{"count": 8, "status":"OK", "data":[{"pols": "[X^4, -3*(3*X+1)*(3*X+2)*(17*X^2+17*X+6), 648*(3*X+1)*(3*X+2)*(3*X+4)*(3*X+5)]", "text": "Hadamard product $B\\ast g$.", "degz": 2, "h3": "36", "sol": "1 36 3780 524160 82952100 14193715536 2558150090496 478581063966720 92098312591711140 18122109528268746000", "n_discr_factors": "2", "c3": "-156", "operator": "4 2 0 0 0 0 1 -36 -264 -723 -918 -459 25920 151632 285768 209952 52488", "new_number": "2.25", "id": 17, "operator_tex": "\\theta^4-3 x(3\\theta+1)(3\\theta+2)(17\\theta^2+17\\theta+6)+2^{3} 3^{4} x^{2}(3\\theta+1)(3\\theta+2)(3\\theta+4)(3\\theta+5)", "superseek": "27 2618", "discriminant": "2 1 -459 52488", "aesz": "138", "n_sing_complex": "0", "inst_int": "", "c2h": "108", "hash": "c524254b716132352b27914640b03c8b", "dim_h": "15", "inst": " 27 189/4 2618 43713 2319057 196286095/2 5214508191 272574896067 14990046252383 3356489455171983/4", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "A_{n}=\\dbinom{2n}{n}\\dbinom{3n}{n}\\sum_{j,k}^{n}(-1)^{j}8^{n-j}\\dbinom{n}{j}\\dbinom{j}{k}^3", "n_sing_rational": "3", "n_sing": "3", "laurent": "None", "discriminant_tex": "(243z-1)(216z-1)", "discr_factors": "52488, z-1/243, z-1/216", "dm_basis": ["-377989751/500000000*I", "21/2", "1", "1", "-9/2", "-18", "-1", "0", "0", "36", "0", "0", "-36", "0", "0", "0"], "q": "0 1 -120 10782 -841288 60234693 -4078954368 264886454966 -16689963727536 1025543560906530", "yuk": "1 27 405 70713 2798037 289882152 21198969351 1788576309540 139558349584341 10927743718057920", "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","36","1","0","0","0","1","1"]},{"re":"1/243","im":"0","approx_re":"0.00411522633745","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["1.+.755979502*I","0","39/2*lambda",".15875139e-1","9/2","1","9/16","-39/2*lambda","0","0","1","0","36","0","9/2","1.-.755979502*I"],"monodromy_dm":["1","-15","-1","-1","0","1","0","0","0","0","1","0","0","0","0","1"]},{"re":"1/216","im":"0","approx_re":"0.00462962962963","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[".84386396e-1+.881341465*I","-.593907697+1.816219110*I",".987405021+.251865740*I","-.18197034e-1-.280246794*I","-.610146073+4.105015738*I","3.086102688+5.881005017*I","1/ln(2)^(8/3)/ln(3)^(8/5)*Zeta(5)^8-1.317777791*I","-.605925748-.688412508*I","-1.084750363+4.722447485*I","1.891556916+7.035664131*I","4.676916900-1.255046419*I","-.642466556-.856579334*I","-4.881168587+32.840125900*I","16.688821505+47.048040140*I","24.445126799-10.542222328*I","-3.847405984-5.507300063*I"],"monodromy_dm":["-2450927/1000000+271203/1000000*I","-7338521/500000+382623/15625*I","299583/500000+49333/125000*I","33897/250000-456113/500000*I","505191/1000000-1/10000*I","3414753/1000000-1697749/500000*I","-3307/40000-1004/15625*I","-7533/250000+131179/1000000*I","-1136679/125000+28/15625*I","-43465553/1000000+61118963/1000000*I","1244077/500000+18072/15625*I","4339/8000-295153/125000*I","378893/50000-1493/1000000*I","18110647/500000-5093247/100000*I","-19377/15625-3012/3125*I","548021/1000000+983843/500000*I"]},{"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, -6*(2*X+1)^2*(3*X^2+3*X+1), -108*(2*X+1)*(X+1)^2*(2*X+3)]", "text": "Hadamard product $I \\ast \\zeta$", "degz": 2, "h3": "36", "sol": "1 6 162 6180 284130 14553756 800506476 46305405432 2780921118690 171927372671340", "n_discr_factors": "1", "c3": "-120", "operator": "4 2 0 0 0 0 1 -6 -42 -114 -144 -72 -324 -1512 -2484 -1728 -432", "new_number": "2.56", "id": 51, "operator_tex": "\\theta^4-2 3 x(2\\theta+1)^2(3\\theta^2+3\\theta+1)-2^{2} 3^{3} x^{2}(2\\theta+1)(\\theta+1)^2(2\\theta+3)", "superseek": "6 608", "discriminant": "2 1 -72 -432", "aesz": "185\n", "n_sing_complex": "0", "inst_int": "", "c2h": "84", "hash": "80506439e4d4fdc41f5b16e246a69fbf", "dim_h": "13", "inst": " 6 93/2 608 11754 275352 7385808 217059960 6828131178 678725472244/3 7810724839074", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "3", "laurent": null, "discriminant_tex": "1-72z-432z^2", "discr_factors": "-432, -1/432+1/6*z+z^2", "dm_basis": ["-120*lambda", "19/2", "1", "1", "-7/2", "-18", "-1", "0", "0", "36", "0", "0", "-36", "0", "0", "0"], "q": "0 1 -18 27 -36 -22167 -482598 -16710093 -589136328 -21533578893", "yuk": "1 6 378 16422 752634 34419006 1595351322 74451566286 3496003915770 164930289771714", "gv2": null, "gv0": "216 1674 21888 423144 9912672 265889088 7814158560 245812722408 8144705666928 281186094206664", "gv1": "0 0 0 0 432 374244 47016720 3817401912 257168084992 15642903869352 894095532071136 49057031338312056 2616721485814811088 136776743210373105060 7042999506203371710528 358568495069148149096088 18095776638485891677952544 906965529519461742959059708 45208728659669539002191355600", "spectrum":[{"re":"-1/12-1/18*3^(1/2)","im":"0","approx_re":"-0.179558","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["8+480*lambda","-7/2-240*lambda","91/72+260/3*lambda","-.302703484-140/3*lambda","26","-12","169/36","-91/72-260/3*lambda","72","-36","14","-7/2-240*lambda","144","-72","26","-6-480*lambda"],"monodromy_dm":["-13","-100","-6","-4","7","51","3","2","-168","-1200","-71","-48","126","900","54","37"]},{"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","36","1","0","0","0","1","1"]},{"re":"-1/12+1/18*3^(1/2)","im":"0","approx_re":"0.012892","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["1+120*lambda","0","35/3*lambda",".9393573e-2","7/2","1","49/144","-35/3*lambda","0","0","1","0","36","0","7/2","1-120*lambda"],"monodromy_dm":["1","-13","-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":["1/2","1","1","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -172*X^4-344*X^3-286*X^2-114*X-18, 36*(X+1)^2*(236*X^2+472*X+187), -32400*(X+1)*(X+2)*(2*X+1)*(2*X+5)]", "text": "Operator equivalent to AESZ 103 =$c \\ast c$.", "degz": 3, "h3": "36", "sol": "1 18 630 28980 1593270 99340668 6771183804 491734025640 37390439327670 2942412630737580", "n_discr_factors": "2", "c3": "-48", "operator": "4 3 0 0 0 0 1 -18 -114 -286 -344 -172 6732 30456 49212 33984 8496 -324000 -1263600 -1587600 -777600 -129600", "new_number": "3.10", "id": 71, "operator_tex": "\\theta^4-2 x\\left(86\\theta^4+172\\theta^3+143\\theta^2+57\\theta+9\\right)+2^{2} 3^{2} x^{2}(\\theta+1)^2(236\\theta^2+472\\theta+187)-2^{4} 3^{4} 5^{2} x^{3}(\\theta+1)(\\theta+2)(2\\theta+1)(2\\theta+5)", "superseek": "10 664", "discriminant": "3 1 -172 8496 -129600", "aesz": "~103", "n_sing_complex": "0", "inst_int": "", "c2h": "72", "hash": "9239615e8ac132ca232c13367a39ae3b", "dim_h": "12", "inst": " 10 24 664 9088 234388 5667648 162977404 4849452496 154029465758 5070777681360", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "-(100z-1)(-1+36z)^2", "discr_factors": "-129600, z-1/100, (-1/36+z)^2", "dm_basis": ["-48*lambda", "9", "1", "1", "-3", "-18", "-1", "0", "0", "36", "0", "0", "-36", "0", "0", "0"], "q": "0 1 -42 1407 -46436 1436487 -44122518 1303343085 -38697997416 1108968963840", "yuk": "1 10 202 17938 581834 29298510 1224230098 55901249582 2482920259786 112287480555520", "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":"1/100","im":"0","approx_re":"0.01","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/36","im":"0","approx_re":"0.0277777777778","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/2","1","2","5/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, 15*X^4+30*X^3+35*X^2+20*X+4, -32*(X+1)^2*(66*X^2+132*X+53), -12544*(X+1)*(X+2)*(2*X+1)*(2*X+5)]", "text": "Operator equivalent to AESZ 100= $ a \\ast a$", "degz": 3, "h3": "36", "sol": "1 -4 132 -1120 72100 -265104 59047296 350118912 63064312740 1096066914800", "n_discr_factors": "2", "c3": "-72", "operator": "4 3 0 0 0 0 1 4 20 35 30 15 -1696 -7616 -12256 -8448 -2112 -125440 -489216 -614656 -301056 -50176", "new_number": "3.8", "id": 103, "operator_tex": "\\theta^4+x\\left(15\\theta^4+30\\theta^3+35\\theta^2+20\\theta+4\\right)-2^{5} x^{2}(\\theta+1)^2(66\\theta^2+132\\theta+53)-2^{8} 7^{2} x^{3}(\\theta+1)(\\theta+2)(2\\theta+1)(2\\theta+5)", "superseek": "5 454", "discriminant": "3 1 15 -2112 -50176", "aesz": "~100", "n_sing_complex": "0", "inst_int": "", "c2h": "72", "hash": "82a1ac6ac6fb9ab2e4d6b5d5790d1d9b", "dim_h": "12", "inst": " 5 42 454 7498 154351 3652254 94572705 2621325434 76541504257 2329054186336", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "-(49z-1)(1+32z)^2", "discr_factors": "-50176, (1/32+z)^2, z-1/49", "dm_basis": null, "q": "0 1 4 -258 -4616 -15963 203304 -9506154 -568626864 -17941215870", "yuk": "1 5 341 12263 480213 19293880 788899463 32438437820 1342119102421 55798756615616", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/32","im":"0","approx_re":"-0.03125","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/49","im":"0","approx_re":"0.0204081632653","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","5/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -639*X^4-558*X^3-447*X^2-168*X-24, 151632*X^4+232848*X^3+204984*X^2+84672*X+12960, -16030656*X^4-31850496*X^3-27661824*X^2-10368000*X-1451520, 3317760*(2*X+1)^2*(51*X^2+69*X+32), -298598400*(2*X+1)^2*(2*X+3)^2]", "text": "This is operator \"5.100\" from ...", "degz": 5, "h3": "36", "sol": "1 24 1944 218400 28488600 4048761024 608371749216 95064025769856 15292201195042200 2515650430048641600", "n_discr_factors": "3", "c3": "-16", "operator": "4 5 0 0 0 0 1 -24 -168 -447 -558 -639 12960 84672 204984 232848 151632 -1451520 -10368000 -27661824 -31850496 -16030656 106168320 653598720 1509580800 1592524800 676823040 -2687385600 -14332723200 -26276659200 -19110297600 -4777574400", "new_number": "5.100", "id": 182, "operator_tex": "\\theta^4-3 x\\left(213\\theta^4+186\\theta^3+149\\theta^2+56\\theta+8\\right)+2^{3} 3^{3} x^{2}\\left(702\\theta^4+1078\\theta^3+949\\theta^2+392\\theta+60\\right)-2^{6} 3^{3} x^{3}\\left(9277\\theta^4+18432\\theta^3+16008\\theta^2+6000\\theta+840\\right)+2^{13} 3^{4} 5 x^{4}(2\\theta+1)^2(51\\theta^2+69\\theta+32)-2^{14} 3^{6} 5^{2} x^{5}(2\\theta+1)^2(2\\theta+3)^2", "superseek": "15 27140/3", "discriminant": "5 1 -639 151632 -16030656 676823040 -4777574400", "aesz": "347\n", "n_sing_complex": "0", "inst_int": "", "c2h": "84", "hash": "f00de20026c099e75b447c475ab287e4", "dim_h": "13", "inst": " 15 1329/4 27140/3 220680 5952570 550577279/3 6782826234 302695932456 138944230607815/9 1711409037498435/2", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "-(192z-1)(1728z^2-207z+1)(-1+120z)^2", "discr_factors": "-4777574400, z-1/192, z^2-23/192*z+1/1728, (-1/120+z)^2", "dm_basis": null, "q": "0 1 -72 2484 -54576 1205874 -26096256 504161136 -10716165216 43953392151", "yuk": "1 15 2673 244275 14126193 744071265 39641811021 2326509398277 154980331543665 11254482679477290", "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":"23/384-11/1152*33^(1/2)","im":"0","approx_re":"0.005043","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/192","im":"0","approx_re":"0.00520833333333","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/120","im":"0","approx_re":"0.00833333333333","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"23/384+11/1152*33^(1/2)","im":"0","approx_re":"0.114748","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": "[81*X^4, -1719*X^4-7758*X^3-6147*X^2-2268*X-324, -231200*X^4-794720*X^3-980288*X^2-517536*X-98208, -3392256*X^4-9179136*X^3-7076096*X^2-1783296*X-46080, -20480*(2*X+1)*(314*X^3+363*X^2+68*X-31), 1638400*(2*X+1)*(X+1)^2*(2*X+3)]", "text": "This is operator \"5.87\" from ...", "degz": 5, "h3": "36", "sol": "1 4 132 4000 179620 8127504 412976256 21605895168 1184481569700 66548256071440", "n_discr_factors": "3", "c3": "-128", "operator": "4 5 0 0 0 0 81 -324 -2268 -6147 -7758 -1719 -98208 -517536 -980288 -794720 -231200 -46080 -1783296 -7076096 -9179136 -3392256 634880 -122880 -10219520 -21299200 -12861440 4915200 22937600 37683200 26214400 6553600", "new_number": "5.87", "id": 301, "operator_tex": "3^{4} \\theta^4-3^{2} x\\left(191\\theta^4+862\\theta^3+683\\theta^2+252\\theta+36\\right)-2^{5} x^{2}\\left(7225\\theta^4+24835\\theta^3+30634\\theta^2+16173\\theta+3069\\right)-2^{8} x^{3}\\left(13251\\theta^4+35856\\theta^3+27641\\theta^2+6966\\theta+180\\right)-2^{12} 5 x^{4}(2\\theta+1)(314\\theta^3+363\\theta^2+68\\theta-31)+2^{16} 5^{2} x^{5}(2\\theta+1)(\\theta+1)^2(2\\theta+3)", "superseek": "35/9 3002/9", "discriminant": "5 81 -1719 -231200 -3392256 -12861440 6553600", "aesz": "321", "n_sing_complex": "0", "inst_int": "", "c2h": "84", "hash": "b786027c217dd5d5c5abac7b1ecc570b", "dim_h": "13", "inst": " 35/9 261/4 3002/9 126800/9 1727129/9 14907123/2 1476084167/9 55207321888/9 1554991360055/9 232053578385767/36", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "(32z+1)(32z^2-71z+1)(9+80z)^2", "discr_factors": "6553600, z+1/32, z^2-71/32*z+1/32, (9/80+z)^2", "dm_basis": null, "q": "0 1 -12 -178 2664 -47355 -234392 -22549626 -420799504 -24839805918", "yuk": "1 35/9 4733/9 81089/9 8119933/9 71963720/3 14489809343/9 506296869316/9 9422052308863/3 1133588701561184/9", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-9/80","im":"0","approx_re":"-0.1125","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/32","im":"0","approx_re":"-0.03125","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":"71/64-17/64*17^(1/2)","im":"0","approx_re":"0.014175","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"71/64+17/64*17^(1/2)","im":"0","approx_re":"2.204575","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","1","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -(10*X^2+10*X+3)*(7*X^2+7*X+2), -71*X^4-1148*X^3-1591*X^2-886*X-192, -5040*X^4+30240*X^3+92808*X^2+69336*X+17280, -20592*X^4-41184*X^3+163872*X^2+184464*X+59616, 362880*X^4+3628800*X^3+2026944*X^2-388800*X-393984, -368064*X^4+4478976*X^3+7397568*X^2+4478976*X+933120, 373248*(10*X^2+10*X+3)*(7*X^2+7*X+2), 26873856*(X+1)^4]", "text": "Hadamard product $a \\ast c$. This operator has a second MUM-point at infinity with the same instanton point. \nIt is reducible to an operator of degree 4 with a single MUM-point defined over $Q(\\sqrt{-2})$", "degz": 8, "h3": "36", "sol": "1 6 150 5208 221094 10478556 534006096 28636761600 1594933457958 91464881448084", "n_discr_factors": "5", "c3": "-60", "operator": "4 8 0 0 0 0 1 -6 -41 -111 -140 -70 -192 -886 -1591 -1148 -71 17280 69336 92808 30240 -5040 59616 184464 163872 -41184 -20592 -393984 -388800 2026944 3628800 362880 933120 4478976 7397568 4478976 -368064 2239488 15303168 41430528 52254720 26127360 26873856 107495424 161243136 107495424 26873856", "new_number": "8.2", "id": 474, "operator_tex": "\\theta^4-x(10\\theta^2+10\\theta+3)(7\\theta^2+7\\theta+2)-x^{2}\\left(71\\theta^4+1148\\theta^3+1591\\theta^2+886\\theta+192\\right)-2^{3} 3^{2} x^{3}\\left(70\\theta^4-420\\theta^3-1289\\theta^2-963\\theta-240\\right)-2^{4} 3^{2} x^{4}\\left(143\\theta^4+286\\theta^3-1138\\theta^2-1281\\theta-414\\right)+2^{6} 3^{4} x^{5}\\left(70\\theta^4+700\\theta^3+391\\theta^2-75\\theta-76\\right)-2^{6} 3^{4} x^{6}\\left(71\\theta^4-864\\theta^3-1427\\theta^2-864\\theta-180\\right)+2^{9} 3^{6} x^{7}(10\\theta^2+10\\theta+3)(7\\theta^2+7\\theta+2)+2^{12} 3^{8} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "7 1271/3", "discriminant": "8 1 -70 -71 -5040 -20592 362880 -368064 26127360 26873856", "aesz": "104", "n_sing_complex": "2", "inst_int": "", "c2h": "72", "hash": "d6bd0d1524954c8ce0a6421d295e9795", "dim_h": "12", "inst": " 7 93/2 1271/3 18507/2 190710 9428013/2 128027760 7423428159/2 339968018663/3 3607055297185", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "5", "n_sing": "7", "laurent": null, "discriminant_tex": "(9z+1)(8z-1)(72z-1)(z+1)(1+72z^2)^2", "discr_factors": "26873856, z+1/9, z-1/8, z-1/72, z+1, (1/72+z^2)^2", "dm_basis": null, "q": "0 1 -17 28 337 -25739 -225296 -10088399 -338161817 -10983844277", "yuk": "1 7 379 11446 592603 23838757 1018237222 43913521687 1900398201307 82612228546555", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1","im":"0","approx_re":"-1.0","approx_im":"0.0","exponents":["0","1","1","2"],"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":"0","im":"-1/12*2^(1/2)","approx_re":"0.0","approx_im":"-0.117851","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":"0","im":"1/12*2^(1/2)","approx_re":"0.0","approx_im":"0.117851","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/72","im":"0","approx_re":"0.0138888888889","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/8","im":"0","approx_re":"0.125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[16*X^4, -288-2400*X-7636*X^2-10472*X^3-5128*X^4, -26424-143496*X-285795*X^2-241290*X^3-85527*X^4, -784728-4313736*X-7404372*X^2-1481328*X^3+1265787*X^4, -8612406-34179894*X-29773818*X^2+29597400*X^3+22024548*X^4, -39234780-121404744*X+67263372*X^2+479110464*X^3-54377568*X^4, -102509064-240211332*X+66371076*X^2-85030560*X^3-1465359984*X^4, -17006112*(2*X+1)*(100*X^3+162*X^2+95*X+21), 1224440064*(2*X+1)*(X+1)^2*(2*X+3)]", "text": "This is operator \"8.30\" from ...", "degz": 8, "h3": "36", "sol": "1 18 1926 310860 61060230 13432459068 3181130504244 793444983882408 205654006502505990 54906028842418516620", "n_discr_factors": "3", "c3": "-204", "operator": "4 8 0 0 0 0 16 -288 -2400 -7636 -10472 -5128 -26424 -143496 -285795 -241290 -85527 -784728 -4313736 -7404372 -1481328 1265787 -8612406 -34179894 -29773818 29597400 22024548 -39234780 -121404744 67263372 479110464 -54377568 -102509064 -240211332 66371076 -85030560 -1465359984 -357128352 -2329837344 -5986151424 -7210591488 -3401222400 3673320192 17142160896 28162121472 19591041024 4897760256", "new_number": "8.30", "id": 475, "operator_tex": "2^{4} \\theta^4-2^{2} x\\left(1282\\theta^4+2618\\theta^3+1909\\theta^2+600\\theta+72\\right)-3^{2} x^{2}\\left(9503\\theta^4+26810\\theta^3+31755\\theta^2+15944\\theta+2936\\right)+3^{4} x^{3}\\left(15627\\theta^4-18288\\theta^3-91412\\theta^2-53256\\theta-9688\\right)+2 3^{6} x^{4}\\left(15106\\theta^4+20300\\theta^3-20421\\theta^2-23443\\theta-5907\\right)-2^{2} 3^{8} x^{5}\\left(2072\\theta^4-18256\\theta^3-2563\\theta^2+4626\\theta+1495\\right)-2^{2} 3^{10} x^{6}\\left(6204\\theta^4+360\\theta^3-281\\theta^2+1017\\theta+434\\right)-2^{5} 3^{12} x^{7}(2\\theta+1)(100\\theta^3+162\\theta^2+95\\theta+21)+2^{8} 3^{14} x^{8}(2\\theta+1)(\\theta+1)^2(2\\theta+3)", "superseek": "229/4 297111/4", "discriminant": "8 16 -5128 -85527 1265787 22024548 -54377568 -1465359984 -3401222400 4897760256", "aesz": "314", "n_sing_complex": "2", "inst_int": "", "c2h": "0", "hash": "893692ba7eb3effcbc0c3b48d405456a", "dim_h": "6", "inst": " 229/4 1293 297111/4 6150238 2540085295/4 74831355661 9685903435429 1342462084703074 392130689138916953/2 29842706359594087140", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "7", "laurent": null, "discriminant_tex": "(z-1)(11664z^3+3888z^2+324z-1)(-4-9z+648z^2)^2", "discr_factors": "4897760256, z-1, (-1/162-1/72*z+z^2)^2, z^3+1/3*z^2+1/36*z-1/11664", "dm_basis": null, "q": "0 1 -78 1029 -60368 -6625650 -865943982 -127452930702 -19739639668632 -3184583094643149", "yuk": "1 229/4 41605/4 4011113/2 1574502533/4 79377665526 32327149677353/2 13289059513408817/4 2749362351046398085/4 142931636191137234925", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/36*2^(1/3)-1/72*2^(2/3)-1/9","im":"-1/36*3^(1/2)*(2^(1/3)-1/2*2^(2/3))","approx_re":"-0.168156","approx_im":"-0.022431","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/36*2^(1/3)-1/72*2^(2/3)-1/9","im":"1/36*3^(1/2)*(2^(1/3)-1/2*2^(2/3))","approx_re":"-0.168156","approx_im":"0.022431","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/144-1/144*129^(1/2)","im":"0","approx_re":"-0.071929","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":"1/18*2^(1/3)+1/36*2^(2/3)-1/9","im":"0","approx_re":"0.002979","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/144+1/144*129^(1/2)","im":"0","approx_re":"0.085818","approx_im":"0.0","exponents":["0","1","3","4"],"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":["1/2","1","1","3/2"],"monodromy":[],"monodromy_dm":[]}]}]}