{"count": 6, "status":"OK", "data":[{"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, -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": "[25*X^4, -2765*X^4-3610*X^3-3055*X^2-1250*X-200, 122496*X^4+302208*X^3+353216*X^2+192640*X+39040, -2805760*X^4-9830400*X^3-14196736*X^2-9093120*X-2048000, 524288*(2*X+1)*(30*X^3+105*X^2+122*X+46), -33554432*(2*X+1)*(X+1)^2*(2*X+3)]", "text": "This is operator \"5.107\" from ...", "degz": 5, "h3": null, "sol": "1 8 120 2240 50680 1387008 43627584 1473838080 51214208760 1801126733120", "n_discr_factors": "2", "c3": null, "operator": "4 5 0 0 0 0 25 -200 -1250 -3055 -3610 -2765 39040 192640 353216 302208 122496 -2048000 -9093120 -14196736 -9830400 -2805760 24117248 112197632 182976512 125829120 31457280 -100663296 -469762048 -771751936 -536870912 -134217728", "new_number": "5.107", "id": 189, "operator_tex": "5^{2} \\theta^4-5 x\\left(553\\theta^4+722\\theta^3+611\\theta^2+250\\theta+40\\right)+2^{6} x^{2}\\left(1914\\theta^4+4722\\theta^3+5519\\theta^2+3010\\theta+610\\right)-2^{12} x^{3}\\left(685\\theta^4+2400\\theta^3+3466\\theta^2+2220\\theta+500\\right)+2^{19} x^{4}(2\\theta+1)(30\\theta^3+105\\theta^2+122\\theta+46)-2^{25} x^{5}(2\\theta+1)(\\theta+1)^2(2\\theta+3)", "superseek": "11/5 71/5", "discriminant": "5 25 -2765 122496 -2805760 31457280 -134217728", "aesz": "364", "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "c5b4bc60bc9d39ea420bd49fad182557", "dim_h": null, "inst": " 11/5 -8/5 71/5 738 26841/5 71028/5 1285026/5 50351594/5 786252554/5 6885546964/5", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "5", "laurent": null, "discriminant_tex": "-(32768z^3-2560z^2+85z-1)(-5+64z)^2", "discr_factors": "-134217728, (-5/64+z)^2, z^3-5/64*z^2+85/32768*z-1/32768", "dm_basis": null, "q": "0 1 -18 277 -4088 49790 -601226 7017898 -81144608 823861259", "yuk": "1 11/5 -53/5 1928/5 236107/5 3355136/5 15343912/5 440763929/5 5156050447 573178113794/5", "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":"-1/768*(388+114*114^(1/2))^(1/3)+55/384/(388+114*114^(1/2))^(1/3)+5/192","im":"0","approx_re":"0.023029","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/1536*(388+114*114^(1/2))^(1/3)-55/768/(388+114*114^(1/2))^(1/3)+5/192","im":"1/2*3^(1/2)*(-1/768*(388+114*114^(1/2))^(1/3)-55/384/(388+114*114^(1/2))^(1/3))","approx_re":"0.027548","approx_im":"-0.023797","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/1536*(388+114*114^(1/2))^(1/3)-55/768/(388+114*114^(1/2))^(1/3)+5/192","im":"-1/2*3^(1/2)*(-1/768*(388+114*114^(1/2))^(1/3)-55/384/(388+114*114^(1/2))^(1/3))","approx_re":"0.027548","approx_im":"0.023797","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"5/64","im":"0","approx_re":"0.078125","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/2","1","1","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -2304*X^4-2880*X^3-2292*X^2-852*X-120, 2011392*X^4+4561920*X^3+4980096*X^2+2588544*X+455040, -842047488*X^4-2579890176*X^3-3289559040*X^2-1872211968*X-341729280, 170272751616*X^4+619173642240*X^3+840184233984*X^2+468680048640*X+83607552000, -1486016741376*(X+1)^2*(3*X+1)*(3*X+5)]", "text": "This is operator \"5.8\" from ...", "degz": 5, "h3": null, "sol": "1 120 34920 13157760 5790070440 2866877133120 1562496801465600 920528890348953600 576774234149057029800 379043061747351173515200", "n_discr_factors": "3", "c3": null, "operator": "4 5 0 0 0 0 1 -120 -852 -2292 -2880 -2304 455040 2588544 4980096 4561920 2011392 -341729280 -1872211968 -3289559040 -2579890176 -842047488 83607552000 468680048640 840184233984 619173642240 170272751616 -7430083706880 -41608468758528 -74300837068800 -53496602689536 -13374150672384", "new_number": "5.8", "id": 304, "operator_tex": "\\theta^4-2^{2} 3 x\\left(192\\theta^4+240\\theta^3+191\\theta^2+71\\theta+10\\right)+2^{7} 3^{2} x^{2}\\left(1746\\theta^4+3960\\theta^3+4323\\theta^2+2247\\theta+395\\right)-2^{12} 3^{4} x^{3}\\left(2538\\theta^4+7776\\theta^3+9915\\theta^2+5643\\theta+1030\\right)+2^{17} 3^{6} x^{4}\\left(1782\\theta^4+6480\\theta^3+8793\\theta^2+4905\\theta+875\\right)-2^{23} 3^{11} x^{5}(\\theta+1)^2(3\\theta+1)(3\\theta+5)", "superseek": "84 1522388/3", "discriminant": "5 1 -2304 2011392 -842047488 170272751616 -13374150672384", "aesz": "", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "f4b2a154823e983e64682b48f6254a15", "dim_h": null, "inst": " 84 9210 1522388/3 120348978 19186016160 14337645775418/3 1105086275262876 300135253167886218 244741945783423164752/3 23794866517166874380880", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "-(-1+864z)(432z-1)^2(288z-1)^2", "discr_factors": "-13374150672384, (z-1/288)^2, -1/864+z, (z-1/432)^2", "dm_basis": null, "q": "0 1 -372 112734 -32614288 8813239341 -2352202637400 603766372001426 -155516566454839104 38705915538575348742", "yuk": "1 84 73764 13701576 7702408356 2398252020084 1032310509605352 379044592415166552 153669249629660151972 59472292825371842736312", "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":"1/864","im":"0","approx_re":"0.00115740740741","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/432","im":"0","approx_re":"0.00231481481481","approx_im":"0.0","exponents":["0","1/6","5/6","1"],"monodromy":[],"monodromy_dm":[]},{"re":"1/288","im":"0","approx_re":"0.00347222222222","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/3","1","1","5/3"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -33*X^4-98*X^3-105*X^2-56*X-12, 272*X^4+2208*X^3+4872*X^2+4656*X+1728, 528*X^4-8160*X^3-45168*X^2-72960*X-40608, -1152*(2*X^2+6*X+5)*(4*X^2+12*X-31), 8448*X^4+231936*X^3+908544*X^2+1268736*X+557568, 69632*X^4+270336*X^3-79872*X^2-1449984*X-1529856, -135168*X^4-1220608*X^3-4116480*X^2-6111232*X-3342336, 65536*(X+3)^4]", "text": "This is operator \"8.55\" from ...", "degz": 8, "h3": null, "sol": "1 12 120 1216 13080 149664 1801312 22528512 290011032 3816913696", "n_discr_factors": "5", "c3": null, "operator": "4 8 0 0 0 0 1 -12 -56 -105 -98 -33 1728 4656 4872 2208 272 -40608 -72960 -45168 -8160 528 178560 145152 -34560 -55296 -9216 557568 1268736 908544 231936 8448 -1529856 -1449984 -79872 270336 69632 -3342336 -6111232 -4116480 -1220608 -135168 5308416 7077888 3538944 786432 65536", "new_number": "8.55", "id": 502, "operator_tex": "\\theta^4-x\\left(33\\theta^4+98\\theta^3+105\\theta^2+56\\theta+12\\right)+2^{3} x^{2}\\left(34\\theta^4+276\\theta^3+609\\theta^2+582\\theta+216\\right)+2^{4} 3 x^{3}\\left(11\\theta^4-170\\theta^3-941\\theta^2-1520\\theta-846\\right)-2^{7} 3^{2} x^{4}(2\\theta^2+6\\theta+5)(4\\theta^2+12\\theta-31)+2^{8} 3 x^{5}\\left(11\\theta^4+302\\theta^3+1183\\theta^2+1652\\theta+726\\right)+2^{11} x^{6}\\left(34\\theta^4+132\\theta^3-39\\theta^2-708\\theta-747\\right)-2^{12} x^{7}\\left(33\\theta^4+298\\theta^3+1005\\theta^2+1492\\theta+816\\right)+2^{16} x^{8}\\left((\\theta+3)^4\\right)", "superseek": "1 68/9", "discriminant": "8 1 -33 272 528 -9216 8448 69632 -135168 65536", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "39ed8ce7572bc79a333f77c892033bcf", "dim_h": null, "inst": " 1 -2 68/9 -30 150 -778 4374 -25438 463459/3 -960634", "cleanlist": "True", "n_sing_real": "7", "sol_explicit": "", "n_sing_rational": "5", "n_sing": "7", "laurent": null, "discriminant_tex": "(z-1)(16z-1)(16z^2-16z+1)(4z-1)^2(4z+1)^2", "discr_factors": "65536, (z-1/4)^2, (z+1/4)^2, z-1, z-1/16, z^2-z+1/16", "dm_basis": null, "q": "0 1 -8 52 -336 2226 -15040 103280 -719520 5072791", "yuk": "1 1 -15 205 -1935 18751 -167859 1500283 -13026191 112620742", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/4","im":"0","approx_re":"-0.25","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/16","im":"0","approx_re":"0.0625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/2-1/4*3^(1/2)","im":"0","approx_re":"0.066987","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/4","im":"0","approx_re":"0.25","approx_im":"0.0","exponents":["0","0","-1","1"],"monodromy":[],"monodromy_dm":[]},{"re":"1/2+1/4*3^(1/2)","im":"0","approx_re":"0.933013","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1","im":"0","approx_re":"1.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["3","3","3","3"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -5*(5*X+1)*(5*X+2)*(5*X+3)*(5*X+4)]", "text": "A-incarnation: $X(5) \\subset P^4$\nB-incarnation: mirror quintic.\nP. Candelas, X. de la Ossa, D. Green, L. Parkes,{\\em An exactly soluble superconformal theory from a mirror pair of Calabi-Yau manifolds}, Phys. Lett. B 258 (1991), no.1-2, 118-126. \n\n", "degz": 1, "h3": "5", "sol": "1 120 113400 168168000 305540235000 623360743125120 1370874167589326400 3177459078523411968000 7656714453153197981835000 19010638202652030712978200000", "n_discr_factors": "1", "c3": "-200", "operator": "4 1 0 0 0 0 1 -120 -1250 -4375 -6250 -3125", "new_number": "1.1", "id": 555, "operator_tex": "\\theta^4-5 x(5\\theta+1)(5\\theta+2)(5\\theta+3)(5\\theta+4)", "superseek": "575 63441275", "discriminant": "1 1 -3125", "aesz": "1", "n_sing_complex": "0", "inst_int": null, "c2h": "50", "hash": "c86f1c284d8c5119801c6ba1343172bb", "dim_h": "5", "inst": " 575 121850 63441275 48493506000 45861177777525 49649948423604400 59018210114169131850 75126432187495320710000 100768102083397048729021250 140857632995690937222697649950", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "A_{n}=\\frac{(5n)!}{n!^5}", "n_sing_rational": "2", "n_sing": "2", "laurent": null, "discriminant_tex": "1-3125z", "discr_factors": "-3125, -1/3125+z", "dm_basis": null, "q": "0 1 -770 171525 -81623000 -35423171250 -54572818340154 -71982448083391590 -102693620674349200800 -152309618533468229185125", "yuk": "1 575 975375 1712915000 3103585359375 5732647222191200 10724388861212440200 20243246069160012225125 38464733280000707788879375 73459946418796448525169406250", "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":"1/3125","im":"0","approx_re":"0.00032","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/5","2/5","3/5","4/5"],"monodromy":[],"monodromy_dm":[]}]}]}