{"count": 77, "status":"OK", "data":[{"pols": "[X^4, -1296*(X+1/2)^4-1152*(X+1/2)^2-33, 443232*(X+1)^4+90072*(X+1)^2+7308, -3779136*(X+3/2)^2*(4*(X+3/2)^2+3), 944784*(2*X+3)*(2*X+5)*(6*X+11)*(6*X+13)]", "text": "YY-Operator equivalent to AESZ 170=$d \\ast h \\tilde B \\ast \\epsilon$", "degz": 4, "h3": null, "sol": "1 402 197010 104962956 58311249066 33214816772676 19237340237054940 11275171083526676040 6667676790890365989882 3970438396828869620358132", "n_discr_factors": "1", "c3": null, "operator": "4 4 0 0 0 0 1 -402 -1800 -3096 -2592 -1296 540612 1953072 2749464 1772928 443232 -102036672 -238085568 -215410752 -90699264 -15116544 2026561680 4202399232 3227382144 1088391168 136048896", "new_number": "4.10", "id": 105, "operator_tex": "\\theta^4-2 3 x\\left(216\\theta^4+432\\theta^3+516\\theta^2+300\\theta+67\\right)+2^{2} 3^{2} x^{2}\\left(12312\\theta^4+49248\\theta^3+76374\\theta^2+54252\\theta+15017\\right)-2^{6} 3^{10} x^{3}(\\theta^2+3\\theta+3)(2\\theta+3)^2+2^{4} 3^{10} x^{4}(2\\theta+3)(2\\theta+5)(6\\theta+11)(6\\theta+13)", "superseek": "-84 -148820", "discriminant": "4 1 -1296 443232 -15116544 136048896", "aesz": null, "n_sing_complex": "1", "inst_int": "", "c2h": null, "hash": "fc2837f1001e57a5cc53749a08d4f2bf", "dim_h": null, "inst": " -84 -5271/2 -148820 -41373213/4 -836813460 -149029320727/2 -7085845912404 -2830424545606623/4 -73374371515541012 -15677869461132014535/2", "cleanlist": "True", "n_sing_real": "1", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "2", "laurent": null, "discriminant_tex": "(1-648z+11664z^2)^2", "discr_factors": "136048896, (1/11664-1/18*z+z^2)^2", "dm_basis": null, "q": "0 1 -192 11916 -559360 30385806 -1707803136 54439705208 -4825641228288 -74261173085595", "yuk": "1 -84 -21168 -4018224 -661992576 -104601682584 -16095170677824 -2430445147954656 -362294342499640320 -53489916834833415972", "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":"s_1","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["-1/2","0","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"s_2","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["-1/2","0","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/36-1/54*2^(1/2)","im":"0","approx_re":"0.001589","approx_im":"0.0","exponents":["0","-1/2","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/36+1/54*2^(1/2)","im":"0","approx_re":"0.053967","approx_im":"0.0","exponents":["0","-1/2","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["3/2","11/6","13/6","5/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -972*(X+1/2)^4-864*(X+1/2)^2-99/4, 196830*(X+1)^4-251505/2*(X+1)^2-46413/4, 4782969*(X+3/2)^2*(4*(X+3/2)^2+3), 43046721/16*(2*X+3)*(2*X+5)*(6*X+11)*(6*X+13)]", "text": "This is operator \"4.11\" from ...", "degz": 4, "h3": null, "sol": "1 603/2 1008855/8 898513875/16 3331190162475/128 3161945411895501/256 6099993792665917011/1024 5952504034504427078115/2048 46875561168026465063658675/32768 46457746073264645346945105225/65536", "n_discr_factors": "1", "c3": null, "operator": "4 4 0 0 0 0 1 -603/2 -1350 -2322 -1944 -972 237897/4 535815 2110455/2 787320 196830 129140163 301327047 272629233 114791256 19131876 92335216545/16 11966988438 18380949867/2 3099363912 387420489", "new_number": "4.11", "id": 106, "operator_tex": "\\theta^4-x\\left(972\\theta^4+1944\\theta^3+2322\\theta^2+1350\\theta+603/2\\right)+x^{2}\\left(196830\\theta^4+787320\\theta^3+2110455/2\\theta^2+535815\\theta+237897/4\\right)+3^{14} x^{3}(\\theta^2+3\\theta+3)(2\\theta+3)^2+x^{4}43046721/16(2\\theta+3)(2\\theta+5)(6\\theta+11)(6\\theta+13)", "superseek": "-63 -96866", "discriminant": "4 1 -972 196830 19131876 387420489", "aesz": null, "n_sing_complex": "1", "inst_int": "", "c2h": null, "hash": "39ed55f37672c58e7ce182c4c33d4a66", "dim_h": null, "inst": " -63 -8757/4 -96866 -6253821 -446217723 -71032541839/2 -3003468049764 -267200854617627 -24665476255290500 -9385209703933096257/4", "cleanlist": "True", "n_sing_real": "1", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "2", "laurent": null, "discriminant_tex": "(-1+486z+19683z^2)^2", "discr_factors": "387420489, (-1/19683+2/81*z+z^2)^2", "dm_basis": null, "q": "0 1 -144 2106 395286 -22796343 -78199830 35931296835 -2490116826726 -108328486058532", "yuk": "1 -63 -17577 -2615445 -400262121 -55777215438 -7671517151571 -1030189541069115 -136806837964487145 -17981132190109389945", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/81-2/243*3^(1/2)","im":"0","approx_re":"-0.026601","approx_im":"0.0","exponents":["0","-1/2","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"s_1","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["-1/2","0","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"s_2","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["-1/2","0","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/81+2/243*3^(1/2)","im":"0","approx_re":"0.00191","approx_im":"0.0","exponents":["0","-1/2","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["3/2","11/6","13/6","5/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -1188*(X+1/2)^4-1092*(X+1/2)^2-141/4, 535086*(X+1)^4+1287495/2*(X+1)^2+223011/4, -820125*(X+3/2)^2*(132*(X+3/2)^2+103), 922640625/16*(2*X+3)*(2*X+5)*(6*X+11)*(6*X+13)]", "text": "YY-operator equivalent to AESZ $=b \\ast h ~B \\ast \\eta$", "degz": 4, "h3": null, "sol": "1 765/2 1009575/8 627988725/16 1505754528075/128 876427978866363/256 992952700080876675/1024 547116035902478345925/2048 2338776827733813875961075/32768 1204708667299330204097718975/65536", "n_discr_factors": "1", "c3": null, "operator": "4 4 0 0 0 0 1 -765/2 -1686 -2874 -2376 -1188 4938345/4 3427839 7708527/2 2140344 535086 -738112500 -1714881375 -1545935625 -649539000 -108256500 1979064140625/16 256494093750 393967546875/2 66430125000 8303765625", "new_number": "4.12", "id": 107, "operator_tex": "\\theta^4-x\\left(1188\\theta^4+2376\\theta^3+2874\\theta^2+1686\\theta+765/2\\right)+x^{2}\\left(535086\\theta^4+2140344\\theta^3+7708527/2\\theta^2+3427839\\theta+4938345/4\\right)-3^{8} 5^{3} x^{3}(33\\theta^2+99\\theta+100)(2\\theta+3)^2+x^{4}922640625/16(2\\theta+3)(2\\theta+5)(6\\theta+11)(6\\theta+13)", "superseek": "-45 7080", "discriminant": "4 1 -1188 535086 -108256500 8303765625", "aesz": null, "n_sing_complex": "1", "inst_int": "", "c2h": null, "hash": "6c95cb50a57e8a1c96a5a4e3e353cb85", "dim_h": null, "inst": " -45 -135 7080 406035 17168436 631199430 17671792905 115936332615 -29577913105800 -2692376094481614", "cleanlist": "True", "n_sing_real": "1", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "2", "laurent": null, "discriminant_tex": "(1-594z+91125z^2)^2", "discr_factors": "8303765625, (1/91125-22/3375*z+z^2)^2", "dm_basis": null, "q": "0 1 -156 18144 -1724866 150548730 -12113124102 936247114643 -69434363509134 5017792372971057", "yuk": "1 -45 -1125 191115 25985115 2146054455 136339266915 6061424966370 59359428283995 -21562298653937085", "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":"s_1","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["-1/2","0","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"s_2","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["-1/2","0","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"11/3375","im":"-2/3375","approx_re":"0.00325925925926","approx_im":"-0.000592592592593","exponents":["0","-1/2","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"11/3375","im":"2/3375","approx_re":"0.00325925925926","approx_im":"0.000592592592593","exponents":["0","-1/2","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["3/2","11/6","13/6","5/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -2560*(X+1/2)^4-2296*(X+1/2)^2-70, 2162688*(X+1)^4+1824768*(X+1)^2+157968, -2097152*(X+3/2)^2*(320*(X+3/2)^2+237), 1073741824*(2*X+3)*(2*X+5)*(4*X+7)*(4*X+9)]", "text": "YY-Operator equivalent to AESZ 37$=C \\ast \\alpha ~tilde c \\ast i$", "degz": 4, "h3": null, "sol": "1 804 655260 563879792 505573095132 465896958146928 437354371109864208 415950446183712897600 399419538832058760105948 386388886442070524565149168", "n_discr_factors": "2", "c3": null, "operator": "4 4 0 0 0 0 1 -804 -3576 -6136 -5120 -2560 4145424 12300288 14800896 8650752 2162688 -4515692544 -10550771712 -9556721664 -4026531840 -671088640 1014686023680 2113123909632 1627792605184 549755813888 68719476736", "new_number": "4.13", "id": 108, "operator_tex": "\\theta^4-2^{2} x\\left(640\\theta^4+1280\\theta^3+1534\\theta^2+894\\theta+201\\right)+2^{4} 3 x^{2}\\left(45056\\theta^4+180224\\theta^3+308352\\theta^2+256256\\theta+86363\\right)-2^{19} x^{3}(320\\theta^2+960\\theta+957)(2\\theta+3)^2+2^{30} x^{4}(2\\theta+3)(2\\theta+5)(4\\theta+7)(4\\theta+9)", "superseek": "-128 -1546624/3", "discriminant": "4 1 -2560 2162688 -671088640 68719476736", "aesz": "~37", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "c03e4e4ca58f9f1f76c98c8616bc2cbd", "dim_h": null, "inst": " -128 -5232 -1546624/3 -64705008 -7960717440 -1089730087792 -162852262064256 -25631728909937136 -12497550359574176128/3 -696752685957410152304", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "(1024z-1)^2(256z-1)^2", "discr_factors": "68719476736, (z-1/1024)^2, (z-1/256)^2", "dm_basis": null, "q": "0 1 -360 70956 -14059968 2347124430 -366393345504 54715249671864 -7875068403264000 1076803003734521061", "yuk": "1 -128 -41984 -13919744 -4141162496 -995089680128 -235381712924672 -55858325888039936 -13123445206028976128 -3036904737376538718848", "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":"1/1024","im":"0","approx_re":"0.0009765625","approx_im":"0.0","exponents":["0","-1/2","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/256","im":"0","approx_re":"0.00390625","approx_im":"0.0","exponents":["0","-1/2","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["3/2","7/4","9/4","5/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -4352*(X+1/2)^4-3788*(X+1/2)^2-101, 4743168*(X+1)^4-16128*(X+1)^2+5760, -16384*(X+3/2)^2*(1088*(X+3/2)^2+777), 262144*(2*X+3)*(2*X+5)*(4*X+7)*(4*X+9)]", "text": "YY-Operator equivalent to AESZ 52 $=C \\ast \\gamma \\tilde g \\ast i$", "degz": 4, "h3": null, "sol": "1 1320 2233320 4108451200 7880762169000 15500666950276032 31002086442385793280 62750084039647601541120 128151536375757747156690600 263545260900330847296670945600", "n_discr_factors": "1", "c3": null, "operator": "4 4 0 0 0 0 1 -1320 -5964 -10316 -8704 -4352 4732800 18940416 28442880 18972672 4743168 -118886400 -278839296 -253378560 -106954752 -17825792 247726080 515899392 397410304 134217728 16777216", "new_number": "4.14", "id": 109, "operator_tex": "\\theta^4-2^{2} x\\left(1088\\theta^4+2176\\theta^3+2579\\theta^2+1491\\theta+330\\right)+2^{7} 3 x^{2}\\left(12352\\theta^4+49408\\theta^3+74070\\theta^2+49324\\theta+12325\\right)-2^{12} x^{3}(1088\\theta^2+3264\\theta+3225)(2\\theta+3)^2+2^{18} x^{4}(2\\theta+3)(2\\theta+5)(4\\theta+7)(4\\theta+9)", "superseek": "-340 -15174100/3", "discriminant": "4 1 -4352 4743168 -17825792 16777216", "aesz": null, "n_sing_complex": "1", "inst_int": "", "c2h": null, "hash": "a961869d91c2f73091913e8f8c4b5fa0", "dim_h": null, "inst": " -340 -31985 -15174100/3 -1036481610 -246612212640 -193707689567825/3 -18075181026722460 -5315792147784226530 -4871206859483840096080/3 -511100579616840965458760", "cleanlist": "True", "n_sing_real": "1", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "2", "laurent": null, "discriminant_tex": "(1-2176z+4096z^2)^2", "discr_factors": "16777216, (1/4096-17/32*z+z^2)^2", "dm_basis": null, "q": "0 1 -684 159966 -18790896 1346499885 -101313680232 1393122481170 -2524801413772992 -640923118711447290", "yuk": "1 -340 -256220 -136567240 -66335079260 -30826526580340 -13946953785706520 -6199787092165804120 -2721685579731859062620 -1183703266854573279914680", "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":"s_1","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["-1/2","0","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"s_2","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["-1/2","0","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"17/64-3/16*2^(1/2)","im":"0","approx_re":"0.00046","approx_im":"0.0","exponents":["0","-1/2","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"17/64+3/16*2^(1/2)","im":"0","approx_re":"0.53079","approx_im":"0.0","exponents":["0","-1/2","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["3/2","7/4","9/4","5/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -1792*(X+1/2)^4-1620*(X+1/2)^2-51, 1466368*(X+1)^4+2265344*(X+1)^2+196992, -1327104*(X+3/2)^2*(448*(X+3/2)^2+335), 1719926784*(2*X+3)*(2*X+5)*(4*X+7)*(4*X+9)]", "text": "YY-Operator equivalent to AESZ 152 $=C \\ast \\delta ~tilde \\alpha \\ast i$", "degz": 4, "h3": null, "sol": "1 568 207720 25669504 -32774007128 -33531981809856 -18504054035460864 -5834315674341826560 490963612772074612392 2144977565489285442014656", "n_discr_factors": "1", "c3": null, "operator": "4 4 0 0 0 0 1 -568 -2516 -4308 -3584 -1792 3928704 10396160 11063552 5865472 1466368 -4010176512 -9360064512 -8470904832 -3567255552 -594542592 1625330810880 3384815910912 2607409004544 880602513408 110075314176", "new_number": "4.15", "id": 110, "operator_tex": "\\theta^4-2^{2} x\\left(448\\theta^4+896\\theta^3+1077\\theta^2+629\\theta+142\\right)+2^{7} x^{2}\\left(11456\\theta^4+45824\\theta^3+86434\\theta^2+81220\\theta+30693\\right)-2^{12} 3^{4} x^{3}(448\\theta^2+1344\\theta+1343)(2\\theta+3)^2+2^{18} 3^{8} x^{4}(2\\theta+3)(2\\theta+5)(4\\theta+7)(4\\theta+9)", "superseek": "-76 415420", "discriminant": "4 1 -1792 1466368 -594542592 110075314176", "aesz": null, "n_sing_complex": "1", "inst_int": "", "c2h": null, "hash": "d8c866a60b2b4edb0c88e03315fa2a7b", "dim_h": null, "inst": " -76 2958 415420 17891650 -1211214176 -318737280294 -23481434881860 1222575736557290 489910761382234864 45969766146854950768", "cleanlist": "True", "n_sing_real": "1", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "2", "laurent": null, "discriminant_tex": "(331776z^2-896z+1)^2", "discr_factors": "110075314176, (z^2-7/2592*z+1/331776)^2", "dm_basis": null, "q": "0 1 -244 67038 -11065488 2080590637 -311558771544 48546840405778 -6877593269132096 978116260390106886", "yuk": "1 -76 23588 11216264 1145089188 -151401772076 -68847241303576 -8054132164478056 625958778262421668 357144945047660432120", "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":"s_1","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["-1/2","0","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"s_2","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["-1/2","0","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"7/5184","im":"-1/1296*2^(1/2)","approx_re":"0.00135030864198","approx_im":"-0.001091","exponents":["0","-1/2","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"7/5184","im":"1/1296*2^(1/2)","approx_re":"0.00135030864198","approx_im":"0.001091","exponents":["0","-1/2","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["3/2","7/4","9/4","5/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -3072*(X+1/2)^4-2704*(X+1/2)^2-76, 2490368*(X+1)^4+462848*(X+1)^2+41472, -1048576*(X+3/2)^2*(192*(X+3/2)^2+139), 67108864*(2*X+3)*(2*X+5)*(4*X+7)*(4*X+9)]", "text": "YY-Operator equivalent to $C \\ast \\epsilon ~d \\ast i$", "degz": 4, "h3": null, "sol": "1 944 1093840 1379945728 1816122981136 2451227225468672 3364375797938504960 4673256047979115089920 6549780543792076135009552 9243985820818857390612566784", "n_discr_factors": "1", "c3": null, "operator": "4 4 0 0 0 0 1 -944 -4240 -7312 -6144 -3072 2994688 10887168 15405056 9961472 2490368 -1347158016 -3155165184 -2863661056 -1207959552 -201326592 63417876480 132070244352 101737037824 34359738368 4294967296", "new_number": "4.16", "id": 111, "operator_tex": "\\theta^4-2^{4} x\\left(192\\theta^4+384\\theta^3+457\\theta^2+265\\theta+59\\right)+2^{9} x^{2}\\left(4864\\theta^4+19456\\theta^3+30088\\theta^2+21264\\theta+5849\\right)-2^{18} x^{3}(192\\theta^2+576\\theta+571)(2\\theta+3)^2+2^{26} x^{4}(2\\theta+3)(2\\theta+5)(4\\theta+7)(4\\theta+9)", "superseek": "-208 -1863312", "discriminant": "4 1 -3072 2490368 -201326592 4294967296", "aesz": null, "n_sing_complex": "1", "inst_int": "", "c2h": null, "hash": "ff22b96c1af3d06292a97d4dee085628", "dim_h": null, "inst": " -208 -15098 -1863312 -284211001 -50414626800 -9859373378738 -2058387737996368 -451368681647582495 -102784607370050148224 -24115956485115626688670", "cleanlist": "True", "n_sing_real": "1", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "2", "laurent": null, "discriminant_tex": "(1-1536z+65536z^2)^2", "discr_factors": "4294967296, (1/65536-3/128*z+z^2)^2", "dm_basis": null, "q": "0 1 -464 73984 -8463360 1129673136 -149983806976 14521322394624 -2003739846541312 96130548058708120", "yuk": "1 -208 -120992 -50309632 -18189625056 -6301828350208 -2129624700237824 -706026994132754432 -231100765021751862496 -74929978772766608364928", "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":"s_1","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["-1/2","0","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"s_2","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["-1/2","0","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"3/256-1/128*2^(1/2)","im":"0","approx_re":"0.00067","approx_im":"0.0","exponents":["0","-1/2","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"3/256+1/128*2^(1/2)","im":"0","approx_re":"0.022767","approx_im":"0.0","exponents":["0","-1/2","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["3/2","7/4","9/4","5/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -2304*(X+1/2)^4-2028*(X+1/2)^2-57, 1105920*(X+1)^4-725760*(X+1)^2-62928, 1327104*(X+3/2)^2*(192*(X+3/2)^2+139), 191102976*(2*X+3)*(2*X+5)*(4*X+7)*(4*X+9)]", "text": "YY-Operator equivalent to $C \\ast \\zeta ~tilde f \\ast i$", "degz": 4, "h3": null, "sol": "1 708 700740 738956400 811309522500 912383013204432 1042806404789628336 1205821890196940427840 1406588787702335655346500 1652031692435448147788250000", "n_discr_factors": "1", "c3": null, "operator": "4 4 0 0 0 0 1 -708 -3180 -5484 -4608 -2304 317232 2972160 5909760 4423680 1105920 1704996864 3993255936 3624321024 1528823808 254803968 180592312320 376090656768 289712111616 97844723712 12230590464", "new_number": "4.17", "id": 112, "operator_tex": "\\theta^4-2^{2} 3 x\\left(192\\theta^4+384\\theta^3+457\\theta^2+265\\theta+59\\right)+2^{4} 3^{2} x^{2}\\left(7680\\theta^4+30720\\theta^3+41040\\theta^2+20640\\theta+2203\\right)+2^{12} 3^{4} x^{3}(192\\theta^2+576\\theta+571)(2\\theta+3)^2+2^{18} 3^{6} x^{4}(2\\theta+3)(2\\theta+5)(4\\theta+7)(4\\theta+9)", "superseek": "-156 -1229332", "discriminant": "4 1 -2304 1105920 254803968 12230590464", "aesz": null, "n_sing_complex": "1", "inst_int": "", "c2h": null, "hash": "245e2566c8da93abbfc4296923ccba12", "dim_h": null, "inst": " -156 -12549 -1229332 -175559052 -27542017056 -4847609100799 -903993545346132 -177568890996902412 -108530823268261557056/3 -7596937360026971320344", "cleanlist": "True", "n_sing_real": "1", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "2", "laurent": null, "discriminant_tex": "(-1+1152z+110592z^2)^2", "discr_factors": "12230590464, (-1/110592+1/96*z+z^2)^2", "dm_basis": null, "q": "0 1 -348 15534 5476048 -832252683 6797095992 8198150318738 -1105289746060224 -45282071782478718", "yuk": "1 -156 -100548 -33192120 -11235879876 -3442752132156 -1047083599065096 -310069786053723432 -90915272201649914820 -26372990054187591556728", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/192-1/288*3^(1/2)","im":"0","approx_re":"-0.011222","approx_im":"0.0","exponents":["0","-1/2","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"s_1","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["-1/2","0","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"s_2","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["-1/2","0","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/192+1/288*3^(1/2)","im":"0","approx_re":"0.000806","approx_im":"0.0","exponents":["0","-1/2","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["3/2","7/4","9/4","5/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -2816*(X+1/2)^4-2564*(X+1/2)^2-83, 3006464*(X+1)^4+3564800*(X+1)^2+308336, -2048000*(X+3/2)^2*(704*(X+3/2)^2+531), 4096000000*(2*X+3)*(2*X+5)*(4*X+7)*(4*X+9)]", "text": "YY-Operator equivalent to $C \\ast \\eta ~b \\ast i$", "degz": 4, "h3": null, "sol": "1 900 701100 515510800 365497137900 251698064854896 168714604297656560 110000961860877172800 69543595786149130545900 42370884564129031005009200", "n_discr_factors": "1", "c3": null, "operator": "4 4 0 0 0 0 1 -900 -3972 -6788 -5632 -2816 6879600 19155456 21603584 12025856 3006464 -9745920000 -22726656000 -20551680000 -8650752000 -1441792000 3870720000000 8060928000000 6209536000000 2097152000000 262144000000", "new_number": "4.18", "id": 113, "operator_tex": "\\theta^4-2^{2} x\\left(704\\theta^4+1408\\theta^3+1697\\theta^2+993\\theta+225\\right)+2^{4} x^{2}\\left(187904\\theta^4+751616\\theta^3+1350224\\theta^2+1197216\\theta+429975\\right)-2^{12} 5^{3} x^{3}(704\\theta^2+2112\\theta+2115)(2\\theta+3)^2+2^{18} 5^{6} x^{4}(2\\theta+3)(2\\theta+5)(4\\theta+7)(4\\theta+9)", "superseek": "-100 126580", "discriminant": "4 1 -2816 3006464 -1441792000 262144000000", "aesz": null, "n_sing_complex": "1", "inst_int": "", "c2h": null, "hash": "3ab4956c5da76dad5e104e338e7c0128", "dim_h": null, "inst": " -100 -1260 126580 12033300 1211646512 95291744220 6051006366100 25532819388820 -62676985866252520 -11991679685845617392", "cleanlist": "True", "n_sing_real": "1", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "2", "laurent": null, "discriminant_tex": "(512000z^2-1408z+1)^2", "discr_factors": "262144000000, (z^2-11/4000*z+1/512000)^2", "dm_basis": null, "q": "0 1 -372 103206 -23318608 4800264705 -906363458040 163308814938546 -28110319795940160 4692035680985357844", "yuk": "1 -100 -10180 3417560 770121020 151455813900 20583020159000 2075495183572200 13072804297196860 -45691522696494669520", "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":"s_1","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["-1/2","0","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"s_2","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["-1/2","0","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"11/8000","im":"-1/4000","approx_re":"0.001375","approx_im":"-0.00025","exponents":["0","-1/2","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"11/8000","im":"1/4000","approx_re":"0.001375","approx_im":"0.00025","exponents":["0","-1/2","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["3/2","7/4","9/4","5/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -17280*(X+1/2)^4-15288*(X+1/2)^2-462, 98537472*(X+1)^4+80745984*(X+1)^2+7061904, -859963392*(X+3/2)^2*(240*(X+3/2)^2+169), 3962711310336*(2*X+3)*(2*X+5)*(3*X+5)*(3*X+7)]", "text": "YY-Operator equivalent to $AESZ 66 =$D \\ast \\alpha \\tilde c \\ast j$", "degz": 4, "h3": null, "sol": "1 5364 29367900 170217457200 1029027458497500 6396798260167351344 40516714072724617533456 260029813122930776438433600 1685090543488031316816654990300 11001488991531550865698731563674800", "n_discr_factors": "2", "c3": null, "operator": "4 4 0 0 0 0 1 -5364 -23928 -41208 -34560 -17280 186345360 555641856 671970816 394149888 98537472 -1371856601088 -3222282829824 -2931615203328 -1238347284480 -206391214080 2080423437926400 4358982441369600 3372267325095936 1141260857376768 142657607172096", "new_number": "4.19", "id": 114, "operator_tex": "\\theta^4-2^{2} 3 x\\left(1440\\theta^4+2880\\theta^3+3434\\theta^2+1994\\theta+447\\right)+2^{4} 3^{4} x^{2}\\left(76032\\theta^4+304128\\theta^3+518496\\theta^2+428736\\theta+143785\\right)-2^{15} 3^{8} x^{3}(240\\theta^2+720\\theta+709)(2\\theta+3)^2+2^{26} 3^{10} x^{4}(2\\theta+3)(2\\theta+5)(3\\theta+5)(3\\theta+7)", "superseek": "-864 -147560800", "discriminant": "4 1 -17280 98537472 -206391214080 142657607172096", "aesz": "~66", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "b9b85f803521c6af3b5f7572d309f89a", "dim_h": null, "inst": " -864 -261684 -147560800 -120568926924 -88009904955744 -72338406331651444 -66286324404529432416 -63605775313297935288396 -62789590294133700641856352 -63763261933532396671270263924", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "(6912z-1)^2(1728z-1)^2", "discr_factors": "142657607172096, (z-1/6912)^2, (z-1/1728)^2", "dm_basis": null, "q": "0 1 -2472 3404844 -4591592384 5333736689358 -5645526028060896 5755473275519706296 -5570409363132277922304 5163552434107359999841509", "yuk": "1 -864 -2094336 -3984142464 -7716413417472 -11001238119468864 -15625095771622947840 -22736209270753595319552 -32566156960416259281076224 -45773611324423467771897423072", "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":"1/6912","im":"0","approx_re":"0.000144675925926","approx_im":"0.0","exponents":["0","-1/2","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/1728","im":"0","approx_re":"0.000578703703704","approx_im":"0.0","exponents":["0","-1/2","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["3/2","5/3","7/3","5/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -640*(X+1/2)^4-584*(X+1/2)^2-18, 135168*(X+1)^4+118272*(X+1)^2+10128, -131072*(X+3/2)^2*(80*(X+3/2)^2+63), 67108864*(X+2)^2*(2*X+3)*(2*X+5)]", "text": "YY-Operator equivalent to AESZ 39=$A \\ast \\alpha$.", "degz": 4, "h3": null, "sol": "1 204 41820 9022160 2025179100 466941326544 109640857502736 26078280865871040 6262163022415481820 1514784810773910635600", "n_discr_factors": "2", "c3": null, "operator": "4 4 0 0 0 0 1 -204 -904 -1544 -1280 -640 263568 777216 929280 540672 135168 -71663616 -166330368 -149815296 -62914560 -10485760 4026531840 8321499136 6375342080 2147483648 268435456", "new_number": "4.1", "id": 115, "operator_tex": "\\theta^4-2^{2} x\\left(160\\theta^4+320\\theta^3+386\\theta^2+226\\theta+51\\right)+2^{4} 3 x^{2}\\left(2816\\theta^4+11264\\theta^3+19360\\theta^2+16192\\theta+5491\\right)-2^{15} x^{3}(80\\theta^2+240\\theta+243)(2\\theta+3)^2+2^{26} x^{4}(\\theta+2)^2(2\\theta+3)(2\\theta+5)", "superseek": "-32 -8736", "discriminant": "4 1 -640 135168 -10485760 268435456", "aesz": "~39", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "462066f711fc3742db1ea9befa2fe01b", "dim_h": null, "inst": " -32 -284 -8736 -283900 -10041888 -1152289940/3 -15976746016 -698105875068 -31627354130464 -1474104208483292", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "(256z-1)^2(64z-1)^2", "discr_factors": "268435456, (z-1/64)^2, (z-1/256)^2", "dm_basis": null, "q": "0 1 -88 4140 -203840 8154830 -320933664 11741625528 -434327971328 14542126994661", "yuk": "1 -32 -2304 -235904 -18171904 -1255236032 -82965113856 -5480023883520 -357430226206720 -23056341161344160", "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":"1/256","im":"0","approx_re":"0.00390625","approx_im":"0.0","exponents":["0","-1/2","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/64","im":"0","approx_re":"0.015625","approx_im":"0.0","exponents":["0","-1/2","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["3/2","2","2","5/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -29376*(X+1/2)^4-25212*(X+1/2)^2-645, 216110592*(X+1)^4-5987520*(X+1)^2+430272, -6718464*(X+3/2)^2*(816*(X+3/2)^2+553), 967458816*(2*X+3)*(2*X+5)*(3*X+5)*(3*X+7)]", "text": "YY-Operator equivalent to AESZ 149=$D \\ast \\gamma ~tilde g \\ast j$", "degz": 4, "h3": null, "sol": "1 8784 99982728 1239742123200 16039070549564328 212836312970070451200 2872358362827386137216512 39233318289531856214440015872 540734177784604434526512261576360 7505029434484718126637814782745333632", "n_discr_factors": "1", "c3": null, "operator": "4 4 0 0 0 0 1 -8784 -39900 -69276 -58752 -29376 210553344 852467328 1290676032 864442368 216110592 -36113423616 -85156531200 -77725910016 -32893599744 -5482266624 507915878400 1064204697600 823307452416 278628139008 34828517376", "new_number": "4.20", "id": 116, "operator_tex": "\\theta^4-2^{2} 3 x\\left(2448\\theta^4+4896\\theta^3+5773\\theta^2+3325\\theta+732\\right)+2^{6} 3^{4} x^{2}\\left(41688\\theta^4+166752\\theta^3+248973\\theta^2+164442\\theta+40616\\right)-2^{8} 3^{8} x^{3}(816\\theta^2+2448\\theta+2389)(2\\theta+3)^2+2^{14} 3^{10} x^{4}(2\\theta+3)(2\\theta+5)(3\\theta+5)(3\\theta+7)", "superseek": "-2484 -1327731388", "discriminant": "4 1 -29376 216110592 -5482266624 34828517376", "aesz": null, "n_sing_complex": "1", "inst_int": "", "c2h": null, "hash": "80035e90a6f24cd6da3d4c5adc98379f", "dim_h": null, "inst": " -2484 -1446309 -1327731388 -1580284433106 -2187358898922144 -3333084983275758103 -5431476536808370628796 -9299939636087488614405114 -16540355956250846925699785968 -30316727187835571138135877667944", "cleanlist": "True", "n_sing_real": "1", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "2", "laurent": null, "discriminant_tex": "(1-14688z+186624z^2)^2", "discr_factors": "34828517376, (1/186624-17/216*z+z^2)^2", "dm_basis": null, "q": "0 1 -4764 8528094 -8141036080 4977670007085 -2438688593316744 1130289677354089490 -1033297716399959256000 48984521650677347996934", "yuk": "1 -2484 -11572956 -35848749960 -101138215291740 -273419862365270484 -719946356423424070680 -1862996452125271125679512 -4761569093676895308790710108 -12057919492106867408870992720632", "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":"s_1","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["-1/2","0","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"s_2","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["-1/2","0","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"17/432-1/36*2^(1/2)","im":"0","approx_re":"6.8e-05","approx_im":"0.0","exponents":["0","-1/2","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"17/432+1/36*2^(1/2)","im":"0","approx_re":"0.078636","approx_im":"0.0","exponents":["0","-1/2","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["3/2","5/3","7/3","5/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -12096*(X+1/2)^4-10788*(X+1/2)^2-339, 8726976+101590848*(X+1)^2+66811392*(X+1)^4, -544195584*(X+3/2)^2*(336*(X+3/2)^2+239), 6347497291776*(2*X+3)*(2*X+5)*(3*X+5)*(3*X+7)]", "text": "This is operator \"4.21\" from ...", "degz": 4, "h3": null, "sol": "1 3792 9275400 7430606400 -68166524583000 -464596341265343232 -1718931909208528295424 -3618348072352420690483200 2300184841205997345252767400 61995153436412843743197951907200", "n_discr_factors": "1", "c3": null, "operator": "4 4 0 0 0 0 1 -3792 -16836 -28932 -24192 -12096 177129216 470427264 502459200 267245568 66811392 -1218317863680 -2858659402752 -2598533913600 -1097098297344 -182849716224 3332436078182400 6982247020953600 5401720195301376 1828079220031488 228509902503936", "new_number": "4.21", "id": 117, "operator_tex": "\\theta^4-2^{2} 3 x\\left(1008\\theta^4+2016\\theta^3+2411\\theta^2+1403\\theta+316\\right)+2^{6} 3^{2} x^{2}\\left(115992\\theta^4+463968\\theta^3+872325\\theta^2+816714\\theta+307516\\right)-2^{8} 3^{12} x^{3}(336\\theta^2+1008\\theta+995)(2\\theta+3)^2+2^{14} 3^{18} x^{4}(2\\theta+3)(2\\theta+5)(3\\theta+5)(3\\theta+7)", "superseek": "-492 136094428", "discriminant": "4 1 -12096 66811392 -182849716224 228509902503936", "aesz": null, "n_sing_complex": "1", "inst_int": "", "c2h": null, "hash": "595707be6cb20abc1dfeecf72492ae5f", "dim_h": null, "inst": " -492 128514 136094428 32416215738 -16919954920032 -25081894126382570 -10798647846388664100 4628276637816545092050 9612599272287001934026096 5072299890987974052401948304", "cleanlist": "True", "n_sing_real": "1", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "2", "laurent": null, "discriminant_tex": "(15116544z^2-6048z+1)^2", "discr_factors": "228509902503936, (z^2-7/17496*z+1/15116544)^2", "dm_basis": null, "q": "0 1 -1668 3129822 -3591051856 4582578534189 -4682795317633080 4948605373685854994 -4702733898277550411328 4489208769582109560324870", "yuk": "1 -492 1027620 3674549064 2074638834852 -2114994365004492 -5417689127623057944 -3703936211311311786792 2369677638564145725964452 7007584869497224413579573048", "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":"s_1","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["-1/2","0","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"s_2","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["-1/2","0","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"7/34992","im":"-1/8748*2^(1/2)","approx_re":"0.000200045724737","approx_im":"-0.000162","exponents":["0","-1/2","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"7/34992","im":"1/8748*2^(1/2)","approx_re":"0.000200045724737","approx_im":"0.000162","exponents":["0","-1/2","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["3/2","5/3","7/3","5/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -20736*(X+1/2)^4-18000*(X+1/2)^2-492, 113467392*(X+1)^4+18330624*(X+1)^2+1939968, -3869835264*(X+3/2)^2*(16*(X+3/2)^2+11), 247669456896*(2*X+3)*(2*X+5)*(3*X+5)*(3*X+7)]", "text": "YY-Operator equivalent to $D \\ast \\epsilon \\tilde d \\ast j$", "degz": 4, "h3": null, "sol": "1 6288 49006800 416705452800 3698851729136400 33681272937781480704 311932982382295022191872 2923944709736219442719846400 27656388114594756400576052989200 263429909404593083347831575185875200", "n_discr_factors": "1", "c3": null, "operator": "4 4 0 0 0 0 1 -6288 -28368 -49104 -41472 -20736 133737984 490530816 699134976 453869568 113467392 -409235079168 -963588980736 -878452604928 -371504185344 -61917364224 130026464870400 272436402585600 210766707818496 71328803586048 8916100448256", "new_number": "4.22", "id": 118, "operator_tex": "\\theta^4-2^{4} 3 x\\left(432\\theta^4+864\\theta^3+1023\\theta^2+591\\theta+131\\right)+2^{9} 3^{2} x^{2}\\left(24624\\theta^4+98496\\theta^3+151722\\theta^2+106452\\theta+29023\\right)-2^{14} 3^{10} x^{3}(16\\theta^2+48\\theta+47)(2\\theta+3)^2+2^{22} 3^{10} x^{4}(2\\theta+3)(2\\theta+5)(3\\theta+5)(3\\theta+7)", "superseek": "-1488 -517984144", "discriminant": "4 1 -20736 113467392 -61917364224 8916100448256", "aesz": null, "n_sing_complex": "1", "inst_int": "", "c2h": null, "hash": "7d70f749f0fd6381c088f4c1fac4d6df", "dim_h": null, "inst": " -1488 -704730 -517984144 -469396561641 -493072108113648 -573124059144496402 -710282017068116797776 -924822665992369737350799 -1250674565943802068474015616 -1742649598747772220671160126270", "cleanlist": "True", "n_sing_real": "1", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "2", "laurent": null, "discriminant_tex": "(2985984z^2-10368z+1)^2", "discr_factors": "8916100448256, (z^2-1/288*z+1/2985984)^2", "dm_basis": null, "q": "0 1 -3216 3831552 -3121472512 2886132664752 -2689021314141696 2061211926480499712 -1595527447063571496960 1098926330327365589088408", "yuk": "1 -1488 -5639328 -13985573376 -30041385584352 -61634013514207488 -123794796789202434048 -243626731854364061638656 -473509204988123346909193440 -911741758573031707931542957440", "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":"s_1","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["-1/2","0","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"s_2","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["-1/2","0","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/576-1/864*2^(1/2)","im":"0","approx_re":"9.9e-05","approx_im":"0.0","exponents":["0","-1/2","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/576+1/864*2^(1/2)","im":"0","approx_re":"0.003373","approx_im":"0.0","exponents":["0","-1/2","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["3/2","5/3","7/3","5/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -15552*(X+1/2)^4-13500*(X+1/2)^2-369, 50388480*(X+1)^4-34292160*(X+1)^2-2702160, 4897760256*(X+3/2)^2*(16*(X+3/2)^2+11), 705277476864*(2*X+3)*(2*X+5)*(3*X+5)*(3*X+7)]", "text": "This is operator \"4.23\" from ...", "degz": 4, "h3": null, "sol": "1 4716 31430916 223425214992 1654537886846532 12553361207715469680 96815184264340183464624 755472658494095667308730816 5947354313754393026474138585412 47142591780478152347203384002983472", "n_discr_factors": "1", "c3": null, "operator": "4 4 0 0 0 0 1 -4716 -21276 -36828 -31104 -15552 13394160 132969600 268038720 201553920 50388480 517938147072 1219542303744 1111791578112 470184984576 78364164096 370270675353600 775805224550400 600191132811264 203119913336832 25389989167104", "new_number": "4.23", "id": 119, "operator_tex": "\\theta^4-2^{2} 3^{2} x\\left(432\\theta^4+864\\theta^3+1023\\theta^2+591\\theta+131\\right)+2^{4} 3^{5} 5 x^{2}\\left(2592\\theta^4+10368\\theta^3+13788\\theta^2+6840\\theta+689\\right)+2^{8} 3^{14} x^{3}(16\\theta^2+48\\theta+47)(2\\theta+3)^2+2^{14} 3^{16} x^{4}(2\\theta+3)(2\\theta+5)(3\\theta+5)(3\\theta+7)", "superseek": "-1116 -349462868", "discriminant": "4 1 -15552 50388480 78364164096 25389989167104", "aesz": null, "n_sing_complex": "1", "inst_int": "", "c2h": null, "hash": "4cde44ecce8658b2c2ca6b3c279f4e62", "dim_h": null, "inst": " -1116 -586989 -349462868 -300569202144 -280354383814176 -296982683718981431 -330942057079152291732 -389740226852216102058576 -475399528533641734868803520 -598109644529459007164316811224", "cleanlist": "True", "n_sing_real": "1", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "2", "laurent": null, "discriminant_tex": "(5038848z^2+7776z-1)^2", "discr_factors": "25389989167104, (z^2+1/648*z-1/5038848)^2", "dm_basis": null, "q": "0 1 -2412 949806 1750469136 -2111572819467 375181321827672 974436435410694930 -921111319627599911616 48784763819176278750594", "yuk": "1 -1116 -4697028 -9435498552 -19236433634244 -35044297976773116 -64148259692740183560 -113513125578149236065192 -199546996148353880687625156 -346566256301024824728793264632", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/1296-1/1944*3^(1/2)","im":"0","approx_re":"-0.001663","approx_im":"0.0","exponents":["0","-1/2","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"s_1","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["-1/2","0","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"s_2","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["-1/2","0","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/1296+1/1944*3^(1/2)","im":"0","approx_re":"0.000119","approx_im":"0.0","exponents":["0","-1/2","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["3/2","5/3","7/3","5/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -19008*(X+1/2)^4-17076*(X+1/2)^2-555, 136982016*(X+1)^4+159091776*(X+1)^2+13734000, -839808000*(X+3/2)^2*(528*(X+3/2)^2+379), 15116544000000*(2*X+3)*(2*X+5)*(3*X+5)*(3*X+7)]", "text": "YY-Operator equivalent to $D \\ast \\eta ~b \\ast j$", "degz": 4, "h3": null, "sol": "1 6012 31439916 155468925360 741919701370860 3440334229212106512 15530980276763547700464 68197609142431078878827712 290322230075367777254926104300 1190585994177540597112900197838800", "n_discr_factors": "1", "c3": null, "operator": "4 4 0 0 0 0 1 -6012 -26580 -45588 -38016 -19008 309807792 866111616 980983872 547928064 136982016 -2960953056000 -6941013120000 -6304438656000 -2660511744000 -443418624000 7936185600000000 16628198400000000 12864178944000000 4353564672000000 544195584000000", "new_number": "4.24", "id": 120, "operator_tex": "\\theta^4-2^{2} 3 x\\left(1584\\theta^4+3168\\theta^3+3799\\theta^2+2215\\theta+501\\right)+2^{4} 3^{2} x^{2}\\left(951264\\theta^4+3805056\\theta^3+6812388\\theta^2+6014664\\theta+2151443\\right)-2^{8} 3^{8} 5^{3} x^{3}(528\\theta^2+1584\\theta+1567)(2\\theta+3)^2+2^{14} 3^{10} 5^{6} x^{4}(2\\theta+3)(2\\theta+5)(3\\theta+5)(3\\theta+7)", "superseek": "-612 51318900", "discriminant": "4 1 -19008 136982016 -443418624000 544195584000000", "aesz": null, "n_sing_complex": "1", "inst_int": "", "c2h": null, "hash": "dc90e303db3462d0c0bd472762000ad5", "dim_h": null, "inst": " -612 -87372 51318900 24336059400 14111081636400 7632101153972412 2689453850253788052 -105216147647189676072 -1507370707788027902059752 -1598466549261264907286790000", "cleanlist": "True", "n_sing_real": "1", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "2", "laurent": null, "discriminant_tex": "(23328000z^2-9504z+1)^2", "discr_factors": "544195584000000, (z^2-11/27000*z+1/23328000)^2", "dm_basis": null, "q": "0 1 -2532 4785318 -7335393424 10147405409025 -12793574387745432 15259861218545289266 -17285394597615440227392 18862018194471740749530900", "yuk": "1 -612 -699588 1385609688 1557507102012 1763885204549388 1648533850642951704 922482670637049301224 -53870667593803607046852 -1098873245977472339215949520", "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":"s_1","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["-1/2","0","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"s_2","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["-1/2","0","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"11/54000","im":"-1/27000","approx_re":"0.000203703703704","approx_im":"-3.7037037037e-05","exponents":["0","-1/2","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"11/54000","im":"1/27000","approx_re":"0.000203703703704","approx_im":"3.7037037037e-05","exponents":["0","-1/2","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["3/2","5/3","7/3","5/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -540*(X+1/2)^4-486*(X+1/2)^2-57/4, 72846*(X+1)^4+6915/2*(X+1)^2+3/4, 14580*(X+3/2)^4+12717*(X+3/2)^2+324, 9/16*(6*X+11)^2*(6*X+13)^2]", "text": "Sporadic YY-Operator", "degz": 4, "h3": null, "sol": "1 339/2 287415/8 131845323/16 251852894379/128 123238332726741/256 122592505348354995/1024 61692704367754625307/2048 250561664907978069535923/32768 128080461905587807503878001/65536", "n_discr_factors": "1", "c3": null, "operator": "4 4 0 0 0 0 1 -339/2 -756 -1296 -1080 -540 305217/4 298299 881067/2 291384 72846 205497/2 234981 209547 87480 14580 184041/16 23166 34911/2 5832 729", "new_number": "4.25", "id": 121, "operator_tex": "\\theta^4-x\\left(540\\theta^4+1080\\theta^3+1296\\theta^2+756\\theta+339/2\\right)+x^{2}\\left(72846\\theta^4+291384\\theta^3+881067/2\\theta^2+298299\\theta+305217/4\\right)+x^{3}\\left(14580\\theta^4+87480\\theta^3+209547\\theta^2+234981\\theta+205497/2\\right)+x^{4}9/16(6\\theta+11)^2(6\\theta+13)^2", "superseek": "-33 -13051", "discriminant": "4 1 -540 72846 14580 729", "aesz": "32", "n_sing_complex": "1", "inst_int": "", "c2h": null, "hash": "bf53401dcbe0436fb67761f590ee3295", "dim_h": null, "inst": " -33 -1995/4 -13051 -435975 -16838124 -2857251193/4 -32366430885 -1539790563111 -76052716745077 -3869806769783889", "cleanlist": "True", "n_sing_real": "1", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "2", "laurent": null, "discriminant_tex": "(-1+270z+27z^2)^2", "discr_factors": "729, (-1/27+10*z+z^2)^2", "dm_basis": null, "q": "0 1 -78 1443 -9854 -69069 -4239612 -241242846 -13365451086 -752315479929", "yuk": "1 -33 -4023 -352410 -27906423 -2104765533 -154291920822 -11101685793588 -788372796219255 -55442430507513543", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-5-26/9*3^(1/2)","im":"0","approx_re":"-10.003702","approx_im":"0.0","exponents":["0","-1/2","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"s_1","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["-1/2","0","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"s_2","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["-1/2","0","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"-5+26/9*3^(1/2)","im":"0","approx_re":"0.003702","approx_im":"0.0","exponents":["0","-1/2","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["11/6","11/6","13/6","13/6"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -248*(X+1/2)^4-232*(X+1/2)^2-15/2, 18832*(X+1)^4+13806*(X+1)^2+1251, -428544*(X+3/2)^4-382296*(X+3/2)^2-9138, 9*(24*X+41)*(24*X+47)*(24*X+49)*(24*X+55)]", "text": "Sporadic YY-Operator", "degz": 4, "h3": null, "sol": "1 81 13837/2 1263327/2 480917043/8 46958960871/8 9328218834137/16 937774718213487/16 761037915101276291/128 77743160915496110811/128", "n_discr_factors": "2", "c3": null, "operator": "4 4 0 0 0 0 1 -81 -356 -604 -496 -248 33889 102940 126798 75328 18832 -3038808 -6932232 -6167640 -2571264 -428544 46739385 94514688 71404416 23887872 2985984", "new_number": "4.26", "id": 122, "operator_tex": "\\theta^4-x\\left(248\\theta^4+496\\theta^3+604\\theta^2+356\\theta+81\\right)+x^{2}\\left(18832\\theta^4+75328\\theta^3+126798\\theta^2+102940\\theta+33889\\right)-2^{3} 3 x^{3}\\left(17856\\theta^4+107136\\theta^3+256985\\theta^2+288843\\theta+126617\\right)+3^{2} x^{4}(24\\theta+41)(24\\theta+47)(24\\theta+49)(24\\theta+55)", "superseek": "-10 -870", "discriminant": "4 1 -248 18832 -428544 2985984", "aesz": "60", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "033b6632bf7cbbfe2a70e1f1eee4bf04", "dim_h": null, "inst": " -10 -65 -870 -13905 -248910 -4882215 -102446770 -2255612945 -51514954750 -1211473161115", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "(108z-1)^2(16z-1)^2", "discr_factors": "2985984, (z-1/16)^2, (z-1/108)^2", "dm_basis": null, "q": "0 1 -32 356 -5528 43410 -599232 96364 -128087616 -2266406377", "yuk": "1 -10 -530 -23500 -890450 -31113760 -1054582460 -35139242120 -1154874718290 -37554402036250", "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":"1/108","im":"0","approx_re":"0.00925925925926","approx_im":"0.0","exponents":["0","-1/2","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/16","im":"0","approx_re":"0.0625","approx_im":"0.0","exponents":["0","-1/2","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["41/24","47/24","49/24","55/24"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -520*(X+1/2)^4-470*(X+1/2)^2-14, 69648*(X+1)^4+10908*(X+1)^2+724, -532480*(X+3/2)^4-439680*(X+3/2)^2-6896, 256*(8*X+13)*(8*X+15)*(8*X+17)*(8*X+19)]", "text": "Sporadic YY-Operator", "degz": 4, "h3": null, "sol": "1 164 32886 7144704 1616497596 374796008496 88334003745624 21064705760170176 5067706001455546614 1227579787297952607736", "n_discr_factors": "2", "c3": null, "operator": "4 4 0 0 0 0 1 -164 -730 -1250 -1040 -520 81280 300408 428796 278592 69648 -3691856 -8507520 -7628160 -3194880 -532480 16124160 32899072 25001984 8388608 1048576", "new_number": "4.27", "id": 123, "operator_tex": "\\theta^4-2 x\\left(260\\theta^4+520\\theta^3+625\\theta^2+365\\theta+82\\right)+2^{2} x^{2}\\left(17412\\theta^4+69648\\theta^3+107199\\theta^2+75102\\theta+20320\\right)-2^{4} x^{3}\\left(33280\\theta^4+199680\\theta^3+476760\\theta^2+531720\\theta+230741\\right)+2^{8} x^{4}(8\\theta+13)(8\\theta+15)(8\\theta+17)(8\\theta+19)", "superseek": "-30 -11360", "discriminant": "4 1 -520 69648 -532480 1048576", "aesz": "189", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "2ce243b7535bf4eefb88252a3c164466", "dim_h": null, "inst": " -30 -885/2 -11360 -365910 -13641180 -558537880 -170942216100/7 -1120886044110 -53410511601050 -2621751030955005", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "(256z-1)^2(4z-1)^2", "discr_factors": "1048576, (z-1/256)^2, (z-1/4)^2", "dm_basis": null, "q": "0 1 -74 1359 -16564 193055 -7606134 -165889059 -11443685608 -589716597852", "yuk": "1 -30 -3570 -306750 -23421810 -1705147530 -120644492370 -8376168588930 -573893678006130 -38936262957472200", "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":"1/256","im":"0","approx_re":"0.00390625","approx_im":"0.0","exponents":["0","-1/2","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/4","im":"0","approx_re":"0.25","approx_im":"0.0","exponents":["0","-1/2","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["13/8","15/8","17/8","19/8"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, 208*(X+1/2)^4+192*(X+1/2)^2+6, 9952*(X+1)^4-1978*(X+1)^2-309, -89856*(X+3/2)^4-82320*(X+3/2)^2-2484, 9*(12*X+23)^2*(12*X+25)^2]", "text": "Sporadic YY-Operator", "degz": 4, "h3": null, "sol": "1 -67 11529/2 -1062425/2 406816235/8 -39863964525/8 7936975166253/16 -799185510570033/16 649330423536226995/128 -66391663951923938705/128", "n_discr_factors": "2", "c3": null, "operator": "4 4 0 0 0 0 1 67 296 504 416 208 7665 35852 57734 39808 9952 -642600 -1460016 -1295376 -539136 -89856 2975625 5961600 4476384 1492992 186624", "new_number": "4.28", "id": 124, "operator_tex": "\\theta^4+x\\left(208\\theta^4+416\\theta^3+504\\theta^2+296\\theta+67\\right)+x^{2}\\left(9952\\theta^4+39808\\theta^3+57734\\theta^2+35852\\theta+7665\\right)-2^{3} 3 x^{3}\\left(3744\\theta^4+22464\\theta^3+53974\\theta^2+60834\\theta+26775\\right)+3^{2} x^{4}(12\\theta+23)^2(12\\theta+25)^2", "superseek": "10 1018", "discriminant": "4 1 208 9952 -89856 186624", "aesz": "244", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "6bf8549841e32615ff2b7798191c0de3", "dim_h": null, "inst": " 10 -167/2 1018 -16457 304664 -12377287/2 134069538 -3047708881 71895701066 -1746715486050", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "(108z+1)^2(4z-1)^2", "discr_factors": "186624, (z+1/108)^2, (z-1/4)^2", "dm_basis": null, "q": "0 1 28 42 -1008 -14525 182616 -4407494 118650368 -3117539943", "yuk": "1 10 -658 27496 -1053906 38083010 -1336720168 45985851544 -1560428000978 52411966104610", "gv2": null, "gv0": null, "gv1": null}, {"pols": "[X^4, 1024*(X+1/2)^4+1076*(X+1/2)^2+43, 393216*(X+1)^4+545792*(X+1)^2+52864, 67108864*(X+3/2)^4+67895296*(X+3/2)^2+2011136, 4194304*(4*X+7)*(4*X+9)*(8*X+15)*(8*X+17)]", "text": "Sporadic YY-Operator.\nCan be reduced to 2.70, so not primary operator.", "degz": 4, "h3": null, "sol": "1 -376 117736 -34499456 9771980456 -2711775741248 742308658737408 -201222249192972288 54149431992142702248 -14489353573673061517248", "n_discr_factors": "1", "c3": null, "operator": "4 4 0 0 0 0 1 376 1588 2612 2048 1024 991872 2664448 2905088 1572864 393216 494514176 1109655552 973864960 402653184 67108864 67381493760 136096776192 102743670784 34359738368 4294967296", "new_number": "4.29", "id": 125, "operator_tex": "\\theta^4+2^{2} x\\left(256\\theta^4+512\\theta^3+653\\theta^2+397\\theta+94\\right)+2^{7} x^{2}\\left(3072\\theta^4+12288\\theta^3+22696\\theta^2+20816\\theta+7749\\right)+2^{12} x^{3}\\left(16384\\theta^4+98304\\theta^3+237760\\theta^2+270912\\theta+120731\\right)+2^{22} x^{4}(4\\theta+7)(4\\theta+9)(8\\theta+15)(8\\theta+17)", "superseek": "-20 -28820/3", "discriminant": "4 1 1024 393216 67108864 4294967296", "aesz": "255", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "86173b300ea0aef95c3f2b60ce5ecf91", "dim_h": null, "inst": " -20 295 -28820/3 454190 -26517920 5315675335/3 -130052490460 10228035566870 -2544287074153040/3 73327006759699320", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "2", "laurent": null, "discriminant_tex": "(256z+1)^4", "discr_factors": "4294967296, (z+1/256)^4", "dm_basis": null, "q": "0 1 84 3294 104464 2008365 80464536 -1641557998 248229425472 -21222256770810", "yuk": "1 -20 2340 -259400 29070500 -3314740020 382728367080 -44608004227800 5236754239307940 -618261759019448120", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/256","im":"0","approx_re":"-0.00390625","approx_im":"0.0","exponents":["-3/8","3/8","-5/8","-11/8"],"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":["7/4","15/8","17/8","9/4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -1088*(X+1/2)^4-964*(X+1/2)^2-27, 296448*(X+1)^4+8256*(X+1)^2+192, -1024*(X+3/2)^2*(272*(X+3/2)^2+207), 16384*(X+2)^2*(2*X+3)*(2*X+5)]", "text": "YY-Operator equivalent to AESZ 44=$ A \\ast \\gamma$", "degz": 4, "h3": null, "sol": "1 336 142728 65762368 31568339880 15533012968704 7770174392268288 3933113259549247488 2008605043302914864808 1032883937290818939314560", "n_discr_factors": "1", "c3": null, "operator": "4 4 0 0 0 0 1 -336 -1508 -2596 -2176 -1088 304896 1202304 1786944 1185792 296448 -1886976 -4396032 -3972096 -1671168 -278528 983040 2031616 1556480 524288 65536", "new_number": "4.2", "id": 126, "operator_tex": "\\theta^4-2^{2} x\\left(272\\theta^4+544\\theta^3+649\\theta^2+377\\theta+84\\right)+2^{6} 3 x^{2}\\left(1544\\theta^4+6176\\theta^3+9307\\theta^2+6262\\theta+1588\\right)-2^{8} x^{3}(272\\theta^2+816\\theta+819)(2\\theta+3)^2+2^{14} x^{4}(\\theta+2)^2(2\\theta+3)(2\\theta+5)", "superseek": "-76 -92996", "discriminant": "4 1 -1088 296448 -278528 65536", "aesz": "~44", "n_sing_complex": "1", "inst_int": "", "c2h": null, "hash": "79f5f70bb79e740c1cd7e835ff99a64c", "dim_h": null, "inst": " -76 -2002 -92996 -5555506 -384650592 -87851559442/3 -2382567781700 -203597635374810 -18066930122752784 -1651905878787792656", "cleanlist": "True", "n_sing_real": "1", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "2", "laurent": null, "discriminant_tex": "(1-544z+256z^2)^2", "discr_factors": "65536, (1/256-17/8*z+z^2)^2", "dm_basis": null, "q": "0 1 -164 7902 -175312 1770797 -88925688 -5015603694 -588849979456 -58902911500026", "yuk": "1 -76 -16092 -2510968 -355568476 -48081324076 -6325314806808 -817220749123176 -104241989667471196 -13170792059489290504", "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":"s_1","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["-1/2","0","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"s_2","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["-1/2","0","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"17/16-3/4*2^(1/2)","im":"0","approx_re":"0.00184","approx_im":"0.0","exponents":["0","-1/2","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"17/16+3/4*2^(1/2)","im":"0","approx_re":"2.12316","approx_im":"0.0","exponents":["0","-1/2","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["3/2","2","2","5/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, 164*(X+1/2)^4+156*(X+1/2)^2+21/4, 12974*(X+1)^4+45175/2*(X+1)^2+8835/4, 512500*(X+3/2)^4+461875*(X+3/2)^2+10840, 15625*(5*X+17/2)*(5*X+19/2)*(5*X+21/2)*(5*X+23/2)]", "text": "Sporadic YY-Operator", "degz": 4, "h3": null, "sol": "1 -109/2 13447/8 58747/16 -556301557/128 80417194613/256 -12564715223389/1024 180567391553131/2048 885175103898923123/32768 -153605363433546271247/65536", "n_discr_factors": "1", "c3": null, "operator": "4 4 0 0 0 0 1 109/2 238 402 328 164 151081/4 97071 200863/2 51896 12974 3644590 8304375 7380625 3075000 512500 2437640625/16 308593750 466796875/2 78125000 9765625", "new_number": "4.30", "id": 127, "operator_tex": "\\theta^4+x\\left(164\\theta^4+328\\theta^3+402\\theta^2+238\\theta+109/2\\right)+x^{2}\\left(12974\\theta^4+51896\\theta^3+200863/2\\theta^2+97071\\theta+151081/4\\right)+5 x^{3}\\left(102500\\theta^4+615000\\theta^3+1476125\\theta^2+1660875\\theta+728918\\right)+x^{4}15625/16(10\\theta+17)(10\\theta+19)(10\\theta+21)(10\\theta+23)", "superseek": "5 -420", "discriminant": "4 1 164 12974 512500 9765625", "aesz": "281", "n_sing_complex": "1", "inst_int": "", "c2h": null, "hash": "d24d5f19c8a8bf23ea9abd62ea9242b2", "dim_h": null, "inst": " 5 95/4 -420 2555 19930 -682645 6463805 40651055 -2112423895 50608382435/2", "cleanlist": "True", "n_sing_real": "1", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "2", "laurent": null, "discriminant_tex": "(1+82z+3125z^2)^2", "discr_factors": "9765625, (1/3125+82/3125*z+z^2)^2", "dm_basis": null, "q": "0 1 20 500 4850 80620 700534 6933915 74473950 730700800", "yuk": "1 5 195 -11335 163715 2491255 -147462465 2217085120 20813503875 -1539957030790", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-41/3125","im":"-38/3125","approx_re":"-0.01312","approx_im":"-0.01216","exponents":["0","-1/2","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"-41/3125","im":"38/3125","approx_re":"-0.01312","approx_im":"0.01216","exponents":["0","-1/2","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"s_1","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["-1/2","0","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"s_2","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["-1/2","0","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["17/10","19/10","21/10","23/10"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -344*(X+1/2)^4-326*(X+1/2)^2-11, 43408*(X+1)^4+51724*(X+1)^2+4816, -2377728*(X+3/2)^4-2088192*(X+3/2)^2-41328, 147456*(3*X+5)*(3*X+7)*(6*X+11)*(6*X+13)]", "text": "This is operator \"4.31\" from ...", "degz": 4, "h3": null, "sol": "1 114 11466 1123804 109952106 10822345380 1074138708940 107525860929960 10849336216894890 1102378579939296660", "n_discr_factors": "2", "c3": null, "operator": "4 4 0 0 0 0 1 -114 -498 -842 -688 -344 99948 277080 312172 173632 43408 -16777008 -38363904 -34187520 -14266368 -2377728 738017280 1502281728 1139982336 382205952 47775744", "new_number": "4.31", "id": 128, "operator_tex": "\\theta^4-2 x\\left(172\\theta^4+344\\theta^3+421\\theta^2+249\\theta+57\\right)+2^{2} x^{2}\\left(10852\\theta^4+43408\\theta^3+78043\\theta^2+69270\\theta+24987\\right)-2^{4} 3 x^{3}\\left(49536\\theta^4+297216\\theta^3+712240\\theta^2+799248\\theta+349521\\right)+2^{14} 3^{2} x^{4}(3\\theta+5)(3\\theta+7)(6\\theta+11)(6\\theta+13)", "superseek": "-10 -340", "discriminant": "4 1 -344 43408 -2377728 47775744", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "dc534a2a8e7bca49a87c29d9ed4e3ae8", "dim_h": null, "inst": " -10 -40 -340 -5820 -114610 -2195680 -41115490 -783867060 -15624406960 -326326810040", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "(108z-1)^2(64z-1)^2", "discr_factors": "47775744, (z-1/64)^2, (z-1/108)^2", "dm_basis": null, "q": "0 1 -42 1101 -24428 428490 -7494594 109149252 -1698087912 21634702887", "yuk": "1 -10 -330 -9190 -372810 -14326260 -474276390 -14102613080 -401340307530 -11390192683030", "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":"1/108","im":"0","approx_re":"0.00925925925926","approx_im":"0.0","exponents":["0","-1/2","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/64","im":"0","approx_re":"0.015625","approx_im":"0.0","exponents":["0","-1/2","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["5/3","11/6","13/6","7/3"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -472*(X+1/2)^4-446*(X+1/2)^2-15, 83344*(X+1)^4+102060*(X+1)^2+9252, -6524928*(X+3/2)^4-5576448*(X+3/2)^2-69888, 9216*(12*X+19)*(12*X+23)*(12*X+25)*(12*X+29)]", "text": "Sporadic YY-Operator.", "degz": 4, "h3": null, "sol": "1 156 21062 2714208 342489420 42745344432 5302680749912 655600683760704 80913588850087846 9978933506757141000", "n_discr_factors": "2", "c3": null, "operator": "4 4 0 0 0 0 1 -156 -682 -1154 -944 -472 194656 537496 602124 333376 83344 -45649344 -104815872 -93662976 -39149568 -6524928 2919859200 5977276416 4551966720 1528823808 191102976", "new_number": "4.32", "id": 129, "operator_tex": "\\theta^4-2 x\\left(236\\theta^4+472\\theta^3+577\\theta^2+341\\theta+78\\right)+2^{2} x^{2}\\left(20836\\theta^4+83344\\theta^3+150531\\theta^2+134374\\theta+48664\\right)-2^{6} 3 x^{3}\\left(33984\\theta^4+203904\\theta^3+487828\\theta^2+545916\\theta+237757\\right)+2^{10} 3^{2} x^{4}(12\\theta+19)(12\\theta+23)(12\\theta+25)(12\\theta+29)", "superseek": "-14 -196", "discriminant": "4 1 -472 83344 -6524928 191102976", "aesz": "356\n", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "e73c971c3ed3a4fd581234510642c285", "dim_h": null, "inst": " -14 -42 -196 -1218 -208446/5 -1249164 -31158358 -665413042 -13244743400 -255577395122", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "(128z-1)^2(108z-1)^2", "discr_factors": "191102976, (z-1/128)^2, (z-1/108)^2", "dm_basis": null, "q": "0 1 -58 2285 -73180 2053050 -53567538 1306009292 -30756537128 694691706071", "yuk": "1 -14 -350 -5306 -78302 -5211164 -269825066 -10687316808 -340691555806 -9655417943906", "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","-1/2","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/108","im":"0","approx_re":"0.00925925925926","approx_im":"0.0","exponents":["0","-1/2","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["19/12","23/12","25/12","29/12"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[9*X^4, -2496*X^4-2688*X^3-1956*X^2-612*X-72, 16384*X^4-475136*X^3-822272*X^2-428544*X-72192, 9437184*X^4+37748736*X^3+30605312*X^2+9437184*X+983040, -16777216*(2*X+1)^4]", "text": "Sporadic operator. There is a second MUM-point\nhiding at infinity, corresponding to Operator 4.56", "degz": 4, "h3": "12", "sol": "1 8 936 108800 16748200 2810179008 509793064704 97163659726848 19240100389996200 3922510470614964800", "n_discr_factors": "3", "c3": "-88", "operator": "4 4 0 0 0 0 9 -72 -612 -1956 -2688 -2496 -72192 -428544 -822272 -475136 16384 983040 9437184 30605312 37748736 9437184 -16777216 -134217728 -402653184 -536870912 -268435456", "new_number": "4.33", "id": 130, "operator_tex": "3^{2} \\theta^4-2^{2} 3 x\\left(208\\theta^4+224\\theta^3+163\\theta^2+51\\theta+6\\right)+2^{9} x^{2}\\left(32\\theta^4-928\\theta^3-1606\\theta^2-837\\theta-141\\right)+2^{16} x^{3}\\left(144\\theta^4+576\\theta^3+467\\theta^2+144\\theta+15\\right)-2^{24} x^{4}\\left((2\\theta+1)^4\\right)", "superseek": "76/3 144196/3", "discriminant": "4 9 -2496 16384 9437184 -268435456", "aesz": "55", "n_sing_complex": "0", "inst_int": "", "c2h": "48", "hash": "7e88cd5b7dc1c51022b66ac6f009218f", "dim_h": "6", "inst": " 76/3 3476/3 144196/3 3563196 309069600 95147523676/3 10621019178308/3 1274833553965780/3 161052568610071312/3 7072463333697906400", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "-(64z+1)(256z-1)(-3+128z)^2", "discr_factors": "-268435456, z-1/256, z+1/64, (-3/128+z)^2", "dm_basis": null, "q": "0 1 -36 -2082 -18768 -4144851 -572787192 -73468972270 -9672435358272 -1347029244663546", "yuk": "1 76/3 27884/3 3893368/3 684161516/3 115901100076/3 20551869035192/3 1214336526053240 652714780314640876/3 117407322516745879816/3", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"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":"1/256","im":"0","approx_re":"0.00390625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"3/128","im":"0","approx_re":"0.0234375","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":["1/2","1/2","1/2","1/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[169*X^4, -59397*X^4-117546*X^3-86827*X^2-28054*X-3380, 102176*X^4-28384*X^3-286368*X^2-185536*X-33904, 17152*X^4+319488*X^3+279296*X^2+79872*X+6656, -4096*(2*X+1)^4]", "text": "Sporadic Operator.\nThere is a second MUM point hidden at infinity. That is operator AESZ 207/4.38\nA-Incarnation: $5 \\times 5$-Pfaffian in P^5\n\nA-Incarnation: 5 \\times 5 Pfaffian in P^5", "degz": 4, "h3": "13", "sol": "1 20 2196 369200 75562900 17321033520 4274237444400 1110816764291520 299987146348074900 83448532078002462800", "n_discr_factors": "2", "c3": "-120", "operator": "4 4 0 0 0 0 169 -3380 -28054 -86827 -117546 -59397 -33904 -185536 -286368 -28384 102176 6656 79872 279296 319488 17152 -4096 -32768 -98304 -131072 -65536", "new_number": "4.34", "id": 131, "operator_tex": "13^{2} \\theta^4-13 x\\left(4569\\theta^4+9042\\theta^3+6679\\theta^2+2158\\theta+260\\right)+2^{4} x^{2}\\left(6386\\theta^4-1774\\theta^3-17898\\theta^2-11596\\theta-2119\\right)+2^{8} x^{3}\\left(67\\theta^4+1248\\theta^3+1091\\theta^2+312\\theta+26\\right)-2^{12} x^{4}\\left((2\\theta+1)^4\\right)", "superseek": "647/13 942613/13", "discriminant": "4 169 -59397 102176 17152 -65536", "aesz": "99", "n_sing_complex": "1", "inst_int": "", "c2h": "58", "hash": "f6c6b846edc829f336d8e4ae1dcb5618", "dim_h": "7", "inst": " 647/13 16166/13 942613/13 80218296/13 8418215008/13 1010635571652/13 133175036459554/13 18790105726249800/13 2793397258503481492/13 432766737883812461716/13", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "3", "laurent": null, "discriminant_tex": "-(256z^2+349z-1)(-13+16z)^2", "discr_factors": "-65536, (-13/16+z)^2, z^2+349/256*z-1/256", "dm_basis": null, "q": "0 1 -86 1891 -93168 -5986827 -897060226 -133756443955 -21091605379872 -3466693323446225", "yuk": "1 647/13 129975/13 25451198/13 5134100919/13 1052276876647/13 218297309057358/13 3513772115817513 9620534136973998519/13 2036386601449063458866/13", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-349/512-85/512*17^(1/2)","im":"0","approx_re":"-1.366141","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":"s_1","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"s_2","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-349/512+85/512*17^(1/2)","im":"0","approx_re":"0.002859","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"13/16","im":"0","approx_re":"0.8125","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":["1/2","1/2","1/2","1/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -368*X^4-224*X^3-208*X^2-96*X-16, 2048*X*(21*X^3+24*X^2+18*X+4), -65536*(2*X+1)*(10*X^3+7*X^2-5*X-4), -8388608*(2*X+1)*(X+1)^2*(2*X+3)]", "text": "Operator equivalent to 3.34, equivalent to\nAESZ 107 $=d \\ast d$.", "degz": 4, "h3": null, "sol": "1 16 912 67840 5839120 545884416 53886556416 5527209971712 583312107240720 62928509796655360", "n_discr_factors": "2", "c3": null, "operator": "4 4 0 0 0 0 1 -16 -96 -208 -224 -368 0 8192 36864 49152 43008 262144 851968 196608 -1572864 -1310720 -25165824 -117440512 -192937984 -134217728 -33554432", "new_number": "4.35", "id": 132, "operator_tex": "\\theta^4-2^{4} x\\left(23\\theta^4+14\\theta^3+13\\theta^2+6\\theta+1\\right)+2^{11} x^{2}\\theta(21\\theta^3+24\\theta^2+18\\theta+4)-2^{16} x^{3}(2\\theta+1)(10\\theta^3+7\\theta^2-5\\theta-4)-2^{23} x^{4}(2\\theta+1)(\\theta+1)^2(2\\theta+3)", "superseek": "-16 -1744", "discriminant": "4 1 -368 43008 -1310720 -33554432", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "cd392ce4c33f242f5d17e59976d0ea4f", "dim_h": null, "inst": " -16 -106 -1744 -29526 -644016 -14437922 -359438736 -9163638478 -246345604992 -6752150271598", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "-(16z+1)(128z-1)^3", "discr_factors": "-33554432, (z-1/128)^3, z+1/16", "dm_basis": null, "q": "0 1 -32 -96 7168 -52944 -857088 -1792512 -175964160 -8774633832", "yuk": "1 -16 -864 -47104 -1890528 -80502016 -3118639104 -123287486464 -4691784791264 -179585946086272", "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":"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","1/2","3/2","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": "[49*X^4, -53424*X^4-105336*X^3-74718*X^2-22050*X-2352, 524448*X^4+457056*X^3-309084*X^2-247296*X-40320, -1181952*X^4+653184*X^3+722304*X^2+154224*X+6048, -15552*(3*X+1)*(2*X+1)^2*(3*X+2)]", "text": "Sporadic Operator.", "degz": 4, "h3": "7", "sol": "1 48 15840 8148000 5126536800 3619570002048 2753811350113824 2207771557753956480 1839938553689058108000 1579830078681015395520000", "n_discr_factors": "2", "c3": "-120", "operator": "4 4 0 0 0 0 49 -2352 -22050 -74718 -105336 -53424 -40320 -247296 -309084 457056 524448 6048 154224 722304 653184 -1181952 -31104 -264384 -824256 -1119744 -559872", "new_number": "4.36", "id": 133, "operator_tex": "7^{2} \\theta^4-2 3 7 x\\left(1272\\theta^4+2508\\theta^3+1779\\theta^2+525\\theta+56\\right)+2^{2} 3 x^{2}\\left(43704\\theta^4+38088\\theta^3-25757\\theta^2-20608\\theta-3360\\right)-2^{4} 3^{3} x^{3}\\left(2736\\theta^4-1512\\theta^3-1672\\theta^2-357\\theta-14\\right)-2^{6} 3^{5} x^{4}(3\\theta+1)(2\\theta+1)^2(3\\theta+2)", "superseek": "1434/7 18676572/7", "discriminant": "4 49 -53424 524448 -1181952 -559872", "aesz": "109", "n_sing_complex": "1", "inst_int": "", "c2h": "46", "hash": "bca2938ac7fa09f5bdc395cab75caf82", "dim_h": "5", "inst": " 1434/7 14718 18676572/7 4988009280/7 1646787631350/7 622466594325132/7 258353389427348430/7 16404944169924970464 53786293452931561754730/7 26254922854681782077900670/7", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "3", "laurent": null, "discriminant_tex": "-(432z^2+1080z-1)(-7+36z)^2", "discr_factors": "-559872, z^2+5/2*z-1/432, (-7/36+z)^2", "dm_basis": null, "q": "0 1 -258 15801 -2799212 -619136580 -289200901266 -135520306538198 -67319605493315208 -34851846790327410108", "yuk": "1 1434/7 825642/7 504268878/7 319233419562/7 205848453920184/7 134452784879321598/7 88615212573580512924/7 58795319905330327562538/7 39210207927187109023467048/7", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-5/4-13/18*3^(1/2)","im":"0","approx_re":"-2.500926","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":"s_1","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"s_2","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-5/4+13/18*3^(1/2)","im":"0","approx_re":"0.000926","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"7/36","im":"0","approx_re":"0.194444444444","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":["1/3","1/2","1/2","2/3"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -4*X*(X+1)*(2*X+1)^2, -32*(2*X+1)*(2*X+3)*(11*X^2+22*X+12), -1200*(2*X+1)*(2*X+3)^2*(2*X+5), -4864*(2*X+1)*(2*X+3)*(2*X+5)*(2*X+7)]", "text": "Sporadic Operator.", "degz": 4, "h3": null, "sol": "1 0 72 1200 44520 1451520 54164880 2075673600 82978295400 3404489088000", "n_discr_factors": "2", "c3": null, "operator": "4 4 0 0 0 0 1 0 -4 -20 -32 -16 -1152 -5184 -8224 -5632 -1408 -54000 -201600 -240000 -115200 -19200 -510720 -1712128 -1673216 -622592 -77824", "new_number": "4.37", "id": 134, "operator_tex": "\\theta^4-2^{2} x\\theta(\\theta+1)(2\\theta+1)^2-2^{5} x^{2}(2\\theta+1)(2\\theta+3)(11\\theta^2+22\\theta+12)-2^{4} 3 5^{2} x^{3}(2\\theta+1)(2\\theta+3)^2(2\\theta+5)-2^{8} 19 x^{4}(2\\theta+1)(2\\theta+3)(2\\theta+5)(2\\theta+7)", "superseek": "4 284", "discriminant": "4 1 -16 -1408 -19200 -77824", "aesz": "206", "n_sing_complex": "1", "inst_int": "", "c2h": null, "hash": "bd5dae321e1369e7fae153775f84a351", "dim_h": null, "inst": " 4 27 284 4368 80968 1722333 40082284 998658176 26202453860 716312822310", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "3", "laurent": null, "discriminant_tex": "-(16z+1)(4864z^3+896z^2+32z-1)", "discr_factors": "-77824, z^3+7/38*z^2+1/152*z-1/4864, z+1/16", "dm_basis": null, "q": "0 1 -4 -174 -1008 5703 -60552 -6912774 -195899200 -4965619785", "yuk": "1 4 220 7672 279772 10121004 372031816 13748223416 511313265884 19101588871612", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/912*(6947+627*33^(1/2))^(1/3)-41/114/(6947+627*33^(1/2))^(1/3)-7/114","im":"-1/8*3^(1/2)*(1/114*(6947+627*33^(1/2))^(1/3)-164/57/(6947+627*33^(1/2))^(1/3))","approx_re":"-0.10185","approx_im":"-0.013248","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/912*(6947+627*33^(1/2))^(1/3)-41/114/(6947+627*33^(1/2))^(1/3)-7/114","im":"1/8*3^(1/2)*(1/114*(6947+627*33^(1/2))^(1/3)-164/57/(6947+627*33^(1/2))^(1/3))","approx_re":"-0.10185","approx_im":"0.013248","exponents":["0","1","1","2"],"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":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"s_1","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"s_3","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"s_2","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/456*(6947+627*33^(1/2))^(1/3)+41/57/(6947+627*33^(1/2))^(1/3)-7/114","im":"0","approx_re":"0.019489","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","3/2","5/2","7/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -17152*X^4+285184*X^3+174208*X^2+31616*X+2320, -6696206336*X^4-15252586496*X^3+5932843008*X^2+1864892416*X+183107584, 255108172480512*X^4+5360119185408*X^3-1702954532864*X^2+1340029796352*X+338497110016, -2973079441506304*(2*X+1)^4]", "text": "Sporadic Operator.\nThere is a further MUM point hidden at infinity.\nThat operator is AESZ 99/4.34", "degz": 4, "h3": null, "sol": "1 -2320 57601296 -2373661139200 121665506430000400 -7045795484316081803520 441185231305801580551430400 -29167850759386124406758964203520 2007006431502831560693698607381552400 -142398548719995442925238316283669698412800", "n_discr_factors": "2", "c3": null, "operator": "4 4 0 0 0 0 1 2320 31616 174208 285184 -17152 183107584 1864892416 5932843008 -15252586496 -6696206336 338497110016 1340029796352 -1702954532864 5360119185408 255108172480512 -2973079441506304 -23784635532050432 -71353906596151296 -95138542128201728 -47569271064100864", "new_number": "4.38", "id": 135, "operator_tex": "\\theta^4-2^{4} x\\left(1072\\theta^4-17824\\theta^3-10888\\theta^2-1976\\theta-145\\right)-2^{17} x^{2}\\left(51088\\theta^4+116368\\theta^3-45264\\theta^2-14228\\theta-1397\\right)+2^{28} 13 x^{3}\\left(73104\\theta^4+1536\\theta^3-488\\theta^2+384\\theta+97\\right)-2^{44} 13^{2} x^{4}\\left((2\\theta+1)^4\\right)", "superseek": "-70944 -3707752060576", "discriminant": "4 1 -17152 -6696206336 255108172480512 -47569271064100864", "aesz": "207", "n_sing_complex": "1", "inst_int": "", "c2h": null, "hash": "eadc0882a9bf59840ef2b4a602f586e8", "dim_h": null, "inst": " -70944 107317768 -3707752060576 66327758316665792 -1970671594871618215520 60918074853294450360703848 -2127431022471079026687146213408 78924771274663026682498993043569600 -3092613530414005042810122048042336112384 126209351142487249207056800988317625590063064", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "3", "laurent": null, "discriminant_tex": "-(16777216z^2-89344z-1)(-1+53248z)^2", "discr_factors": "-47569271064100864, z^2-349/65536*z-1/16777216, (-1/53248+z)^2", "dm_basis": null, "q": "0 1 22336 197970016 3517928839168 -2806303023423952 1476770832531571582976 -41107586288642233464430080 1919442885482411246327352655872 -80488023757262364556958491706762600", "yuk": "1 -70944 858471200 -100109305706496 4244976533125081888 -246333949358952277010944 13158304168311501169464866816 -729708840707580106153691151269888 40409482892627469665684460971432717088 -2254515263671809676208578973122972331634432", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"349/131072-85/131072*17^(1/2)","im":"0","approx_re":"-1.1e-05","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":"s_2","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"s_1","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/53248","im":"0","approx_re":"1.87800480769e-05","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"349/131072+85/131072*17^(1/2)","im":"0","approx_re":"0.005336","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","1/2","1/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[25*X^4, 700+6100*X+19620*X^2+27040*X^3+13760*X^4, -4240-20160*X+1536*X^2+112128*X^3+93696*X^4, 5120+30720*X+70656*X^2+122880*X^3+180224*X^4, 4096*(2*X+1)^4]", "text": "Sporadic operator. There is a second MUM point hidden at infinity; Operator AESZ 211/4.40", "degz": 4, "h3": null, "sol": "1 -28 4716 -1226800 389349100 -138518544528 53075018337264 -21423107233015488 8987125431289905900 -3883840846842483326800", "n_discr_factors": "2", "c3": null, "operator": "4 4 0 0 0 0 25 700 6100 19620 27040 13760 -4240 -20160 1536 112128 93696 5120 30720 70656 122880 180224 4096 32768 98304 131072 65536", "new_number": "4.39", "id": 136, "operator_tex": "5^{2} \\theta^4+2^{2} 5 x\\left(688\\theta^4+1352\\theta^3+981\\theta^2+305\\theta+35\\right)+2^{4} x^{2}\\left(5856\\theta^4+7008\\theta^3+96\\theta^2-1260\\theta-265\\right)+2^{10} x^{3}\\left(176\\theta^4+120\\theta^3+69\\theta^2+30\\theta+5\\right)+2^{12} x^{4}\\left((2\\theta+1)^4\\right)", "superseek": "-444/5 -1501908/5", "discriminant": "4 25 13760 93696 180224 65536", "aesz": "210", "n_sing_complex": "1", "inst_int": "", "c2h": null, "hash": "155d0198a5b26de08a0c2caf680f0786", "dim_h": null, "inst": " -444/5 16653/5 -1501908/5 199965534/5 -6573697776 6182943292991/5 -1276877706329844/5 56474709239438358 -65798958247981094232/5 3195763572038478592884", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "3", "laurent": null, "discriminant_tex": "(256z^2+544z+1)(5+16z)^2", "discr_factors": "65536, z^2+17/8*z+1/256, (5/16+z)^2", "dm_basis": null, "q": "0 1 132 4326 353936 -36794751 8644090200 -2015530567694 498256837667904 -128350330837545324", "yuk": "1 -444/5 26556 -8110392 12797926956/5 -4108561110444/5 267103142173464 -437969053271136936/5 144575255665760123436/5 -47967440562778258247088/5", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-17/16-3/4*2^(1/2)","im":"0","approx_re":"-2.12316","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-5/16","im":"0","approx_re":"-0.3125","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-17/16+3/4*2^(1/2)","im":"0","approx_re":"-0.00184","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":"s_1","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"s_2","im":"0","approx_re":"0.0","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","1/2","1/2","1/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -448*(X+1/2)^4-412*(X+1/2)^2-13, 91648*(X+1)^4+144448*(X+1)^2+12736, -82944*(X+3/2)^2*(112*(X+3/2)^2+89), 107495424*(X+2)^2*(2*X+3)*(2*X+5)]", "text": "YY-Operator equivalent to AESZ 150=$ A \\ast \\delta $", "degz": 4, "h3": null, "sol": "1 144 13320 432320 -127603800 -33213869568 -4622348436992 -369487705466880 6608967774500520 8246344074310742400", "n_discr_factors": "1", "c3": null, "operator": "4 4 0 0 0 0 1 -144 -636 -1084 -896 -448 248832 655488 694336 366592 91648 -63638784 -147557376 -132793344 -55738368 -9289728 6449725440 13329432576 10212065280 3439853568 429981696", "new_number": "4.3", "id": 137, "operator_tex": "\\theta^4-2^{2} x\\left(112\\theta^4+224\\theta^3+271\\theta^2+159\\theta+36\\right)+2^{6} x^{2}\\left(1432\\theta^4+5728\\theta^3+10849\\theta^2+10242\\theta+3888\\right)-2^{8} 3^{4} x^{3}(112\\theta^2+336\\theta+341)(2\\theta+3)^2+2^{14} 3^{8} x^{4}(\\theta+2)^2(2\\theta+3)(2\\theta+5)", "superseek": "-20 5924", "discriminant": "4 1 -448 91648 -9289728 429981696", "aesz": null, "n_sing_complex": "1", "inst_int": "", "c2h": null, "hash": "4163e7dfeb4b46f62bda072d071020fc", "dim_h": null, "inst": " -20 199 5924 82010 -1170848 -92226419 -2051645148 18334803698 2749155476112 79788570171384", "cleanlist": "True", "n_sing_real": "1", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "2", "laurent": null, "discriminant_tex": "(1-224z+20736z^2)^2", "discr_factors": "429981696, (1/20736-7/648*z+z^2)^2", "dm_basis": null, "q": "0 1 -60 4062 -161456 7582509 -281492040 10960968978 -395542087104 14279572541190", "yuk": "1 -20 1572 159928 5250212 -146356020 -19920744984 -703714285784 9387424743588 2004134342245576", "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":"s_1","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["-1/2","0","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"s_2","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["-1/2","0","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"7/1296","im":"-1/324*2^(1/2)","approx_re":"0.0054012345679","approx_im":"-0.004365","exponents":["0","-1/2","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"7/1296","im":"1/324*2^(1/2)","approx_re":"0.0054012345679","approx_im":"0.004365","exponents":["0","-1/2","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["3/2","2","2","5/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, 208+2368*X+9792*X^2+14848*X^3+11264*X^4, -495616-3981312*X-6684672*X^2+19267584*X^3+23986176*X^4, 36700160+125829120*X-314572800*X^2+503316480*X^3+14428405760*X^4, 6710886400*(2*X+1)^4]", "text": "Sporadic Operator. There is a second MUM point hidden at infinity. That corresponds to Operator AESZ210/", "degz": 4, "h3": null, "sol": "1 -208 531216 -2168300800 10900554288400 -61672477170302208 376545976212867842304 -2424693725877235737120768 16238936215019821475553123600 -112091305560797352029300969708800", "n_discr_factors": "2", "c3": null, "operator": "4 4 0 0 0 0 1 208 2368 9792 14848 11264 -495616 -3981312 -6684672 19267584 23986176 36700160 125829120 -314572800 503316480 14428405760 6710886400 53687091200 161061273600 214748364800 107374182400", "new_number": "4.40", "id": 138, "operator_tex": "\\theta^4+2^{4} x\\left(704\\theta^4+928\\theta^3+612\\theta^2+148\\theta+13\\right)+2^{12} x^{2}\\left(5856\\theta^4+4704\\theta^3-1632\\theta^2-972\\theta-121\\right)+2^{20} 5 x^{3}\\left(2752\\theta^4+96\\theta^3-60\\theta^2+24\\theta+7\\right)+2^{28} 5^{2} x^{4}\\left((2\\theta+1)^4\\right)", "superseek": "-2400 -2956977632", "discriminant": "4 1 11264 23986176 14428405760 107374182400", "aesz": "211", "n_sing_complex": "1", "inst_int": "", "c2h": null, "hash": "c923c78e33e72a3a2b294bf3f2749298", "dim_h": null, "inst": " -2400 1830480 -2956977632 7117422755016 -21319886408804640 73220641843081488400 -276237242831635556694624 1116165003675243068387169096 -4752240098387465208494919826688 21084899505584266915675933560347760", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "3", "laurent": null, "discriminant_tex": "(65536z^2+8704z+1)(1+1280z)^2", "discr_factors": "107374182400, z^2+17/128*z+1/65536, (1/1280+z)^2", "dm_basis": null, "q": "0 1 1536 -472224 1670150144 -5922808911312 23097698733133824 -97617640594997652992 437400929237401712197632 -2047254291356326075951592808", "yuk": "1 -2400 14641440 -79838398464 455515070962464 -2664985801100582400 15815658638025777739776 -94749374291250995946258432 571476481881724906529301539616 -3464383031724462136992876392054016", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-17/256-3/64*2^(1/2)","im":"0","approx_re":"-0.132698","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/1280","im":"0","approx_re":"-0.00078125","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-17/256+3/64*2^(1/2)","im":"0","approx_re":"-0.000115","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":"s_1","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"s_2","im":"0","approx_re":"0.0","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","1/2","1/2","1/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -320*X^4-896*X^3-608*X^2-160*X-16, -86016*X^4-245760*X^3-267264*X^2-137216*X-25600, -65536*(2*X+1)^2*(23*X^2+55*X+39), -8388608*(2*X+1)^2*(2*X+3)^2]", "text": "Sporadic Operator.\nReducible to 3.32, so not a primary operator.\nB-Incarnation: 81111- x 82--11\n", "degz": 4, "h3": "8", "sol": "1 16 3600 851200 257328400 86333942016 31204775137536 11874454884864000 4695209743316835600 1912190218793129017600", "n_discr_factors": "2", "c3": "-8", "operator": "4 4 0 0 0 0 1 -16 -160 -608 -896 -320 -25600 -137216 -267264 -245760 -86016 -2555904 -13828096 -26148864 -20447232 -6029312 -75497472 -402653184 -738197504 -536870912 -134217728", "new_number": "4.41", "id": 139, "operator_tex": "\\theta^4-2^{4} x\\left(20\\theta^4+56\\theta^3+38\\theta^2+10\\theta+1\\right)-2^{10} x^{2}\\left(84\\theta^4+240\\theta^3+261\\theta^2+134\\theta+25\\right)-2^{16} x^{3}(2\\theta+1)^2(23\\theta^2+55\\theta+39)-2^{23} x^{4}(2\\theta+1)^2(2\\theta+3)^2", "superseek": "128 382592", "discriminant": "4 1 -320 -86016 -6029312 -134217728", "aesz": "220", "n_sing_complex": "0", "inst_int": "", "c2h": "32", "hash": "671a1aa788ead53985e13ad6774d0189", "dim_h": "4", "inst": " 128 4084 382592 51510860 8644861312 1659459740132 349956800171136 79045292244127852 18815837160365104128 4668098318162928620860", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "-(512z-1)(64z+1)^3", "discr_factors": "-134217728, (z+1/64)^3, z-1/512", "dm_basis": null, "q": "0 1 -96 -3360 47104 -59645904 -11999339520 -2746669569536 -697657825099776 -183142363318091112", "yuk": "1 128 32800 10330112 3296727840 1080607664128 358443314231296 120035182458699776 40471189632290188064 13716745289906171239424", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/64","im":"0","approx_re":"-0.015625","approx_im":"0.0","exponents":["0","1/2","3/2","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":"1/512","im":"0","approx_re":"0.001953125","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, -200-1550*X-4545*X^2-5990*X^3-2035*X^4, -87040-518400*X-1069824*X^2-895872*X^3-269184*X^4, -409600-3932160*X-12619776*X^2-15728640*X^3-5681152*X^4, -2097152*(2*X+1)^4]", "text": "Sporadic Operator. There is a second MUM-point hiding at infinity, corresponding to Operator AESZ225/4.43", "degz": 4, "h3": "20", "sol": "1 8 504 36800 3518200 365275008 41121267264 4856185331712 596136147492600 75323913126862400", "n_discr_factors": "2", "c3": "-128", "operator": "4 4 0 0 0 0 25 -200 -1550 -4545 -5990 -2035 -87040 -518400 -1069824 -895872 -269184 -409600 -3932160 -12619776 -15728640 -5681152 -2097152 -16777216 -50331648 -67108864 -33554432", "new_number": "4.42", "id": 140, "operator_tex": "5^{2} \\theta^4-5 x\\left(407\\theta^4+1198\\theta^3+909\\theta^2+310\\theta+40\\right)-2^{7} x^{2}\\left(2103\\theta^4+6999\\theta^3+8358\\theta^2+4050\\theta+680\\right)-2^{12} x^{3}\\left(1387\\theta^4+3840\\theta^3+3081\\theta^2+960\\theta+100\\right)-2^{21} x^{4}\\left((2\\theta+1)^4\\right)", "superseek": "69/5 29081/5", "discriminant": "4 25 -2035 -269184 -5681152 -33554432", "aesz": "222", "n_sing_complex": "1", "inst_int": "", "c2h": "68", "hash": "aad7a72e711c9c463396d319e0bf7603", "dim_h": "9", "inst": " 69/5 1383/4 29081/5 346080 72023607/5 3784067515/4 281702428686/5 20053762156416/5 1409669129591222/5 85799281232555565/4", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "3", "laurent": null, "discriminant_tex": "-(8192z^2+107z-1)(5+64z)^2", "discr_factors": "-33554432, z^2+107/8192*z-1/8192, (5/64+z)^2", "dm_basis": null, "q": "0 1 -30 -507 15896 -864690 -19722342 -2270250854 -140407232352 -12748761975909", "yuk": "1 69/5 13899/5 785256/5 110759499/5 9002950944/5 1021699028136/5 96623933039367/5 10267526334844491/5 1027648795472786094/5", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-5/64","im":"0","approx_re":"-0.078125","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-107/16384-51/16384*17^(1/2)","im":"0","approx_re":"-0.019365","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":"s_1","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"s_2","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-107/16384+51/16384*17^(1/2)","im":"0","approx_re":"0.006304","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","1/2","1/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -784-16768*X-153216*X^2-272896*X^3+355072*X^4, 17825792+1849688064*X+17012097024*X^2-46858764288*X^3+35282485248*X^4, -16578573762560-131941395333120*X-381393095884800*X^2-527765581332480*X^3+559376540631040*X^4, -900719925474099200*(2*X+1)^4]", "text": "Sporadic Operator. There is a second MUM-point\nhiding at infinity, corresponding to Operator\nAESZ 222/4.42", "degz": 4, "h3": "4", "sol": "1 784 3226896 20413907200 157477179235600 1361831571773616384 12684795211912342692096 124477818005324688955674624 1269631592734724062413342973200 13341061142213717890728655538233600", "n_discr_factors": "2", "c3": "640", "operator": "4 4 0 0 0 0 1 -784 -16768 -153216 -272896 355072 17825792 1849688064 17012097024 -46858764288 35282485248 -16578573762560 -131941395333120 -381393095884800 -527765581332480 559376540631040 -900719925474099200 -7205759403792793600 -21617278211378380800 -28823037615171174400 -14411518807585587200", "new_number": "4.43", "id": 141, "operator_tex": "\\theta^4+2^{4} x\\left(22192\\theta^4-17056\\theta^3-9576\\theta^2-1048\\theta-49\\right)+2^{20} x^{2}\\left(33648\\theta^4-44688\\theta^3+16224\\theta^2+1764\\theta+17\\right)+2^{34} 5 x^{3}\\left(6512\\theta^4-6144\\theta^3-4440\\theta^2-1536\\theta-193\\right)-2^{55} 5^{2} x^{4}\\left((2\\theta+1)^4\\right)", "superseek": "93984 25265152551072", "discriminant": "4 1 355072 35282485248 559376540631040 -14411518807585587200", "aesz": "225", "n_sing_complex": "1", "inst_int": "", "c2h": "-8", "hash": "5993002ccf811247be9232b089dd8e3a", "dim_h": "0", "inst": " 93984 -1084521600 25265152551072 -787700706860008320 28889437619654310485088 -1175123711760789859743048320 51358422489334818184115432720928 -2366123613298324781338140979519579008 113498527327558067922532188570410940202752 -5620696211385822025421692623281080034910450048", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "3", "laurent": null, "discriminant_tex": "-(536870912z^2-27392z-1)(1+163840z)^2", "discr_factors": "-14411518807585587200, z^2-107/2097152*z-1/536870912, (1/163840+z)^2", "dm_basis": null, "q": "0 1 -13632 349655136 -12475753895936 522338315529567792 -24006084551026067761152 1172497234208292982798672384 -59770287497610147774288093118464 3145077533503728165711567034217978520", "yuk": "1 93984 -8676078816 682159118972928 -50412845247716611296 3611179702456788810729984 -253826721740329927554055636992 17615938913841842637151593423372288 -1211455290008742288095541026761741063392 82740426421789831515525965468511734526779136", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"107/4194304-51/4194304*17^(1/2)","im":"0","approx_re":"-2.5e-05","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/163840","im":"0","approx_re":"-6.103515625e-06","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":"s_2","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"s_1","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"107/4194304+51/4194304*17^(1/2)","im":"0","approx_re":"7.6e-05","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","1/2","1/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[25*X^4, -600-5250*X-16895*X^2-23290*X^3-13085*X^4, -165120-1038720*X-1974144*X^2-935232*X^3+129216*X^4, 921600+9400320*X+32044032*X^2+39813120*X^3+8801280*X^4, -3538944*(3*X+1)*(2*X+1)^2*(3*X+2)]", "text": "Sporadic Operator.", "degz": 4, "h3": "10", "sol": "1 24 3960 974400 292030200 98002929024 35404004091456 13469740411944960 5325269471817867000 2168604409044940152000", "n_discr_factors": "3", "c3": "-120", "operator": "4 4 0 0 0 0 25 -600 -5250 -16895 -23290 -13085 -165120 -1038720 -1974144 -935232 129216 921600 9400320 32044032 39813120 8801280 -7077888 -60162048 -187564032 -254803968 -127401984", "new_number": "4.44", "id": 142, "operator_tex": "5^{2} \\theta^4-5 x\\left(2617\\theta^4+4658\\theta^3+3379\\theta^2+1050\\theta+120\\right)+2^{6} 3 x^{2}\\left(673\\theta^4-4871\\theta^3-10282\\theta^2-5410\\theta-860\\right)+2^{10} 3^{2} x^{3}\\left(955\\theta^4+4320\\theta^3+3477\\theta^2+1020\\theta+100\\right)-2^{17} 3^{3} x^{4}(3\\theta+1)(2\\theta+1)^2(3\\theta+2)", "superseek": "379/5 1364199/5", "discriminant": "4 25 -13085 129216 8801280 -127401984", "aesz": "232", "n_sing_complex": "0", "inst_int": "", "c2h": "52", "hash": "8d5ff690c87757ed51a092dee764eede", "dim_h": "6", "inst": " 379/5 3346 1364199/5 177727432/5 5658116533 5162925665472/5 1034132839801394/5 44368440569992104 50146684202347697994/5 2362720295938250247382", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "-(27z+1)(512z-1)(-5+96z)^2", "discr_factors": "-127401984, (-5/96+z)^2, z-1/512, z+1/27", "dm_basis": null, "q": "0 1 -114 1029 -116984 -43625010 -7822436202 -1800503860710 -431538538385184 -107734627015030629", "yuk": "1 379/5 134219/5 36833752/5 11374689867/5 3536322833504/5 1115191980709544/5 354707564051878521/5 113583207870554476107/5 36556932783511508671378/5", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/27","im":"0","approx_re":"-0.037037037037","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":"1/512","im":"0","approx_re":"0.001953125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"5/96","im":"0","approx_re":"0.0520833333333","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":["1/3","1/2","1/2","2/3"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -48-384*X-1136*X^2-1504*X^3-1328*X^4, 61440+436224*X+1069056*X^2+1173504*X^3+620544*X^4, -6488064-60162048*X-196411392*X^2-254803968*X^3-119734272*X^4, 226492416*(3*X+1)*(2*X+1)^2*(3*X+2)]", "text": "Sporadic Operator.", "degz": 4, "h3": "16", "sol": "1 48 9360 2553600 813027600 283184149248 104664044669184 40361741131345920 16073129967819210000 6564949660340509152000", "n_discr_factors": "3", "c3": "-72", "operator": "4 4 0 0 0 0 1 -48 -384 -1136 -1504 -1328 61440 436224 1069056 1173504 620544 -6488064 -60162048 -196411392 -254803968 -119734272 452984832 3850371072 12004098048 16307453952 8153726976", "new_number": "4.45", "id": 143, "operator_tex": "\\theta^4-2^{4} x\\left(83\\theta^4+94\\theta^3+71\\theta^2+24\\theta+3\\right)+2^{11} 3 x^{2}\\left(101\\theta^4+191\\theta^3+174\\theta^2+71\\theta+10\\right)-2^{16} 3^{2} x^{3}\\left(203\\theta^4+432\\theta^3+333\\theta^2+102\\theta+11\\right)+2^{23} 3^{3} x^{4}(3\\theta+1)(2\\theta+1)^2(3\\theta+2)", "superseek": "80 104976", "discriminant": "4 1 -1328 620544 -119734272 8153726976", "aesz": "233", "n_sing_complex": "0", "inst_int": "", "c2h": "64", "hash": "03f67459f6d678669f766c99281b1e79", "dim_h": "8", "inst": " 80 2794 104976 5367454 508265072 71026691490 10979503341520 1741443998259494 281028365633566080 46168051267005890030", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "(512z-1)(432z-1)(-1+192z)^2", "discr_factors": "8153726976, z-1/432, z-1/512, (-1/192+z)^2", "dm_basis": null, "q": "0 1 -192 20256 -1451008 76300080 -3901906944 74979753472 -15535962980352 -1686551922782568", "yuk": "1 80 22432 2834432 343539488 63533134080 15341768218624 3765969646141440 891619327452400416 204869678546872506752", "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":"1/512","im":"0","approx_re":"0.001953125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/432","im":"0","approx_re":"0.00231481481481","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","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/3","1/2","1/2","2/3"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -48-432*X-1456*X^2-2048*X^3-736*X^4, 30720+195072*X+354816*X^2+24576*X^3-113664*X^4, 737280+7520256*X+25804800*X^2+31850496*X^3+2064384*X^4, 14155776*(3*X+1)*(2*X+1)^2*(3*X+2)]", "text": "This is operator \"4.46\" from ...", "degz": 4, "h3": "8", "sol": "1 48 12240 4972800 2489533200 1401972219648 851613132674304 545396655633223680 363197708573488074000 249238571558094285024000", "n_discr_factors": "3", "c3": "-78", "operator": "4 4 0 0 0 0 1 -48 -432 -1456 -2048 -736 30720 195072 354816 24576 -113664 737280 7520256 25804800 31850496 2064384 28311552 240648192 750256128 1019215872 509607936", "new_number": "4.46", "id": 144, "operator_tex": "\\theta^4-2^{4} x\\left(46\\theta^4+128\\theta^3+91\\theta^2+27\\theta+3\\right)-2^{9} 3 x^{2}\\left(74\\theta^4-16\\theta^3-231\\theta^2-127\\theta-20\\right)+2^{14} 3^{2} x^{3}\\left(14\\theta^4+216\\theta^3+175\\theta^2+51\\theta+5\\right)+2^{19} 3^{3} x^{4}(3\\theta+1)(2\\theta+1)^2(3\\theta+2)", "superseek": "208 1218192", "discriminant": "4 1 -736 -113664 2064384 509607936", "aesz": "237", "n_sing_complex": "0", "inst_int": "", "c2h": "44", "hash": "52c18dd4477f6548dd3b185e97b94c20", "dim_h": "5", "inst": " 208 5874 1218192 220754467 56417503216 15951074497098 4990351864917072 1668543662657027085 588098857643537702784 215992440329420333366982", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "(864z-1)(64z-1)(1+96z)^2", "discr_factors": "509607936, z-1/864, z-1/64, (1/96+z)^2", "dm_basis": null, "q": "0 1 -240 26496 -4041728 210043824 -104028553728 -16599411155968 -8521760778977280 -3068823070013161320", "yuk": "1 208 47200 32891392 14128333088 7052187902208 3445432124311552 1711690689666555904 854294355294526200608 428724067222139018220928", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/96","im":"0","approx_re":"-0.0104166666667","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":"1/864","im":"0","approx_re":"0.00115740740741","approx_im":"0.0","exponents":["0","1","1","2"],"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":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/3","1/2","1/2","2/3"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -144-1536*X-6288*X^2-9504*X^3+432*X^4, 92160+497664*X-1492992*X^2-22394880*X^3-8957952*X^4, -398131200-3439853568*X-10749542400*X^2-15479341056*X^3-14189395968*X^4, -55037657088*(3*X+1)^2*(3*X+2)^2]", "text": "Sporadic Operator.", "degz": 4, "h3": "4", "sol": "1 144 147600 239904000 479672701200 1078954420287744 2618634987667835136 6702283021504364236800 17840666902138413842480400 48944005664385888179529120000", "n_discr_factors": "3", "c3": "-18", "operator": "4 4 0 0 0 0 1 -144 -1536 -6288 -9504 432 92160 497664 -1492992 -22394880 -8957952 -398131200 -3439853568 -10749542400 -15479341056 -14189395968 -220150628352 -1981355655168 -6439405879296 -8916100448256 -4458050224128", "new_number": "4.47", "id": 145, "operator_tex": "\\theta^4+2^{4} 3 x\\left(9\\theta^4-198\\theta^3-131\\theta^2-32\\theta-3\\right)-2^{11} 3^{2} x^{2}\\left(486\\theta^4+1215\\theta^3+81\\theta^2-27\\theta-5\\right)-2^{16} 3^{5} x^{3}\\left(891\\theta^4+972\\theta^3+675\\theta^2+216\\theta+25\\right)-2^{23} 3^{8} x^{4}(3\\theta+1)^2(3\\theta+2)^2", "superseek": "1584 171534960", "discriminant": "4 1 432 -8957952 -14189395968 -4458050224128", "aesz": "239", "n_sing_complex": "0", "inst_int": "", "c2h": "28", "hash": "8e610c3437d7f38e552038bc55399495", "dim_h": "3", "inst": " 1584 -17874 171534960 30012731550 105934107802896 63775249469817750 127749832497630077616 131860871041114114038054 224001851211067044692907648 298697681537718689647638089370", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "-(432z+1)(3456z-1)(1+1728z)^2", "discr_factors": "-4458050224128, z+1/432, z-1/3456, (1/1728+z)^2", "dm_basis": null, "q": "0 1 -960 456480 -333224960 150643621680 -220108476321792 37434112216317440 -259405759761365729280 -112198587502907767173480", "yuk": "1 1584 -141408 4631445504 1920814677792 13241763475363584 13775453890111936512 43818192546687116623872 67512765973052347202161440 163297349532867875585761120896", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/432","im":"0","approx_re":"-0.00231481481481","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/1728","im":"0","approx_re":"-0.000578703703704","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":"1/3456","im":"0","approx_re":"0.000289351851852","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":["1/3","1/3","2/3","2/3"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -2432*X^4-2560*X^3-1760*X^2-480*X-48, 1314816*X^4+540672*X^3-918528*X^2-522240*X-76800, -160432128*X^4+254803968*X^3+212336640*X^2+60162048*X+5898240, -452984832*(3*X+1)*(2*X+1)^2*(3*X+2)]", "text": "Sporadic Operator.", "degz": 4, "h3": "4", "sol": "1 48 26640 21907200 22048765200 24896521698048 30291889001197824 38838210495451361280 51763875861113556426000 71081695744396302602208000", "n_discr_factors": "3", "c3": "-60", "operator": "4 4 0 0 0 0 1 -48 -480 -1760 -2560 -2432 -76800 -522240 -918528 540672 1314816 5898240 60162048 212336640 254803968 -160432128 -905969664 -7700742144 -24008196096 -32614907904 -16307453952", "new_number": "4.48", "id": 146, "operator_tex": "\\theta^4-2^{4} x\\left(152\\theta^4+160\\theta^3+110\\theta^2+30\\theta+3\\right)+2^{10} 3 x^{2}\\left(428\\theta^4+176\\theta^3-299\\theta^2-170\\theta-25\\right)-2^{17} 3^{2} x^{3}\\left(136\\theta^4-216\\theta^3-180\\theta^2-51\\theta-5\\right)-2^{24} 3^{3} x^{4}(3\\theta+1)(2\\theta+1)^2(3\\theta+2)", "superseek": "320 19748928", "discriminant": "4 1 -2432 1314816 -160432128 -16307453952", "aesz": "241", "n_sing_complex": "0", "inst_int": "", "c2h": "28", "hash": "b4d16d8dd1eb7839630ecf8e8d242023", "dim_h": "3", "inst": " 320 61084 19748928 9428973876 5618509433280 3845253330631020 2892405836819922752 2330756708127722933332 1979363847140433024517632 1751890593945326994096072180", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "-(64z+1)(1728z-1)(-1+384z)^2", "discr_factors": "-16307453952, z-1/1728, z+1/64, (-1/384+z)^2", "dm_basis": null, "q": "0 1 -288 -36384 -12797952 -9672066000 -7623005064192 -6428933441480192 -5742516718520303616 -5358500671498636447080", "yuk": "1 320 488992 533221376 603454817056 702313679160320 830574719950010368 992095202029233504256 1193347434561997596683040 1442956244565375675406575104", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"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":"1/1728","im":"0","approx_re":"0.000578703703704","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/384","im":"0","approx_re":"0.00260416666667","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":["1/3","1/2","1/2","2/3"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -240-1152*X+3200*X^2+8704*X^3-41728*X^4, 2457600+44433408*X+228851712*X^2-20447232*X^3+602406912*X^4, -71722598400-616059371520*X-1987093463040*X^2-2609192632320*X^3-3466843914240*X^4, 185542587187200*(3*X+1)*(2*X+1)^2*(3*X+2)]", "text": "Sporadic Operator.", "degz": 4, "h3": null, "sol": "1 240 314640 627244800 1516001533200 4094087979421440 11884911941180678400 36300175078346941132800 115133172782432615437770000 375951272283181983269083488000", "n_discr_factors": "3", "c3": null, "operator": "4 4 0 0 0 0 1 -240 -1152 3200 8704 -41728 2457600 44433408 228851712 -20447232 602406912 -71722598400 -616059371520 -1987093463040 -2609192632320 -3466843914240 371085174374400 3154223982182400 9833757120921600 13359066277478400 6679533138739200", "new_number": "4.49", "id": 147, "operator_tex": "\\theta^4-2^{4} x\\left(2608\\theta^4-544\\theta^3-200\\theta^2+72\\theta+15\\right)+2^{15} 3 x^{2}\\left(6128\\theta^4-208\\theta^3+2328\\theta^2+452\\theta+25\\right)-2^{24} 3^{2} 5 x^{3}\\left(4592\\theta^4+3456\\theta^3+2632\\theta^2+816\\theta+95\\right)+2^{38} 3^{3} 5^{2} x^{4}(3\\theta+1)(2\\theta+1)^2(3\\theta+2)", "superseek": "-5408 -22147077792", "discriminant": "4 1 -41728 602406912 -3466843914240 6679533138739200", "aesz": "254", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "2539c1ff260271c9f7de53e267e2e8cf", "dim_h": null, "inst": " -5408 -8033784 -22147077792 -80392290665536 -341267541912723040 -1602847446037479408792 -8079852834459698409455648 -42914074726041652762709296192 -237265022009205198040468166397696 -1354215442630423202636402572509429800", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "(6912z-1)(4096z-1)(-1+15360z)^2", "discr_factors": "6679533138739200, z-1/6912, z-1/4096, (-1/15360+z)^2", "dm_basis": null, "q": "0 1 -192 1099872 5207496704 27460983332400 152900481294968832 888512735116263776768 5335998355191653406474240 32883442094805154065008188056", "yuk": "1 -5408 -64275680 -597971105792 -5145106666869984 -42658442739090385408 -346215048344693587675136 -2771389522219676554443292672 -21972006259733331359613826520288 -172966201044710589371501891275026176", "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":"1/15360","im":"0","approx_re":"6.51041666667e-05","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/6912","im":"0","approx_re":"0.000144675925926","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/4096","im":"0","approx_re":"0.000244140625","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":["1/3","1/2","1/2","2/3"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -768*(X+1/2)^4-688*(X+1/2)^2-20, 155648*(X+1)^4+33792*(X+1)^2+2560, -65536*(X+3/2)^2*(48*(X+3/2)^2+37), 4194304*(X+2)^2*(2*X+3)*(2*X+5)]", "text": "YY-Operator equivalent to $d \\ast e \\tilde A \\ast \\epsilon$", "degz": 4, "h3": null, "sol": "1 240 69840 22068480 7268490000 2454176533248 842484478035200 292657474471464960 102568871255144271120 36197101681461712992000", "n_discr_factors": "1", "c3": null, "operator": "4 4 0 0 0 0 1 -240 -1072 -1840 -1536 -768 192000 690176 967680 622592 155648 -21381120 -49741824 -44892160 -18874368 -3145728 251658240 520093696 398458880 134217728 16777216", "new_number": "4.4", "id": 148, "operator_tex": "\\theta^4-2^{4} x\\left(48\\theta^4+96\\theta^3+115\\theta^2+67\\theta+15\\right)+2^{9} x^{2}\\left(304\\theta^4+1216\\theta^3+1890\\theta^2+1348\\theta+375\\right)-2^{14} x^{3}(48\\theta^2+144\\theta+145)(2\\theta+3)^2+2^{22} x^{4}(\\theta+2)^2(2\\theta+3)(2\\theta+5)", "superseek": "-48 -32368", "discriminant": "4 1 -768 155648 -3145728 16777216", "aesz": null, "n_sing_complex": "1", "inst_int": "", "c2h": null, "hash": "a0903e578f379289d79849a566639775", "dim_h": null, "inst": " -48 -910 -32368 -1409193 -71439120 -3981781302 -237026585776 -14815169111887 -961469537214592 -64284018963892410", "cleanlist": "True", "n_sing_real": "1", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "2", "laurent": null, "discriminant_tex": "(1-384z+4096z^2)^2", "discr_factors": "16777216, (1/4096-3/32*z+z^2)^2", "dm_basis": null, "q": "0 1 -112 3840 -105472 3238320 -112316928 1366733824 -143396667392 -4299522787176", "yuk": "1 -48 -7328 -873984 -90195680 -8929890048 -860065642496 -81300118921216 -7585366675481824 -700911292630311552", "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":"s_1","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["-1/2","0","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"s_2","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["-1/2","0","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"3/64-1/32*2^(1/2)","im":"0","approx_re":"0.002681","approx_im":"0.0","exponents":["0","-1/2","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"3/64+1/32*2^(1/2)","im":"0","approx_re":"0.091069","approx_im":"0.0","exponents":["0","-1/2","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["3/2","2","2","5/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, 768*X^4+1344*X^3+960*X^2+288*X+32, 41984*X^4+26624*X^3-36864*X^2-25600*X-4352, 458752*X^4-786432*X^3-720896*X^2-196608*X-16384, -262144*(2*X+1)^4]", "text": "Sporadic Operator. There is a second MUM-point hiding at infinity, corresponding to Operator AESZ 257/4.51\nB-Incarnation: \nFibre product 4*11-- x 25311, \nDouble octic; D.O.257\n", "degz": 4, "h3": null, "sol": "1 -32 7056 -2393600 991152400 -460213996032 230179225377024 -121290760948211712 66430105210645347600 -37482175378957980070400", "n_discr_factors": "2", "c3": null, "operator": "4 4 0 0 0 0 1 32 288 960 1344 768 -4352 -25600 -36864 26624 41984 -16384 -196608 -720896 -786432 458752 -262144 -2097152 -6291456 -8388608 -4194304", "new_number": "4.50", "id": 149, "operator_tex": "\\theta^4+2^{5} x\\left(24\\theta^4+42\\theta^3+30\\theta^2+9\\theta+1\\right)+2^{8} x^{2}\\left(164\\theta^4+104\\theta^3-144\\theta^2-100\\theta-17\\right)+2^{14} x^{3}\\left(28\\theta^4-48\\theta^3-44\\theta^2-12\\theta-1\\right)-2^{18} x^{4}\\left((2\\theta+1)^4\\right)", "superseek": "-128 -800384", "discriminant": "4 1 768 41984 458752 -4194304", "aesz": "256", "n_sing_complex": "1", "inst_int": "", "c2h": null, "hash": "05e172cfdecc836685981a2b01b75d1d", "dim_h": null, "inst": " -128 6884 -800384 143245314 -31691939200 8025855746580 -2232088078371968 664849069328894234 -208686013683816528896 68267832094620590369420", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "3", "laurent": null, "discriminant_tex": "-(4096z^2-704z-1)(1+32z)^2", "discr_factors": "-4194304, (1/32+z)^2, z^2-11/64*z-1/4096", "dm_basis": null, "q": "0 1 160 3488 567296 -146232016 40997010432 -12949875538432 4306781227515904 -1492964611561167208", "yuk": "1 -128 54944 -21610496 9167755040 -3961492400128 1733584819705856 -765606210881585152 340402723505561602848 -152132103975502271175680", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/32","im":"0","approx_re":"-0.03125","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"11/128-5/128*5^(1/2)","im":"0","approx_re":"-0.001409","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":"s_1","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"s_2","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"11/128+5/128*5^(1/2)","im":"0","approx_re":"0.173284","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","1/2","1/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -112-1152*X-4480*X^2-6656*X^3-1792*X^4, 94208+655360*X+884736*X^2-3670016*X^3-2686976*X^4, -8388608-50331648*X-100663296*X^2-201326592*X^3-805306368*X^4, -1073741824*(2*X+1)^4]", "text": "Sporadic Operator. There is a second MUM-point\nhiding at infinity, corresponding to Operator\nAESZ 256/4.50", "degz": 4, "h3": "4", "sol": "1 112 93456 124614400 204621667600 378083696723712 753817928330928384 1585000160053962043392 3466049211031541759024400 7811601850118304222490105600", "n_discr_factors": "2", "c3": "-32", "operator": "4 4 0 0 0 0 1 -112 -1152 -4480 -6656 -1792 94208 655360 884736 -3670016 -2686976 -8388608 -50331648 -100663296 -201326592 -805306368 -1073741824 -8589934592 -25769803776 -34359738368 -17179869184", "new_number": "4.51", "id": 150, "operator_tex": "\\theta^4-2^{4} x\\left(112\\theta^4+416\\theta^3+280\\theta^2+72\\theta+7\\right)-2^{12} x^{2}\\left(656\\theta^4+896\\theta^3-216\\theta^2-160\\theta-23\\right)-2^{23} x^{3}\\left(96\\theta^4+24\\theta^3+12\\theta^2+6\\theta+1\\right)-2^{30} x^{4}\\left((2\\theta+1)^4\\right)", "superseek": "992 63721056", "discriminant": "4 1 -1792 -2686976 -805306368 -17179869184", "aesz": null, "n_sing_complex": "1", "inst_int": "", "c2h": "28", "hash": "1d45a05c9bcf007b5042b0f7a5672551", "dim_h": "3", "inst": " 992 98792 63721056 40943244128 36122052633760 35496785398316488 38573077037369045216 44817555891320272923488 54895973186351629390948608 70071414152078519333405737080", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "3", "laurent": null, "discriminant_tex": "-(65536z^2+2816z-1)(1+512z)^2", "discr_factors": "-17179869184, (1/512+z)^2, z^2+11/256*z-1/65536", "dm_basis": null, "q": "0 1 -704 164960 -83273728 -15505781200 -38649728440320 -41146063608995328 -55445056673294450688 -74461017216300912797032", "yuk": "1 992 791328 1720469504 2620368415520 4515256579220992 7667305647757621248 13230565423817582510080 22946588616358600105241376 40019164452850337827722004736", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-11/512-5/512*5^(1/2)","im":"0","approx_re":"-0.043321","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/512","im":"0","approx_re":"-0.001953125","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":"s_2","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"s_1","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-11/512+5/512*5^(1/2)","im":"0","approx_re":"0.000352","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","1/2","1/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -80-704*X-2496*X^2-3584*X^3-256*X^4, 180224+1081344*X+1966080*X^2-786432*X^3-786432*X^4, 20971520+201326592*X+654311424*X^2+805306368*X^3-67108864*X^4, 4294967296*(2*X+1)^4]", "text": "Sporadic Operator.", "degz": 4, "h3": "8", "sol": "1 80 24336 11398400 6632189200 4375826945280 3128385870086400 2363772411985121280 1859710567888951549200 1508986129076374769849600", "n_discr_factors": "3", "c3": "48", "operator": "4 4 0 0 0 0 1 -80 -704 -2496 -3584 -256 180224 1081344 1966080 -786432 -786432 20971520 201326592 654311424 805306368 -67108864 4294967296 34359738368 103079215104 137438953472 68719476736", "new_number": "4.52", "id": 151, "operator_tex": "\\theta^4-2^{4} x\\left(16\\theta^4+224\\theta^3+156\\theta^2+44\\theta+5\\right)-2^{14} x^{2}\\left(48\\theta^4+48\\theta^3-120\\theta^2-66\\theta-11\\right)-2^{22} x^{3}\\left(16\\theta^4-192\\theta^3-156\\theta^2-48\\theta-5\\right)+2^{32} x^{4}\\left((2\\theta+1)^4\\right)", "superseek": "480 4215904", "discriminant": "4 1 -256 -786432 -67108864 68719476736", "aesz": "258", "n_sing_complex": "0", "inst_int": "", "c2h": "32", "hash": "bfb9f01124fd9980817cbf1b50f789c3", "dim_h": "4", "inst": " 480 -16536 4215904 -242723592 151800032928 -1451841658552 9691266849668832 875056266892499832 896019960722254141696 184580570409555186384120", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "(1024z-1)(256z-1)(1+512z)^2", "discr_factors": "68719476736, (1/512+z)^2, z-1/256, z-1/1024", "dm_basis": null, "q": "0 1 -384 109920 -32946176 9269408304 -2759387652096 772834218570240 -235800183728504832 65119631126813469336", "yuk": "1 480 -131808 113829888 -15534441696 18975004116480 -313597684549632 3324104529436409856 448028808633425472288 653198551366523383126272", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/512","im":"0","approx_re":"-0.001953125","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":"1/1024","im":"0","approx_re":"0.0009765625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/256","im":"0","approx_re":"0.00390625","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","1/2","1/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, 54272*X^4-149504*X^3-92224*X^2-17472*X-1488, -767557632*X^4-5976883200*X^3+3050569728*X^2+1019609088*X+127008768, -48975512076288*X^4+29222957481984*X^3+22678232629248*X^2+6899864961024*X+706052358144, 5818615534190592*(3*X+1)*(2*X+1)^2*(3*X+2)]", "text": "Sporadic Operator.", "degz": 4, "h3": null, "sol": "1 1488 11258640 139962144000 2191135140810000 38974397455048543488 751331497587692755878144 15309166093451866932684410880 324854354868556524654614201802000 7110379597953671718924752104334880000", "n_discr_factors": "3", "c3": null, "operator": "4 4 0 0 0 0 1 -1488 -17472 -92224 -149504 54272 127008768 1019609088 3050569728 -5976883200 -767557632 706052358144 6899864961024 22678232629248 29222957481984 -48975512076288 11637231068381184 98916464081240064 308386623312101376 418940318461722624 209470159230861312", "new_number": "4.53", "id": 152, "operator_tex": "\\theta^4+2^{4} x\\left(3392\\theta^4-9344\\theta^3-5764\\theta^2-1092\\theta-93\\right)-2^{17} 3 x^{2}\\left(1952\\theta^4+15200\\theta^3-7758\\theta^2-2593\\theta-323\\right)-2^{26} 3^{2} 7 x^{3}\\left(11584\\theta^4-6912\\theta^3-5364\\theta^2-1632\\theta-167\\right)+2^{42} 3^{3} 7^{2} x^{4}(3\\theta+1)(2\\theta+1)^2(3\\theta+2)", "superseek": "37216 464865119712", "discriminant": "4 1 54272 -767557632 -48975512076288 209470159230861312", "aesz": "264", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "625990ef22ba977bc3dd247ccc791780", "dim_h": null, "inst": " 37216 -75619080 464865119712 -2749454414283384 24030314100181942560 -191383188745885984500840 1918781328189011299017081440 -17585890849315381700538391366648 189589583226526216469072379366702336 -1886080110730882688589570690078662613720", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "(27648z-1)(4096z-1)(1+43008z)^2", "discr_factors": "209470159230861312, z-1/27648, z-1/4096, (1/43008+z)^2", "dm_basis": null, "q": "0 1 -11520 113529696 -1214705154048 13157995272423984 -148726278032418975744 1697462238453740960502272 -19896484803451373102238793728 234703506604410766518669936478872", "yuk": "1 37216 -604915424 12551358269440 -175965083119052000 3003789262522742857216 -41338768769098821898864640 658141995568830875562858971136 -9003976114849475606640739498775776 138210806172137611805953777109684272384", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/43008","im":"0","approx_re":"-2.32514880952e-05","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":"1/27648","im":"0","approx_re":"3.61689814815e-05","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/4096","im":"0","approx_re":"0.000244140625","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":["1/3","1/2","1/2","2/3"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -48-576*X-2880*X^2-4608*X^3+4608*X^4, 663552+5062656*X+12926976*X^2-3538944*X^3+7077888*X^4, 651165696+5775556608*X+18459131904*X^2+24461180928*X^3+8153726976*X^4, 260919263232*(3*X+1)*(2*X+1)^2*(3*X+2)]", "text": "Sporadic Operator.", "degz": 4, "h3": null, "sol": "1 48 -30960 -11961600 15342742800 7954873774848 -12530615872110336 -7309310076290027520 12708986986974242250000 7899153737186997034464000", "n_discr_factors": "2", "c3": null, "operator": "4 4 0 0 0 0 1 -48 -576 -2880 -4608 4608 663552 5062656 12926976 -3538944 7077888 651165696 5775556608 18459131904 24461180928 8153726976 521838526464 4435627474944 13828720951296 18786186952704 9393093476352", "new_number": "4.54", "id": 153, "operator_tex": "\\theta^4+2^{4} 3 x\\left(96\\theta^4-96\\theta^3-60\\theta^2-12\\theta-1\\right)+2^{13} 3 x^{2}\\left(288\\theta^4-144\\theta^3+526\\theta^2+206\\theta+27\\right)+2^{20} 3^{3} x^{3}\\left(288\\theta^4+864\\theta^3+652\\theta^2+204\\theta+23\\right)+2^{30} 3^{5} x^{4}(3\\theta+1)(2\\theta+1)^2(3\\theta+2)", "superseek": "1056 138459552", "discriminant": "4 1 4608 7077888 8153726976 9393093476352", "aesz": "265", "n_sing_complex": "1", "inst_int": "", "c2h": null, "hash": "fad89ac60b7ab4118edfed4cf6350d0c", "dim_h": null, "inst": " 1056 -360672 138459552 -50965971720 20236543243104 -13170624491809632 12113064315942213408 -9804996648203015791752 5994631594454921823729408 -2985511969943689684958167968", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "3", "laurent": null, "discriminant_tex": "(1769472z^2+1)(1+2304z)^2", "discr_factors": "9393093476352, (1/2304+z)^2, z^2+1/1769472", "dm_basis": null, "q": "0 1 -384 404832 -344262656 273686721072 -212302805336064 171402228919792128 -147807218604086919168 130795389166230698977944", "yuk": "1 1056 -2884320 3738408960 -3261825074400 2529567905389056 -2844854886495356928 4154781060368179200000 -5020158283883205910451424 4370086432357638013237147392", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/2304","im":"0","approx_re":"-0.000434027777778","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"-1/2304*3^(1/2)","approx_re":"0.0","approx_im":"-0.000752","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":"s_1","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"s_2","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"1/2304*3^(1/2)","approx_re":"0.0","approx_im":"0.000752","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/3","1/2","1/2","2/3"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -884736*X^4+221184*X^3+49152*X^2-61440*X-10608, 269072990208*X^4-24461180928*X^3+124004597760*X^2+15627976704*X-350355456, -32462531054272512*X^4-24346898290704384*X^3-20063647665487872*X^2-5748573207527424*X-632272604626944, 37396835774521933824*(3*X+1)*(2*X+1)^2*(3*X+2)]", "text": "Sporadic Operator.", "degz": 4, "h3": null, "sol": "1 10608 477012240 30101658720000 2213759644568010000 177668697182907783460608 15088164580638663840569827584 1333046580962138038084343998279680 121271152939302640973806084533106122000 11283491291004292519857771628719454324320000", "n_discr_factors": "2", "c3": null, "operator": "4 4 0 0 0 0 1 -10608 -61440 49152 221184 -884736 -350355456 15627976704 124004597760 -24461180928 269072990208 -632272604626944 -5748573207527424 -20063647665487872 -24346898290704384 -32462531054272512 74793671549043867648 635746208166872875008 1982032296049662492672 2692572175765579235328 1346286087882789617664", "new_number": "4.55", "id": 154, "operator_tex": "\\theta^4-2^{4} 3 x\\left(18432\\theta^4-4608\\theta^3-1024\\theta^2+1280\\theta+221\\right)+2^{17} 3^{4} x^{2}\\left(25344\\theta^4-2304\\theta^3+11680\\theta^2+1472\\theta-33\\right)-2^{28} 3^{8} x^{3}\\left(18432\\theta^4+13824\\theta^3+11392\\theta^2+3264\\theta+359\\right)+2^{46} 3^{12} x^{4}(3\\theta+1)(2\\theta+1)^2(3\\theta+2)", "superseek": "-188832 -101990911789344", "discriminant": "4 1 -884736 269072990208 -32462531054272512 1346286087882789617664", "aesz": "276", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "797e27181bf0a060708a3d221ec79699", "dim_h": null, "inst": " -188832 -3134817768 -101990911789344 -4414817659429205136 -223930278487379610386400 -12564756782029250056315926984 -756084427757279862134160044718240 -47893479034932888828760434508479466128 -3155272971995361246683107063324659407162112 -214420998567951184530459743151255837994639150200", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "(331776z-1)^2(110592z-1)^2", "discr_factors": "1346286087882789617664, (z-1/110592)^2, (z-1/331776)^2", "dm_basis": null, "q": "0 1 -19008 -23078304 -2109955663872 -58663430042147280 -1165406273347008669696 46373781500553478336676352 9887126966617517473134145830912 1091619463009810876015404632360942232", "yuk": "1 -188832 -25078730976 -2753754618501120 -282548330228547859680 -27991284810922451298488832 -2713987464918320765943937271808 -259336958720746992712016895338545152 -24521461265885639080607890798570034517216 -2300193996584618348831985049166430462439680768", "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":"1/331776","im":"0","approx_re":"3.01408179012e-06","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/110592","im":"0","approx_re":"9.04224537037e-06","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":["1/3","1/2","1/2","2/3"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -208-2368*X-11584*X^2-18432*X^3+9216*X^4, -4194304*X^4-130023424*X^3+21757952*X^2+7471104*X+786432, -5033164800-38654705664*X-111937585152*X^2-154618822656*X^3-167503724544*X^4, -9895604649984*(2*X+1)^4]", "text": "Sporadic Operator. There is a second MUM-point hiding at\ninfinity, corresponding to Operator 4.33, reducible to 3.35.", "degz": 4, "h3": "4", "sol": "1 208 254736 490988800 1163138813200 3099609712459008 8912821490498306304 27028629149428355125248 85250093313365034252541200 277129736008042959585497324800", "n_discr_factors": "3", "c3": "136", "operator": "4 4 0 0 0 0 1 -208 -2368 -11584 -18432 9216 786432 7471104 21757952 -130023424 -4194304 -5033164800 -38654705664 -111937585152 -154618822656 -167503724544 -9895604649984 -79164837199872 -237494511599616 -316659348799488 -158329674399744", "new_number": "4.56", "id": 155, "operator_tex": "\\theta^4+2^{4} x\\left(576\\theta^4-1152\\theta^3-724\\theta^2-148\\theta-13\\right)-2^{17} x^{2}\\left(32\\theta^4+992\\theta^3-166\\theta^2-57\\theta-6\\right)-2^{26} 3 x^{3}\\left(832\\theta^4+768\\theta^3+556\\theta^2+192\\theta+25\\right)-2^{40} 3^{2} x^{4}\\left((2\\theta+1)^4\\right)", "superseek": "4192 2124587232", "discriminant": "4 1 9216 -4194304 -167503724544 -158329674399744", "aesz": "277", "n_sing_complex": "0", "inst_int": "", "c2h": "16", "hash": "9d905a8d31566f4976cbeb2d3bf0624c", "dim_h": "2", "inst": " 4192 -1708008 2124587232 -2777042329304 4857272052090400 -8662038695645169608 17457595917396214851936 -35803804676519586643377240 78149966571561860853262927104 -173301643054058182072314357680760", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "-(1024z+1)(4096z-1)(1+6144z)^2", "discr_factors": "-158329674399744, z+1/1024, z-1/4096, (1/6144+z)^2", "dm_basis": null, "q": "0 1 -1536 2019168 -3416864768 6362636991024 -13293690316296192 28972568094420308480 -66676440369195119542272 157105050052992014772439704", "yuk": "1 4192 -13659872 57363859456 -177730722735328 607159006511304192 -1871000358202006439936 5987955399666901694218240 -18331547994378206092131882208 56971325630668596562086037718272", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/1024","im":"0","approx_re":"-0.0009765625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/6144","im":"0","approx_re":"-0.000162760416667","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":"1/4096","im":"0","approx_re":"0.000244140625","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","1/2","1/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -72-600*X-1923*X^2-2646*X^3-837*X^4, 143856+905904*X+1781190*X^2+831060*X^3-34992*X^4, 7243344+72275976*X+242652024*X^2+306110016*X^3+71567388*X^4, 229582512*(3*X+1)*(2*X+1)^2*(3*X+2)]", "text": "Sporadic Operator.", "degz": 4, "h3": null, "sol": "1 72 18360 6552000 2767980600 1299283457472 656117126368704 349624543068852480 194103929303224083000 111279944461816742040000", "n_discr_factors": "3", "c3": null, "operator": "4 4 0 0 0 0 1 -72 -600 -1923 -2646 -837 143856 905904 1781190 831060 -34992 7243344 72275976 242652024 306110016 71567388 459165024 3902902704 12167873136 16529940864 8264970432", "new_number": "4.57", "id": 156, "operator_tex": "\\theta^4-3 x\\left(279\\theta^4+882\\theta^3+641\\theta^2+200\\theta+24\\right)-2 3^{5} x^{2}\\left(72\\theta^4-1710\\theta^3-3665\\theta^2-1864\\theta-296\\right)+2^{2} 3^{9} x^{3}\\left(909\\theta^4+3888\\theta^3+3082\\theta^2+918\\theta+92\\right)+2^{4} 3^{15} x^{4}(3\\theta+1)(2\\theta+1)^2(3\\theta+2)", "superseek": "243 513936", "discriminant": "4 1 -837 -34992 71567388 8264970432", "aesz": "278", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "b30f6ac0da69cf91ab39089e6bf1ac8c", "dim_h": null, "inst": " 243 -3402 513936 2470824 6888345300 521184197574 177276531680712 27272307827975184 7090947333466041546 1462038119518392451530", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "(729z-1)(432z-1)(1+162z)^2", "discr_factors": "8264970432, (1/162+z)^2, z-1/729, z-1/432", "dm_basis": null, "q": "0 1 -312 72504 -15282248 2942883132 -551629499184 98423117795516 -17576968135443600 2995643349545507766", "yuk": "1 243 -26973 13876515 158105763 861043162743 112575800525283 60805850366484459 13963421608081399971 5169300606096758163549", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/162","im":"0","approx_re":"-0.00617283950617","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":"1/729","im":"0","approx_re":"0.00137174211248","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/432","im":"0","approx_re":"0.00231481481481","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":["1/3","1/2","1/2","2/3"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[25*X^4, -26960*X^4-15040*X^3-10420*X^2-2900*X-300, 7382016*X^4-2322432*X^3-9465984*X^2-4847040*X-758160, -134369280*X^4+2418647040*X^3+1941636096*X^2+604661760*X+67184640, -6530347008*(2*X+1)^4]", "text": "Sporadic Operator. There is a second MUM-point hiding at infinity,corresponding to the Operator AESZ 283/4.59", "degz": 4, "h3": null, "sol": "1 12 3564 1081200 418200300 179605378512 83081624727024 40457677635131328 20469840205440869100 10666939181821718624400", "n_discr_factors": "2", "c3": null, "operator": "4 4 0 0 0 0 25 -300 -2900 -10420 -15040 -26960 -758160 -4847040 -9465984 -2322432 7382016 67184640 604661760 1941636096 2418647040 -134369280 -6530347008 -52242776064 -156728328192 -208971104256 -104485552128", "new_number": "4.58", "id": 157, "operator_tex": "5^{2} \\theta^4-2^{2} 5 x\\left(1348\\theta^4+752\\theta^3+521\\theta^2+145\\theta+15\\right)+2^{4} 3^{4} x^{2}\\left(5696\\theta^4-1792\\theta^3-7304\\theta^2-3740\\theta-585\\right)-2^{10} 3^{8} x^{3}\\left(20\\theta^4-360\\theta^3-289\\theta^2-90\\theta-10\\right)-2^{12} 3^{13} x^{4}\\left((2\\theta+1)^4\\right)", "superseek": "364/5 1264916", "discriminant": "4 25 -26960 7382016 -134369280 -104485552128", "aesz": "282", "n_sing_complex": "1", "inst_int": "", "c2h": null, "hash": "582c9abe0a0b8176a2a06ec6c223bef4", "dim_h": null, "inst": " 364/5 43384/5 1264916 1297643028/5 323354425968/5 18440179245448 28857052915378692/5 9671474245508827972/5 3415046183767896342328/5 1256493105328411899065696/5", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "3", "laurent": null, "discriminant_tex": "-(62208z^2+560z-1)(-5+1296z)^2", "discr_factors": "-104485552128, z^2+35/3888*z-1/62208, (-5/1296+z)^2", "dm_basis": null, "q": "0 1 -68 -11994 -1583120 -386690559 -120243104472 -41467710508110 -15241609913408064 -5869609473593985516", "yuk": "1 364/5 347436/5 170764024/5 83049501228/5 40419303246364/5 19915393756194936/5 1979593829994978344 4951794813783569422892/5 2489568667966796604321136/5", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-35/7776-13/7776*13^(1/2)","im":"0","approx_re":"-0.010529","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":"s_1","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"s_2","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-35/7776+13/7776*13^(1/2)","im":"0","approx_re":"0.001527","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"5/1296","im":"0","approx_re":"0.00385802469136","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":["1/2","1/2","1/2","1/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, 80*X^4+1600*X^3+1124*X^2+324*X+36, -273408*X^4-632832*X^3-188544*X^2-30144*X-1872, 62115840*X^4+89579520*X^3+65203200*X^2+22394880*X+2903040, -223948800*(2*X+1)^4]", "text": "Sporadic Operator. There is a second MUM-point hiding at\ninfinity, corresponding to AESZ 282/4.58", "degz": 4, "h3": null, "sol": "1 -36 7236 -2257200 860876100 -368431728336 169912498328496 -82574431174737216 41716012918529535300 -21713202716348915600400", "n_discr_factors": "2", "c3": null, "operator": "4 4 0 0 0 0 1 36 324 1124 1600 80 -1872 -30144 -188544 -632832 -273408 2903040 22394880 65203200 89579520 62115840 -223948800 -1791590400 -5374771200 -7166361600 -3583180800", "new_number": "4.59", "id": 158, "operator_tex": "\\theta^4+2^{2} x\\left(20\\theta^4+400\\theta^3+281\\theta^2+81\\theta+9\\right)-2^{4} 3 x^{2}\\left(5696\\theta^4+13184\\theta^3+3928\\theta^2+628\\theta+39\\right)+2^{10} 3^{2} 5 x^{3}\\left(1348\\theta^4+1944\\theta^3+1415\\theta^2+486\\theta+63\\right)-2^{12} 3^{7} 5^{2} x^{4}\\left((2\\theta+1)^4\\right)", "superseek": "-188 -807540", "discriminant": "4 1 80 -273408 62115840 -3583180800", "aesz": "283", "n_sing_complex": "1", "inst_int": "", "c2h": null, "hash": "987222cb05e8a3d02c76c47abefbb9f4", "dim_h": null, "inst": " -188 831 -807540 39235244 -18812436256 7173900127847/3 -834950967787188 168214381357365724 -52798584988609383360 13387294633108573801288", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "3", "laurent": null, "discriminant_tex": "-(62208z^2-560z-1)(-1+240z)^2", "discr_factors": "-3583180800, (-1/240+z)^2, z^2-35/3888*z-1/62208", "dm_basis": null, "q": "0 1 180 14766 1912976 138964725 44605408536 447565207954 2001210504259392 -211324510074233214", "yuk": "1 -188 6460 -21803768 2511062076 -2351554532188 516520787407864 -286388181951005672 86125763257482312764 -38490168456696262273208", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"35/7776-13/7776*13^(1/2)","im":"0","approx_re":"-0.001527","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":"s_1","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"s_2","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/240","im":"0","approx_re":"0.00416666666667","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"35/7776+13/7776*13^(1/2)","im":"0","approx_re":"0.010529","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","1/2","1/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -576*(X+1/2)^4-516*(X+1/2)^2-15, 69120*(X+1)^4-43200*(X+1)^2-4176, 82944*(X+3/2)^2*(48*(X+3/2)^2+37), 11943936*(X+2)^2*(2*X+3)*(2*X+5)]", "text": "YY-Operator equivalent to $d \\ast e \\tilde A\\st \\epsilon$", "degz": 4, "h3": null, "sol": "1 180 44676 11798640 3241596996 911927850768 260684645619888 75383026726593600 21988913736501928260 6457716149904879040080", "n_discr_factors": "1", "c3": null, "operator": "4 4 0 0 0 0 1 -180 -804 -1380 -1152 -576 21744 190080 371520 276480 69120 27060480 62954496 56816640 23887872 3981312 716636160 1481048064 1134673920 382205952 47775744", "new_number": "4.5", "id": 159, "operator_tex": "\\theta^4-2^{2} 3 x\\left(48\\theta^4+96\\theta^3+115\\theta^2+67\\theta+15\\right)+2^{4} 3^{2} x^{2}\\left(480\\theta^4+1920\\theta^3+2580\\theta^2+1320\\theta+151\\right)+2^{8} 3^{4} x^{3}(48\\theta^2+144\\theta+145)(2\\theta+3)^2+2^{14} 3^{6} x^{4}(\\theta+2)^2(2\\theta+3)(2\\theta+5)", "superseek": "-36 -62596/3", "discriminant": "4 1 -576 69120 3981312 47775744", "aesz": null, "n_sing_complex": "1", "inst_int": "", "c2h": null, "hash": "f5b4785eb6dd46eea771050179115d33", "dim_h": null, "inst": " -36 -756 -62596/3 -839088 -37432800 -5568714004/3 -97940149740 -5432676734880 -312731103096896 -18548876430404064", "cleanlist": "True", "n_sing_real": "1", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "2", "laurent": null, "discriminant_tex": "(-1+288z+6912z^2)^2", "discr_factors": "47775744, (-1/6912+1/24*z+z^2)^2", "dm_basis": null, "q": "0 1 -84 558 79088 -2506251 -15199704 1128529682 -69405940032 -2821201832574", "yuk": "1 -36 -6084 -563400 -53707716 -4679100036 -400947977736 -33593471360856 -2781530541966276 -227980974158200584", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/48-1/72*3^(1/2)","im":"0","approx_re":"-0.04489","approx_im":"0.0","exponents":["0","-1/2","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"s_1","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["-1/2","0","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"s_2","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["-1/2","0","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/48+1/72*3^(1/2)","im":"0","approx_re":"0.003223","approx_im":"0.0","exponents":["0","-1/2","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["3/2","2","2","5/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -432-4416*X-16960*X^2-25088*X^3-7936*X^4, 7962624+63995904*X+154337280*X^2+74711040*X^3-3145728*X^4, 5096079360+53452210176*X+192216563712*X^2+260919263232*X^3+61001957376*X^4, 463856467968*(4*X+1)*(3*X+1)*(3*X+2)*(4*X+3)]", "text": "Sporadic Operator.", "degz": 4, "h3": "4", "sol": "1 432 982800 3259872000 12958462717200 57507674287295232 275104725474922447104 1389843863969427389952000 7317666838199613923550666000 39788554502561698105541549280000", "n_discr_factors": "3", "c3": "24", "operator": "4 4 0 0 0 0 1 -432 -4416 -16960 -25088 -7936 7962624 63995904 154337280 74711040 -3145728 5096079360 53452210176 192216563712 260919263232 61001957376 2783138807808 27367531610112 94162862997504 133590662774784 66795331387392", "new_number": "4.60", "id": 160, "operator_tex": "\\theta^4-2^{4} x\\left(496\\theta^4+1568\\theta^3+1060\\theta^2+276\\theta+27\\right)-2^{15} 3 x^{2}\\left(32\\theta^4-760\\theta^3-1570\\theta^2-651\\theta-81\\right)+2^{22} 3^{2} x^{3}\\left(1616\\theta^4+6912\\theta^3+5092\\theta^2+1416\\theta+135\\right)+2^{34} 3^{3} x^{4}(4\\theta+1)(3\\theta+1)(3\\theta+2)(4\\theta+3)", "superseek": "3616 264403872", "discriminant": "4 1 -7936 -3145728 61001957376 66795331387392", "aesz": "288", "n_sing_complex": "0", "inst_int": "", "c2h": "28", "hash": "3373ebdbe30d220b5562cfd77d4e8f96", "dim_h": "3", "inst": " 3616 114144 264403872 424149521656 710239010095456 1276165652786715744 2488282041160304300320 5231049591044378569431928 11643937059631017192549541632 27039505146615533040287139508896", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "(6912z-1)(4096z-1)(1+1536z)^2", "discr_factors": "66795331387392, (1/1536+z)^2, z-1/6912, z-1/4096", "dm_basis": null, "q": "0 1 -2688 4828512 -7377668096 9370263876144 -11657738493517824 11810397522454737408 -14798269700120886116352 8694811319106031657675416", "yuk": "1 3616 916768 7138908160 27145570302752 88779876261935616 275651781009070422016 853480740117984375013376 2678297390614748973119449888 8488430116471011533375754757888", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/1536","im":"0","approx_re":"-0.000651041666667","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":"1/6912","im":"0","approx_re":"0.000144675925926","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/4096","im":"0","approx_re":"0.000244140625","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":["1/4","1/3","2/3","3/4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -528-6272*X-28032*X^2-43520*X^3-6400*X^4, 5799936+48627712*X+104333312*X^2-206045184*X^3-139984896*X^4, 2264924160+28185722880*X+116098334720*X^2+128849018880*X^3-393257943040*X^4, 1717986918400*(4*X+1)*(2*X+1)^2*(4*X+3)]", "text": "Sporadic Operator.", "degz": 4, "h3": "2", "sol": "1 528 2434320 18496262400 174225386134800 1851234419251945728 21250689818684006064384 257431429480165678405324800 3244695401066105343290660298000 42160560700757556279415471133856000", "n_discr_factors": "3", "c3": "-16", "operator": "4 4 0 0 0 0 1 -528 -6272 -28032 -43520 -6400 5799936 48627712 104333312 -206045184 -139984896 2264924160 28185722880 116098334720 128849018880 -393257943040 5153960755200 48103633715200 158054796492800 219902325555200 109951162777600", "new_number": "4.61", "id": 161, "operator_tex": "\\theta^4-2^{4} x\\left(400\\theta^4+2720\\theta^3+1752\\theta^2+392\\theta+33\\right)-2^{15} x^{2}\\left(4272\\theta^4+6288\\theta^3-3184\\theta^2-1484\\theta-177\\right)-2^{24} 5 x^{3}\\left(4688\\theta^4-1536\\theta^3-1384\\theta^2-336\\theta-27\\right)+2^{36} 5^{2} x^{4}(4\\theta+1)(2\\theta+1)^2(4\\theta+3)", "superseek": "8224 15542388128", "discriminant": "4 1 -6400 -139984896 -393257943040 109951162777600", "aesz": "289", "n_sing_complex": "0", "inst_int": "", "c2h": "20", "hash": "673413653f5554d4f0cc1a8af33e8bbe", "dim_h": "2", "inst": " 8224 3407456 15542388128 54609260446560 282477571639256928 1593403948509786474208 9996790950092404250694432 66959132321618107208146692960 472988575734717866146656912684800 3481362951036082771628823802703192096", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "(16384z-1)(256z-1)(1+5120z)^2", "discr_factors": "109951162777600, z-1/256, (1/5120+z)^2, z-1/16384", "dm_basis": null, "q": "0 1 -4160 6816864 -20920440832 -2801293291984 -274110763911579648 -1409140353520807566848 -11677853297001700102111232 -88913392568086581572177028456", "yuk": "1 8224 27267872 419644487680 3494992695847712 35309696454907124224 344175252878533550176256 3428899295881694657988198400 34283075748668474385563802643232 344808671710609324420913308991706880", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/5120","im":"0","approx_re":"-0.0001953125","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":"1/16384","im":"0","approx_re":"6.103515625e-05","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/256","im":"0","approx_re":"0.00390625","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":["1/4","1/2","1/2","3/4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[9*X^4, -55632*X^4-95136*X^3-64164*X^2-16596*X-1512, 30232576*X^4+26054656*X^3-13438976*X^2-8615424*X-1128960, -4130603008*X^4+1056964608*X^3+1151926272*X^2+231211008*X+12386304, -822083584*(4*X+1)*(2*X+1)^2*(4*X+3)]", "text": "Sporadic Operator.", "degz": 4, "h3": null, "sol": "1 168 279720 737721600 2391487698600 8717511682047168 34277910683556443904 142115219255002478284800 612718123704257507465529000 2722381600280229607324028424000", "n_discr_factors": "2", "c3": null, "operator": "4 4 0 0 0 0 9 -1512 -16596 -64164 -95136 -55632 -1128960 -8615424 -13438976 26054656 30232576 12386304 231211008 1151926272 1056964608 -4130603008 -2466250752 -23018340352 -75631689728 -105226698752 -52613349376", "new_number": "4.62", "id": 162, "operator_tex": "3^{2} \\theta^4-2^{2} 3 x\\left(4636\\theta^4+7928\\theta^3+5347\\theta^2+1383\\theta+126\\right)+2^{9} x^{2}\\left(59048\\theta^4+50888\\theta^3-26248\\theta^2-16827\\theta-2205\\right)-2^{16} 7 x^{3}\\left(9004\\theta^4-2304\\theta^3-2511\\theta^2-504\\theta-27\\right)-2^{24} 7^{2} x^{4}(4\\theta+1)(2\\theta+1)^2(4\\theta+3)", "superseek": "4300/3 1701817028/3", "discriminant": "4 9 -55632 30232576 -4130603008 -52613349376", "aesz": "292", "n_sing_complex": "1", "inst_int": "", "c2h": null, "hash": "bce26f214ee56f65c7a275cd8fdcc0c7", "dim_h": null, "inst": " 4300/3 1768292/3 1701817028/3 2484553593752/3 1500880129466144 9350482662153015820/3 7110166243548551297772 52120041107300527753842568/3 134207871085060188820318570256/3 360162480402539472681189005683360/3", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "3", "laurent": null, "discriminant_tex": "-(65536z^2+5584z-1)(-3+896z)^2", "discr_factors": "-52613349376, z^2+349/4096*z-1/65536, (-3/896+z)^2", "dm_basis": null, "q": "0 1 -1172 98526 -341830288 -694093661395 -1640092990169880 -4223070324113649134 -11497369531205203223360 -32654543280727574249164026", "yuk": "1 4300/3 14150636/3 45949064056/3 159011444150764/3 562830048549808300/3 2019704255071014627512/3 7316361064611459285411688/3 8895153682312676407137181860 97837538021008877650058186780680/3", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-349/8192-85/8192*17^(1/2)","im":"0","approx_re":"-0.085384","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":"s_1","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"s_2","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-349/8192+85/8192*17^(1/2)","im":"0","approx_re":"0.000179","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"3/896","im":"0","approx_re":"0.00334821428571","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":["1/4","1/2","1/2","3/4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -300800*X^4+233984*X^3+130944*X^2+13952*X+528, 26671579136*X^4-28290580480*X^3+19652411392*X^2+3958374400*X+312213504, -731020613648384*X^4-897201488265216*X^3-654355447414784*X^2-196262825558016*X-20863877382144, 325385073077518336*(4*X+1)*(2*X+1)^2*(4*X+3)]", "text": "Sporadic Operator.", "degz": 4, "h3": null, "sol": "1 -528 -16919280 -95988076800 3707387171888400 92316039956860591872 -376022945639941423439616 -57681657382036442491508428800 -758273177515629707148382382646000 24441589252062441804429772019780448000", "n_discr_factors": "2", "c3": null, "operator": "4 4 0 0 0 0 1 528 13952 130944 233984 -300800 312213504 3958374400 19652411392 -28290580480 26671579136 -20863877382144 -196262825558016 -654355447414784 -897201488265216 -731020613648384 976155219232555008 9110782046170513408 29935426723131686912 41649289353922347008 20824644676961173504", "new_number": "4.63", "id": 163, "operator_tex": "\\theta^4-2^{4} x\\left(18800\\theta^4-14624\\theta^3-8184\\theta^2-872\\theta-33\\right)+2^{18} x^{2}\\left(101744\\theta^4-107920\\theta^3+74968\\theta^2+15100\\theta+1191\\right)-2^{30} 17 x^{3}\\left(40048\\theta^4+49152\\theta^3+35848\\theta^2+10752\\theta+1143\\right)+2^{50} 17^{2} x^{4}(4\\theta+1)(2\\theta+1)^2(4\\theta+3)", "superseek": "-80416 -15561562691488", "discriminant": "4 1 -300800 26671579136 -731020613648384 20824644676961173504", "aesz": "294", "n_sing_complex": "1", "inst_int": "", "c2h": null, "hash": "f6b5a258285779facb6702e1a2a891bb", "dim_h": null, "inst": " -80416 -872844376 -15561562691488 -341695175348542432 -8482586861983707669856 -229990965583686463160181624 -6684153834033483822411985673504 -205357401406348084399132422536082400 -6590661926453126413976895123706345809664 -218749445548560046467613128308268224607619144", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "3", "laurent": null, "discriminant_tex": "(1073741824z^2-22272z+1)(-1+139264z)^2", "discr_factors": "20824644676961173504, (-1/139264+z)^2, z^2-87/4194304*z+1/1073741824", "dm_basis": null, "q": "0 1 11840 379358304 12601567188992 433089953113026096 15214560424671659280384 544494807023048742027960832 19826879547002446065059280584704 733701731317333290029840263361436312", "yuk": "1 -80416 -6982835424 -420162192750592 -21868491229289551072 -1060323357747963458812416 -49678048566076696211774736384 -2292664765073484951087311086092288 -105142989520050219234224291567763739872 -4804592544384329155789156545602088287995648", "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":"s_1","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"s_2","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/139264","im":"0","approx_re":"7.18060661765e-06","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"87/8388608","im":"-91/8388608*7^(1/2)","approx_re":"1.03712081909e-05","approx_im":"-2.9e-05","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"87/8388608","im":"91/8388608*7^(1/2)","approx_re":"1.03712081909e-05","approx_im":"2.9e-05","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/4","1/2","1/2","3/4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -13056*X^4+23040*X^3+14464*X^2+2944*X+272, 6029312+42991616*X+113246208*X^2-155189248*X^3+20971520*X^4, -11811160064-103079215104*X-317827579904*X^2-412316860416*X^3+85899345920*X^4, 35184372088832*(2*X+1)^4]", "text": "Sporadic Operator. There is a second MUM-point hiding at\ninfinity, corresponding to Operator AESZ 296/4.65", "degz": 4, "h3": "4", "sol": "1 -272 93456 194502400 -587215823600 640732932419328 776446344050598144 -4713772249712944484352 8322330312713357740285200 2292816132708062002706579200", "n_discr_factors": "2", "c3": "192", "operator": "4 4 0 0 0 0 1 272 2944 14464 23040 -13056 6029312 42991616 113246208 -155189248 20971520 -11811160064 -103079215104 -317827579904 -412316860416 85899345920 35184372088832 281474976710656 844424930131968 1125899906842624 562949953421312", "new_number": "4.64", "id": 164, "operator_tex": "\\theta^4-2^{4} x\\left(816\\theta^4-1440\\theta^3-904\\theta^2-184\\theta-17\\right)+2^{18} x^{2}\\left(80\\theta^4-592\\theta^3+432\\theta^2+164\\theta+23\\right)+2^{30} x^{3}\\left(80\\theta^4-384\\theta^3-296\\theta^2-96\\theta-11\\right)+2^{45} x^{4}\\left((2\\theta+1)^4\\right)", "superseek": "-5408 -4296119968", "discriminant": "4 1 -13056 20971520 85899345920 562949953421312", "aesz": "295", "n_sing_complex": "1", "inst_int": "", "c2h": "4", "hash": "e40629f953a095a2a764c68394321139", "dim_h": "1", "inst": " -5408 -3839480 -4296119968 -6482749129792 -11816577914904160 -23775821454252033176 -50868108154251421892640 -114383780266640218792887360 -267794278217800769868007067392 -646609344110586651247479818403880", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "3", "laurent": null, "discriminant_tex": "(8388608z^2+3328z+1)(-1+8192z)^2", "discr_factors": "562949953421312, z^2+13/32768*z+1/8388608, (-1/8192+z)^2", "dm_basis": null, "q": "0 1 1856 4507744 10996029440 27530323566128 70984202464897024 187308349528583004672 502803073483807579570176 1368671554155217410108316312", "yuk": "1 -5408 -30721248 -115995244544 -414895975027936 -1477072239363025408 -5135577434234465126400 -17447761096908237709180928 -58564495496520206917933356256 -195222028820776761233893147373312", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-13/65536","im":"-7/65536*7^(1/2)","approx_re":"-0.000198364257812","approx_im":"-0.000283","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-13/65536","im":"7/65536*7^(1/2)","approx_re":"-0.000198364257812","approx_im":"0.000283","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":"s_1","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"s_2","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/8192","im":"0","approx_re":"0.0001220703125","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":["1/2","1/2","1/2","1/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -16-128*X-400*X^2-544*X^3-80*X^4, 16384+96256*X+184320*X^2+96256*X^3+10240*X^4, 327680+3145728*X+10158080*X^2+12582912*X^3+3342336*X^4, 8388608*(2*X+1)^4]", "text": "Sporadic Operator. There is a second MUM-point hiding at infinity,\ncorresponding to Operator AESZ 295/4.64", "degz": 4, "h3": null, "sol": "1 16 144 -70400 -9858800 -437923584 86893906176 20978388946944 1721357631536400 -139493166549651200", "n_discr_factors": "2", "c3": null, "operator": "4 4 0 0 0 0 1 -16 -128 -400 -544 -80 16384 96256 184320 96256 10240 327680 3145728 10158080 12582912 3342336 8388608 67108864 201326592 268435456 134217728", "new_number": "4.65", "id": 165, "operator_tex": "\\theta^4-2^{4} x\\left(5\\theta^4+34\\theta^3+25\\theta^2+8\\theta+1\\right)+2^{11} x^{2}\\left(5\\theta^4+47\\theta^3+90\\theta^2+47\\theta+8\\right)+2^{16} x^{3}\\left(51\\theta^4+192\\theta^3+155\\theta^2+48\\theta+5\\right)+2^{23} x^{4}\\left((2\\theta+1)^4\\right)", "superseek": "48 -9104", "discriminant": "4 1 -80 10240 3342336 134217728", "aesz": null, "n_sing_complex": "1", "inst_int": "", "c2h": null, "hash": "5ec2790b5eda514313634b7aeb0a295c", "dim_h": null, "inst": " 48 -1298 -9104 387230 102374160 -102845098 -458716656464 -25010987919066 2318527766431360 305371018298604250", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "3", "laurent": null, "discriminant_tex": "(32768z^2-208z+1)(1+64z)^2", "discr_factors": "134217728, (1/64+z)^2, z^2-13/2048*z+1/32768", "dm_basis": null, "q": "0 1 -64 5920 -343040 19349296 -1367195648 82913836544 -3043803922432 240495514046104", "yuk": "1 48 -10336 -245760 24772384 12796770048 -22214797312 -157339813167104 -12805625789789408 1690206741728215680", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/64","im":"0","approx_re":"-0.015625","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":"s_1","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"s_2","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"13/4096","im":"-7/4096*7^(1/2)","approx_re":"0.003173828125","approx_im":"-0.004522","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"13/4096","im":"7/4096*7^(1/2)","approx_re":"0.003173828125","approx_im":"0.004522","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","1/2","1/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, 240+2560*X+9456*X^2+13792*X^3+5936*X^4, 1628160+13957120*X+33556480*X^2+21186560*X^3+2293760*X^4, -3422617600*X^4-12288000000*X^3-9065267200*X^2-2457600000*X-221184000, 1048576000*(5*X+1)*(5*X+2)*(5*X+3)*(5*X+4)]", "text": "Sporadic Operator.", "degz": 4, "h3": "4", "sol": "1 -240 378000 -941740800 2908743037200 -10151874959466240 38309871295625529600 -152614322407866908160000 632640146605662882986442000 -2703686438960809804123990368000", "n_discr_factors": "2", "c3": "-130", "operator": "4 4 0 0 0 0 1 240 2560 9456 13792 5936 1628160 13957120 33556480 21186560 2293760 -221184000 -2457600000 -9065267200 -12288000000 -3422617600 25165824000 262144000000 917504000000 1310720000000 655360000000", "new_number": "4.66", "id": 166, "operator_tex": "\\theta^4+2^{4} x\\left(371\\theta^4+862\\theta^3+591\\theta^2+160\\theta+15\\right)+2^{11} 5 x^{2}\\left(224\\theta^4+2069\\theta^3+3277\\theta^2+1363\\theta+159\\right)-2^{16} 5^{2} x^{3}\\left(2089\\theta^4+7500\\theta^3+5533\\theta^2+1500\\theta+135\\right)+2^{23} 5^{3} x^{4}(5\\theta+1)(5\\theta+2)(5\\theta+3)(5\\theta+4)", "superseek": "-1616 -283183120", "discriminant": "4 1 5936 2293760 -3422617600 655360000000", "aesz": "300", "n_sing_complex": "1", "inst_int": "", "c2h": "28", "hash": "edc54887effd2ebcaa636dcc93baf0b7", "dim_h": "3", "inst": " -1616 265534 -283183120 351860487150 -525536710386800 905847882475840870 -1717463745183584163280 3484895489379071632856310 -7449697893532490934280447360 16596414766862442506943198303050", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "3", "laurent": null, "discriminant_tex": "(6400000z^2+6576z+1)(-1+320z)^2", "discr_factors": "655360000000, (-1/320+z)^2, z^2+411/400000*z+1/6400000", "dm_basis": null, "q": "0 1 1600 1355040 1290306560 604823942960 991922734264320 -645735308412019200 2416007564491479449600 -5155873649461458449879400", "yuk": "1 -1616 2122656 -7645945856 22519073300256 -65692088798351616 195663142607137806336 -589090064597969368006656 1784266490562107195095730976 -5430829764385185891098092071296", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-411/800000-41/800000*41^(1/2)","im":"0","approx_re":"-0.000842","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-411/800000+41/800000*41^(1/2)","im":"0","approx_re":"-0.000186","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":"s_2","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"s_1","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/320","im":"0","approx_re":"0.003125","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":["1/5","2/5","3/5","4/5"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, 3914496*X^4-4557312*X^3-2577024*X^2-298368*X-18192, 3434983981056*X^4-9176113741824*X^3+4366371127296*X^2+708682186752*X+61483253760, -673764507704623104*X^4+718183403077238784*X^3+511336816029204480*X^2+169571081282125824*X+19011157339668480, 6863918177676863471616*(3*X+1)*(2*X+1)^2*(3*X+2)]", "text": "Sporadic Operator.", "degz": 4, "h3": null, "sol": "1 18192 178183440 -132466290835200 -18938901463932265200 282304649798820482625792 544025342147050978269112721664 77358678591550894632666959343390720 -5270208916811993788352647120507759158000 -3635009303061777629147893706848630014470496000", "n_discr_factors": "2", "c3": null, "operator": "4 4 0 0 0 0 1 -18192 -298368 -2577024 -4557312 3914496 61483253760 708682186752 4366371127296 -9176113741824 3434983981056 19011157339668480 169571081282125824 511336816029204480 718183403077238784 -673764507704623104 13727836355353726943232 116686609020506679017472 363787663416873763995648 494202108792734169956352 247101054396367084978176", "new_number": "4.67", "id": 167, "operator_tex": "\\theta^4+2^{4} 3 x\\left(81552\\theta^4-94944\\theta^3-53688\\theta^2-6216\\theta-379\\right)+2^{20} 3 x^{2}\\left(1091952\\theta^4-2917008\\theta^3+1388032\\theta^2+225284\\theta+19545\\right)-2^{34} 3^{3} 7 x^{3}\\left(207504\\theta^4-221184\\theta^3-157480\\theta^2-52224\\theta-5855\\right)+2^{59} 3^{5} 7^{2} x^{4}(3\\theta+1)(2\\theta+1)^2(3\\theta+2)", "superseek": "1565472 28381748186959008", "discriminant": "4 1 3914496 3434983981056 -673764507704623104 247101054396367084978176", "aesz": "305", "n_sing_complex": "1", "inst_int": "", "c2h": null, "hash": "4ce63e568901a8cef3f9c2f60b6ce2d2", "dim_h": null, "inst": " 1565472 -155959736064 28381748186959008 -6798945051352302862848 1905341636283453444266170464 -590118540566665289038917553171200 195838862292900201138732110989989469728 -68365830048103279856913191359489981496173056 24808485062489308191032724928857595913888866950912 -9282274996751937341538274580909889850415716996031065344", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "3", "laurent": null, "discriminant_tex": "(57982058496z^2-214272z+1)(1+2064384z)^2", "discr_factors": "247101054396367084978176, z^2-31/8388608*z+1/57982058496, (1/2064384+z)^2", "dm_basis": null, "q": "0 1 -225600 71291658336 -24815856020559872 9170258377289976086064 -3534254432448465680615761920 1405086479689249444194265869640192 -572039330156820750689594699070142808064 237291944702520899095519161464882298725980824", "yuk": "1 1565472 -1247676323040 766307201049458688 -435132483287795059545312 238167704535431680533272873472 -127465604762399701666100238113409024 67172729766464768990585114069566389682176 -35003304984628879286739989108542158321100149984 18085385610554705671262856473137188187532185056673536", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/2064384","im":"0","approx_re":"-4.84406001984e-07","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":"s_1","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"s_2","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"31/16777216","im":"-145/150994944*15^(1/2)","approx_re":"1.84774398804e-06","approx_im":"-4e-06","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"31/16777216","im":"145/150994944*15^(1/2)","approx_re":"1.84774398804e-06","approx_im":"4e-06","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/3","1/2","1/2","2/3"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[25*X^4, -52245*X^4-91530*X^3-63615*X^2-17850*X-1800, 9051264*X^4+10240992*X^3+69984*X^2-1244160*X-213120, -458535168*X^4-302330880*X^3-186437376*X^2-67184640*X-8709120, 53747712*(3*X+1)^2*(3*X+2)^2]", "text": "Sporadic Operator.", "degz": 4, "h3": null, "sol": "1 72 41400 37396800 41397463800 51465849507072 68974101299847744 97431256231311974400 143088412046096191217400 216526904351285764733640000", "n_discr_factors": "2", "c3": null, "operator": "4 4 0 0 0 0 25 -1800 -17850 -63615 -91530 -52245 -213120 -1244160 69984 10240992 9051264 -8709120 -67184640 -186437376 -302330880 -458535168 214990848 1934917632 6288482304 8707129344 4353564672", "new_number": "4.68", "id": 168, "operator_tex": "5^{2} \\theta^4-3 5 x\\left(3483\\theta^4+6102\\theta^3+4241\\theta^2+1190\\theta+120\\right)+2^{5} 3^{2} x^{2}\\left(31428\\theta^4+35559\\theta^3+243\\theta^2-4320\\theta-740\\right)-2^{8} 3^{5} x^{3}\\left(7371\\theta^4+4860\\theta^3+2997\\theta^2+1080\\theta+140\\right)+2^{13} 3^{8} x^{4}(3\\theta+1)^2(3\\theta+2)^2", "superseek": "2043/5 88982631/5", "discriminant": "4 25 -52245 9051264 -458535168 4353564672", "aesz": "337", "n_sing_complex": "1", "inst_int": "", "c2h": null, "hash": "dc26e94a7c1daba6f627be36c42019b7", "dim_h": null, "inst": " 2043/5 279018/5 88982631/5 8604708876 25774859896713/5 17683308060957072/5 13325172014008420146/5 10754726369310113746644/5 1829462967322461406625346 8108517336265913904915653934/5", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "3", "laurent": null, "discriminant_tex": "(23328z^2-1917z+1)(-5+432z)^2", "discr_factors": "4353564672, (-5/432+z)^2, z^2-71/864*z+1/23328", "dm_basis": null, "q": "0 1 -426 27621 -13241608 -7686485202 -6081843427074 -5184549890041414 -4670074254201955296 -4386070348249547118789", "yuk": "1 2043/5 2234187/5 480506616 2753509074507/5 3221857487091168/5 3819594543571492776/5 4570534000804888112121/5 1101283980217906349471247 1333678503178074365910383850", "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":"s_1","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"s_2","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"71/1728-17/1728*17^(1/2)","im":"0","approx_re":"0.000525","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":"71/1728+17/1728*17^(1/2)","im":"0","approx_re":"0.081651","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":["1/3","1/3","2/3","2/3"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -24-184*X-545*X^2-722*X^3-289*X^4, 5136*X^4+65616*X^3+116664*X^2+63360*X+11232, 72576+746496*X+2449152*X^2+2985984*X^3+801216*X^4, 746496*(2*X+1)^4]", "text": "Sporadic Operator. There is a second MUM-point hiding at infinity, corresponding to Operator AESZ 351/4.70", "degz": 4, "h3": "18", "sol": "1 24 1944 232800 34133400 5649061824 1011627229536 191367704601216 37683808295304600 7651704687834292800", "n_discr_factors": "3", "c3": "-64", "operator": "4 4 0 0 0 0 1 -24 -184 -545 -722 -289 11232 63360 116664 65616 5136 72576 746496 2449152 2985984 801216 746496 5971968 17915904 23887872 11943936", "new_number": "4.69", "id": 169, "operator_tex": "\\theta^4-x\\left(24+184\\theta+545\\theta^2+722\\theta^3+289\\theta^4\\right)+2^{3} 3 x^{2}\\left(214\\theta^4+2734\\theta^3+4861\\theta^2+2640\\theta+468\\right)+2^{6} 3^{2} x^{3}\\left(1391\\theta^4+5184\\theta^3+4252\\theta^2+1296\\theta+126\\right)+2^{10} 3^{6} x^{4}\\left((2\\theta+1)^4\\right)", "superseek": "49 173876/9", "discriminant": "4 1 -289 5136 801216 11943936", "aesz": "350", "n_sing_complex": "0", "inst_int": "", "c2h": "60", "hash": "e6de16eb3758d2ed5687f4b2a2abf36b", "dim_h": "8", "inst": " 49 136 173876/9 781152 57087750 12201523592/3 338790123846 29537353606592 24592780153285625/9 262707875156521480", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "(256z-1)(81z-1)(1+24z)^2", "discr_factors": "11943936, z-1/256, (1/24+z)^2, z-1/81", "dm_basis": null, "q": "0 1 -88 4980 -282064 12865650 -690703872 23666776560 -1799987151264 3529620262935", "yuk": "1 49 1137 521677 49994865 7135968799 878510221389 116205012479227 15123125096569969 1992015192416657302", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/24","im":"0","approx_re":"-0.0416666666667","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":"1/256","im":"0","approx_re":"0.00390625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/81","im":"0","approx_re":"0.0123456790123","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","1/2","1/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -704*(X+1/2)^4-652*(X+1/2)^2-21, 187904*(X+1)^4+228672*(X+1)^2+19824, -128000*(X+3/2)^2*(176*(X+3/2)^2+141), 256000000*(X+2)^2*(2*X+3)*(2*X+5)]", "text": "YY-operator equivalent to AESZ 121 =$b \\ast e \\tilde A \\ast \\eta$", "degz": 4, "h3": null, "sol": "1 228 44716 8258768 1469227500 253733647728 42642370753264 6970600688094528 1105114457148006124 168933127196275073200", "n_discr_factors": "1", "c3": null, "operator": "4 4 0 0 0 0 1 -228 -1004 -1708 -1408 -704 436400 1208960 1356096 751616 187904 -154656000 -358272000 -322176000 -135168000 -22528000 15360000000 31744000000 24320000000 8192000000 1024000000", "new_number": "4.6", "id": 170, "operator_tex": "\\theta^4-2^{2} x\\left(176\\theta^4+352\\theta^3+427\\theta^2+251\\theta+57\\right)+2^{4} x^{2}\\left(11744\\theta^4+46976\\theta^3+84756\\theta^2+75560\\theta+27275\\right)-2^{8} 5^{3} x^{3}(176\\theta^2+528\\theta+537)(2\\theta+3)^2+2^{14} 5^{6} x^{4}(\\theta+2)^2(2\\theta+3)(2\\theta+5)", "superseek": "-28 1036", "discriminant": "4 1 -704 187904 -22528000 1024000000", "aesz": null, "n_sing_complex": "1", "inst_int": "", "c2h": null, "hash": "e42780ff25b428328423d5eea814a37a", "dim_h": null, "inst": " -28 -21 1036 53976 1260496 31899337 507180268 3964357416 -299161562136 -16443487872164", "cleanlist": "True", "n_sing_real": "1", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "2", "laurent": null, "discriminant_tex": "(1-352z+32000z^2)^2", "discr_factors": "1024000000, (1/32000-11/1000*z+z^2)^2", "dm_basis": null, "q": "0 1 -92 6310 -354928 18451201 -887962344 41276142642 -1847354908608 80878912980756", "yuk": "1 -28 -196 27944 3454268 157561972 6890284568 173962831896 2029754451260 -218088778769200", "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":"s_1","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["-1/2","0","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"s_2","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["-1/2","0","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"11/2000","im":"-1/1000","approx_re":"0.0055","approx_im":"-0.001","exponents":["0","-1/2","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"11/2000","im":"1/1000","approx_re":"0.0055","approx_im":"0.001","exponents":["0","-1/2","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["3/2","2","2","5/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -5136-60544*X-368000*X^2-614912*X^3+356096*X^4, 1974730752+15712911360*X+61209575424*X^2-130572877824*X^3+12117344256*X^4, 49313740750848+450868486864896*X+1308771024371712*X^2+1803473947459584*X^3-3619472019554304*X^4, 4155203974946881536*(2*X+1)^4]", "text": "Sporadic Operator. There is a second\nMUM-point hiding at infinity, corresponding to\nOperator AESZ 350/4.69", "degz": 4, "h3": null, "sol": "1 5136 98870544 2900370796800 105956691416931600 4412931536513801339136 200024695553870048140452096 9610127151374411353958342529024 481646920959477742785210040171568400 24925288199370479336346978920708674924800", "n_discr_factors": "3", "c3": null, "operator": "4 4 0 0 0 0 1 -5136 -60544 -368000 -614912 356096 1974730752 15712911360 61209575424 -130572877824 12117344256 49313740750848 450868486864896 1308771024371712 1803473947459584 -3619472019554304 4155203974946881536 33241631799575052288 99724895398725156864 132966527198300209152 66483263599150104576", "new_number": "4.70", "id": 171, "operator_tex": "\\theta^4+2^{4} x\\left(22256\\theta^4-38432\\theta^3-23000\\theta^2-3784\\theta-321\\right)+2^{18} 3^{3} x^{2}\\left(1712\\theta^4-18448\\theta^3+8648\\theta^2+2220\\theta+279\\right)-2^{30} 3^{6} x^{3}\\left(4624\\theta^4-2304\\theta^3-1672\\theta^2-576\\theta-63\\right)+2^{46} 3^{10} x^{4}\\left((2\\theta+1)^4\\right)", "superseek": "177184 45194569320864", "discriminant": "4 1 356096 12117344256 -3619472019554304 66483263599150104576", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "56776b8a011d3f76a664ac5c7f492c1a", "dim_h": null, "inst": " 177184 -1960034336 45194569320864 -1351787074724461344 47485667264376266736480 -1839007798945759694042445216 76327836914996076109358397605664 -3331558964842891392980226676888998688 151158280898727092917597478771287519172352 -7071069840039563002592832982104646794439280480", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "(65536z-1)(20736z-1)(1+221184z)^2", "discr_factors": "66483263599150104576, z-1/65536, z-1/20736, (1/221184+z)^2", "dm_basis": null, "q": "0 1 -40000 1663374432 -74681178560512 3519608472117628464 -172025274470483532318720 8639617070915457513339167232 -443247092807915286936511963594752 23130783780245130032578789032783780504", "yuk": "1 177184 -15680097504 1220253371840512 -86514372798045623520 5935708408047033342237184 -397225684572282873675476600832 26180448061843654105509930378919936 -1705758189999560393292390431365212951776 110194386775172050736928562025488854848485120", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/221184","im":"0","approx_re":"-4.52112268519e-06","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":"1/65536","im":"0","approx_re":"1.52587890625e-05","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/20736","im":"0","approx_re":"4.8225308642e-05","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","1/2","1/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -12-68*X-148*X^2-160*X^3-208*X^4, 1968+11008*X+24192*X^2+24576*X^3+15360*X^4, -152832-720896*X-1327104*X^2-1179648*X^3-458752*X^4, 16384*(4*X+5)^2*(4*X+3)^2]", "text": "Sporadic Operator, reducible to 3.33, so not a primary operator.", "degz": 4, "h3": null, "sol": "1 12 324 11856 504900 23475312 1155060144 59120134848 3115322063172 167873343726000", "n_discr_factors": "2", "c3": null, "operator": "4 4 0 0 0 0 1 -12 -68 -148 -160 -208 1968 11008 24192 24576 15360 -152832 -720896 -1327104 -1179648 -458752 3686400 15728640 24641536 16777216 4194304", "new_number": "4.71", "id": 172, "operator_tex": "\\theta^4-2^{2} x\\left(52\\theta^4+40\\theta^3+37\\theta^2+17\\theta+3\\right)+2^{4} x^{2}\\left(960\\theta^4+1536\\theta^3+1512\\theta^2+688\\theta+123\\right)-2^{8} x^{3}\\left(1792\\theta^4+4608\\theta^3+5184\\theta^2+2816\\theta+597\\right)+2^{14} x^{4}(4\\theta+5)^2(4\\theta+3)^2", "superseek": "-4 -1580/9", "discriminant": "4 1 -208 15360 -458752 4194304", "aesz": "353", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "33845d8200fe810109063e352fbfc8b1", "dim_h": null, "inst": " -4 -24 -1580/9 -1580 -17120 -621272/3 -2660236 -35601596 -493759552 -7061891648", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "(16z-1)(64z-1)^3", "discr_factors": "4194304, z-1/16, (z-1/64)^3", "dm_basis": null, "q": "0 1 -20 174 -1808 10485 -97368 267922 -6478144 -38096766", "yuk": "1 -4 -196 -4744 -101316 -2140004 -44736520 -912460952 -18228118468 -359950718152", "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":"1/64","im":"0","approx_re":"0.015625","approx_im":"0.0","exponents":["0","1/2","3/2","2"],"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":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["3/4","3/4","5/4","5/4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -12-92*X-268*X^2-352*X^3-320*X^4, 7344+46656*X+104448*X^2+99840*X^3+44544*X^4, -165888-1492992*X-4709376*X^2-5971968*X^3-2506752*X^4, 2985984*(2*X+1)^4]", "text": "Sporadic Operator. There is a second MUM-point hiding at infinity, corresponding to Operator AESZ 362/4.73", "degz": 4, "h3": null, "sol": "1 12 324 -6000 -2778300 -361782288 -30344052816 -1087320117312 175645509682500 45289843467726000", "n_discr_factors": "2", "c3": null, "operator": "4 4 0 0 0 0 1 -12 -92 -268 -352 -320 7344 46656 104448 99840 44544 -165888 -1492992 -4709376 -5971968 -2506752 2985984 23887872 71663616 95551488 47775744", "new_number": "4.72", "id": 173, "operator_tex": "\\theta^4-2^{2} x\\left(80\\theta^4+88\\theta^3+67\\theta^2+23\\theta+3\\right)+2^{4} 3 x^{2}\\left(928\\theta^4+2080\\theta^3+2176\\theta^2+972\\theta+153\\right)-2^{10} 3^{2} x^{3}\\left(272\\theta^4+648\\theta^3+511\\theta^2+162\\theta+18\\right)+2^{12} 3^{6} x^{4}\\left((2\\theta+1)^4\\right)", "superseek": "20 -119332/9", "discriminant": "4 1 -320 44544 -2506752 47775744", "aesz": "361", "n_sing_complex": "1", "inst_int": "", "c2h": null, "hash": "f55eaa640956f064f5230c04d8173d60", "dim_h": null, "inst": " 20 -139 -119332/9 -462222 -2113440 9744926503/9 86597298876 2523690015938 -1608859520322496/9 -27901291082883368", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "3", "laurent": null, "discriminant_tex": "(20736z^2-224z+1)(-1+48z)^2", "discr_factors": "47775744, z^2-7/648*z+1/20736, (-1/48+z)^2", "dm_basis": null, "q": "0 1 -44 1902 -14192 942453 -28814376 -3593659182 -207641592000 1037108780802", "yuk": "1 20 -1092 -357976 -29583300 -264179980 233877876984 29702873514488 1292129258576956 -130317621146480152", "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":"s_1","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"s_2","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"7/1296","im":"-1/324*2^(1/2)","approx_re":"0.0054012345679","approx_im":"-0.004365","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"7/1296","im":"1/324*2^(1/2)","approx_re":"0.0054012345679","approx_im":"0.004365","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/48","im":"0","approx_re":"0.0208333333333","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":["1/2","1/2","1/2","1/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -48+64*X+3392*X^2+6656*X^3-17408*X^4, 995328+11943936*X+49545216*X^2-24772608*X^3+102629376*X^4, -6879707136-55037657088*X-168170618880*X^2-220150628352*X^3-244611809280*X^4, 15850845241344*(2*X+1)^4]", "text": "Sporadic Operator. There is a second MUM-point corresponding to Operator AESZ 361/4.72", "degz": 4, "h3": null, "sol": "1 48 -40176 -103200000 -153639990000 -149648032541952 -2121925296750336 407721053691675389952 1129764626181960087805200 1886020876540975307019744000", "n_discr_factors": "2", "c3": null, "operator": "4 4 0 0 0 0 1 -48 64 3392 6656 -17408 995328 11943936 49545216 -24772608 102629376 -6879707136 -55037657088 -168170618880 -220150628352 -244611809280 15850845241344 126806761930752 380420285792256 507227047723008 253613523861504", "new_number": "4.73", "id": 174, "operator_tex": "\\theta^4-2^{4} x\\left(1088\\theta^4-416\\theta^3-212\\theta^2-4\\theta+3\\right)+2^{12} 3^{3} x^{2}\\left(928\\theta^4-224\\theta^3+448\\theta^2+108\\theta+9\\right)-2^{20} 3^{6} x^{3}\\left(320\\theta^4+288\\theta^3+220\\theta^2+72\\theta+9\\right)+2^{28} 3^{10} x^{4}\\left((2\\theta+1)^4\\right)", "superseek": "-2656 -2493879008", "discriminant": "4 1 -17408 102629376 -244611809280 253613523861504", "aesz": "362", "n_sing_complex": "1", "inst_int": "", "c2h": null, "hash": "57a424b3b32b72260817cb8c45a8ae8f", "dim_h": null, "inst": " -2656 -1985680 -2493879008 -3906525894360 -6910084057179168 -13205144335837069648 -26643849974502474584928 -56014700550896392414559320 -121694131730070927522488317184 -271695197484747225091573920363824", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "3", "laurent": null, "discriminant_tex": "(5308416z^2-3584z+1)(-1+6912z)^2", "discr_factors": "253613523861504, z^2-7/10368*z+1/5308416, (-1/6912+z)^2", "dm_basis": null, "q": "0 1 256 741216 1628698624 3774036294192 9014129277775872 21978114893585650176 54410587501632422412288 136359425294572151505521304", "yuk": "1 -2656 -15888096 -67334735872 -250017673127136 -863760507147398656 -2852311176608157665280 -9138840541254348782632960 -28679526682059202933927498976 -88715022031221706163961317963008", "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":"s_2","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"s_1","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/6912","im":"0","approx_re":"0.000144675925926","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"7/20736","im":"-1/5184*2^(1/2)","approx_re":"0.000337577160494","approx_im":"-0.000273","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"7/20736","im":"1/5184*2^(1/2)","approx_re":"0.000337577160494","approx_im":"0.000273","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","1/2","1/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, 72+648*X+2079*X^2+2862*X^3+2079*X^4, 194400+1492992*X+3633336*X^2+3604176*X^3+1504656*X^4, 20995200+211631616*X+730632960*X^2+967458816*X^3+399328704*X^4, 544195584*(4*X+1)*(2*X+1)^2*(4*X+3)]", "text": "Sporadic Operator.", "degz": 4, "h3": null, "sol": "1 -72 22680 -9424800 4199995800 -1795109988672 621876550879584 -53512702860988800 -199819112547934737000 286500726415890938952000", "n_discr_factors": "2", "c3": null, "operator": "4 4 0 0 0 0 1 72 648 2079 2862 2079 194400 1492992 3633336 3604176 1504656 20995200 211631616 730632960 967458816 399328704 1632586752 15237476352 50065993728 69657034752 34828517376", "new_number": "4.74", "id": 175, "operator_tex": "\\theta^4+3^{2} x\\left(231\\theta^4+318\\theta^3+231\\theta^2+72\\theta+8\\right)+2^{3} 3^{5} x^{2}\\left(774\\theta^4+1854\\theta^3+1869\\theta^2+768\\theta+100\\right)+2^{6} 3^{8} x^{3}\\left(951\\theta^4+2304\\theta^3+1740\\theta^2+504\\theta+50\\right)+2^{10} 3^{12} x^{4}(4\\theta+1)(2\\theta+1)^2(4\\theta+3)", "superseek": "-207 621972", "discriminant": "4 1 2079 1504656 399328704 34828517376", "aesz": "363", "n_sing_complex": "1", "inst_int": "", "c2h": null, "hash": "15f3be0c25c6a6ea1d78414f1cb31713", "dim_h": null, "inst": " -207 5544 621972 -241386048 59946723846 -11102975438472 729574413105222 578068512191684640 -359085841181915842191 128078952652171203999912", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "3", "laurent": null, "discriminant_tex": "(746496z^2+1647z+1)(1+216z)^2", "discr_factors": "34828517376, z^2+61/27648*z+1/746496, (1/216+z)^2", "dm_basis": null, "q": "0 1 360 87156 14045232 2327439474 244965088512 30694301605872 7556208374936160 -1751386443391367145", "yuk": "1 -207 44145 16793037 -15448662927 7493340480543 -2398242677872563 250244023695090939 295971078226693872753 -261773578221616632164202", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/216","im":"0","approx_re":"-0.00462962962963","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-61/55296","im":"-5/55296*15^(1/2)","approx_re":"-0.00110315393519","approx_im":"-0.00035","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-61/55296","im":"5/55296*15^(1/2)","approx_re":"-0.00110315393519","approx_im":"0.00035","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":"s_1","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"s_2","im":"0","approx_re":"0.0","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":["1/4","1/2","1/2","3/4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, 270*X^4+450*X^3+432*X^2+207*X+39, 3*(3*X+2)*(3039*X^3+8104*X^2+9017*X+3783), 4563*(3*X+2)*(3*X+5)*(30*X^2+80*X+63), 257049*(3*X+2)*(3*X+5)^2*(3*X+8)]", "text": "Sporadic Operator. Where did it come from?", "degz": 4, "h3": null, "sol": "1 -39 1989 -110604 6425757 -383377995 23285576223 -1432520205246 88975404777051 -5567350763238303", "n_discr_factors": "1", "c3": null, "operator": "4 4 0 0 0 0 1 39 207 432 450 270 22698 88149 129777 91170 27351 2874690 9687249 11621961 6160050 1232010 102819600 316170270 326195181 138806460 20820969", "new_number": "4.75", "id": 176, "operator_tex": "\\theta^4+3 x\\left(90\\theta^4+150\\theta^3+144\\theta^2+69\\theta+13\\right)+3 x^{2}(3\\theta+2)(3039\\theta^3+8104\\theta^2+9017\\theta+3783)+3^{3} 13^{2} x^{3}(3\\theta+2)(3\\theta+5)(30\\theta^2+80\\theta+63)+3^{2} 13^{4} x^{4}(3\\theta+2)(3\\theta+5)^2(3\\theta+8)", "superseek": "6 389", "discriminant": "4 1 270 27351 1232010 20820969", "aesz": null, "n_sing_complex": "1", "inst_int": "", "c2h": null, "hash": "1e24ac15c33e7bc66a4211a6f86ad179", "dim_h": null, "inst": " 6 33 389 6393 128769 2960438 74625204 2013080277 57201249791 1693527030393", "cleanlist": "True", "n_sing_real": "1", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "2", "laurent": null, "discriminant_tex": "(1+135z+4563z^2)^2", "discr_factors": "20820969, (1/4563+5/169*z+z^2)^2", "dm_basis": null, "q": "0 1 51 2388 107783 4772193 208849338 9069802248 391736133087 16851323413863", "yuk": "1 6 270 10509 409422 16096131 639465381 25596444978 1030697511246 41699711108148", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-5/338","im":"-1/3042*3^(1/2)","approx_re":"-0.0147928994083","approx_im":"-0.000569","exponents":["0","1/3","1","4/3"],"monodromy":[],"monodromy_dm":[]},{"re":"-5/338","im":"1/3042*3^(1/2)","approx_re":"-0.0147928994083","approx_im":"0.000569","exponents":["0","1/3","1","4/3"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"s_1","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1/3","1","4/3"],"monodromy":[],"monodromy_dm":[]},{"re":"s_2","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1/3","1","4/3"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["2/3","5/3","5/3","8/3"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -8613*X^4-32778*X^3-21207*X^2-4818*X-408, -65178432*X^4-86453568*X^3+29870208*X^2+15230592*X+1804032, -94629565440*X^4-5804752896*X^3+194835456*X^2-1370566656*X-295612416, -69657034752*(3*X+1)*(2*X+1)^2*(3*X+2)]", "text": "Sporadic Operator.\nB-Incarnation as Diagonal.", "degz": 4, "h3": null, "sol": "1 408 1616760 10409448000 82877787531000 743753159270529408 7208204617559837795904 73708776291129009523384320 784124563334024663223333003000 8598812308406488588724561520120000", "n_discr_factors": "3", "c3": null, "operator": "4 4 0 0 0 0 1 -408 -4818 -21207 -32778 -8613 1804032 15230592 29870208 -86453568 -65178432 -295612416 -1370566656 194835456 -5804752896 -94629565440 -139314069504 -1184169590784 -3691822841856 -5015306502144 -2507653251072", "new_number": "4.76", "id": 177, "operator_tex": "\\theta^4-3 x\\left(2871\\theta^4+10926\\theta^3+7069\\theta^2+1606\\theta+136\\right)-2^{6} 3^{4} x^{2}\\left(12573\\theta^4+16677\\theta^3-5762\\theta^2-2938\\theta-348\\right)-2^{10} 3^{8} x^{3}\\left(14085\\theta^4+864\\theta^3-29\\theta^2+204\\theta+44\\right)-2^{17} 3^{12} x^{4}(3\\theta+1)(2\\theta+1)^2(3\\theta+2)", "superseek": "6015 9668470011", "discriminant": "4 1 -8613 -65178432 -94629565440 -2507653251072", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "f16cc33931b60f0c5d3a1a0239a01062", "dim_h": null, "inst": " 6015 3451026 9668470011 32924097729576 144270059475420597 719319787652485401792 3944086411161197102835210 23158185018934890566297522088 143297456357348110689521077046850 924087060671515383906523935916297302", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "-(27z+1)(13824z-1)(1+2592z)^2", "discr_factors": "-2507653251072, z+1/27, z-1/13824, (1/2592+z)^2", "dm_basis": null, "q": "0 1 -3186 2615301 -7866499320 -17294023962162 -125478777327166314 -748332330474756704742 -4938290845294248979509024 -33715211837556295359772728165", "yuk": "1 6015 27614223 261048696312 2107142282307087 18033757434427580640 155373074133197923091592 1352821639028290606272483045 11856990729694666077086613616143 104463845684506772692661126215849962", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/27","im":"0","approx_re":"-0.037037037037","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/2592","im":"0","approx_re":"-0.000385802469136","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":"1/13824","im":"0","approx_re":"7.2337962963e-05","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":["1/3","1/2","1/2","2/3"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -16-80*X-161*X^2-162*X^3-81*X^4, 3520+11840*X+15616*X^2+9696*X^3+2424*X^4, -64*(124*X^2+372*X+263)*(2*X+3)^2, 38400*(X+1)*(2*X+5)*(2*X+3)*(X+3)]", "text": "Sporadic Operator.\nB-Incarnation: SII4411\n", "degz": 4, "h3": null, "sol": "1 16 280 5152 98200 1924096 38567776 788141440 16375619992 345184309120", "n_discr_factors": "3", "c3": null, "operator": "4 4 0 0 0 0 1 -16 -80 -161 -162 -81 3520 11840 15616 9696 2424 -151488 -416256 -424448 -190464 -31744 1728000 4147200 3494400 1228800 153600", "new_number": "4.77", "id": 178, "operator_tex": "\\theta^4-x\\left(16+80\\theta+161\\theta^2+162\\theta^3+81\\theta^4\\right)+2^{3} x^{2}\\left(303\\theta^4+1212\\theta^3+1952\\theta^2+1480\\theta+440\\right)-2^{6} x^{3}(124\\theta^2+372\\theta+263)(2\\theta+3)^2+2^{9} 3 5^{2} x^{4}(\\theta+1)(2\\theta+5)(2\\theta+3)(\\theta+3)", "superseek": "1 68/9", "discriminant": "4 1 -81 2424 -31744 153600", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "f9623221ffe8be4c1e31a6e6ce195a37", "dim_h": null, "inst": " 1 -2 68/9 -30 150 -778 4374 -25438 463459/3 -960634", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "(25z-1)(24z-1)(-1+16z)^2", "discr_factors": "153600, z-1/25, (-1/16+z)^2, z-1/24", "dm_basis": null, "q": "0 1 -16 228 -3088 40434 -516960 6493584 -80458272 986088855", "yuk": "1 1 -15 205 -1935 18751 -167859 1500283 -13026191 112620742", "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":"1/25","im":"0","approx_re":"0.04","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/24","im":"0","approx_re":"0.0416666666667","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/16","im":"0","approx_re":"0.0625","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","3/2","5/2","3"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -1080*(X+1/2)^4-978*(X+1/2)^2-30, 384912*(X+1)^4+331452*(X+1)^2+28512, -1679616*(X+3/2)^2*(30*(X+3/2)^2+23), 15116544*(2*X+3)*(2*X+5)*(6*X+11)*(6*X+13)]", "text": "YY-operator equivalent to (:AESZ 50), $\\tilde B \\ast \\alpha$", "degz": 4, "h3": null, "sol": "1 342 117990 42901884 16240501782 6316625715444 2502293810634972 1004195277488806200 406869404168584931958 166067564374448102903364", "n_discr_factors": "2", "c3": null, "operator": "4 4 0 0 0 0 1 -342 -1518 -2598 -2160 -1080 744876 2202552 2640924 1539648 384912 -342011808 -796137984 -718875648 -302330880 -50388480 32424986880 67238387712 51638114304 17414258688 2176782336", "new_number": "4.7", "id": 179, "operator_tex": "\\theta^4-2 3 x\\left(180\\theta^4+360\\theta^3+433\\theta^2+253\\theta+57\\right)+2^{2} 3^{4} 11 x^{2}\\left(108\\theta^4+432\\theta^3+741\\theta^2+618\\theta+209\\right)-2^{5} 3^{8} x^{3}(60\\theta^2+180\\theta+181)(2\\theta+3)^2+2^{8} 3^{10} x^{4}(2\\theta+3)(2\\theta+5)(6\\theta+11)(6\\theta+13)", "superseek": "-54 -40552", "discriminant": "4 1 -1080 384912 -50388480 2176782336", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "ee8508b4e5567367ca11f74e074e8099", "dim_h": null, "inst": " -54 -864 -40552 -2192400 -123334380 -7606782112 -510067786500 -35999557094448 -2629631770323490 -197665963831332576", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "(432z-1)^2(108z-1)^2", "discr_factors": "2176782336, (z-1/108)^2, (z-1/432)^2", "dm_basis": null, "q": "0 1 -150 12159 -1012316 69674055 -4599819306 286902654701 -17623474911768 1008452921121792", "yuk": "1 -54 -6966 -1094958 -140320566 -15416797554 -1643066038062 -174953250769554 -18431773372677942 -1917001560566919168", "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":"1/432","im":"0","approx_re":"0.00231481481481","approx_im":"0.0","exponents":["0","-1/2","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/108","im":"0","approx_re":"0.00925925925926","approx_im":"0.0","exponents":["0","-1/2","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["3/2","11/6","13/6","5/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -1836*(X+1/2)^4-1614*(X+1/2)^2-177/4, 844182*(X+1)^4+23571/2*(X+1)^2+2835/4, -6561*(X+3/2)^2*(204*(X+3/2)^2+151), 59049/16*(2*X+3)*(2*X+5)*(6*X+11)*(6*X+13)]", "text": "YY-Operator equivalent to AESZ 53 =$B \\ast \\gamma \\tilde g \\ast h$", "degz": 4, "h3": null, "sol": "1 1125/2 3219615/8 5002535925/16 32404173968475/128 53796434927016771/256 181612568805465855915/1024 310214532003511738962645/2048 4276965511967012944282192275/32768 7422128578198801501629900794775/65536", "n_discr_factors": "1", "c3": null, "operator": "4 4 0 0 0 0 1 -1125/2 -2532 -4368 -3672 -1836 3426705/4 3400299 10153755/2 3376728 844182 -18009945/2 -21041127 -19059705 -8030664 -1338444 126660105/16 16415622 25213923/2 4251528 531441", "new_number": "4.8", "id": 180, "operator_tex": "\\theta^4-x\\left(1836\\theta^4+3672\\theta^3+4368\\theta^2+2532\\theta+1125/2\\right)+x^{2}\\left(844182\\theta^4+3376728\\theta^3+10153755/2\\theta^2+3400299\\theta+3426705/4\\right)-x^{3}6561/2(2\\theta+3)^2(102\\theta^2+306\\theta+305)+x^{4}59049/16(2\\theta+3)(2\\theta+5)(6\\theta+11)(6\\theta+13)", "superseek": "-135 -417685", "discriminant": "4 1 -1836 844182 -1338444 531441", "aesz": null, "n_sing_complex": "1", "inst_int": "", "c2h": null, "hash": "f5702d0b3fd53e9b80a42c76a335b648", "dim_h": null, "inst": " -135 -22815/4 -417685 -78983235/2 -4331084310 -2089942400125/4 -67374991615680 -18252405254369835/2 -1283816640590794765 -372187037770688515995/2", "cleanlist": "True", "n_sing_real": "1", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "2", "laurent": null, "discriminant_tex": "(1-918z+729z^2)^2", "discr_factors": "531441, (1/729-34/27*z+z^2)^2", "dm_basis": null, "q": "0 1 -282 25119 -1071652 25356255 -1131124770 -48836642899 -12516628400052 -1895689264678308", "yuk": "1 -135 -45765 -11277630 -2527509285 -541385538885 -112856900930010 -23109622124178375 -4672615747646187045 -935902330990700661315", "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":"s_1","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["-1/2","0","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"s_2","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["-1/2","0","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"17/27-4/9*2^(1/2)","im":"0","approx_re":"0.00109","approx_im":"0.0","exponents":["0","-1/2","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"17/27+4/9*2^(1/2)","im":"0","approx_re":"1.258169","approx_im":"0.0","exponents":["0","-1/2","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["3/2","11/6","13/6","5/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -756*(X+1/2)^4-690*(X+1/2)^2-87/4, 260982*(X+1)^4+815427/2*(X+1)^2+142947/4, -531441*(X+3/2)^2*(84*(X+3/2)^2+65), 387420489/16*(2*X+3)*(2*X+5)*(6*X+11)*(6*X+13)]", "text": "YY-operator equivalent to AESZ 151=$B \\ast \\delta$", "degz": 4, "h3": null, "sol": "1 483/2 300015/8 32162403/16 -132658029189/128 -115627249605483/256 -108197209270259109/1024 -29009247623259989085/2048 15099017488656585094611/32768 59767409101296884745991233/65536", "n_discr_factors": "1", "c3": null, "operator": "4 4 0 0 0 0 1 -483/2 -1068 -1824 -1512 -756 2817729/4 1859355 3947211/2 1043928 260982 -607437063/2 -706285089 -637197759 -267846264 -44641044 831016948905/16 107702895942 165428548803/2 27894275208 3486784401", "new_number": "4.9", "id": 181, "operator_tex": "\\theta^4-x\\left(756\\theta^4+1512\\theta^3+1824\\theta^2+1068\\theta+483/2\\right)+x^{2}\\left(260982\\theta^4+1043928\\theta^3+3947211/2\\theta^2+1859355\\theta+2817729/4\\right)-x^{3}531441/2(2\\theta+3)^2(42\\theta^2+126\\theta+127)+x^{4}387420489/16(2\\theta+3)(2\\theta+5)(6\\theta+11)(6\\theta+13)", "superseek": "-33 29693", "discriminant": "4 1 -756 260982 -44641044 3486784401", "aesz": null, "n_sing_complex": "1", "inst_int": "", "c2h": null, "hash": "c444fb1a912bd488ee5947b8bc1e2c53", "dim_h": null, "inst": " -33 1095/2 29693 1241103/2 -16117818 -3980319827/2 -68679466944 2495037536247/2 260588508312917 11634569245959975", "cleanlist": "True", "n_sing_real": "1", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "2", "laurent": null, "discriminant_tex": "(1-378z+59049z^2)^2", "discr_factors": "3486784401, (1/59049-14/2187*z+z^2)^2", "dm_basis": null, "q": "0 1 -102 11727 -799756 63350367 -3980423214 261400863725 -15763834861404 952935785688204", "yuk": "1 -33 4347 801678 39719643 -2014727283 -429873735258 -23557057161825 638729648998875 189969022560918171", "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":"s_1","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["-1/2","0","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"s_2","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["-1/2","0","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"7/2187","im":"-4/2187*2^(1/2)","approx_re":"0.00320073159579","approx_im":"-0.002587","exponents":["0","-1/2","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"7/2187","im":"4/2187*2^(1/2)","approx_re":"0.00320073159579","approx_im":"0.002587","exponents":["0","-1/2","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["3/2","11/6","13/6","5/2"],"monodromy":[],"monodromy_dm":[]}]}]}