{"count": 4, "status":"OK", "data":[{"pols": "[X^4, -13*X^4-14*X^3-16*X^2-9*X-2, 33*X^4-88*X^3-265*X^2-324*X-148, 217*X^4+2362*X^3+6403*X^2+8178*X+4160, -1354*X^4-8268*X^3-16178*X^2-12420*X-720, 1812*X^4-15192*X^3-139320*X^2-347460*X-301320, 7580*X^4+149208*X^3+707964*X^2+1423392*X+1075344, -38540*X^4-356680*X^3-743540*X^2+429576*X+2089856, 47256*X^4-85088*X^3-3329000*X^2-13330608*X-16415360, 94304*X^4+2569088*X^3+16637888*X^2+42511200*X+38564800, -391808*X^4-5430528*X^3-25443520*X^2-46255680*X-22811520, 433728*X^4+2572416*X^3-8937408*X^2-87598848*X-152957952, 1152*(X+4)*(371*X^3+8580*X^2+53325*X+101564), -27648*(X+4)*(X+5)*(51*X^2+519*X+1330), 829440*(X+4)*(X+5)^2*(X+6)]", "text": "This is operator \"14.1\" from ...", "degz": 14, "h3": null, "sol": "1 2 16 48 264 1008 5008 21824 106792 500496", "n_discr_factors": "9", "c3": null, "operator": "4 14 0 0 0 0 1 -2 -9 -16 -14 -13 -148 -324 -265 -88 33 4160 8178 6403 2362 217 -720 -12420 -16178 -8268 -1354 -301320 -347460 -139320 -15192 1812 1075344 1423392 707964 149208 7580 2089856 429576 -743540 -356680 -38540 -16415360 -13330608 -3329000 -85088 47256 38564800 42511200 16637888 2569088 94304 -22811520 -46255680 -25443520 -5430528 -391808 -152957952 -87598848 -8937408 2572416 433728 468006912 362723328 100967040 11593728 427392 -735436800 -617932800 -194116608 -27039744 -1410048 497664000 406425600 123586560 16588800 829440", "new_number": "14.1", "id": 380, "operator_tex": "\\theta^4-x\\left(13\\theta^4+14\\theta^3+16\\theta^2+9\\theta+2\\right)+x^{2}\\left(33\\theta^4-88\\theta^3-265\\theta^2-324\\theta-148\\right)+x^{3}\\left(217\\theta^4+2362\\theta^3+6403\\theta^2+8178\\theta+4160\\right)-2 x^{4}\\left(677\\theta^4+4134\\theta^3+8089\\theta^2+6210\\theta+360\\right)+2^{2} 3 x^{5}\\left(151\\theta^4-1266\\theta^3-11610\\theta^2-28955\\theta-25110\\right)+2^{2} x^{6}\\left(1895\\theta^4+37302\\theta^3+176991\\theta^2+355848\\theta+268836\\right)-2^{2} x^{7}\\left(9635\\theta^4+89170\\theta^3+185885\\theta^2-107394\\theta-522464\\right)+2^{3} x^{8}\\left(5907\\theta^4-10636\\theta^3-416125\\theta^2-1666326\\theta-2051920\\right)+2^{5} x^{9}\\left(2947\\theta^4+80284\\theta^3+519934\\theta^2+1328475\\theta+1205150\\right)-2^{6} x^{10}\\left(6122\\theta^4+84852\\theta^3+397555\\theta^2+722745\\theta+356430\\right)+2^{6} 3 x^{11}\\left(2259\\theta^4+13398\\theta^3-46549\\theta^2-456244\\theta-796656\\right)+2^{7} 3^{2} x^{12}(\\theta+4)(371\\theta^3+8580\\theta^2+53325\\theta+101564)-2^{10} 3^{3} x^{13}(\\theta+4)(\\theta+5)(51\\theta^2+519\\theta+1330)+2^{11} 3^{4} 5 x^{14}(\\theta+4)(\\theta+5)^2(\\theta+6)", "superseek": "0 0", "discriminant": "14 1 -13 33 217 -1354 1812 7580 -38540 47256 94304 -391808 433728 427392 -1410048 829440", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "a8cf56492aecc07971e82c9104785180", "dim_h": null, "inst": " 0 1/4 0 -1/2 0 28/9 0 -14 0 2223/20", "cleanlist": "True", "n_sing_real": "9", "sol_explicit": "", "n_sing_rational": "9", "n_sing": "11", "laurent": null, "discriminant_tex": "(z-1)(6z-1)(4z-1)(3z+1)(4z+1)(5z-1)(2z+1)^2(2z-1)^2(6z^2-2z+1)^2", "discr_factors": "829440, z+1/4, z-1/4, z-1/6, (z-1/2)^2, (z^2-1/3*z+1/6)^2, z-1, (z+1/2)^2, z-1/5, z+1/3", "dm_basis": null, "q": "0 1 -1 -5 11 26 -99 -146 871 717", "yuk": "1 0 2 0 -30 0 674 0 -7198 0", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/2","im":"0","approx_re":"-0.5","approx_im":"0.0","exponents":["0","0","-1","1"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/3","im":"0","approx_re":"-0.333333333333","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","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":"1/6","im":"-1/6*5^(1/2)","approx_re":"0.166666666667","approx_im":"-0.372678","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/6","im":"0","approx_re":"0.166666666667","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/6","im":"1/6*5^(1/2)","approx_re":"0.166666666667","approx_im":"0.372678","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/5","im":"0","approx_re":"0.2","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","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/2","im":"0","approx_re":"0.5","approx_im":"0.0","exponents":["0","0","-1","1"],"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":["4","5","5","6"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -1080*X^4-108*X^3+108*X^2+162*X+54, 607796*X^4-57016*X^3-280716*X^2-170380*X-24864, -231759792*X^4+94404096*X^3+206143920*X^2+64618776*X-13611240, 65227123968*X^4-48564192768*X^3-72099465040*X^2-8122273840*X+11596005984, -14066373012480*X^4+15195333003264*X^3+13999572187200*X^2-1687316230656*X-3282545328192, 2359816716720128*X^4-3290695102746624*X^3-1528486967623936*X^2+843457210205952*X+458342842795776, -27899909581049856-158500070146934784*X+74461221541942272*X^2+509776698302005248*X^3-307095565445406720*X^4, 30422938491488960512*X^4-56950223173721391104*X^3+2252759436976885760*X^2+17467780737296838656*X-803082528013074432, -2214843187307211915264*X^4+4610937478802466668544*X^3-508085941259030446080*X^2-1211755384935017938944*X+266244995514218692608, -19224668449399085531136+53196928087690737156096*X+21013167072375093657600*X^2-273629387456451706355712*X^3+111058393005347629694976*X^4, -3268770702689219367665664*X^4+12147398436951383819157504*X^3+434303782324614709641216*X^2-1574875925775946403020800*X+727482384391255017652224, 19397619377463692818907136*X^4-403354081997251933655531520*X^3-47495566182530791099072512*X^2+45502562207831923164708864*X-21912310182848197400985600, 2180210994862646014186094592*X^4+8651143024324447900614524928*X^3-1078411184992932449715486720*X^2-1904418975224600987713929216*X+514185729032199203129917440, -229256481029845155840*X*(269358010*X^3+131761607*X^2-826543489*X-380205376), -30702027939516863270092800*X*(X+1)*(1997*X^2+119865*X+91208), 16446462326640393316523311104000*X*(X+2)*(X+1)^2]", "text": "This is operator \"16.1\" from ...", "degz": 16, "h3": null, "sol": "1 -54 -1362 -73548 -4170906 -246754836 -13172025396 -427220212248 35101755954198 10995363622275516", "n_discr_factors": null, "c3": null, "operator": "4 16 0 0 0 0 1 54 162 108 -108 -1080 -24864 -170380 -280716 -57016 607796 -13611240 64618776 206143920 94404096 -231759792 11596005984 -8122273840 -72099465040 -48564192768 65227123968 -3282545328192 -1687316230656 13999572187200 15195333003264 -14066373012480 458342842795776 843457210205952 -1528486967623936 -3290695102746624 2359816716720128 -27899909581049856 -158500070146934784 74461221541942272 509776698302005248 -307095565445406720 -803082528013074432 17467780737296838656 2252759436976885760 -56950223173721391104 30422938491488960512 266244995514218692608 -1211755384935017938944 -508085941259030446080 4610937478802466668544 -2214843187307211915264 -19224668449399085531136 53196928087690737156096 21013167072375093657600 -273629387456451706355712 111058393005347629694976 727482384391255017652224 -1574875925775946403020800 434303782324614709641216 12147398436951383819157504 -3268770702689219367665664 -21912310182848197400985600 45502562207831923164708864 -47495566182530791099072512 -403354081997251933655531520 19397619377463692818907136 514185729032199203129917440 -1904418975224600987713929216 -1078411184992932449715486720 8651143024324447900614524928 2180210994862646014186094592 0 87164546570389144697925795840 189490451706270528237742325760 -30207202355657412694643834880 -61752069509801841785202278400 0 -2800270564307454065138624102400 -6480369143277642881008297574400 -3741410528765403991820048793600 -61311949795215175950375321600 0 32892924653280786633046622208000 82232311633201966582616555520000 65785849306561573266093244416000 16446462326640393316523311104000", "new_number": "16.1", "id": 570, "operator_tex": "\\theta^4-2 3^{3} x\\left(20\\theta^4+2\\theta^3-2\\theta^2-3\\theta-1\\right)+2^{2} x^{2}\\left(151949\\theta^4-14254\\theta^3-70179\\theta^2-42595\\theta-6216\\right)-2^{3} 3^{3} x^{3}\\left(1072962\\theta^4-437056\\theta^3-954370\\theta^2-299161\\theta+63015\\right)+2^{4} x^{4}\\left(4076695248\\theta^4-3035262048\\theta^3-4506216565\\theta^2-507642115\\theta+724750374\\right)-2^{6} 3^{3} x^{5}\\left(8140262160\\theta^4-8793595488\\theta^3-8101604275\\theta^2+976456152\\theta+1899621139\\right)+2^{8} x^{6}\\left(9218034049688\\theta^4-12854277745104\\theta^3-5970652217281\\theta^2+3294754727367\\theta+1790401729671\\right)-2^{10} 3^{3} x^{7}\\left(11107333819640\\theta^4-18438103960576\\theta^3-2693186543039\\theta^2+5732786101958\\theta+1009111312972\\right)+2^{12} x^{8}\\left(7427475217648672\\theta^4-13903863079521824\\theta^3+549990096918185\\theta^2+4264594906566611\\theta-196065070315692\\right)-2^{14} 3^{3} x^{9}\\left(5006788889131248\\theta^4-10423307017692208\\theta^3+1148559437524935\\theta^2+2739247379862508\\theta-601863144518181\\right)+2^{16} 3^{4} x^{10}\\left(20921192499862036\\theta^4-51546334623445432\\theta^3+3958462764104225\\theta^2+10021243264975981\\theta-3621545193405921\\right)-2^{18} 3^{7} x^{11}\\left(5701586950847588\\theta^4-21188224783674368\\theta^3-757538843568497\\theta^2+2746993547213600\\theta-1268918638558608\\right)+2^{23} 3^{10} x^{12}\\left(39160297802908\\theta^4-814299201549560\\theta^3-95884988762411\\theta^2+91861472904467\\theta-44237005356800\\right)+2^{28} 3^{13} x^{13}\\left(5094274414759\\theta^4+20214234618156\\theta^3-2519812312315\\theta^2-4449859616032\\theta+1201444818880\\right)-2^{35} 3^{16} 5 31 x^{14}\\theta(269358010\\theta^3+131761607\\theta^2-826543489\\theta-380205376)-2^{40} 3^{19} 5^{2} 31^{2} x^{15}\\theta(\\theta+1)(1997\\theta^2+119865\\theta+91208)+2^{47} 3^{22} 5^{3} 31^{3} x^{16}\\theta(\\theta+2)(\\theta+1)^2", "superseek": "0 0", "discriminant": null, "aesz": null, "n_sing_complex": null, "inst_int": null, "c2h": null, "hash": "ce5c5b062cf22bc8935e236748d3c341", "dim_h": null, "inst": " 0 12293/4 0 -8127101 0 41236218451 0 -276447980501616 0 4329637201512212709/2", "cleanlist": "True", "n_sing_real": null, "sol_explicit": null, "n_sing_rational": null, "n_sing": null, "laurent": null, "discriminant_tex": null, "discr_factors": null, "dm_basis": null, "q": "0 1 -54 -433 204228 850519 -1293038154 -6904309651 10578727730088 73530074294464", "yuk": "1 0 24586 0 -520109878 0 8907023210002 0 -141541366536937270 0", "gv2": null, "gv0": null, "gv1": null}, {"pols": "[3*X^4, -1200*X^4-1500*X^3-1500*X^2-750*X-150, 187740*X^4+435960*X^3+557100*X^2+354780*X+89400, -14322000*X^4-45360000*X^3-66078000*X^2-45909000*X-12219000, 532800000*X^4+1994400000*X^3+3029250000*X^2+2059950000*X+523800000, -15000000*(X+1)^2*(524*X^2+1096*X+611), 2000000000*(X+1)^2*(X+2)^2]", "text": "This is operator \"6.13\" from ...", "degz": 6, "h3": null, "sol": "1 50 3450 267500 22029250 1882312500 40070712812500/243 8582299119171875000/583443 28749442551877343750/21609 638895192146725039062500/5250987", "n_discr_factors": null, "c3": null, "operator": "4 6 0 0 0 0 3 -150 -750 -1500 -1500 -1200 89400 354780 557100 435960 187740 -12219000 -45909000 -66078000 -45360000 -14322000 523800000 2059950000 3029250000 1994400000 532800000 -9165000000 -34770000000 -49905000000 -32160000000 -7860000000 8000000000 24000000000 26000000000 12000000000 2000000000", "new_number": "6.13", "id": 583, "operator_tex": "3 \\theta^4-2 3 5^{2} x\\left(8\\theta^4+10\\theta^3+10\\theta^2+5\\theta+1\\right)+2^{2} 3 5 x^{2}\\left(3129\\theta^4+7266\\theta^3+9285\\theta^2+5913\\theta+1490\\right)-2^{3} 3 5^{3} x^{3}\\left(4774\\theta^4+15120\\theta^3+22026\\theta^2+15303\\theta+4073\\right)+2^{4} 3 5^{5} x^{4}\\left(3552\\theta^4+13296\\theta^3+20195\\theta^2+13733\\theta+3492\\right)-2^{6} 3 5^{7} x^{5}(\\theta+1)^2(524\\theta^2+1096\\theta+611)+2^{10} 5^{9} x^{6}(\\theta+1)^2(\\theta+2)^2", "superseek": "0 0", "discriminant": null, "aesz": null, "n_sing_complex": null, "inst_int": null, "c2h": null, "hash": "b7b28238d79425febad0c26d36cce7ef", "dim_h": null, "inst": " 0 165/4 0 -44335/8 0 13953739445/6561 185200000000000/2470629 48581886883225/15552 2872156814000000000000/26795786661 83062447138990159/36450", "cleanlist": "True", "n_sing_real": null, "sol_explicit": null, "n_sing_rational": null, "n_sing": null, "laurent": null, "discriminant_tex": null, "discr_factors": null, "dm_basis": null, "q": "0 1 -50 1635 -38500 687275 -9888750 87784671125/729 -24861386713175000/12252303 19044062514606250/1361367", "yuk": "1 0 330 0 -354350 0 111629995750/243 185200000000000/7203 388655008958750/243 2872156814000000000000/36756909", "gv2": null, "gv0": null, "gv1": null}, {"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":[]}]}]}