{"count": 5, "status":"OK", "data":[{"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, -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, -594*X^4-216*X^3-234*X^2-126*X-24, 137052*X^4+128304*X^3+136728*X^2+60588*X+10224, -15274008*X^4-26453952*X^3-28308528*X^2-14224248*X-2807136, 816293376*X^4+2244806784*X^3+2692634400*X^2+1527715728*X+331304256, -51018336*(3*X+2)*(3*X+4)*(6*X+5)*(6*X+7)]", "text": "This is operator \"5.12\" from ...", "degz": 5, "h3": "72", "sol": "1 24 1152 71520 5101200 396676224 32692889376 2808042450048 248675352512400 22544379039811200", "n_discr_factors": "3", "c3": "450", "operator": "4 5 0 0 0 0 1 -24 -126 -234 -216 -594 10224 60588 136728 128304 137052 -2807136 -14224248 -28308528 -26453952 -15274008 331304256 1527715728 2692634400 2244806784 816293376 -14285134080 -61528113216 -96883820064 -66119763456 -16529940864", "new_number": "5.12", "id": 214, "operator_tex": "\\theta^4-2 3 x\\left(99\\theta^4+36\\theta^3+39\\theta^2+21\\theta+4\\right)+2^{2} 3^{2} x^{2}\\left(3807\\theta^4+3564\\theta^3+3798\\theta^2+1683\\theta+284\\right)-2^{3} 3^{5} x^{3}\\left(7857\\theta^4+13608\\theta^3+14562\\theta^2+7317\\theta+1444\\right)+2^{4} 3^{9} x^{4}\\left(2592\\theta^4+7128\\theta^3+8550\\theta^2+4851\\theta+1052\\right)-2^{5} 3^{13} x^{5}(3\\theta+2)(3\\theta+4)(6\\theta+5)(6\\theta+7)", "superseek": "-30 -14632", "discriminant": "5 1 -594 137052 -15274008 816293376 -16529940864", "aesz": "74", "n_sing_complex": "0", "inst_int": "", "c2h": "-36", "hash": "e668180adb7c88d4e5fbab5eb7ee61c7", "dim_h": "9", "inst": " -30 -516 -14632 -4227807/8 -22139868 -1021798708 -50464650036 -2619966661332 -141334834087546 -7859316901635348", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "-(-1+54z)(162z-1)^2(108z-1)^2", "discr_factors": "-16529940864, (z-1/108)^2, -1/54+z, (z-1/162)^2", "dm_basis": null, "q": "0 1 -30 495 -8236 58839 -2049570 -24155251 -973292856 1233846432", "yuk": "1 -30 -4158 -395094 -33826614 -2767483530 -220708920150 -17309374962378 -1341422964428598 -103033094050216128", "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":"1/162","im":"0","approx_re":"0.00617283950617","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/108","im":"0","approx_re":"0.00925925925926","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"1/54","im":"0","approx_re":"0.0185185185185","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":["2/3","5/6","7/6","4/3"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[16*X^4, -240-1536*X-4020*X^2-4968*X^3-1944*X^4, 73116+319248*X+512001*X^2+294462*X^3+32913*X^4, -2386260-7989840*X-7779645*X^2+196830*X^3+1120230*X^4, -10731609-64892664*X-136142937*X^2-126964098*X^3-22652946*X^4, -177343830-419641560*X-134926965*X^2+124199730*X^3-149492385*X^4, 30114990+1562436540*X+5464984950*X^2+6557981940*X^3+3059328690*X^4, -239148450-3348078300*X-12515435550*X^2-18334714500*X^3-9526079925*X^4, -1076168025*(X+1)^4]", "text": "This operator has a second MUM-point at infininty corresponding to operator 8.31", "degz": 8, "h3": "11", "sol": "1 15 459 19545 1019259 60504165 3910479525 267933366135 19147233606075 1412455648664085", "n_discr_factors": "3", "c3": "-88", "operator": "4 8 0 0 0 0 16 -240 -1536 -4020 -4968 -1944 73116 319248 512001 294462 32913 -2386260 -7989840 -7779645 196830 1120230 -10731609 -64892664 -136142937 -126964098 -22652946 -177343830 -419641560 -134926965 124199730 -149492385 30114990 1562436540 5464984950 6557981940 3059328690 -239148450 -3348078300 -12515435550 -18334714500 -9526079925 -1076168025 -4304672100 -6457008150 -4304672100 -1076168025", "new_number": "8.32", "id": 477, "operator_tex": "2^{4} \\theta^4-2^{2} 3 x\\left(162\\theta^4+414\\theta^3+335\\theta^2+128\\theta+20\\right)+3^{3} x^{2}\\left(1219\\theta^4+10906\\theta^3+18963\\theta^2+11824\\theta+2708\\right)+3^{5} 5 x^{3}\\left(922\\theta^4+162\\theta^3-6403\\theta^2-6576\\theta-1964\\right)-3^{7} x^{4}\\left(10358\\theta^4+58054\\theta^3+62251\\theta^2+29672\\theta+4907\\right)-3^{9} 5 x^{5}\\left(1519\\theta^4-1262\\theta^3+1371\\theta^2+4264\\theta+1802\\right)+2 3^{11} 5 x^{6}\\left(1727\\theta^4+3702\\theta^3+3085\\theta^2+882\\theta+17\\right)-3^{13} 5^{2} x^{7}\\left(239\\theta^4+460\\theta^3+314\\theta^2+84\\theta+6\\right)-3^{16} 5^{2} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "69/4 14365/12", "discriminant": "8 16 -1944 32913 1120230 -22652946 -149492385 3059328690 -9526079925 -1076168025", "aesz": "317", "n_sing_complex": "3", "inst_int": "", "c2h": "50", "hash": "cda8cce31025f51636125bea67a820d1", "dim_h": "6", "inst": " 69/4 -30 14365/12 3015/2 1376205/4 9897421/3 388901931/2 7471470879/2 636889759589/4 4303811481090", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "7", "laurent": null, "discriminant_tex": "-(27z-1)(243z^3+2214z^2-117z+1)(-4-45z+405z^2)^2", "discr_factors": "-1076168025, z-1/27, (-4/405-1/9*z+z^2)^2, z^3+82/9*z^2-13/27*z+1/243", "dm_basis": null, "q": "0 1 -36 972 -26604 669816 -17273412 416721960 -10686110652 249004225278", "yuk": "1 69/4 -891/4 64677/2 385029/4 86012847/2 1425292821/2 266786724735/4 7650786565125/4 464292634869735/4", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/108*(-4526396+3852*I*107^(1/2))^(1/3)-6841/27/(-4526396+3852*I*107^(1/2))^(1/3)-82/27+1/6*I*3^(1/2)*(1/18*(-4526396+3852*I*107^(1/2))^(1/3)-13682/9/(-4526396+3852*I*107^(1/2))^(1/3))","im":"0","approx_re":"-9.163702","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/18-1/90*105^(1/2)","im":"0","approx_re":"-0.058299","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":"-1/108*(-4526396+3852*I*107^(1/2))^(1/3)-6841/27/(-4526396+3852*I*107^(1/2))^(1/3)-82/27-1/6*I*3^(1/2)*(1/18*(-4526396+3852*I*107^(1/2))^(1/3)-13682/9/(-4526396+3852*I*107^(1/2))^(1/3))","im":"0","approx_re":"0.010727","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/27","im":"0","approx_re":"0.037037037037","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/54*(-4526396+3852*I*107^(1/2))^(1/3)+13682/27/(-4526396+3852*I*107^(1/2))^(1/3)-82/27","im":"0","approx_re":"0.041864","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/18+1/90*105^(1/2)","im":"0","approx_re":"0.169411","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","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -33*X^4-98*X^3-105*X^2-56*X-12, 272*X^4+2208*X^3+4872*X^2+4656*X+1728, 528*X^4-8160*X^3-45168*X^2-72960*X-40608, -1152*(2*X^2+6*X+5)*(4*X^2+12*X-31), 8448*X^4+231936*X^3+908544*X^2+1268736*X+557568, 69632*X^4+270336*X^3-79872*X^2-1449984*X-1529856, -135168*X^4-1220608*X^3-4116480*X^2-6111232*X-3342336, 65536*(X+3)^4]", "text": "This is operator \"8.55\" from ...", "degz": 8, "h3": null, "sol": "1 12 120 1216 13080 149664 1801312 22528512 290011032 3816913696", "n_discr_factors": "5", "c3": null, "operator": "4 8 0 0 0 0 1 -12 -56 -105 -98 -33 1728 4656 4872 2208 272 -40608 -72960 -45168 -8160 528 178560 145152 -34560 -55296 -9216 557568 1268736 908544 231936 8448 -1529856 -1449984 -79872 270336 69632 -3342336 -6111232 -4116480 -1220608 -135168 5308416 7077888 3538944 786432 65536", "new_number": "8.55", "id": 502, "operator_tex": "\\theta^4-x\\left(33\\theta^4+98\\theta^3+105\\theta^2+56\\theta+12\\right)+2^{3} x^{2}\\left(34\\theta^4+276\\theta^3+609\\theta^2+582\\theta+216\\right)+2^{4} 3 x^{3}\\left(11\\theta^4-170\\theta^3-941\\theta^2-1520\\theta-846\\right)-2^{7} 3^{2} x^{4}(2\\theta^2+6\\theta+5)(4\\theta^2+12\\theta-31)+2^{8} 3 x^{5}\\left(11\\theta^4+302\\theta^3+1183\\theta^2+1652\\theta+726\\right)+2^{11} x^{6}\\left(34\\theta^4+132\\theta^3-39\\theta^2-708\\theta-747\\right)-2^{12} x^{7}\\left(33\\theta^4+298\\theta^3+1005\\theta^2+1492\\theta+816\\right)+2^{16} x^{8}\\left((\\theta+3)^4\\right)", "superseek": "1 68/9", "discriminant": "8 1 -33 272 528 -9216 8448 69632 -135168 65536", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "39ed8ce7572bc79a333f77c892033bcf", "dim_h": null, "inst": " 1 -2 68/9 -30 150 -778 4374 -25438 463459/3 -960634", "cleanlist": "True", "n_sing_real": "7", "sol_explicit": "", "n_sing_rational": "5", "n_sing": "7", "laurent": null, "discriminant_tex": "(z-1)(16z-1)(16z^2-16z+1)(4z-1)^2(4z+1)^2", "discr_factors": "65536, (z-1/4)^2, (z+1/4)^2, z-1, z-1/16, z^2-z+1/16", "dm_basis": null, "q": "0 1 -8 52 -336 2226 -15040 103280 -719520 5072791", "yuk": "1 1 -15 205 -1935 18751 -167859 1500283 -13026191 112620742", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/4","im":"0","approx_re":"-0.25","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":"1/16","im":"0","approx_re":"0.0625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/2-1/4*3^(1/2)","im":"0","approx_re":"0.066987","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/4","im":"0","approx_re":"0.25","approx_im":"0.0","exponents":["0","0","-1","1"],"monodromy":[],"monodromy_dm":[]},{"re":"1/2+1/4*3^(1/2)","im":"0","approx_re":"0.933013","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1","im":"0","approx_re":"1.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["3","3","3","3"],"monodromy":[],"monodromy_dm":[]}]}]}