{"count": 5, "status":"OK", "data":[{"pols": "[X^4, 112+384*X-384*X^2-1536*X^3+3840*X^4, -143360+491520*X+3883008*X^2-786432*X^3+3735552*X^4, 10485760-327155712*X-1744830464*X^2+2415919104*X^3-503316480*X^4, -692026605568-2141041197056*X-2595233988608*X^2-2834678415360*X^3-1108101562368*X^4, -422556062449664-1432113895178240*X-1825739057922048*X^2-721279627821056*X^3+63771674411008*X^4, 265167020247482368+947022559143002112*X+1436014962433589248*X^2+834291830970384384*X^3+96264442035044352*X^4, 166759287002274725888+408242299021880721408*X+245932568451448045568*X^2-32570032505143427072*X^3-13258597302978740224*X^4, -81290189446819566583808-230501290573037702217728*X-229915606448697423953920*X^2-52462540145629964795904*X^3+1051464412201444442112*X^4, -2927867219379180032491520+4037623342853546657710080*X+24476025480713371142586368*X^2+11588687348962109354409984*X^3+524182679598530618720256*X^4, 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z^2-700/10917*z+625/294759, (z-25/378)^2, z-25/128, z+25/72, z-25/153", "dm_basis": null, "q": "0 1 -228/25 81984/625 -25313602/15625 9587396256/390625 -3604099625118/9765625 1398183577941279/244140625 -554924800284557862/6103515625 224200628657466750036/152587890625", "yuk": "1 7/2 -379/2 3203 -196187/2 4076757/2 -41453141 878084977 -35942168923/2 357127269722", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-25/72","im":"0","approx_re":"-0.347222222222","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"175/80046-625/80046*57^(1/2)","im":"0","approx_re":"-0.056763","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":"25/978","im":"-625/8802*3^(1/2)","approx_re":"0.0255623721881","approx_im":"-0.122987","exponents":["0","0","-1","1"],"monodromy":[],"monodromy_dm":[]},{"re":"25/978","im":"625/8802*3^(1/2)","approx_re":"0.0255623721881","approx_im":"0.122987","exponents":["0","0","-1","1"],"monodromy":[],"monodromy_dm":[]},{"re":"350/10917","im":"-625/32751*3^(1/2)","approx_re":"0.0320600897683","approx_im":"-0.033053","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"350/10917","im":"625/32751*3^(1/2)","approx_re":"0.0320600897683","approx_im":"0.033053","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"175/80046+625/80046*57^(1/2)","im":"0","approx_re":"0.061135","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"25/378","im":"0","approx_re":"0.0661375661376","approx_im":"0.0","exponents":["0","-1","1","-2"],"monodromy":[],"monodromy_dm":[]},{"re":"25/153","im":"0","approx_re":"0.16339869281","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"25/128","im":"0","approx_re":"0.1953125","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","6","7","8"],"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": "[27*X^4, 432*X^4-540-2628*X-5760*X^3-5508*X^2, 295872*X+306240*X^2+112464-33792*X^3-129024*X^4, -1102080+17825792*X^3+6772736*X^2+1005568*X+335872*X^4, -65896448*X+209977344*X^4-7311360-67010560*X^2-67633152*X^3, -8728018944-20230963200*X-14659092480*X^3-3407872000*X^4-20752105472*X^2, -66441969664*X^2+32568770560*X-88264933376*X^4-76369887232*X^3+50988056576, 11803408990208+10383083438080*X^3+25540291461120*X+22371679338496*X^2+1950720458752*X^4, 14018773254144*X^3+16522739187712*X^4-88707717660672-43752831844352*X^2-124506806943744*X, -11378553778077696*X-8578509978992640*X^2-428603376402432*X^4-5853482078699520-3110518394978304*X^3, 20472631631282176*X^2+44573995231608832-2308974418329600*X^3+58566861243023360*X-2196824232296448*X^4, 1383827742532829184*X^2+1060244769013235712+1993713648320643072*X+419679190275588096*X^3+43980465111040000*X^4, -3489322140979691520+790803947068588032*X^2+250512729272483840*X^4+1173187702930014208*X^3-2883851873889026048*X, -86645879130887815168*X^2-137928368087755653120*X-76746685674950754304-21527206218830970880*X^3-1639310264362860544*X^4, -454233058416588226560*X^2-640682082989726760960*X-14771806777775226880*X^4-138350580552821637120*X^3-332635868477584834560, -28823037615171174400*(X+2)^4]", "text": "This is operator \"15.3\" from ...", "degz": 15, "h3": null, "sol": "1 20 388 7344 141636 2777360 55728816 1143301440 23982011716 513499103440", "n_discr_factors": "5", "c3": null, "operator": "4 15 0 0 0 0 27 -540 -2628 -5508 -5760 432 112464 295872 306240 -33792 -129024 -1102080 1005568 6772736 17825792 335872 -7311360 -65896448 -67010560 -67633152 209977344 -8728018944 -20230963200 -20752105472 -14659092480 -3407872000 50988056576 32568770560 -66441969664 -76369887232 -88264933376 11803408990208 25540291461120 22371679338496 10383083438080 1950720458752 -88707717660672 -124506806943744 -43752831844352 14018773254144 16522739187712 -5853482078699520 -11378553778077696 -8578509978992640 -3110518394978304 -428603376402432 44573995231608832 58566861243023360 20472631631282176 -2308974418329600 -2196824232296448 1060244769013235712 1993713648320643072 1383827742532829184 419679190275588096 43980465111040000 -3489322140979691520 -2883851873889026048 790803947068588032 1173187702930014208 250512729272483840 -76746685674950754304 -137928368087755653120 -86645879130887815168 -21527206218830970880 -1639310264362860544 -332635868477584834560 -640682082989726760960 -454233058416588226560 -138350580552821637120 -14771806777775226880 -461168601842738790400 -922337203685477580800 -691752902764108185600 -230584300921369395200 -28823037615171174400", "new_number": "15.3", "id": 391, "operator_tex": "3^{3} \\theta^4+2^{2} 3^{2} x\\left(12\\theta^4-160\\theta^3-153\\theta^2-73\\theta-15\\right)-2^{4} 3 x^{2}\\left(2688\\theta^4+704\\theta^3-6380\\theta^2-6164\\theta-2343\\right)+2^{8} x^{3}\\left(1312\\theta^4+69632\\theta^3+26456\\theta^2+3928\\theta-4305\\right)+2^{12} x^{4}\\left(51264\\theta^4-16512\\theta^3-16360\\theta^2-16088\\theta-1785\\right)-2^{16} x^{5}\\left(52000\\theta^4+223680\\theta^3+316652\\theta^2+308700\\theta+133179\\right)-2^{21} x^{6}\\left(42088\\theta^4+36416\\theta^3+31682\\theta^2-15530\\theta-24313\\right)+2^{25} x^{7}\\left(58136\\theta^4+309440\\theta^3+666728\\theta^2+761160\\theta+351769\\right)+2^{29} x^{8}\\left(30776\\theta^4+26112\\theta^3-81496\\theta^2-231912\\theta-165231\\right)-2^{33} 3 x^{9}\\left(16632\\theta^4+120704\\theta^3+332890\\theta^2+441546\\theta+227145\\right)-2^{36} x^{10}\\left(31968\\theta^4+33600\\theta^3-297916\\theta^2-852260\\theta-648637\\right)+2^{40} x^{11}\\left(40000\\theta^4+381696\\theta^3+1258584\\theta^2+1813272\\theta+964287\\right)+2^{44} x^{12}\\left(14240\\theta^4+66688\\theta^3+44952\\theta^2-163928\\theta-198345\\right)-2^{48} x^{13}\\left(5824\\theta^4+76480\\theta^3+307828\\theta^2+490020\\theta+272659\\right)-2^{54} 5 x^{14}\\left(164\\theta^4+1536\\theta^3+5043\\theta^2+7113\\theta+3693\\right)-2^{60} 5^{2} x^{15}\\left((\\theta+2)^4\\right)", "superseek": "44/3 220588/81", "discriminant": "15 27 432 -129024 335872 209977344 -3407872000 -88264933376 1950720458752 16522739187712 -428603376402432 -2196824232296448 43980465111040000 250512729272483840 -1639310264362860544 -14771806777775226880 -28823037615171174400", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "ae51313cd958206bb1b7a3c8ae23e509", "dim_h": null, "inst": " 44/3 -1421/9 220588/81 -14752264/243 1138508000/729 -10709297389/243 26132550216580/19683 -2479083315913288/59049 37209718959808/27 -222890635279564684376/4782969", "cleanlist": "True", "n_sing_real": "8", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "8", "laurent": null, "discriminant_tex": "-(1+16z)(1280z^2-32z-1)^2(256z^2+16z-1)^2(16z+3)^3(16z-1)^3", "discr_factors": "-28823037615171174400, (z^2-1/40*z-1/1280)^2, (z+3/16)^3, (z^2+1/16*z-1/256)^2, 1/16+z, (z-1/16)^3", "dm_basis": null, "q": "0 1 -52/3 1034/3 -685232/81 58632847/243 -7584520 1665120615890/6561 -174404409876800/19683 956870278022/3", "yuk": "1 44/3 -11236/9 73544 -944448268/243 142313510692/729 -9519303176 8963464724575624/19683 -1269290887248532580/59049 1004662411988360", "gv2": null, "gv0": null, "gv1": null, 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{"pols": "[25*X^4, -300-1100*X-1660*X^2-1120*X^3-10480*X^4, 680960*X+1964544*X^4+632832*X^3+969344*X^2+158320, -37018880-144348160*X-209849344*X^2-139444224*X^3-217964544*X^4, 15973089280*X^4+17656250368*X+5061877760+16775118848*X^3+25085739008*X^2, -450117763072-1433513492480*X-1922996109312*X^2-1260052807680*X^3-817352409088*X^4, 101136447045632*X^2+63277149192192*X^3+81033617735680*X+30113106231296*X^4+27403069947904, -1172226564947968-3250626939060224*X-3763978341711872*X^2-2205773333528576*X^3-811916054233088*X^4, 54428574353981440*X^3+16123384538595328*X^4+93195756621529088*X+100329190494044160*X^2+35629414452559872, -769799426687369216-1907350033615814656*X-1916083179597332480*X^2-957108379304591360*X^3-235396918291726336*X^4, 2501498904353177600*X^4+11941558294763536384*X^3+27594548875410538496*X+25978776955975106560*X^2+11710476134977110016, -122831035499414552576-276522424495432007680*X-245184900544560365568*X^2-104031884754863259648*X^3-18970780111600615424*X^4, 1852920498288670539776*X+856593656325123080192+613444312443390001152*X^3+99284105585196269568*X^4+1556901146581421522944*X^2, -3736042135678487625728-7821275372064774029312*X-6275928210327371513856*X^2-2315642842002852151296*X^3-338526576790185443328*X^4, 14379237005456595484672*X^2+673306158690398633984*X^4+18603541398336082804736*X+5017514388048998039552*X^3+9112691572412518498304, -590295810358705651712*(X+2)^4]", "text": "This is operator \"15.4\" from ...", "degz": 15, "h3": null, "sol": "1 12 44 -3792 -207124 -8325552 -309616912 -11277235008 -410187134228 -15004164993648", "n_discr_factors": "5", "c3": null, "operator": "4 15 0 0 0 0 25 -300 -1100 -1660 -1120 -10480 158320 680960 969344 632832 1964544 -37018880 -144348160 -209849344 -139444224 -217964544 5061877760 17656250368 25085739008 16775118848 15973089280 -450117763072 -1433513492480 -1922996109312 -1260052807680 -817352409088 27403069947904 81033617735680 101136447045632 63277149192192 30113106231296 -1172226564947968 -3250626939060224 -3763978341711872 -2205773333528576 -811916054233088 35629414452559872 93195756621529088 100329190494044160 54428574353981440 16123384538595328 -769799426687369216 -1907350033615814656 -1916083179597332480 -957108379304591360 -235396918291726336 11710476134977110016 27594548875410538496 25978776955975106560 11941558294763536384 2501498904353177600 -122831035499414552576 -276522424495432007680 -245184900544560365568 -104031884754863259648 -18970780111600615424 856593656325123080192 1852920498288670539776 1556901146581421522944 613444312443390001152 99284105585196269568 -3736042135678487625728 -7821275372064774029312 -6275928210327371513856 -2315642842002852151296 -338526576790185443328 9112691572412518498304 18603541398336082804736 14379237005456595484672 5017514388048998039552 673306158690398633984 -9444732965739290427392 -18889465931478580854784 -14167099448608935641088 -4722366482869645213696 -590295810358705651712", "new_number": "15.4", "id": 392, "operator_tex": "5^{2} \\theta^4-2^{2} 5 x\\left(524\\theta^4+56\\theta^3+83\\theta^2+55\\theta+15\\right)+2^{4} x^{2}\\left(122784\\theta^4+39552\\theta^3+60584\\theta^2+42560\\theta+9895\\right)-2^{8} x^{3}\\left(851424\\theta^4+544704\\theta^3+819724\\theta^2+563860\\theta+144605\\right)+2^{13} x^{4}\\left(1949840\\theta^4+2047744\\theta^3+3062224\\theta^2+2155304\\theta+617905\\right)-2^{18} x^{5}\\left(3117952\\theta^4+4806720\\theta^3+7335648\\theta^2+5468420\\theta+1717063\\right)+2^{22} x^{6}\\left(7179524\\theta^4+15086448\\theta^3+24112808\\theta^2+19319920\\theta+6533401\\right)-2^{26} x^{7}\\left(12098492\\theta^4+32868584\\theta^3+56087648\\theta^2+48438116\\theta+17467537\\right)+2^{31} x^{8}\\left(7508036\\theta^4+25345280\\theta^3+46719420\\theta^2+43397656\\theta+16591239\\right)-2^{38} x^{9}\\left(856369\\theta^4+3481940\\theta^3+6970670\\theta^2+6938899\\theta+2800514\\right)+2^{42} x^{10}\\left(568775\\theta^4+2715196\\theta^3+5906890\\theta^2+6274274\\theta+2662654\\right)-2^{46} x^{11}\\left(269591\\theta^4+1478382\\theta^3+3484287\\theta^2+3929620\\theta+1745534\\right)+2^{51} x^{12}\\left(44091\\theta^4+272424\\theta^3+691403\\theta^2+822862\\theta+380404\\right)-2^{57} x^{13}\\left(2349\\theta^4+16068\\theta^3+43548\\theta^2+54271\\theta+25924\\right)+2^{63} x^{14}\\left(73\\theta^4+544\\theta^3+1559\\theta^2+2017\\theta+988\\right)-2^{69} x^{15}\\left((\\theta+2)^4\\right)", "superseek": "52/5 13436/5", "discriminant": "15 25 -10480 1964544 -217964544 15973089280 -817352409088 30113106231296 -811916054233088 16123384538595328 -235396918291726336 2501498904353177600 -18970780111600615424 99284105585196269568 -338526576790185443328 673306158690398633984 -590295810358705651712", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "2306e85a3af0a97d616dedf03cc93f69", "dim_h": null, "inst": " 52/5 115 13436/5 89632 18465296/5 871619621/5 45240257244/5 503650715312 147905271435016/5 9063969995240684/5", "cleanlist": "True", "n_sing_real": "8", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "8", "laurent": null, "discriminant_tex": "-(-1+32z)(256z^2-48z+1)^2(512z^2-128z+5)^2(64z-1)^3(16z-1)^3", "discr_factors": "-590295810358705651712, (z-1/16)^3, (z^2-1/4*z+5/512)^2, -1/32+z, (z-1/64)^3, (z^2-3/16*z+1/256)^2", "dm_basis": null, "q": "0 1 4 422 23056 1452289 97060696 6773971762 487971107392 36012102833428", "yuk": "1 52/5 4652/5 362824/5 28686892/5 2308162052/5 37654041112 15517408234744/5 1289345859885612/5 107822942876489488/5", "gv2": null, "gv0": null, "gv1": null, 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