{"count": 4, "status":"OK", "data":[{"pols": "[X^4, -352*X^4-128*X^3-144*X^2-80*X-16, 48128*X^4+45056*X^3+49664*X^2+23040*X+4096, -3178496*X^4-5505024*X^3-6078464*X^2-3194880*X-671744, 100663296*X^4+276824064*X^3+341311488*X^2+202899456*X+47185920, -1207959552*(X+1)^4]", "text": "There is a second MUM-point hiding at infinity, corresponding to Operator...", "degz": 5, "h3": "128", "sol": "1 16 464 17152 725776 33449216 1633531136 83137654784 4362766699792 234378319042816", "n_discr_factors": "3", "c3": "544", "operator": "4 5 0 0 0 0 1 -16 -80 -144 -128 -352 4096 23040 49664 45056 48128 -671744 -3194880 -6078464 -5505024 -3178496 47185920 202899456 341311488 276824064 100663296 -1207959552 -4831838208 -7247757312 -4831838208 -1207959552", "new_number": "5.9", "id": 315, "operator_tex": "\\theta^4-2^{4} x\\left(22\\theta^4+8\\theta^3+9\\theta^2+5\\theta+1\\right)+2^{9} x^{2}\\left(94\\theta^4+88\\theta^3+97\\theta^2+45\\theta+8\\right)-2^{14} x^{3}\\left(194\\theta^4+336\\theta^3+371\\theta^2+195\\theta+41\\right)+2^{19} 3 x^{4}\\left(64\\theta^4+176\\theta^3+217\\theta^2+129\\theta+30\\right)-2^{27} 3^{2} x^{5}\\left((\\theta+1)^4\\right)", "superseek": "-16 -3280", "discriminant": "5 1 -352 48128 -3178496 100663296 -1207959552", "aesz": "56", "n_sing_complex": "0", "inst_int": "", "c2h": "-64", "hash": "58a7f24bf18cb98b526885069667f9f0", "dim_h": "16", "inst": " -16 -178 -3280 -76197 -2046896 -60450314 -1908455824 -63296186075 -2180416654720 -77402940045830", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "-(-1+32z)(96z-1)^2(64z-1)^2", "discr_factors": "-1207959552, -1/32+z, (z-1/64)^2, (z-1/96)^2", "dm_basis": null, "q": "0 1 -16 128 -1024 1968 -48640 781312 74416128 4319629464", "yuk": "1 -16 -1440 -88576 -4878048 -255862016 -13057357824 -654600347648 -32407652148448 -1589523741379456", "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":"1/96","im":"0","approx_re":"0.0104166666667","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/64","im":"0","approx_re":"0.015625","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"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":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -152*X^4-200*X^3-212*X^2-112*X-24, 9872*X^4+25568*X^3+37776*X^2+28992*X+9376, -364032*X^4-1399808*X^3-2642176*X^2-2539008*X-1014016, 8529920*X^4+43130880*X^3+98770944*X^2+112343040*X+52101120, -135135232*X^4-830013440*X^3-2213789696*X^2-2879913984*X-1501495296, 1517879296*X^4+10569777152*X^3+31405178880*X^2+45223772160*X+25817448448, -12704546816*X^4-93967089664*X^3-293598134272*X^2-446554963968*X-269278511104, 83248545792*X^4+626159255552*X^3+1939722993664*X^2+2903272062976*X+1730242674688, -436207616000*X^4-3331284008960*X^3-10178669838336*X^2-14365726081024*X-7823954018304, 1791001362432*X^4+13958643712000*X^3+44105019162624*X^2+63200443760640*X+33853200662528, -5634997092352*X^4-43843026157568*X^3-140393890971648*X^2-210762635149312*X-122007135977472, 13194139533312*X^4+107752139522048*X^3+340298848796672*X^2+490931941801984*X+272060408397824, -1099511627776*(2*X+5)^4]", "text": "This is operator \"13.3\" from ...", "degz": 13, "h3": null, "sol": "1 24 464 8832 178960 4010368 100357376 2772019200 82738408720 2613822935424", "n_discr_factors": "4", "c3": null, "operator": "4 13 0 0 0 0 1 -24 -112 -212 -200 -152 9376 28992 37776 25568 9872 -1014016 -2539008 -2642176 -1399808 -364032 52101120 112343040 98770944 43130880 8529920 -1501495296 -2879913984 -2213789696 -830013440 -135135232 25817448448 45223772160 31405178880 10569777152 1517879296 -269278511104 -446554963968 -293598134272 -93967089664 -12704546816 1730242674688 2903272062976 1939722993664 626159255552 83248545792 -7823954018304 -14365726081024 -10178669838336 -3331284008960 -436207616000 33853200662528 63200443760640 44105019162624 13958643712000 1791001362432 -122007135977472 -210762635149312 -140393890971648 -43843026157568 -5634997092352 272060408397824 490931941801984 340298848796672 107752139522048 13194139533312 -687194767360000 -1099511627776000 -659706976665600 -175921860444160 -17592186044416", "new_number": "13.3", "id": 371, "operator_tex": "\\theta^4-2^{2} x\\left(38\\theta^4+50\\theta^3+53\\theta^2+28\\theta+6\\right)+2^{4} x^{2}\\left(617\\theta^4+1598\\theta^3+2361\\theta^2+1812\\theta+586\\right)-2^{8} x^{3}\\left(1422\\theta^4+5468\\theta^3+10321\\theta^2+9918\\theta+3961\\right)+2^{11} x^{4}\\left(4165\\theta^4+21060\\theta^3+48228\\theta^2+54855\\theta+25440\\right)-2^{14} x^{5}\\left(8248\\theta^4+50660\\theta^3+135119\\theta^2+175776\\theta+91644\\right)+2^{16} x^{6}\\left(23161\\theta^4+161282\\theta^3+479205\\theta^2+690060\\theta+393943\\right)-2^{20} x^{7}\\left(12116\\theta^4+89614\\theta^3+279997\\theta^2+425868\\theta+256804\\right)+2^{23} x^{8}\\left(9924\\theta^4+74644\\theta^3+231233\\theta^2+346097\\theta+206261\\right)-2^{27} x^{9}\\left(3250\\theta^4+24820\\theta^3+75837\\theta^2+107033\\theta+58293\\right)+2^{28} x^{10}\\left(6672\\theta^4+52000\\theta^3+164304\\theta^2+235440\\theta+126113\\right)-2^{32} x^{11}\\left(1312\\theta^4+10208\\theta^3+32688\\theta^2+49072\\theta+28407\\right)+2^{36} x^{12}\\left(192\\theta^4+1568\\theta^3+4952\\theta^2+7144\\theta+3959\\right)-2^{40} x^{13}\\left((2\\theta+5)^4\\right)", "superseek": "4 52", "discriminant": "13 1 -152 9872 -364032 8529920 -135135232 1517879296 -12704546816 83248545792 -436207616000 1791001362432 -5634997092352 13194139533312 -17592186044416", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "9127ce057848ca38f220a7bb67e245a2", "dim_h": null, "inst": " 4 7/2 52 500 2796 108891/2 523876 8014175 112614496 3281174301/2", "cleanlist": "True", "n_sing_real": "6", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "8", "laurent": null, "discriminant_tex": "-(1-48z+256z^2)(8z-1)^2(512z^3-32z^2+20z-1)^2(16z-1)^3", "discr_factors": "-17592186044416, (z^3-1/16*z^2+5/128*z-1/512)^2, 1/256-3/16*z+z^2, (z-1/8)^2, (z-1/16)^3", "dm_basis": null, "q": "0 1 -16 192 -2304 24240 -254976 2316288 -22216704 157621400", "yuk": "1 4 32 1408 32032 349504 11761664 179689472 4103289632 82095968992", "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":"-1/96*(64+3*3165^(1/2))^(1/3)+29/96/(64+3*3165^(1/2))^(1/3)+1/48","im":"-1/8*3^(1/2)*(1/12*(64+3*3165^(1/2))^(1/3)+29/12/(64+3*3165^(1/2))^(1/3))","approx_re":"0.005863","approx_im":"-0.196043","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/96*(64+3*3165^(1/2))^(1/3)+29/96/(64+3*3165^(1/2))^(1/3)+1/48","im":"1/8*3^(1/2)*(1/12*(64+3*3165^(1/2))^(1/3)+29/12/(64+3*3165^(1/2))^(1/3))","approx_re":"0.005863","approx_im":"0.196043","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"3/32-1/32*5^(1/2)","im":"0","approx_re":"0.023873","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/48*(64+3*3165^(1/2))^(1/3)-29/48/(64+3*3165^(1/2))^(1/3)+1/48","im":"0","approx_re":"0.050774","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","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/8","im":"0","approx_re":"0.125","approx_im":"0.0","exponents":["0","0","-1","1"],"monodromy":[],"monodromy_dm":[]},{"re":"3/32+1/32*5^(1/2)","im":"0","approx_re":"0.163627","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":["5/2","5/2","5/2","5/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[25*X^4, 380*X^4+1720*X^3+1460*X^2+600*X+100, 11344*X^4+68032*X^3+117424*X^2+77280*X+18640, -107520*X^4-29184*X^3+843264*X^2+1013760*X+339200, -971776*X^4-6944768*X^3-11622400*X^2-7904256*X-1934336, 5386240*X^4+17539072*X^3+29487104*X^2+23527424*X+6926336, 10043392*X^4+25559040*X^3+15941632*X^2-3538944*X-4079616, -2883584-10223616*X-10485760*X^2-524288*X^3+2883584*X^4, -1048576*(X+1)^4]", "text": "This is operator \"8.45\" from ...", "degz": 8, "h3": null, "sol": "1 -4 -4 464 -4244 -64304 2188976 -10994624 -630978836 14385797456", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 25 100 600 1460 1720 380 18640 77280 117424 68032 11344 339200 1013760 843264 -29184 -107520 -1934336 -7904256 -11622400 -6944768 -971776 6926336 23527424 29487104 17539072 5386240 -4079616 -3538944 15941632 25559040 10043392 -2883584 -10223616 -10485760 -524288 2883584 -1048576 -4194304 -6291456 -4194304 -1048576", "new_number": "8.45", "id": 491, "operator_tex": "5^{2} \\theta^4+2^{2} 5 x\\left(19\\theta^4+86\\theta^3+73\\theta^2+30\\theta+5\\right)+2^{4} x^{2}\\left(709\\theta^4+4252\\theta^3+7339\\theta^2+4830\\theta+1165\\right)-2^{8} x^{3}\\left(420\\theta^4+114\\theta^3-3294\\theta^2-3960\\theta-1325\\right)-2^{10} x^{4}\\left(949\\theta^4+6782\\theta^3+11350\\theta^2+7719\\theta+1889\\right)+2^{12} x^{5}\\left(1315\\theta^4+4282\\theta^3+7199\\theta^2+5744\\theta+1691\\right)+2^{14} x^{6}\\left(613\\theta^4+1560\\theta^3+973\\theta^2-216\\theta-249\\right)+2^{18} x^{7}\\left(11\\theta^4-2\\theta^3-40\\theta^2-39\\theta-11\\right)-2^{20} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "-12/5 -20", "discriminant": "8 25 380 11344 -107520 -971776 5386240 10043392 2883584 -1048576", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "52e4f6959f297529016ddef66a399c12", "dim_h": null, "inst": " -12/5 -83/5 -20 3941/20 -13872/5 -197789/5 173580 57625509/20 -244692056/5 -480447172", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "7", "laurent": null, "discriminant_tex": "-(8z+1)(128z^3-624z^2-20z-1)(-5+32z+32z^2)^2", "discr_factors": "-1048576, z^3-39/8*z^2-5/32*z-1/128, z+1/8, (-5/32+z+z^2)^2", "dm_basis": null, "q": "0 1 8 126 1280 12209 135664 1558810 14866944 131815364", "yuk": "1 -12/5 -676/5 -2712/5 12476 -1734012/5 -8545160 297689688/5 7376127532/5 -178380511536/5", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/2-1/8*26^(1/2)","im":"0","approx_re":"-1.137377","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","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/48*(61128+177*177^(1/2))^(1/3)-517/16/(61128+177*177^(1/2))^(1/3)+13/8","im":"-1/8*3^(1/2)*(1/6*(61128+177*177^(1/2))^(1/3)-517/2/(61128+177*177^(1/2))^(1/3))","approx_re":"-0.016083","approx_im":"-0.036516","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/48*(61128+177*177^(1/2))^(1/3)-517/16/(61128+177*177^(1/2))^(1/3)+13/8","im":"1/8*3^(1/2)*(1/6*(61128+177*177^(1/2))^(1/3)-517/2/(61128+177*177^(1/2))^(1/3))","approx_re":"-0.016083","approx_im":"0.036516","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":"-1/2+1/8*26^(1/2)","im":"0","approx_re":"0.137377","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/24*(61128+177*177^(1/2))^(1/3)+517/8/(61128+177*177^(1/2))^(1/3)+13/8","im":"0","approx_re":"4.907166","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": "[27*X^4, -1080*X^4-2448*X^3-1944*X^2-720*X-108, 6192*X^4+49728*X^3+69360*X^2+30048*X+2736, 419840*X^4+1034752*X^3+1820032*X^2+1866368*X+754752, -4396032*X^4+860160*X^3+26789888*X^2+17959936*X+3554304, 4685824*X^4-47063040*X^3-539981824*X^2-543836160*X-18164736, 1038209024*X^4+1100398592*X^3-1724329984*X^2-4393951232*X-2630938624, -4405100544*X^4+15843262464*X^3+3547955200*X^2+2510028800*X+2922299392, -18063097856*X^4-24164696064*X^3-250203865088*X^2-75539939328*X+15624830976, 651701518336*X^4-81321263104*X^3-94561632256*X^2+128318439424*X+226505523200, 149315125248*X^4+4151480156160*X^3+12803802923008*X^2+16455131201536*X+8119969120256, -21217440432128*X^4-70266805813248*X^3-137193184034816*X^2-135180991856640*X-54832664674304, -860067201024*X^4+18563117088768*X^3-13890326888448*X^2-110554874118144*X-92799345098752, 286583303438336*X^4+1784789765980160*X^3+5121708503597056*X^2+6995398723895296*X+3665801697558528, -8990977163264*X^4-1444558562918400*X^3-6453041796481024*X^2-10447448891719680*X-60878325131771904, -1941368167464960*X^4-15574539257774080*X^3-52954726261587968*X^2-84935160121786368*X-50239772207087616, -347647537840128*X^4+10096815277867008*X^3+70731960971952128*X^2+152715739827011584*X+105689730586247168, 7556977777442816*X^4+60106108802433024*X^3+167509943656644608*X^2+211352179540230144*X+98574395705917440, 4944435070631936*X^4+14362095759917056*X^3-10464945514741760*X^2-101598860136153088*X-95841748533641216, -21130414462599168*X^4-186492565233598464*X^3-509670368718356480*X^2-472903799397154816*X-84379545972506624, -11272193207959552*X^4-22430037206630400*X^3-6772991627100160*X^2+43844125669195776*X+51558299249672192, 25297563531870208*X^4+174197826211807232*X^3+449031752690696192*X^2+503796227846963200*X+212667539044433920, 26194765020135424*X^4+151644643702865920*X^3+296129267685654528*X^2+236614902297395200*X+66656792922292224, -37295434414161920*X^4-240661105087610880*X^3-591801138534154240*X^2-658651445502935040*X-280419445547991040, 7036874417766400*(X+2)^4]", "text": "This is operator \"24.14\" from ...", "degz": 24, "h3": null, "sol": "1 4 52 464 1412 -693765232/5625 -6731441951024/1366875 -61182688180883776/468838125 -1257035453283020332/468838125 -40668093989763282842512/1025348979375", "n_discr_factors": "1", "c3": null, "operator": "4 24 0 0 0 0 27 -108 -720 -1944 -2448 -1080 2736 30048 69360 49728 6192 754752 1866368 1820032 1034752 419840 3554304 17959936 26789888 860160 -4396032 -18164736 -543836160 -539981824 -47063040 4685824 -2630938624 -4393951232 -1724329984 1100398592 1038209024 2922299392 2510028800 3547955200 15843262464 -4405100544 15624830976 -75539939328 -250203865088 -24164696064 -18063097856 226505523200 128318439424 -94561632256 -81321263104 651701518336 8119969120256 16455131201536 12803802923008 4151480156160 149315125248 -54832664674304 -135180991856640 -137193184034816 -70266805813248 -21217440432128 -92799345098752 -110554874118144 -13890326888448 18563117088768 -860067201024 3665801697558528 6995398723895296 5121708503597056 1784789765980160 286583303438336 -60878325131771904 -10447448891719680 -6453041796481024 -1444558562918400 -8990977163264 -50239772207087616 -84935160121786368 -52954726261587968 -15574539257774080 -1941368167464960 105689730586247168 152715739827011584 70731960971952128 10096815277867008 -347647537840128 98574395705917440 211352179540230144 167509943656644608 60106108802433024 7556977777442816 -95841748533641216 -101598860136153088 -10464945514741760 14362095759917056 4944435070631936 -84379545972506624 -472903799397154816 -509670368718356480 -186492565233598464 -21130414462599168 51558299249672192 43844125669195776 -6772991627100160 -22430037206630400 -11272193207959552 212667539044433920 503796227846963200 449031752690696192 174197826211807232 25297563531870208 66656792922292224 236614902297395200 296129267685654528 151644643702865920 26194765020135424 -280419445547991040 -658651445502935040 -591801138534154240 -240661105087610880 -37295434414161920 112589990684262400 225179981368524800 168884986026393600 56294995342131200 7036874417766400", "new_number": "24.14", "id": 589, "operator_tex": "3^{3} \\theta^4-2^{2} 3^{2} x\\left(30\\theta^4+68\\theta^3+54\\theta^2+20\\theta+3\\right)+2^{4} 3 x^{2}\\left(129\\theta^4+1036\\theta^3+1445\\theta^2+626\\theta+57\\right)+2^{6} x^{3}\\left(6560\\theta^4+16168\\theta^3+28438\\theta^2+29162\\theta+11793\\right)-2^{10} x^{4}\\left(4293\\theta^4-840\\theta^3-26162\\theta^2-17539\\theta-3471\\right)+2^{10} x^{5}\\left(4576\\theta^4-45960\\theta^3-527326\\theta^2-531090\\theta-17739\\right)+2^{12} x^{6}\\left(253469\\theta^4+268652\\theta^3-420979\\theta^2-1072742\\theta-642319\\right)-2^{14} x^{7}\\left(268866\\theta^4-966996\\theta^3-216550\\theta^2-153200\\theta-178363\\right)-2^{16} x^{8}\\left(275621\\theta^4+368724\\theta^3+3817808\\theta^2+1152648\\theta-238416\\right)+2^{19} x^{9}\\left(1243022\\theta^4-155108\\theta^3-180362\\theta^2+244748\\theta+432025\\right)+2^{21} x^{10}\\left(71199\\theta^4+1979580\\theta^3+6105329\\theta^2+7846418\\theta+3871903\\right)-2^{23} x^{11}\\left(2529316\\theta^4+8376456\\theta^3+16354702\\theta^2+16114830\\theta+6536563\\right)-2^{27} x^{12}\\left(6408\\theta^4-138306\\theta^3+103491\\theta^2+823698\\theta+691409\\right)+2^{27} x^{13}\\left(2135212\\theta^4+13297720\\theta^3+38159702\\theta^2+52119782\\theta+27312351\\right)-2^{29} x^{14}\\left(16747\\theta^4+2690700\\theta^3+12019727\\theta^2+19459890\\theta+113394717\\right)-2^{31} x^{15}\\left(904020\\theta^4+7252460\\theta^3+24658966\\theta^2+39551016\\theta+23394717\\right)-2^{32} x^{16}\\left(80943\\theta^4-2350848\\theta^3-16468568\\theta^2-35556904\\theta-24607808\\right)+2^{34} x^{17}\\left(439874\\theta^4+3498636\\theta^3+9750362\\theta^2+12302316\\theta+5737785\\right)+2^{36} x^{18}\\left(71951\\theta^4+208996\\theta^3-152285\\theta^2-1478458\\theta-1394681\\right)-2^{38} x^{19}\\left(76872\\theta^4+678456\\theta^3+1854170\\theta^2+1720414\\theta+306971\\right)-2^{42} x^{20}\\left(2563\\theta^4+5100\\theta^3+1540\\theta^2-9969\\theta-11723\\right)+2^{42} x^{21}\\left(5752\\theta^4+39608\\theta^3+102098\\theta^2+114550\\theta+48355\\right)+2^{44} x^{22}\\left(1489\\theta^4+8620\\theta^3+16833\\theta^2+13450\\theta+3789\\right)-2^{46} 5 x^{23}\\left(106\\theta^4+684\\theta^3+1682\\theta^2+1872\\theta+797\\right)+2^{48} 5^{2} x^{24}\\left((\\theta+2)^4\\right)", "superseek": "16/3 -880/81", "discriminant": "24 27 -1080 6192 419840 -4396032 4685824 1038209024 -4405100544 -18063097856 651701518336 149315125248 -21217440432128 -860067201024 286583303438336 -8990977163264 -1941368167464960 -347647537840128 7556977777442816 4944435070631936 -21130414462599168 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