*X^2+8*X+3), 36864*(6*X+1)*(6*X+5)*(6*X+7)*(6*X+11)]", "text": "", "degz": 2, "h3": null, "sol": "1 720 2273040 9605756160 46308725583120 240786868817214720 1315120893663838060800 7435757049324458453913600 43135804200964730778389552400 255247151546465636305978354924800", "n_discr_factors": "1", "c3": null, "operator": "4 2 0 0 0 0 1 -720 -7104 -20928 -27648 -13824 14192640 122093568 252149760 191102976 47775744", "new_number": "2.19", "id": 10, "operator_tex": "\\theta^4-2^{4} 3 x(6\\theta+1)(6\\theta+5)(8\\theta^2+8\\theta+3)+2^{12} 3^{2} x^{2}(6\\theta+1)(6\\theta+5)(6\\theta+7)(6\\theta+11)", "superseek": "-288 -96055968", "discriminant": "2 1 -13824 47775744", "aesz": "112", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "9a988f0cb0ca922885043cdadf98dd79", "dim_h": null, "inst": " -288 162504 -96055968 106571782296 -135291308081760 202640200069218600 -331236087493837278240 582773446380820280519448 -1081357063366546927831256832 2094880412576670910662188706840", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "A_{n}=\\dbinom{3n}{n}\\dbinom{6n}{3n}\\sum_{k=0}^{n}4^{n-k}\\dbinom{2k}{k}^2\\dbinom{2n-2k}{n-k}", "n_sing_rational": "2", "n_sing": "2", "laurent": null, "discriminant_tex": "(6912z-1)^2", "discr_factors": "47775744, (z-1/6912)^2", "dm_basis": ["7/6+96920449/100000000*I", "-4/3", "1/2", "1", "5/3", "0", "-1", "0", "2", "-4", "0", "0", "4", "0", "0", "0"], "q": "0 1 -4224 15018336 -49622038528 157618249425456 -488487774278467584 1488716329019728343552 -4482147177792048362422272 13370796738913860479184841368", "yuk": "1 -288 1299744 -2593511424 6820595366688 -16911413510220288 43770283212359006208 -113613978010386186436608 298380004546986804221324064 -788309299194212710391579741952", "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":"1/6912","im":"0","approx_re":"0.000144675925926","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":["-.16666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666667-.969204490*I","-100*lambda","-35/72-250/3*lambda","-.234839336","-5/3","1/6","-25/36","-35/72+250/3*lambda","-2","0","1/6","100*lambda","-4","-2","-5/3","-.16666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666667+.969204490*I"],"monodromy_dm":["-3","3","0","-1","-1","1","1/4","0","0","0","1","0","1","0","-1/4","1"]},{"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, -4*(2*X+1)^2*(7*X^2+7*X+2), -128*(2*X+1)^2*(2*X+3)^2]", "text": "Hadamard product $A \\ast a$, where $A$ is (:case 2.1.1)", "degz": 2, "h3": "24", "sol": "1 8 360 22400 1695400 143011008 12963734784 1236284375040 122432502277800 12483618390900800", "n_discr_factors": "2", "c3": "-120", "operator": "4 2 0 0 0 0 1 -8 -60 -172 -224 -112 -1152 -6144 -11264 -8192 -2048", "new_number": "2.1", "id": 11, "operator_tex": "\\theta^4-2^{2} x(2\\theta+1)^2(7\\theta^2+7\\theta+2)-2^{7} x^{2}(2\\theta+1)^2(2\\theta+3)^2", "superseek": "12 3204", "discriminant": "2 1 -112 -2048", "aesz": "45", "n_sing_complex": "0", "inst_int": "", "c2h": "72", "hash": "cdf289f6febf84eb577a238542a57457", "dim_h": "10", "inst": " 12 163 3204 107582 4203360 190881921 9458941572 502640311894 28123887334416 1640055889524440", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "A_{n}=\\dbinom{2n}{n}^2\\sum_{k=0}^{n}\\dbinom{n}{k}^3", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "-(16z+1)(128z-1)", "discr_factors": "-2048, z+1/16, z-1/128", "dm_basis": ["-120*lambda", "7", "1", "1", "-3", "-12", "-1", "0", "0", "24", "0", "0", "-24", "0", "0", "0"], "q": "0 1 -28 -34 1488 -200915 -6984840 -407799534 -24230964160 -1498995588346", "yuk": "1 12 1316 86520 6886564 525420012 41230582760 3244416959208 257351846576292 20502313866875784", "gv2": null, "gv0": null, "gv1": null, 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\\times P^2$", "degz": 2, "h3": "18", "sol": "1 12 900 94080 11988900 1704214512 260453217024 41886697881600 6996546610936740 1203384096358158000", "n_discr_factors": "2", "c3": "-162", "operator": "4 2 0 0 0 0 1 -12 -96 -285 -378 -189 -2880 -16848 -31752 -23328 -5832", "new_number": "2.2", "id": 22, "operator_tex": "\\theta^4-3 x(3\\theta+1)(3\\theta+2)(7\\theta^2+7\\theta+2)-2^{3} 3^{2} x^{2}(3\\theta+1)(3\\theta+2)(3\\theta+4)(3\\theta+5)", "superseek": "21 15894", "discriminant": "2 1 -189 -5832", "aesz": "15", "n_sing_complex": "0", "inst_int": "", "c2h": "72", "hash": "c8053e0e9c05ef468263fafd5e3fc764", "dim_h": "9", "inst": " 21 480 15894 894075 58703151 4482271260 373469554929 33373998306933 3140252369423073 307963083118697496", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "A_{n}=\\dbinom{2n}{n}\\dbinom{3n}{n}\\sum_{k=0}^{n}\\dbinom{n}{k}^3", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "-(27z+1)(216z-1)", "discr_factors": "-5832, z-1/216, z+1/27", "dm_basis": ["-162*lambda", "6", "1", "1", "-3", "-9", "-1", "0", "0", "18", "0", "0", "-18", "0", "0", "0"], "q": "0 1 -48 -18 7976 -1697115 -90056880 -9049527514 -907472920848 -94324071435966", "yuk": "1 21 3861 429159 57224661 7337893896 968171025159 128100057340668 17087487190374357 2289243977309849376", "gv2": null, "gv0": null, "gv1": null, 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null, "sol": "1 208 107280 70739200 52362595600 41461910961408 34312891463794944 29296232075376414720 25600334691287493680400 22775767478675463632723200", "n_discr_factors": "1", "c3": null, "operator": "4 2 0 0 0 0 1 -208 -1344 -3392 -4096 -2048 589824 3145728 5767168 4194304 1048576", "new_number": "2.31", "id": 24, "operator_tex": "\\theta^4-2^{4} x(2\\theta+1)^2(32\\theta^2+32\\theta+13)+2^{16} x^{2}(2\\theta+1)^2(2\\theta+3)^2", "superseek": "96 -12064", "discriminant": "2 1 -2048 1048576", "aesz": "7**", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "2c494088fc85599f73fb344776dbbb28", "dim_h": null, "inst": " 96 -3560 -12064 1941800 -489007584 15548813880 -394413008544 -171180770262104 16579352954127616 -1400497594980275320", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "A_{n}=\\dbinom{2n}{n}^2 64^{n}\\sum_{k=0}^{n}(-1)^{k}\\dbinom{-3/4}{k}\\dbinom{-1/4}{n-k}^2", "n_sing_rational": "2", "n_sing": "2", "laurent": null, "discriminant_tex": "(1024z-1)^2", "discr_factors": "1048576, (z-1/1024)^2", "dm_basis": ["4/3-1708656527755053726527184603581775358292629291158824225586117747415508815310392346494291960809911989/1296284848710416017198988117968146871699058960076991381465223285947803281706700313960088400294610326*I", "4/3", "1/2", "1", "-2/3", "0", "-1", "0", "4", "-8", "0", "0", "8", "0", "0", "0"], "q": "0 1 -512 184160 -54147072 13983267376 -3286874001408 718480223310336 -148143858554765312 29102163801683888792", "yuk": "1 96 -28384 -325632 124246816 -61125947904 3358543443968 -135283661930496 -87644554249950432 12086348303558706432", "gv2": null, "gv0": null, "gv1": null, 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370278354600 494087772290112 689377183045334784 992589121714676428800 1462960664781344542705320 2195516997392906825183832000", "n_discr_factors": "1", "c3": null, "operator": "4 2 0 0 0 0 1 -312 -2172 -5628 -6912 -3456 1474560 8626176 16257024 11943936 2985984", "new_number": "2.32", "id": 25, "operator_tex": "\\theta^4-2^{2} 3 x(3\\theta+1)(3\\theta+2)(32\\theta^2+32\\theta+13)+2^{12} 3^{2} x^{2}(3\\theta+1)(3\\theta+2)(3\\theta+4)(3\\theta+5)", "superseek": "60 307860", "discriminant": "2 1 -3456 2985984", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "c2f30268af49d0bdc6a36f8b0fce3367", "dim_h": null, "inst": " 60 -7635 307860 -44194980 3687387360 -529261811985 59851829292180 -8702630989366980 1145485558395197520 -170278663020690678360", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "2", "laurent": null, "discriminant_tex": "(1728z-1)^2", "discr_factors": "2985984, (z-1/1728)^2", "dm_basis": ["9/8-872284041/1000000000*I", "3/4", "1/2", "1", "-1/4", "0", "-1", "0", "3", "-6", "0", "0", "6", "0", "0", "0"], "q": "0 1 -924 641502 -384412592 211122136365 -109362688829064 54312562744453394 -26126834906167052736 12257965850615612177670", "yuk": "1 60 -61020 8312280 -2828539740 460923420060 -114320543137560 20529177447217800 -4455747069384433500 835058972070107304360", "gv2": null, "gv0": null, "gv1": null, 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"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*(6*X+1)*(6*X+5)*(32*X^2+32*X+13), 589824*(6*X+1)*(6*X+5)*(6*X+7)*(6*X+11)]", "text": "This is operator \"2.34\" from ...", "degz": 2, "h3": null, "sol": "1 3120 41302800 722261379840 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{"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 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"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, -144*(6*X+1)*(6*X+5)*(72*X^2+72*X+31), 26873856*(6*X+1)*(6*X+5)*(6*X+7)*(6*X+11)]", "text": "This is operator \"2.38\" from ...", "degz": 2, "h3": null, "sol": "1 22320 2060205840 248752033770240 33839074380496104720 4926073728361876482712320 749194858233182245286174572800 117487375958799957656057364367257600 18846055960583055120397409171606683491600 3076205051128442319770710298722602167292076800", "n_discr_factors": "1", "c3": null, "operator": "4 2 0 0 0 0 1 -22320 -212544 -585792 -746496 -373248 10346434560 89006211072 183817175040 139314069504 34828517376", "new_number": "2.38", "id": 31, "operator_tex": "\\theta^4-2^{4} 3^{2} x(6\\theta+1)(6\\theta+5)(72\\theta^2+72\\theta+31)+2^{12} 3^{8} x^{2}(6\\theta+1)(6\\theta+5)(6\\theta+7)(6\\theta+11)", "superseek": "-41184 -5124430612320", "discriminant": "2 1 -373248 34828517376", "aesz": "61", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "191cd9ad5f43862072f3be6811803748", "dim_h": null, "inst": " -41184 251271360 -5124430612320 160031225395327320 -6251395923736354968480 281719052768887766413067712 -14011445466133465751932493202912 749010431161713344489247392127781848 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"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","-1","1","0","0","0","1","1"]},{"re":"1/186624","im":"0","approx_re":"5.35836762689e-06","approx_im":"0.0","exponents":["0","1/6","5/6","1"],"monodromy":["25/48+62*lambda","23/32+31*lambda","-23/1152+31/12*lambda",".598529843","-1/24","47/48","-1/576","-23/1152-31/12*lambda","-1/2","3/4","47/48","23/32-31*lambda","-1","-1/2","-1/24","25/48-62*lambda"],"monodromy_dm":["0","0","0","-1","-1","1","1","0","0","0","1","0","1","0","-1","1"]},{"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, -25000*X^4-50000*X^3-58750*X^2-33750*X-7380, 62500*(5*X+4)*(5*X+6)*(10*X+9)*(10*X+11)]", "text": "Operator equivalent to $\\hat{1}$ of AESZ", "degz": 2, "h3": null, "sol": "1 7380 71382150 753157832000 8295076883047500 93726316432903124880 1077149095096618172301400 12529720486181268162877032000 147074411811887111318222704803750 1738540308895317125093331817556175000", "n_discr_factors": "1", "c3": null, "operator": "4 2 0 0 0 0 1 -7380 -33750 -58750 -50000 -25000 148500000 609375000 929687500 625000000 156250000", "new_number": "2.39", "id": 32, "operator_tex": "\\theta^4-2 5 x\\left(2500\\theta^4+5000\\theta^3+5875\\theta^2+3375\\theta+738\\right)+2^{2} 5^{6} x^{2}(5\\theta+4)(5\\theta+6)(10\\theta+9)(10\\theta+11)", "superseek": "-2450 -623291900", "discriminant": "2 1 -25000 156250000", "aesz": "~80,~81", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "a4500006693bca99ed7ce6d889944382", "dim_h": null, "inst": " -2450 -1825075/2 -623291900 -559511912750 -584671005670010 -673451164806825125 -830084686854071771850 -1075470806925727201508750 -1447735232516675963825615000 -4017525496970769764539679543535/2", "cleanlist": "True", 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10240000000000", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "43d26d7aa358d5634e12c133ddc42a01", "dim_h": null, "inst": " -791200 -41486886600 -4288711075194400 -585926703697412494000 -93381074165698184340671200 -16421870367225302857764612297000 -3092357851211380948661702496840925600 -612347664575452201470599184003859731790000 -126021073706771913403503319306672564968118240000 -26737673346377145201494037670832279422104903618584600", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "2", "laurent": null, "discriminant_tex": "(3200000z-1)^2", "discr_factors": "10240000000000, (z-1/3200000)^2", "dm_basis": ["cy[DM_basis]"], "q": "0 1 -1180480 712317218400 -305628937322752000 106814581184582290110000 -32562911531924497607789316096 9005113062419133863092531588252160 -2315089785174434657443087105496085299200 562384780333848834709856243777406772912143000", "yuk": "1 -791200 -331895884000 -115795199031040000 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equivalent to $\\hat{4}$", "degz": 2, "h3": null, "sol": "1 1746 3951990 9740271348 25043989159350 66042700202991996 177115354806794088636 480730042522583271956520 1316595143051828406693466038 3631103407214519008442157554220", "n_discr_factors": "1", "c3": null, "operator": "4 2 0 0 0 0 1 -1746 -7938 -13770 -11664 -5832 8266860 33539832 50782140 34012224 8503056", "new_number": "2.41", "id": 35, "operator_tex": "\\theta^4-2 3^{2} x\\left(324\\theta^4+648\\theta^3+765\\theta^2+441\\theta+97\\right)+2^{2} 3^{10} x^{2}(\\theta+1)^2(6\\theta+5)(6\\theta+7)", "superseek": "-522 -9879192", "discriminant": "2 1 -5832 8503056", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "73d9f98b2c49f1c35df531f020cf1721", "dim_h": null, "inst": " -522 -105291/2 -9879192 -2420127936 -689420749716 -216357353050266 -72634690919277180 -25626633195551666544 -9392840331059964324510 -3548231463433108407572043", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", 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-6912 -3456 2944656 11860992 17874432 11943936 2985984", "new_number": "2.42", "id": 36, "operator_tex": "\\theta^4-2^{2} 3 x\\left(288\\theta^4+576\\theta^3+682\\theta^2+394\\theta+87\\right)+2^{4} 3^{2} x^{2}(12\\theta+11)^2(12\\theta+13)^2", "superseek": "-288 -2339616", "discriminant": "2 1 -3456 2985984", "aesz": "~98", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "acfee9d4b5fefd1a945cfa6b1bc61373", "dim_h": null, "inst": " -288 -19260 -2339616 -369882612 -67925445408 -13734698150652 -2970077356698912 -674863643068399476 -159284190765874022688 -38744013465690133817340", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "2", "laurent": null, "discriminant_tex": "(1728z-1)^2", "discr_factors": "2985984, (z-1/1728)^2", "dm_basis": ["cy[DM_basis]"], "q": "0 1 -552 110124 -11982784 856080078 -51663236832 1031263062200 -385043380763136 -82129565005671195", "yuk": "1 -288 -154368 -63169920 -23672641536 -8490680676288 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97242114301200 360178063906003200 1356749640538778886400 5172512382206532116582400 19898163319859501951876144400 77083664438817200822729212627200", "n_discr_factors": "1", "c3": null, "operator": "4 2 0 0 0 0 1 -2448 -11136 -19328 -16384 -8192 16257024 66060288 100139008 67108864 16777216", "new_number": "2.43", "id": 37, "operator_tex": "\\theta^4-2^{4} x\\left(512\\theta^4+1024\\theta^3+1208\\theta^2+696\\theta+153\\right)+2^{12} x^{2}(8\\theta+7)^2(8\\theta+9)^2", "superseek": "-736 -26911072", "discriminant": "2 1 -8192 16777216", "aesz": "~77, ~78,~97", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "3d2cd06eccf32145816b35cb63878900", "dim_h": null, "inst": " -736 -104512 -26911072 -9061573696 -3547993303456 -1530399290794816 -706174923240052704 -342448719852185551936 -172519195336759383650560 -89575561850786528483940032", "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": ["cy[DM_basis]"], "q": "0 1 -1344 706656 -215652352 46108515888 -7894967838720 1022037674254848 -174681633392295936 -10758058868434117992", "yuk": "1 -736 -836832 -726599680 -579941553376 -443499162932736 -330566247539116032 -242217998671338078208 -175333744564898944144608 -125766493400497591407857920", "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":"1/4096","im":"0","approx_re":"0.000244140625","approx_im":"0.0","exponents":["0","-1/2","1","3/2"],"monodromy":["2/3*2^(1/2)","-.657917825*I","1/36*2^(1/2)","0","0","-2/3*2^(1/2)","0","1/36*2^(1/2)","2*2^(1/2)","0","-2/3*2^(1/2)",".657917825*I","0","2*2^(1/2)","0","2/3*2^(1/2)"],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["7/8","7/8","9/8","9/8"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -524288*X^4-1048576*X^3-1224704*X^2-700416*X-151920, 67108864*(4*X+3)*(4*X+5)*(8*X+7)*(8*X+9)]", "text": "Operator equivalent to $\\hat{7}$", "degz": 2, "h3": null, "sol": "1 151920 30692221200 6779721385465600 1564471951791288368400 370493832457036401465800448 89258116706936665170335023571200 21767755998162599072984961685675929600 5357233967257499355463258918065806253104400 1327823893497481863487305564306244762320744441600", "n_discr_factors": "1", "c3": null, "operator": "4 2 0 0 0 0 1 -151920 -700416 -1224704 -1048576 -524288 63417876480 264140488704 406948151296 274877906944 68719476736", "new_number": "2.44", "id": 38, "operator_tex": "\\theta^4-2^{4} x\\left(32768\\theta^4+65536\\theta^3+76544\\theta^2+43776\\theta+9495\\right)+2^{26} x^{2}(4\\theta+3)(4\\theta+5)(8\\theta+7)(8\\theta+9)", "superseek": "-57760 -3869123234080", "discriminant": "2 1 -524288 68719476736", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "db68f352287fb91ca91e65eb38318ac4", "dim_h": null, "inst": " -57760 -354010600 -3869123234080 -56296618019665040 -953499788550226132960 -17813617123936487275117000 -356229909523606259341010401440 -7489549705807505315397189724146320 -163626381743508013909772817434163055360 -3685030185299576694719376172259466214804600", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "2", "laurent": null, "discriminant_tex": "(262144z-1)^2", "discr_factors": "68719476736, (z-1/262144)^2", "dm_basis": ["cy[DM_basis]"], "q": "0 1 -92736 4038056544 -117107769501696 2638127284267525680 -50014687815673718581248 836030055713573243974320640 -12703406069017803154088700542976 178838007104675528418336611065199256", "yuk": "1 -57760 -2832142560 -104466327377920 -3602983556090705120 -119187473568778266677760 -3847741298770385720584734720 -122186858966596946953966567751680 -3834649449373442725086344694853620960 -119283632291017342140224384013971194735360", "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":"1/262144","im":"0","approx_re":"3.81469726562e-06","approx_im":"0.0","exponents":["0","-1/2","1","3/2"],"monodromy":["1.355287997","-2.055993202*I","-.591710883","0","0","-1.355287997","0","-.591710883","2^(1/2)","0","-1.355287997","2.055993202*I","0","2^(1/2)","0","1.355287997"],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["3/4","7/8","9/8","5/4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -93312*X^4-186624*X^3-218376*X^2-125064*X-27180, 944784*(4*X+3)*(4*X+5)*(12*X+11)*(12*X+13)]", "text": "Operator equivalent to $\\hat{8}$", "degz": 2, "h3": null, "sol": "1 27180 978471900 38487760088400 1581137831289447900 66654404951318519548752 2858362029664386414591517200 124076717229240558940488795806400 5435193332731790102697615748399911900 239776279063575461111567904104639807816400", "n_discr_factors": "1", "c3": null, "operator": "4 2 0 0 0 0 1 -27180 -125064 -218376 -186624 -93312 2026561680 8404798464 12909528576 8707129344 2176782336", "new_number": "2.45", "id": 39, "operator_tex": "\\theta^4-2^{2} 3^{2} x\\left(2592\\theta^4+5184\\theta^3+6066\\theta^2+3474\\theta+755\\right)+2^{4} 3^{10} x^{2}(4\\theta+3)(4\\theta+5)(12\\theta+11)(12\\theta+13)", "superseek": "-10080 -24400330080", "discriminant": "2 1 -93312 2176782336", "aesz": "~82", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "11afa89027677e0616228cad62a9f990", "dim_h": null, "inst": " -10080 -11338740 -24400330080 -69157402598340 -228492096441648480 -832633261381593237300 -3247929059465910369725280 -13320222474220854131715112260 -56766484061340352943587658383200 -249381504208512964566809294280601140", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "2", "laurent": null, "discriminant_tex": "(46656z-1)^2", "discr_factors": "2176782336, (z-1/46656)^2", "dm_basis": ["cy[DM_basis]"], "q": "0 1 -16344 123097644 -614114232384 2383466617921230 -7821147556235151648 22735736283182442819768 -60473754046179889792943616 149467076765156908624259683557", "yuk": "1 -10080 -90720000 -658808922240 -4426073857013760 -28561512055206070080 -179848784459083038888960 -1114039667396807256815781120 -6819953906801081741511994490880 -41382766880717117295876061770275040", "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":"1/46656","im":"0","approx_re":"2.14334705075e-05","approx_im":"0.0","exponents":["0","-1/2","1","3/2"],"monodromy":["5/8*3^(1/2)","-1.175097994*I","-.99232078e-1","0","0","-1.082531755","0","-.99232078e-1","3^(1/2)","0","-1.082531755","1.175097994*I","0","3^(1/2)","0","5/8*3^(1/2)"],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["3/4","11/12","13/12","5/4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -23887872*X^4-47775744*X^3-55655424*X^2-31767552*X-6870384, 247669456896*(4*X+3)*(4*X+5)*(6*X+5)*(6*X+7)]", "text": "Operator equivalent to $\\hat{9}$", "degz": 2, "h3": null, "sol": "1 6870384 63135105483024 634962415293388429056 6673257595142837863377354000 71986102406989118904362479364208384 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"(16384z-1)^2", "discr_factors": "268435456, (z-1/16384)^2", "dm_basis": ["cy[DM_basis]"], "q": "0 1 -5696 14731872 -25158641664 33504667231792 -37915203736676352 38163064333720814080 -35396658050856552890368 30499890168434563551328920", "yuk": "1 -3488 -11251936 -30852552704 -77543336129760 -187501744589951488 -442274176720152856576 -1026300761020352658341888 -2353628981095692850840556768 -5350063041231453839341901122304", "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":"1/16384","im":"0","approx_re":"6.103515625e-05","approx_im":"0.0","exponents":["0","-1/2","1","3/2"],"monodromy":["11/12","-152*lambda","23/288","0","0","-11/12","0","23/288","2","0","-11/12","152*lambda","0","2","0","11/12"],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["3/4","1","1","5/4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -13824*X^4-27648*X^3-32520*X^2-18696*X-4092, 144*(24*X+19)*(24*X+23)*(24*X+25)*(24*X+29)]", "text": "Operator equivalent to $\\hat{11}$", "degz": 2, "h3": null, "sol": "1 4092 21900060 127808119824 778493560064220 4864445835281624592 30915154660467325392144 198862416703795769079629760 1290800054231513804581286528988 8437496176936232602005911969147280", "n_discr_factors": "1", "c3": null, "operator": "4 2 0 0 0 0 1 -4092 -18696 -32520 -27648 -13824 45622800 186789888 284497920 191102976 47775744", "new_number": "2.48", "id": 42, "operator_tex": "\\theta^4-2^{2} 3 x\\left(1152\\theta^4+2304\\theta^3+2710\\theta^2+1558\\theta+341\\right)+2^{4} 3^{2} x^{2}(24\\theta+19)(24\\theta+23)(24\\theta+25)(24\\theta+29)", "superseek": "-1344 -109320512", "discriminant": "2 1 -13824 47775744", "aesz": "~94", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "892e497a83d12667b7f189a3d743fb7c", "dim_h": null, "inst": " -1344 -278040 -109320512 -56290146024 -33748229589312 -22302392373176216 -15771533154433137984 -11723446028913912315624 -9054198967017255005869376 -7207637261805347748730595736", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "2", "laurent": null, "discriminant_tex": "(6912z-1)^2", "discr_factors": "47775744, (z-1/6912)^2", "dm_basis": ["cy[DM_basis]"], "q": "0 1 -2328 2278188 -1383422528 625233942222 -233196156074016 74363982398450360 -22369416215841486336 5254730843664863999205", "yuk": "1 -1344 -2225664 -2951655168 -3602571571200 -4218528698665344 -4817316755559942144 -5409635871970566329856 -6002404366807525677170688 -6600511046955578902230430272", "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":"1/6912","im":"0","approx_re":"0.000144675925926","approx_im":"0.0","exponents":["0","-1/2","1","3/2"],"monodromy":[".918558654","-.664735808*I",".63788795e-1","0","0","-3/8*2^(1/2)*3^(1/2)","0",".63788795e-1","6^(1/2)","0","-3/8*2^(1/2)*3^(1/2)",".664735808*I","0","6^(1/2)","0",".918558654"],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["19/24","23/24","25/24","29/24"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -221184*X^4-442368*X^3-515712*X^2-294528*X-63600, 36864*(24*X+17)*(24*X+23)*(24*X+25)*(24*X+31)]", "text": "Operator equivalent to $\\hat{12}$", "degz": 2, "h3": null, "sol": "1 63600 5412963600 504140776339200 49063316029156400400 4900834313134236868495104 498038988869289806296472674560 51235571015156106280999811512627200 5319255578266046598386345996291701808400 556172914124215399621824817465692077732140800", "n_discr_factors": "1", "c3": null, "operator": "4 2 0 0 0 0 1 -63600 -294528 -515712 -442368 -221184 11170713600 46798995456 72321859584 48922361856 12230590464", "new_number": "2.49", "id": 43, "operator_tex": "\\theta^4-2^{4} 3 x\\left(4608\\theta^4+9216\\theta^3+10744\\theta^2+6136\\theta+1325\\right)+2^{12} 3^{2} x^{2}(24\\theta+17)(24\\theta+23)(24\\theta+25)(24\\theta+31)", "superseek": "-26400 -230398034080", "discriminant": "2 1 -221184 12230590464", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "ffdc338b55d1f4e1f989f4359b06df6c", "dim_h": null, "inst": " -26400 -52511160 -230398034080 -1287524740195200 -8504689433002312800 -61708584266076354876760 -480359168720881336785453600 -3929326831161598997422750327680 -33415396076795648446867221703540480 -292926267946968919350834362619359155560", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "2", "laurent": null, "discriminant_tex": "(110592z-1)^2", "discr_factors": "12230590464, (z-1/110592)^2", "dm_basis": ["cy[DM_basis]"], "q": "0 1 -40128 799887456 -11209830459392 127623510290284080 -1268317275250676520960 11455455573164588853879296 -96422158858235765058842787840 768678921354095883869980973128344", "yuk": "1 -26400 -420115680 -6220746946560 -82401583792608480 -1063086179125289126400 -13329054201478713820416000 -164763194871262298517410611200 -2011815337554738769082031960380640 -24359823739984027717766210842627956480", "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":"1/110592","im":"0","approx_re":"9.04224537037e-06","approx_im":"0.0","exponents":["0","-1/2","1","3/2"],"monodromy":["1.001734607","-1.096529708*I","-.2455232e-2","0","0","-1.001734607","0","-.2455232e-2","2^(1/2)","0","-1.001734607","1.096529708*I","0","2^(1/2)","0","1.001734607"],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["17/24","23/24","25/24","31/24"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -12*(6*X+1)*(6*X+5)*(7*X^2+7*X+2), -1152*(6*X+1)*(6*X+5)*(6*X+7)*(6*X+11)]", "text": "Hadamard product D*a", "degz": 2, "h3": "6", "sol": "1 120 138600 228708480 463140798120 1049021939085120 2558060804992492800 6569302147162140672000 17530836228424587378796200 48188316359473969642904740800", "n_discr_factors": "2", "c3": "-366", "operator": "4 2 0 0 0 0 1 -120 -1284 -4308 -6048 -3024 -443520 -3815424 -7879680 -5971968 -1492992", "new_number": "2.4", "id": 44, "operator_tex": "\\theta^4-2^{2} 3 x(6\\theta+1)(6\\theta+5)(7\\theta^2+7\\theta+2)-2^{7} 3^{2} x^{2}(6\\theta+1)(6\\theta+5)(6\\theta+7)(6\\theta+11)", "superseek": "372 71562236", "discriminant": "2 1 -3024 -1492992", "aesz": "62", "n_sing_complex": "0", "inst_int": "", "c2h": "72", "hash": "07a3fd7577f878056e765831c6820f3d", "dim_h": "7", "inst": " 372 136182 71562236 63364481358 65860679690400 79731159343319570 105274670715264426492 149145928602499979170278 222456686052033401879944688 345847268611005007252536310320", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "A_{n}=\\frac{(6n)!}{(3n)!(2n)!n!}\\sum_{k=0}^{n}\\dbinom{n}{k}^3", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "-(432z+1)(3456z-1)", "discr_factors": "-1492992, z+1/432, z-1/3456", "dm_basis": ["-366*lambda", "4", "1", "1", "-3", "-3", "-1", "0", "0", "6", "0", "0", "-6", "0", "0", "0"], "q": "0 1 -804 60894 33466160 -125049218259 -73798244967672 -137218105849556206 -217758218544315797568 -356855888534213849342202", "yuk": "1 372 1089828 1932180744 4055327896740 8232584961300372 17221930420090297320 36109212055335698287128 76362715444484044663079076 162170924131932349972411858296", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/432","im":"0","approx_re":"-0.00231481481481","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["4.+3.547288434*I","-3/2-366*lambda","1.7500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+2.069251586*I",".298604603-366*lambda","7","-5/2","49/12","-1.7500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000-2.069251586*I","6","-3","9/2","-3/2-366*lambda","12","-6","7","-2.-3.547288434*I"],"monodromy_dm":["-5","-18","-3","-2","3","10","3/2","1","-12","-36","-5","-4","9","27","9/2","4"]},{"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","6","1","0","0","0","1","1"]},{"re":"1/3456","im":"0","approx_re":"0.000289351851852","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["1+366*lambda","0","183*lambda",".524302301","3","1","3/2","-183*lambda","0","0","1","0","6","0","3","1-366*lambda"],"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":["1/6","5/6","7/6","11/6"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -1492992*X^4-2985984*X^3-3462912*X^2-1969920*X-421488, 61917364224*(X+1)^2*(3*X+2)*(3*X+4)]", "text": "Operator equivalent to $\\hat{13}$ of AESZ", "degz": 2, "h3": null, "sol": "1 421488 241251334416 151434902650832640 99396938275247309913360 66982705221295861052979103488 45930793402209870606388009729630464 31886179044933974315938584958002702348288 22340825763852816148179255097826365737157270800 15765005459624533462430649410473718251082308459411200", "n_discr_factors": "1", "c3": null, "operator": "4 2 0 0 0 0 1 -421488 -1969920 -3462912 -2985984 -1492992 495338913792 2105190383616 3281620303872 2229025112064 557256278016", "new_number": "2.50", "id": 45, "operator_tex": "\\theta^4-2^{4} 3^{2} x\\left(10368\\theta^4+20736\\theta^3+24048\\theta^2+13680\\theta+2927\\right)+2^{20} 3^{10} x^{2}(\\theta+1)^2(3\\theta+2)(3\\theta+4)", "superseek": "-201888 -40177844666400", "discriminant": "2 1 -1492992 557256278016", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "5309f0b5a4362f22faafad07a0eb1bb8", "dim_h": null, "inst": " -201888 -1567499400 -40177844666400 -988883543512335600 -35724019937142805037280 -1195288040031739680397888488 -49312571274502247527094531355552 -1905860636049170652686484217667001072 -84374002677576442597036996400924744725248 -3545810526263846884467644423184211250751003480", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "2", "laurent": null, "discriminant_tex": "(746496z-1)^2", "discr_factors": "557256278016, (z-1/746496)^2", "dm_basis": ["cy[DM_basis]"], "q": "0 1 -283968 43688105568 -5012704879896576 485518167363736868400 -42145587318746541132269568 3389377748957383965350280086016 -257686932189379034887694891704516608 18767233043532518749154918865211905653400", "yuk": "1 -201888 -12540197088 -1084801806194688 -63288546797329675488 -4465502492142850629861888 -258182216646856855780290103296 -16914211947154270901793424255156224 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8115450239232 197661638029770000 4939323290720374102272 125545467132215522356011264 3229945005723515366266945769472 83854302031408839697482462668004624 2192358351404405686911606811524026476800", "n_discr_factors": "1", "c3": null, "operator": "4 2 0 0 0 0 1 -16272 -74496 -129792 -110592 -55296 722534400 2972712960 4544004096 3057647616 764411904", "new_number": "2.51", "id": 46, "operator_tex": "\\theta^4-2^{4} 3 x\\left(1152\\theta^4+2304\\theta^3+2704\\theta^2+1552\\theta+339\\right)+2^{16} 3^{2} x^{2}(6\\theta+5)^2(6\\theta+7)^2", "superseek": "-5472 -6444589536", "discriminant": "2 1 -55296 764411904", "aesz": "~88,~89", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "02d09c6c320ab036e45834cf0d3951e7", "dim_h": null, "inst": " -5472 -4476528 -6444589536 -12228845295024 -27012506850929952 -65769234065535209904 -171356481979219041756768 -469285283914523702214769584 -1335325854497322666224363076864 -3916395562729225852578594898891728", "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": ["cy[DM_basis]"], "q": "0 1 -9408 38014560 -95305603072 175967420118576 -262791111112390656 332714240865107067392 -378185551721944620859392 367629071696971948082543256", "yuk": "1 -5472 -35817696 -174003922944 -782646134699232 -3376563356366249472 -14206154558329645074432 -58775273318872131322576896 -240274065364236918180096726240 -973452547928548223677734686956800", "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":"1/27648","im":"0","approx_re":"3.61689814815e-05","approx_im":"0.0","exponents":["0","-1/2","1","3/2"],"monodromy":["7/6","I*(-7/8-1/8*ln(2)^(1/2)-1/4/ln(2)^(1/2))","-13/72","0","0","-7/6","0","-13/72","2","0","-7/6","I*(7/8+1/8*ln(2)^(1/2)+1/4/ln(2)^(1/2))","0","2","0","7/6"],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["5/6","5/6","7/6","7/6"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -4*(2*X+1)^2*(5*X^2+5*X+2), 256*(2*X+1)*(X+1)^2*(2*X+3)]", "text": "Hadamard product $I \\ast \\alpha$\nA-Incarnation: diagonal subfamily of 1,1,1,1-intersection in $P^1 \\times P^1 \\times P^1 \\times \\P^1$\nB-Incarnations:\nFibre products: 62211- x 632--1, S62211\n", "degz": 2, "h3": "48", "sol": "1 8 168 5120 190120 7939008 357713664 16993726464 839358285480 42714450658880", "n_discr_factors": "2", "c3": "-128", "operator": "4 2 0 0 0 0 1 -8 -52 -132 -160 -80 768 3584 5888 4096 1024", "new_number": "2.52", "id": 47, "operator_tex": "\\theta^4-2^{2} x(2\\theta+1)^2(5\\theta^2+5\\theta+2)+2^{8} x^{2}(2\\theta+1)(\\theta+1)^2(2\\theta+3)", "superseek": "4 644/3", "discriminant": "2 1 -80 1024", "aesz": "16", "n_sing_complex": "0", "inst_int": "", "c2h": "96", "hash": "05af0662662bfbec63e3186c4f363313", "dim_h": "16", "inst": " 4 20 644/3 3072 52512 1027868 22083628 507552272 36850292240/3 309706589472", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "(64z-1)(16z-1)", "discr_factors": "1024, z-1/64, z-1/16", "dm_basis": ["-310145437/500000000*I", "12", "1", "1", "-4", "-24", "-1", "0", "0", "48", "0", "0", "-48", "0", "0", "0"], "q": "0 1 -20 222 -2704 21293 -307224 80402 -67101504 -1187407098", "yuk": "1 4 164 5800 196772 6564004 222025448 7574684408 259866960036 8954621020120", "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","48","1","0","0","0","1","1"]},{"re":"1/64","im":"0","approx_re":"0.015625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["1.+.620290874*I","0","32/3*lambda",".8015849e-2","4","1","1/3","-32/3*lambda","0","0","1","0","48","0","4","1.-.620290874*I"],"monodromy_dm":["1","-16","-1","-1","0","1","0","0","0","0","1","0","0","0","0","1"]},{"re":"1/16","im":"0","approx_re":"0.0625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["5+512*lambda","-1.-.620290874*I","1/3+128/3*lambda","-1/7*7^(5/8)*exp(-9/4)*Zeta(5)^(1/4)-64/3*lambda","16","-3","4/3","-1/3-128/3*lambda","48","-12","5","-1.-.620290874*I","192","-48","16","-3-512*lambda"],"monodromy_dm":["-7","-88","-5","-4","2","23","5/4","1","-48","-528","-29","-24","32","352","20","17"]},{"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, -2*(2*X+1)^2*(17*X^2+17*X+5), 4*(2*X+1)*(X+1)^2*(2*X+3)]", "text": "Hadamard product $I \\ast \\gamma$", "degz": 2, "h3": "24", "sol": "1 10 438 28900 2310070 206389260 19829802300 2005342876680 210655032909750 22787749078623100", "n_discr_factors": "1", "c3": "-116", "operator": "4 2 0 0 0 0 1 -10 -74 -210 -272 -136 12 56 92 64 16", "new_number": "2.53", "id": 48, "operator_tex": "\\theta^4-2 x(2\\theta+1)^2(17\\theta^2+17\\theta+5)+2^{2} x^{2}(2\\theta+1)(\\theta+1)^2(2\\theta+3)", "superseek": "14 10424/3", "discriminant": "2 1 -136 16", "aesz": "29", "n_sing_complex": "0", "inst_int": "", "c2h": "72", "hash": "92e8a038051b3fb8e0cc6ad6a52b8bfb", "dim_h": "10", "inst": " 14 303/2 10424/3 113664 4579068 632241922/3 10640861204 575106521678 98235955748510/3 1942800973152771", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "3", "laurent": null, "discriminant_tex": "1-136z+16z^2", "discr_factors": "16, 1/16-17/2*z+z^2", "dm_basis": ["-116*lambda", "7", "1", "1", "-3", "-12", "-1", "0", "0", "24", "0", "0", "-24", "0", "0", "0"], "q": "0 1 -34 303 -5396 -122185 -7247646 -411600019 -24878258760 -1565584028352", "yuk": "1 14 1226 93830 7275722 572383514 45521513426 3649815392986 294454546374858 23871337246981760", "gv2": null, "gv0": "336 3636 83392 2727936 109897632 5057935376 255380668896 13802556520272 785887645988080 46627223355666504", "gv1": "0 0 0 66 121056 29099400 4233172704 496392888006 51960605375840 5085222689866104 476714409804578496 43409205232304770480 3872757884182127506368 340410931084603171622976 29592091293200835428214720 2550862857452554085533481862 218456411713150420229553031392 18613027853364203337165477519080 1579429134513012615638126828947296", "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":"17/4-3*2^(1/2)","im":"0","approx_re":"0.007359","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["1+116*lambda","0","29/2*lambda","79/6000","3","1","3/8","-29/2*lambda","0","0","1","0","24","0","3","1-116*lambda"],"monodromy_dm":["1","-10","-1","-1","0","1","0","0","0","0","1","0","0","0","0","1"]},{"re":"17/4+3*2^(1/2)","im":"0","approx_re":"8.492641","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["21.+14.053465106*I","-8.-5.621386042*I","5/2+725/2*lambda","-.337500198-580/3*lambda","75","-29","75/8","-5/2-725/2*lambda","240","-96","31","-8.-5.621386042*I","600+1/1000000000*I","-240","75","-19.-14.053465106*I"],"monodromy_dm":["-49","-370","-35","-25","20","149","14","10","-240","-1776","-167","-120","140","1036","98","71"]},{"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, -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":[]}]}, 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{"pols": "[X^4, -65*X^4-130*X^3-105*X^2-40*X-6, 4*(4*X+3)*(X+1)^2*(4*X+5)]", "text": "A-incarnation: $X(1, 1, 1, 1, 1, 1) \\subset  Grass(3, 6)$", "degz": 2, "h3": "42", "sol": "1 6 126 3948 149310 6300756 285675516 13625781336 674863457598 34412622769140", "n_discr_factors": "2", "c3": "-96", "operator": "4 2 0 0 0 0 1 -6 -40 -105 -130 -65 60 248 380 256 64", "new_number": "2.62", "id": 58, "operator_tex": "\\theta^4-x\\left(65\\theta^4+130\\theta^3+105\\theta^2+40\\theta+6\\right)+2^{2} x^{2}(4\\theta+3)(\\theta+1)^2(4\\theta+5)", "superseek": "5 312", "discriminant": "2 1 -65 64", "aesz": "28", "n_sing_complex": "0", "inst_int": "", "c2h": "84", "hash": "06dd455cafc5097e4f671d385984c1a2", "dim_h": "14", "inst": " 5 28 312 4808 91048 1965908 325780668/7 1178954560 31456810796 874502186004", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "(64z-1)(z-1)", "discr_factors": "64, z-1/64, z-1", 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{"pols": "[X^4, 4*(2*X+1)^2*(7*X^2+7*X+3), 48*(2*X+1)*(4*X+3)*(4*X+5)*(2*X+3)]", "text": "This is operator \"2.65\" from ...", "degz": 2, "h3": null, "sol": "1 -12 324 -11280 447300 -19241712 876207024 -41638753728 2046133011780 -103313778625200", "n_discr_factors": "2", "c3": null, "operator": "4 2 0 0 0 0 1 12 76 188 224 112 2160 10368 17472 12288 3072", "new_number": "2.65", "id": 61, "operator_tex": "\\theta^4+2^{2} x(2\\theta+1)^2(7\\theta^2+7\\theta+3)+2^{4} 3 x^{2}(2\\theta+1)(4\\theta+3)(4\\theta+5)(2\\theta+3)", "superseek": "-4 -556/9", "discriminant": "2 1 112 3072", "aesz": "183", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "04a3788c3f9ed53281ae824deb33d833", "dim_h": null, "inst": " -4 8 -556/9 624 -8928 1199704/9 -2132876 35762384 -5668837952/9 11571895488", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "A_{n}=\\binom{2n}{n}\\sum_{j,k=0}^{n}(-4)^{n-j}\\binom{n}{j}\\binom{n}{k}\\binom{j}{k}\\binom{2j}{j}\\binom{2n-3k}{n}", "n_sing_rational": "3", 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"spectrum":[{"re":"-1/48","im":"0","approx_re":"-0.0208333333333","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["3.666666992+1.240581667*I","-.888889273-.413527825*I",".296296213+.137842738*I","-.38694844e-1-.45947515e-1*I","16.000002509-.2845e-5*I","-4.333336913-.1390e-5*I","1.777778225+.1587e-5*I","-.296296073-.137842774*I","48.000008758-.8909e-5*I","-16.000011149-.4045e-5*I","6.333334810+.4721e-5*I","-.888888245-.413528325*I","144.000033661-.28975e-4*I","-48.000035910-.11385e-4*I","16.000005252+.13912e-4*I","-1.666664890-1.240584998*I"],"monodromy_dm":["5","-32000009/1000000-11/1000000*I","-1666667/1000000","-2","666667/1000000","-866667/200000-1/500000*I","-138889/500000","-333333/1000000","-24","96000037/500000+29/500000*I","2200001/200000","3000001/250000-3/1000000*I","17333333/1000000","-866667/6250-21/500000*I","-3611113/500000","-766667/100000+1/500000*I"]},{"re":"-1/64","im":"0","approx_re":"-0.015625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["5.+.620290874*I","-2-64*lambda","7/9+224/9*lambda","-.216878323-.68921208e-1*I","14","-6","49/18","-7/9-224/9*lambda","36","-18","8","-2-64*lambda","72","-36","14","-3.-.620290874*I"],"monodromy_dm":["1","-22","-1","-1","0","1","0","0","0","0","1","0","0","0","0","1"]},{"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":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/2","3/4","5/4","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, -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": "[X^4, -512*X^4-896*X^3-788*X^2-340*X-56, 128*(2*X+1)*(4*X+5)*(8*X+5)*(8*X+9)]", "text": "This is operator \"2.68\" from ...", "degz": 2, "h3": null, "sol": "1 56 7272 1200000 222009000 43921717056 9081017922816 1937046075973632 422903091123513000 94005817066113867200", "n_discr_factors": "1", "c3": null, "operator": "4 2 0 0 0 0 1 -56 -340 -788 -896 -512 28800 152320 287744 229376 65536", "new_number": "2.68", "id": 64, "operator_tex": "\\theta^4-2^{2} x\\left(128\\theta^4+224\\theta^3+197\\theta^2+85\\theta+14\\right)+2^{7} x^{2}(2\\theta+1)(4\\theta+5)(8\\theta+5)(8\\theta+9)", "superseek": "-12 -1668", "discriminant": "2 1 -512 65536", "aesz": "406", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "d3a5c69671a7189e15cf1394437380a2", "dim_h": null, "inst": " -12 -186 -1668 -25974 -243552 671682 177300348 8359166898 303112795632 9856817477424", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "2", "laurent": null, "discriminant_tex": "(256z-1)^2", "discr_factors": "65536, (z-1/256)^2", "dm_basis": ["-934817/40000000-934817/40000000*I", "-1+I", "-I", "1", "-1+I", "6-6*I", "I", "0", "0", "-12+12*I", "0", "0", "12-12*I", "0", "0", "0"], "q": "0 1 -116 8670 -507024 25668397 -1171976280 49631564562 -1982182861632 75496123082502", "yuk": "1 -12 -1500 -45048 -1663836 -30444012 145036776 60814019352 4279891787940 220969227970680", "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","-12-12*I","1","0","0","0","-I","1"]},{"re":"1/256","im":"0","approx_re":"0.00390625","approx_im":"0.0","exponents":["0","1/4","1","5/4"],"monodromy":["1.023370425+.23370425e-1*I","1/4-1/4*I","9*I*lambda-9*lambda",".18840283e-1-.18840283e-1*I","1-I","1/2-1/2*I","-1/6+1/6*I","-9*I*lambda+9*lambda","0","3-3*I","1/2-1/2*I","1/4-1/4*I","-12+12*I","0","1-I","-.23370425e-1-1.023370425*I"],"monodromy_dm":["-I","0","I","-1","0","-1+I","-1/4*I","0","0","-20","2-2*I","0","0","-20*I","2+I","1"]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/2","5/8","9/8","5/4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -59*X^4-118*X^3-105*X^2-46*X-8, 96*(X+1)^2*(3*X+2)*(3*X+4)]", "text": "This is operator \"2.69\" from ...", "degz": 2, "h3": "160", "sol": "1 8 120 2240 46840 1051008 24757824 604538880 15179095800 389772468800", "n_discr_factors": "2", "c3": "-128", "operator": "4 2 0 0 0 0 1 -8 -46 -105 -118 -59 768 3264 5088 3456 864", "new_number": "2.69", "id": 65, "operator_tex": "\\theta^4-x\\left(59\\theta^4+118\\theta^3+105\\theta^2+46\\theta+8\\right)+2^{5} 3 x^{2}(\\theta+1)^2(3\\theta+2)(3\\theta+4)", "superseek": "1 5", "discriminant": "2 1 -59 864", "aesz": "205", "n_sing_complex": "0", "inst_int": "", "c2h": "160", "hash": "4fb2e7002e630237d0458c3985cd6a18", "dim_h": "40", "inst": " 1 7/4 5 24 759/5 4475/4 8822 72536 615358 107517313/20", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "(32z-1)(27z-1)", "discr_factors": "864, z-1/27, z-1/32", "dm_basis": ["-310145437/500000000*I", "100/3", "1", "1", "-20/3", "-80", "-1", "0", "0", "160", "0", "0", "-160", "0", "0", "0"], "q": "0 1 -14 133 -1032 6990 -43798 253594 -1428704 7475227", "yuk": "1 1 15 136 1551 18976 241800 3025947 37139983 448596118", "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","160","1","0","0","0","1","1"]},{"re":"1/32","im":"0","approx_re":"0.03125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["1.+.620290874*I","0","16/3*lambda",".2404755e-2","20/3","1","5/18","-16/3*lambda","0","0","1","0","160","0","20/3","1.-.620290874*I"],"monodromy_dm":["1","-40","-1","-1","0","1","0","0","0","0","1","0","0","0","0","1"]},{"re":"1/27","im":"0","approx_re":"0.037037037037","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["3.333327178+1.235680918*I","-.293785798-.155290034*I",".97173439e-1+.52174089e-1*I","-.12126753e-1-.18089273e-1*I","13.327492354-.18865422e-1*I","-.677351606+.3680160e-2*I",".556724039+.2392839e-2*I","-.96900942e-1-.51907518e-1*I","39.969803488-.74697659e-1*I","-5.030457990+.13317419e-1*I","2.669647034+1/243*I*Pi^(1/6)*Zeta(5)^7","-.290681436-.15554156171284634760705289672544080604534005037783375314861460957178841309823677581863979848866498740554156171284634760705289672544080604534005037783375314861460957178841309823677581863979848866498741*I","319.859816505-.452770130*I","-40.256438534+.88323845e-1*I","13.361376945+.57428145e-1*I","-1.325622606-1.245780435*I"],"monodromy_dm":["-3001219/1000000-1031/500000*I","-50063529/500000+81061/1000000*I","-2250727/1000000+1691/500000*I","-499781/250000+283/100000*I","249997/500000+31/1000000*I","6755959/500000-15801/1000000*I","70313/250000-11/20000*I","249811/1000000-467/1000000*I","-39999541/1000000-2481/1000000*I","-500476737/500000+1264109/1000000*I","-21500131/1000000+5501/125000*I","-9992451/500000+37349/1000000*I","27999679/1000000+1737/1000000*I","87583429/125000-221219/250000*I","3937523/250000-6161/200000*I","14989431/1000000-817/31250*I"]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["2/3","1","1","4/3"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -3*(3*X+1)*(3*X+2)*(11*X^2+11*X+3), -9*(3*X+1)*(3*X+2)*(3*X+4)*(3*X+5)]", "text": "Hadamard product B*b\nRelated to (:case 7.19), (:case 8.18)\nThis operator corresponds to $(Grass(2,5)\\vert 1,1,3)_{-150}$ from arXiv:0802.2908", "degz": 2, "h3": "15", "sol": "1 18 1710 246960 43347150 8515775268 1800376001424 400791767238720 92704190534597070 22085208822810919500", "n_discr_factors": "1", "c3": "-150", "operator": "4 2 0 0 0 0 1 -18 -147 -444 -594 -297 -360 -2106 -3969 -2916 -729", "new_number": "2.6", "id": 66, "operator_tex": "\\theta^4-3 x(3\\theta+1)(3\\theta+2)(11\\theta^2+11\\theta+3)-3^{2} x^{2}(3\\theta+1)(3\\theta+2)(3\\theta+4)(3\\theta+5)", "superseek": "36 41421", "discriminant": "2 1 -297 -729", "aesz": "24", "n_sing_complex": "0", "inst_int": "", "c2h": "66", "hash": "5e8f8f32b5e99693a2956e1240b9fdff", "dim_h": "8", "inst": " 36 837 41421 2992851 266362506 27112272624 3028463890677 362170461839895 45632464971618513 5991507998411065245", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "A_{n}=\\dbinom{2n}{n}\\dbinom{3n}{n}\\sum_{k=0}^{n}\\dbinom{n}{k}^2\\dbinom{n+k}{n}", "n_sing_rational": "1", "n_sing": "3", "laurent": null, "discriminant_tex": "1-297z-729z^2", "discr_factors": "-729, -1/729+11/27*z+z^2", "dm_basis": ["-150*lambda", "21/4", "1", "1", "-11/4", "-15/2", "-1", "0", "0", "15", "0", "0", "-15", "0", "0", "0"], "q": "0 1 -75 1539 -60073 -2978346 -380743659 -48420276097 -6463392140319 -900815105135718", "yuk": "1 36 6732 1118403 191549196 33295313286 5856252011883 1038763114502247 185431276653575436 33266066964311014380", "gv2": null, "gv0": "540 12555 621315 44892765 3995437590 406684089360 45426958360155 5432556927598425 684486974574277695 89872619976165978675", "gv1": "0 0 -1 13095 17230617 6648808835 1831575868830 433375127634753 94416986839804040 19571240651198871015 3928385495739192861123 771467376541495393981885 149185114850267499674332737 28527921575954705632251978558 5410017459416672999118331855100 1019499107689707626552267048965731 191190228044755566196801759890402648 35719045727096113630007361726280466678 6653312019338283509139215063697202862643", "spectrum":[{"re":"-11/54-5/54*5^(1/2)","im":"0","approx_re":"-0.410747","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["11/2+600*lambda","-9/4-300*lambda","21/20+140*lambda","-.196596398-90*lambda","14","-6","49/15","-21/20-140*lambda","30","-15","8","-9/4-300*lambda","60","-30","14","-7/2-600*lambda"],"monodromy_dm":["-9","-50","-6","-4","5","26","3","2","-45","-225","-26","-18","30","150","18","13"]},{"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","15","1","0","0","0","1","1"]},{"re":"-11/54+5/54*5^(1/2)","im":"0","approx_re":"0.00334","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["1+150*lambda","0","55/2*lambda",".35225900e-1","11/4","1","121/240","-55/2*lambda","0","0","1","0","15","0","11/4","1-150*lambda"],"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":["1/3","2/3","4/3","5/3"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -216-948*X-1652*X^2-1408*X^3-512*X^4, 128*(4*X+5)*(2*X+3)*(8*X+9)*(8*X+13)]", "text": "Operator equivalent to (:aesz 255)", "degz": 2, "h3": null, "sol": "1 216 49896 11872896 2872063656 702039514176 172843800197376 42778986061971456 10630400741354546856 2649973379832808922816", "n_discr_factors": "1", "c3": null, "operator": "4 2 0 0 0 0 1 -216 -948 -1652 -1408 -512 224640 667392 738304 360448 65536", "new_number": "2.70", "id": 67, "operator_tex": "\\theta^4-2^{2} x\\left(128\\theta^4+352\\theta^3+413\\theta^2+237\\theta+54\\right)+2^{7} x^{2}(4\\theta+5)(2\\theta+3)(8\\theta+9)(8\\theta+13)", "superseek": "20 28820/3", "discriminant": "2 1 -512 65536", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "336ddc1188eadae2f4b4c470a17f4ec1", "dim_h": null, "inst": " 20 290 28820/3 454190 26517920 5315668130/3 130052490460 10228035566870 2544287074153040/3 73327006753069840", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "2", "laurent": null, "discriminant_tex": "(256z-1)^2", "discr_factors": "65536, (z-1/256)^2", "dm_basis": ["60*I*lambda+1/2+1/2*I-60*lambda", "3-3*I", "-I", "1", "-1+I", "-6+6*I", "I", "0", "0", "12-12*I", "0", "0", "-12+12*I", "0", "0", "0"], "q": "0 1 -84 3294 -104464 2008365 -80464536 -1641557998 -248229425472 -21222256770810", "yuk": "1 20 2340 259400 29070500 3314740020 382728367080 44608004227800 5236754239307940 618261759019448120", "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+12*I","1","0","0","0","-I","1"]},{"re":"1/256","im":"0","approx_re":"0.00390625","approx_im":"0.0","exponents":["0","1/4","-3/4","1"],"monodromy":["1/2-60*I*lambda+I*(-1/2-60*I*lambda)","1/12-1/12*I","-5*I*lambda+5*lambda","-.20732598e-1+.20732598e-1*I","1-I","1/2-1/2*I","1/3-1/3*I","5*I*lambda-5*lambda","0","-1+I","1/2-1/2*I","1/12-1/12*I","12-12*I","0","1-I","1/2+60*I*lambda+I*(-1/2+60*I*lambda)"],"monodromy_dm":["-I","-4+4*I","I","-1","0","1-I","-83333/1000000*I","0","0","-12","0","0","0","4-8*I","333333/1000000-666667/1000000*I","1"]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["9/8","5/4","3/2","13/8"],"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":[]}]}, {"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, -4*(2*X+1)^2*(10*X^2+10*X+3), 144*(2*X+1)^2*(2*X+3)^2]", "text": "Hadamard product A*c", "degz": 2, "h3": "24", "sol": "1 12 540 37200 3131100 295484112 30026448144 3213620879040 357404511707100 40942438891582800", "n_discr_factors": "2", "c3": "-112", "operator": "4 2 0 0 0 0 1 -12 -88 -248 -320 -160 1296 6912 12672 9216 2304", "new_number": "2.9", "id": 70, "operator_tex": "\\theta^4-2^{2} x(2\\theta+1)^2(10\\theta^2+10\\theta+3)+2^{4} 3^{2} x^{2}(2\\theta+1)^2(2\\theta+3)^2", "superseek": "16 11056/3", "discriminant": "2 1 -160 2304", "aesz": "58", "n_sing_complex": "0", "inst_int": "", "c2h": "72", "hash": "1ca6d3d1c4514db0651efce420265f5a", "dim_h": "10", "inst": " 16 142 11056/3 121470 4971792 232972910 11970852368 658336558910 114422902654000/3 2302523619150318", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "A_{n}=\\dbinom{2n}{n}^2\\sum_{k=0}^{n}\\dbinom{n}{k}^2\\dbinom{2k}{k}", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "(144z-1)(16z-1)", "discr_factors": "2304, z-1/144, z-1/16", "dm_basis": ["-112*lambda", "7", "1", "1", "-3", "-12", "-1", "0", "0", "24", "0", "0", "-24", "0", "0", "0"], "q": "0 1 -40 684 -15808 79566 -10214112 -374227528 -26140953088 -1633455293211", "yuk": "1 16 1152 99520 7775232 621474016 50322249216 4106002362240 337068325937152 27804765345021520", "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":"1/144","im":"0","approx_re":"0.00694444444444","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["1+112*lambda","0","14*lambda",".12274269e-1","3","1","3/8","-14*lambda","0","0","1","0","24","0","3","1-112*lambda"],"monodromy_dm":["1","-10","-1","-1","0","1","0","0","0","0","1","0","0","0","0","1"]},{"re":"1/16","im":"0","approx_re":"0.0625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["4.+1.628263543*I","-1-112*lambda","3/8+42*lambda","-.88177192e-1-28*lambda","9","-2","9/8","-3/8-42*lambda","24","-8","4","-1-112*lambda","72","-24","9","-2.-1.628263543*I"],"monodromy_dm":["-5","-42","-4","-3","2","15","1333333/1000000","1","-24","-168","-15","-12","16","112","10666667/1000000","9"]},{"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": "[X^4, -256*X^4-512*X^3-448*X^2-192*X-32, 256*(2*X+1)*(4*X+3)*(4*X+5)*(2*X+3)]", "text": "This is operator is equivalent to [2.33]. Transformation:.....", "degz": 2, "h3": null, "sol": "1 32 2160 181760 17021200 1698181632 176677611264 18937576120320 2075622689471760 231465995770380800", "n_discr_factors": "1", "c3": null, "operator": "4 2 0 0 0 0 1 -32 -192 -448 -512 -256 11520 55296 93184 65536 16384", "new_number": "2.71", "id": 614, "operator_tex": "\\theta^4-2^{5} x(2\\theta+1)^2(2\\theta^2+2\\theta+1)+2^{8} x^{2}(2\\theta+1)(4\\theta+3)(4\\theta+5)(2\\theta+3)", "superseek": "0 0", "discriminant": "2 1 -256 16384", "aesz": null, "n_sing_complex": "0", "inst_int": null, "c2h": null, "hash": "757b011780c5986bd45a5bf434c76c28", "dim_h": null, "inst": " 0 -20 0 -865 0 -67460 0 -6821070 0 -800369820", "cleanlist": "False", "n_sing_real": "2", "sol_explicit": null, "n_sing_rational": "2", "n_sing": "2", "laurent": null, "discriminant_tex": "(-1+128z)^2", "discr_factors": "16384, (-1/128+z)^2", "dm_basis": null, "q": "0 1 -64 2912 -110592 3772720 -119642112 3598125568 -103922663424 2907171436184", "yuk": "1 0 -160 0 -55520 0 -14571520 0 -3492443360 0", "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":"1/128","im":"0","approx_re":"0.0078125","approx_im":"0.0","exponents":["0","1/4","3/4","1"],"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":[]}]}]}