{"count": 7, "status":"OK", "data":[{"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", "n_sing": "3", "laurent": null, "discriminant_tex": "(48z+1)(64z+1)", "discr_factors": "3072, z+1/64, z+1/48", "dm_basis": ["-4-310145437/500000000*I", "8", "1/2", "1", "-14", "0", "-1", "0", "-36", "72", "0", "0", "-72", "0", "0", "0"], "q": "0 1 28 558 9520 144885 2085960 28114706 372061120 4641274242", "yuk": "1 -4 60 -1672 39996 -1116004 28791288 -731576472 18310380604 -459175875784", "gv2": null, "gv0": null, "gv1": null, "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": "[25*X^4, 11920*X^4+10880*X^3+7940*X^2+2500*X+300, 1442304*X^4+709632*X^3-638976*X^2-525120*X-101520, 44015616*X^4-46448640*X^3-62567424*X^2-28200960*X-4527360, -2985984*(2*X+1)^2*(76*X^2+196*X+139), -1289945088*(2*X+1)^2*(2*X+3)^2]", "text": "This is operator \"5.54\" from ...", "degz": 5, "h3": null, "sol": "1 -12 1260 -188400 34353900 -7001506512 1534951790064 -354249360653760 84935226474341100 -20972495427496813200", "n_discr_factors": "3", "c3": null, "operator": "4 5 0 0 0 0 25 300 2500 7940 10880 11920 -101520 -525120 -638976 709632 1442304 -4527360 -28200960 -62567424 -46448640 44015616 -415051776 -2245459968 -4228153344 -3248750592 -907739136 -11609505792 -61917364224 -113515167744 -82556485632 -20639121408", "new_number": "5.54", "id": 265, "operator_tex": "5^{2} \\theta^4+2^{2} 5 x\\left(596\\theta^4+544\\theta^3+397\\theta^2+125\\theta+15\\right)+2^{4} 3 x^{2}\\left(30048\\theta^4+14784\\theta^3-13312\\theta^2-10940\\theta-2115\\right)+2^{8} 3^{3} x^{3}\\left(6368\\theta^4-6720\\theta^3-9052\\theta^2-4080\\theta-655\\right)-2^{12} 3^{6} x^{4}(2\\theta+1)^2(76\\theta^2+196\\theta+139)-2^{16} 3^{9} x^{5}(2\\theta+1)^2(2\\theta+3)^2", "superseek": "-188/5 -450516/5", "discriminant": "5 25 11920 1442304 44015616 -907739136 -20639121408", "aesz": "260\n", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "03ff8e2e94b897c3891e6981e7fb4ec9", "dim_h": null, "inst": " -188/5 7693/5 -450516/5 37785946/5 -790482672 477405507903/5 -63469802544116/5 9043012469852634/5 -1358060663800759128/5 42517080906522247284", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "-(16z+1)(6912z^2-288z-1)(5+432z)^2", "discr_factors": "-20639121408, z+1/16, z^2-1/24*z-1/6912, (5/432+z)^2", "dm_basis": null, "q": "0 1 52 -1434 68048 -9335935 1310920056 -197169539470 31225147414848 -5156649487420524", "yuk": "1 -188/5 61356/5 -2432824 483672380 -494051670188/5 103119577604472/5 -21770142272631976/5 4630022386982910508/5 -990026223910765568432/5", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/16","im":"0","approx_re":"-0.0625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-5/432","im":"0","approx_re":"-0.0115740740741","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/48-1/72*3^(1/2)","im":"0","approx_re":"-0.003223","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/48+1/72*3^(1/2)","im":"0","approx_re":"0.04489","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/2","1/2","3/2","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[25*X^4, 5840*X^4+7360*X^3+5780*X^2+2100*X+300, 395776*X^4+698368*X^3+622976*X^2+303680*X+59760, 11575296*X^4+26542080*X^3+29159424*X^2+15344640*X+3018240, 331776*(2*X+1)*(232*X^3+588*X^2+590*X+207), 191102976*(2*X+1)*(X+1)^2*(2*X+3)]", "text": "This is operator \"5.55\" from ...", "degz": 5, "h3": null, "sol": "1 -12 492 -32880 2743020 -257986512 26170078704 -2797796574144 310918611526380 -35596887110962320", "n_discr_factors": "3", "c3": null, "operator": "4 5 0 0 0 0 25 300 2100 5780 7360 5840 59760 303680 622976 698368 395776 3018240 15344640 29159424 26542080 11575296 68677632 333103104 586579968 467140608 153944064 573308928 2675441664 4395368448 3057647616 764411904", "new_number": "5.55", "id": 266, "operator_tex": "5^{2} \\theta^4+2^{2} 5 x\\left(292\\theta^4+368\\theta^3+289\\theta^2+105\\theta+15\\right)+2^{4} x^{2}\\left(24736\\theta^4+43648\\theta^3+38936\\theta^2+18980\\theta+3735\\right)+2^{9} 3^{2} x^{3}\\left(2512\\theta^4+5760\\theta^3+6328\\theta^2+3330\\theta+655\\right)+2^{12} 3^{4} x^{4}(2\\theta+1)(232\\theta^3+588\\theta^2+590\\theta+207)+2^{18} 3^{6} x^{5}(2\\theta+1)(\\theta+1)^2(2\\theta+3)", "superseek": "-76/5 -24836/5", "discriminant": "5 25 5840 395776 11575296 153944064 764411904", "aesz": "261", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "adadb5e720011482371f48cfa73dab99", "dim_h": null, "inst": " -76/5 1103/5 -24836/5 847456/5 -36542448/5 1806132437/5 -97926149796/5 5684771847792/5 -69550113320856 22170307605956652/5", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "(1+144z)(16z+1)^2(144z+5)^2", "discr_factors": "764411904, (z+1/16)^2, (z+5/144)^2, 1/144+z", "dm_basis": null, "q": "0 1 36 422 11664 -77567 12260376 -650003662 43465220160 -2919137690348", "yuk": "1 -76/5 8748/5 -670648/5 54245932/5 -4567806076/5 390123944568/5 -33588669380104/5 2910603240315436/5 -253510163055190768/5", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/16","im":"0","approx_re":"-0.0625","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"-5/144","im":"0","approx_re":"-0.0347222222222","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/144","im":"0","approx_re":"-0.00694444444444","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/2","1","1","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[25*X^4, 2720*X^4+4480*X^3+3940*X^2+1700*X+300, 89344*X^4+259072*X^3+350784*X^2+236800*X+63280, 1245184*X^4+4669440*X^3+7458816*X^2+5621760*X+1597440, 7602176*X^4+30932992*X^3+48431104*X^2+32964608*X+8208384, 16777216*(X+1)^4]", "text": "There is a second MUM-point at infinity,\ncorresponding to the Operator AESZ 263/5.57", "degz": 5, "h3": null, "sol": "1 -12 236 -6384 217836 -8674512 381058544 -17846749632 873802015468 -44205033911952", "n_discr_factors": "3", "c3": null, "operator": "4 5 0 0 0 0 25 300 1700 3940 4480 2720 63280 236800 350784 259072 89344 1597440 5621760 7458816 4669440 1245184 8208384 32964608 48431104 30932992 7602176 16777216 67108864 100663296 67108864 16777216", "new_number": "5.56", "id": 267, "operator_tex": "5^{2} \\theta^4+2^{2} 5 x\\left(136\\theta^4+224\\theta^3+197\\theta^2+85\\theta+15\\right)+2^{4} x^{2}\\left(5584\\theta^4+16192\\theta^3+21924\\theta^2+14800\\theta+3955\\right)+2^{11} x^{3}\\left(608\\theta^4+2280\\theta^3+3642\\theta^2+2745\\theta+780\\right)+2^{14} x^{4}\\left(464\\theta^4+1888\\theta^3+2956\\theta^2+2012\\theta+501\\right)+2^{24} x^{5}\\left((\\theta+1)^4\\right)", "superseek": "-28/5 -1268/5", "discriminant": "5 25 2720 89344 1245184 7602176 16777216", "aesz": "262", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "4899f97226a5ec3b1ded2994470e9fdc", "dim_h": null, "inst": " -28/5 153/5 -1268/5 18598/5 -320048/5 6328003/5 -137296404/5 3185758982/5 -77892222744/5 1984455155124/5", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "(1+64z)(32z+5)^2(16z+1)^2", "discr_factors": "16777216, (z+1/16)^2, 1/64+z, (z+5/32)^2", "dm_basis": null, "q": "0 1 20 230 2896 22145 310968 -432142 67997504 -1435072876", "yuk": "1 -28/5 1196/5 -34264/5 1191468/5 -40006028/5 1366815608/5 -9418533320 1631109790252/5 -11356686082928", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-5/32","im":"0","approx_re":"-0.15625","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/16","im":"0","approx_re":"-0.0625","approx_im":"0.0","exponents":["0","0","1","1"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/64","im":"0","approx_re":"-0.015625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, 12+56*X+100*X^2+88*X^3+172*X^4, 12048*X^4+14784*X^3+17712*X^2+9952*X+2256, 432256*X^4+923904*X^3+1185408*X^2+737792*X+186240, 7751680*X^4+25311232*X^3+35200000*X^2+22459392*X+5437440, 33214464*X^4+188669952*X^3+212963328*X^2-3096576*X-67424256, -1147650048*X^4-4994629632*X^3-12364333056*X^2-15859777536*X-7297449984, -17323130880*X^4-99635429376*X^3-245132034048*X^2-295728316416*X-130689662976, -3737124864*X^4-44845498368*X^3-20978860032*X^2-20384317440*X-23272095744, 1353518678016*X^4+9702935101440*X^3+28091627864064*X^2+35372906053632*X+15653117362176, 48922361856*(X+1)*(109*X^3+651*X^2+1373*X+933), -1174136684544*(X+1)*(X+2)*(27*X^2+153*X+199), -169075682574336*(X+1)*(X+2)^2*(X+3)]", "text": "This is operator \"12.5\" from ...", "degz": 12, "h3": null, "sol": "1 -12 180 -2736 42948 -691632 11651184 -208526400 3997652292 -81421375536", "n_discr_factors": "5", "c3": null, "operator": "4 12 0 0 0 0 1 12 56 100 88 172 2256 9952 17712 14784 12048 186240 737792 1185408 923904 432256 5437440 22459392 35200000 25311232 7751680 -67424256 -3096576 212963328 188669952 33214464 -7297449984 -15859777536 -12364333056 -4994629632 -1147650048 -130689662976 -295728316416 -245132034048 -99635429376 -17323130880 -23272095744 -20384317440 -20978860032 -44845498368 -3737124864 15653117362176 35372906053632 28091627864064 9702935101440 1353518678016 45644563611648 112814966439936 99018860396544 37180995010560 5332537442304 -467306400448512 -1060245426143232 -835985319395328 -274747984183296 -31701690482688 -2028908190892032 -4734119112081408 -3888740699209728 -1352605460594688 -169075682574336", "new_number": "12.5", "id": 358, "operator_tex": "\\theta^4+2^{2} x\\left(43\\theta^4+22\\theta^3+25\\theta^2+14\\theta+3\\right)+2^{4} x^{2}\\left(753\\theta^4+924\\theta^3+1107\\theta^2+622\\theta+141\\right)+2^{7} x^{3}\\left(3377\\theta^4+7218\\theta^3+9261\\theta^2+5764\\theta+1455\\right)+2^{10} x^{4}\\left(7570\\theta^4+24718\\theta^3+34375\\theta^2+21933\\theta+5310\\right)+2^{12} 3^{2} x^{5}\\left(901\\theta^4+5118\\theta^3+5777\\theta^2-84\\theta-1829\\right)-2^{14} 3^{2} x^{6}\\left(7783\\theta^4+33872\\theta^3+83851\\theta^2+107556\\theta+49489\\right)-2^{17} 3^{3} x^{7}\\left(4895\\theta^4+28154\\theta^3+69267\\theta^2+83564\\theta+36929\\right)-2^{20} 3^{4} x^{8}\\left(44\\theta^4+528\\theta^3+247\\theta^2+240\\theta+274\\right)+2^{23} 3^{5} x^{9}\\left(664\\theta^4+4760\\theta^3+13781\\theta^2+17353\\theta+7679\\right)+2^{26} 3^{6} x^{10}(\\theta+1)(109\\theta^3+651\\theta^2+1373\\theta+933)-2^{29} 3^{7} x^{11}(\\theta+1)(\\theta+2)(27\\theta^2+153\\theta+199)-2^{33} 3^{9} x^{12}(\\theta+1)(\\theta+2)^2(\\theta+3)", "superseek": "4 2252/9", "discriminant": "12 1 172 12048 432256 7751680 33214464 -1147650048 -17323130880 -3737124864 1353518678016 5332537442304 -31701690482688 -169075682574336", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "bb257a283455fdd1fa17fef9649505e3", "dim_h": null, "inst": " 4 -31 2252/9 -11109/4 33312 -4091081/9 6559596 -399687825/4 1577400224 -25647405040", "cleanlist": "True", "n_sing_real": "6", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "8", "laurent": null, "discriminant_tex": "-(16z+1)(432z^2+36z+1)(24z+1)^2(288z^2+48z+1)^2(8z-1)^3", "discr_factors": "-169075682574336, (z^2+1/6*z+1/288)^2, z^2+1/12*z+1/432, (z+1/24)^2, (z-1/8)^3, z+1/16", "dm_basis": null, "q": "0 1 8 54 -128 -2875 -72144 -100310 -7419904 102483090", "yuk": "1 4 -244 6760 -177988 4164004 -98179432 2249941432 -51160219588 1149924770056", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/12-1/24*2^(1/2)","im":"0","approx_re":"-0.142259","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/16","im":"0","approx_re":"-0.0625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/24","im":"-1/72*3^(1/2)","approx_re":"-0.0416666666667","approx_im":"-0.024056","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/24","im":"0","approx_re":"-0.0416666666667","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/24","im":"1/72*3^(1/2)","approx_re":"-0.0416666666667","approx_im":"0.024056","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/12+1/24*2^(1/2)","im":"0","approx_re":"-0.024408","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/8","im":"0","approx_re":"0.125","approx_im":"0.0","exponents":["0","1/2","3/2","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","2","2","3"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, 12+54*X+94*X^2+80*X^3+146*X^4, 2456+9092*X+14064*X^2+10896*X^3+9396*X^4, 210848+676592*X+920344*X^2+642432*X^3+352728*X^4, 9914944+28603392*X+34693728*X^2+21707072*X^3+8626912*X^4, 286847488+760763904*X+836176384*X^2+469761024*X^3+145606400*X^4, 5430845440+13443704832*X+13582102528*X^2+6899736576*X^3+1753843712*X^4, 69713803264+163008135168*X+153273556992*X^2+71104528384*X^3+15376457728*X^4, 619062042624+1381508808704*X+1222573686784*X^2+523627331584*X^3+99110846464*X^4, 3835533262848+8246965305344*X+6940439085056*X^2+2775432822784*X^3+470517284864*X^4, 16544582598656+34586228686848*X+27958274162688*X^2+10557532930048*X^3+1634704818176*X^4, 49013967552512+100486178930688*X+78794027171840*X^2+28418456420352*X^3+4089110855680*X^4, 96980135051264+196496062414848*X+150874785579008*X^2+52568789090304*X^3+7142262177792*X^4, 121818627178496+245231895183360*X+185897458860032*X^2+63264868270080*X^3+8239894757376*X^4, 87756919275520+175803748843520*X+132317204971520*X^2+44409961840640*X^3+5626407157760*X^4, 1717986918400*(X+2)^4]", "text": "This is operator \"15.2\" from ...", "degz": 15, "h3": null, "sol": "1 -12 136 -1632 21296 -302016 4597120 -73944576 1239638800 -21432549312", "n_discr_factors": "5", "c3": null, "operator": "4 15 0 0 0 0 1 12 54 94 80 146 2456 9092 14064 10896 9396 210848 676592 920344 642432 352728 9914944 28603392 34693728 21707072 8626912 286847488 760763904 836176384 469761024 145606400 5430845440 13443704832 13582102528 6899736576 1753843712 69713803264 163008135168 153273556992 71104528384 15376457728 619062042624 1381508808704 1222573686784 523627331584 99110846464 3835533262848 8246965305344 6940439085056 2775432822784 470517284864 16544582598656 34586228686848 27958274162688 10557532930048 1634704818176 49013967552512 100486178930688 78794027171840 28418456420352 4089110855680 96980135051264 196496062414848 150874785579008 52568789090304 7142262177792 121818627178496 245231895183360 185897458860032 63264868270080 8239894757376 87756919275520 175803748843520 132317204971520 44409961840640 5626407157760 27487790694400 54975581388800 41231686041600 13743895347200 1717986918400", "new_number": "15.2", "id": 390, "operator_tex": "\\theta^4+2 x\\left(73\\theta^4+40\\theta^3+47\\theta^2+27\\theta+6\\right)+2^{2} x^{2}\\left(2349\\theta^4+2724\\theta^3+3516\\theta^2+2273\\theta+614\\right)+2^{3} x^{3}\\left(44091\\theta^4+80304\\theta^3+115043\\theta^2+84574\\theta+26356\\right)+2^{5} x^{4}\\left(269591\\theta^4+678346\\theta^3+1084179\\theta^2+893856\\theta+309842\\right)+2^{8} x^{5}\\left(568775\\theta^4+1835004\\theta^3+3266314\\theta^2+2971734\\theta+1120498\\right)+2^{11} x^{6}\\left(856369\\theta^4+3369012\\theta^3+6631886\\theta^2+6564309\\theta+2651780\\right)+2^{11} x^{7}\\left(7508036\\theta^4+34719008\\theta^3+74840604\\theta^2+79593816\\theta+34039943\\right)+2^{13} x^{8}\\left(12098492\\theta^4+63919352\\theta^3+149239952\\theta^2+168641212\\theta+75569097\\right)+2^{16} x^{9}\\left(7179524\\theta^4+42349744\\theta^3+105902696\\theta^2+125838704\\theta+58525593\\right)+2^{19} x^{10}\\left(3117952\\theta^4+20136896\\theta^3+53326176\\theta^2+65967996\\theta+31556287\\right)+2^{21} x^{11}\\left(1949840\\theta^4+13550976\\theta^3+37571920\\theta^2+47915544\\theta+23371681\\right)+2^{23} x^{12}\\left(851424\\theta^4+6266688\\theta^3+17985676\\theta^2+23424156\\theta+11560933\\right)+2^{26} x^{13}\\left(122784\\theta^4+942720\\theta^3+2770088\\theta^2+3654240\\theta+1815239\\right)+2^{31} 5 x^{14}\\left(524\\theta^4+4136\\theta^3+12323\\theta^2+16373\\theta+8173\\right)+2^{36} 5^{2} x^{15}\\left((\\theta+2)^4\\right)", "superseek": "2 38", "discriminant": "15 1 146 9396 352728 8626912 145606400 1753843712 15376457728 99110846464 470517284864 1634704818176 4089110855680 7142262177792 8239894757376 5626407157760 1717986918400", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "76d5c5e186c39f14d8f32dfa0f13e22a", "dim_h": null, "inst": " 2 -29/4 38 -2077/8 2034 -69631/4 158858 -12172903/8 15129336 -619853933/4", "cleanlist": "True", "n_sing_real": "8", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "8", "laurent": null, "discriminant_tex": "(4z+1)(64z^2+24z+1)^2(160z^2+32z+1)^2(2z+1)^3(8z+1)^3", "discr_factors": "1717986918400, z+1/4, (z+1/8)^3, (z+1/2)^3, (z^2+3/8*z+1/64)^2, (z^2+1/5*z+1/160)^2", "dm_basis": null, "q": "0 1 6 22 96 190 1472 -3540 55296 -451314", "yuk": "1 2 -56 1028 -16672 254252 -3759104 54488296 -779082464 11029286972", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/2","im":"0","approx_re":"-0.5","approx_im":"0.0","exponents":["0","2","3","5"],"monodromy":[],"monodromy_dm":[]},{"re":"-3/16-1/16*5^(1/2)","im":"0","approx_re":"-0.327254","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/4","im":"0","approx_re":"-0.25","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/10-1/40*6^(1/2)","im":"0","approx_re":"-0.161237","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/8","im":"0","approx_re":"-0.125","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"-3/16+1/16*5^(1/2)","im":"0","approx_re":"-0.047746","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/10+1/40*6^(1/2)","im":"0","approx_re":"-0.038763","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":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["2","2","2","2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[25*X^4, 5*X^2*(-1-2*X+107*X^2), 4800+20800*X+34276*X^2+23768*X^3+8696*X^4, -190080-604260*X-613836*X^2-152928*X^3+11088*X^4, -2115072-7610544*X-10054080*X^2-5688000*X^3-1016640*X^4, -13379904-41383872*X-44831232*X^2-20601216*X^3-4567104*X^4, -19968768-43390080*X-11736576*X^2+24634368*X^3+12358656*X^4, 39191040+151352064*X+204353280*X^2+106002432*X^3+12690432*X^4, -26873856*(X+1)^4]", "text": "This is operator \"8.84\" from ...", "degz": 8, "h3": null, "sol": "1 0 -12 144 324 -21600 182400 2116800 -59931900 239904000", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 25 0 0 -5 -10 535 4800 20800 34276 23768 8696 -190080 -604260 -613836 -152928 11088 -2115072 -7610544 -10054080 -5688000 -1016640 -13379904 -41383872 -44831232 -20601216 -4567104 -19968768 -43390080 -11736576 24634368 12358656 39191040 151352064 204353280 106002432 12690432 -26873856 -107495424 -161243136 -107495424 -26873856", "new_number": "8.84", "id": 534, "operator_tex": "5^{2} \\theta^4+5 x\\theta^2(-1-2\\theta+107\\theta^2)+2^{2} x^{2}\\left(2174\\theta^4+5942\\theta^3+8569\\theta^2+5200\\theta+1200\\right)+2^{2} 3^{2} x^{3}\\left(308\\theta^4-4248\\theta^3-17051\\theta^2-16785\\theta-5280\\right)-2^{4} 3^{2} x^{4}\\left(7060\\theta^4+39500\\theta^3+69820\\theta^2+52851\\theta+14688\\right)-2^{6} 3^{4} x^{5}\\left(881\\theta^4+3974\\theta^3+8648\\theta^2+7983\\theta+2581\\right)+2^{7} 3^{4} x^{6}\\left(1192\\theta^4+2376\\theta^3-1132\\theta^2-4185\\theta-1926\\right)+2^{8} 3^{6} x^{7}\\left(68\\theta^4+568\\theta^3+1095\\theta^2+811\\theta+210\\right)-2^{12} 3^{8} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "1/5 224/5", "discriminant": "8 25 535 8696 11088 -1016640 -4567104 12358656 12690432 -26873856", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "258fab6f0a4f132fe597fc6f30e54eea", "dim_h": null, "inst": " 1/5 -6 224/5 -448/5 -4334/5 162734/15 4944/5 -5368254/5 52756707/5 93552762/5", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "7", "laurent": null, "discriminant_tex": "-(9z-1)(576z^3+368z^2+16z+1)(-5-36z+72z^2)^2", "discr_factors": "-26873856, z-1/9, (-5/72-1/2*z+z^2)^2, z^3+23/36*z^2+1/36*z+1/576", "dm_basis": null, "q": "0 1 0 28 -324 1306 -6192 2566 -308712 9605779", "yuk": "1 1/5 -239/5 6049/5 -28911/5 -541749/5 11722657/5 1695793/5 -2748574959/5 38459645452/5", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/216*(76276+3348*93^(1/2))^(1/3)-421/54/(76276+3348*93^(1/2))^(1/3)-23/108","im":"0","approx_re":"-0.597246","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/4-1/12*19^(1/2)","im":"0","approx_re":"-0.113242","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/432*(76276+3348*93^(1/2))^(1/3)+421/108/(76276+3348*93^(1/2))^(1/3)-23/108","im":"1/8*3^(1/2)*(-1/54*(76276+3348*93^(1/2))^(1/3)+842/27/(76276+3348*93^(1/2))^(1/3))","approx_re":"-0.020821","approx_im":"-0.049733","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/432*(76276+3348*93^(1/2))^(1/3)+421/108/(76276+3348*93^(1/2))^(1/3)-23/108","im":"-1/8*3^(1/2)*(-1/54*(76276+3348*93^(1/2))^(1/3)+842/27/(76276+3348*93^(1/2))^(1/3))","approx_re":"-0.020821","approx_im":"0.049733","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/9","im":"0","approx_re":"0.111111111111","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/4+1/12*19^(1/2)","im":"0","approx_re":"0.613242","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","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}]}