{"count": 4, "status":"OK", "data":[{"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": "[49*X^4, 98-336*X^3-840*X^4+126*X^2+294*X, -31108-25968*X^4-186660*X^2-120768*X^3-123144*X, 58112*X^4-440832*X^3-1217328-2142720*X^2-2782080*X, 61952+7815168*X^2+3895296*X+5259264*X^3+909312*X^4, 17874944+42074112*X+7864320*X^3+33030144*X^2-786432*X^4, -524288*(2*X+3)^4]", "text": "This is operator \"6.36\" from ...", "degz": 6, "h3": null, "sol": "1 -2 38 204 7462 129284 3308860 75931544 1941436582 49216354516", "n_discr_factors": "4", "c3": null, "operator": "4 6 0 0 0 0 49 98 294 126 -336 -840 -31108 -123144 -186660 -120768 -25968 -1217328 -2782080 -2142720 -440832 58112 61952 3895296 7815168 5259264 909312 17874944 42074112 33030144 7864320 -786432 -42467328 -113246208 -113246208 -50331648 -8388608", "new_number": "6.36", "id": 421, "operator_tex": "7^{2} \\theta^4-2 7 x\\left(60\\theta^4+24\\theta^3-9\\theta^2-21\\theta-7\\right)-2^{2} x^{2}\\left(6492\\theta^4+30192\\theta^3+46665\\theta^2+30786\\theta+7777\\right)+2^{4} x^{3}\\left(3632\\theta^4-27552\\theta^3-133920\\theta^2-173880\\theta-76083\\right)+2^{9} x^{4}\\left(1776\\theta^4+10272\\theta^3+15264\\theta^2+7608\\theta+121\\right)-2^{14} x^{5}\\left(48\\theta^4-480\\theta^3-2016\\theta^2-2568\\theta-1091\\right)-2^{19} x^{6}\\left((2\\theta+3)^4\\right)", "superseek": "10/7 508/7", "discriminant": "6 49 -840 -25968 58112 909312 -786432 -8388608", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "b890cacbc73012eb6554263c3ea04707", "dim_h": null, "inst": " 10/7 100/7 508/7 808 59910/7 855864/7 12382494/7 200115472/7 3327848026/7 58373507100/7", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "5", "n_sing": "5", "laurent": null, "discriminant_tex": "-(16z+1)(32z-1)(4z+1)^2(32z-7)^2", "discr_factors": "-8388608, z+1/16, (z+1/4)^2, z-1/32, (z-7/32)^2", "dm_basis": null, "q": "0 1 -2 -71 -236 -580 -16018 -462550 -8253320 -151220156", "yuk": "1 10/7 810/7 13726/7 362794/7 7488760/7 184881150/7 4247195452/7 102459484458/7 2426001224680/7", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/4","im":"0","approx_re":"-0.25","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","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":"1/32","im":"0","approx_re":"0.03125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"7/32","im":"0","approx_re":"0.21875","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":["3/2","3/2","3/2","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[1849*X^4, -43*X*(142*X^3+890*X^2+574*X+129), -647269*X^4-2441818*X^3-3538503*X^2-2423953*X-650848, -7200000*X^4-34423908*X^3-65337898*X^2-57379329*X-19251960, -37610765*X^4-220029964*X^3-499781264*X^2-511393545*X-194039928, -2*(X+1)*(54978121*X^3+324737370*X^2+665066226*X+466789876), -(X+1)*(X+2)*(185181547*X^2+915931425*X+1176131796), -1212*(X+3)*(X+2)*(X+1)*(138979*X+413408), -64266300*(X+1)*(X+2)*(X+3)*(X+4)]", "text": "This is operator \"8.51\" from ...", "degz": 8, "h3": null, "sol": "1 0 22 204 3474 57000 1031080 19368720 377712370 7565838000", "n_discr_factors": "5", "c3": null, "operator": "4 8 0 0 0 0 1849 0 -5547 -24682 -38270 -6106 -650848 -2423953 -3538503 -2441818 -647269 -19251960 -57379329 -65337898 -34423908 -7200000 -194039928 -511393545 -499781264 -220029964 -37610765 -933579752 -2263712204 -1979607192 -759430982 -109956242 -2352263592 -5360258238 -4294289165 -1471476066 -185181547 -3006302976 -6522210744 -4859171004 -1511705784 -168442548 -1542391200 -3213315000 -2249320500 -642663000 -64266300", "new_number": "8.51", "id": 498, "operator_tex": "43^{2} \\theta^4-43 x\\theta(142\\theta^3+890\\theta^2+574\\theta+129)-x^{2}\\left(647269\\theta^4+2441818\\theta^3+3538503\\theta^2+2423953\\theta+650848\\right)-x^{3}\\left(7200000\\theta^4+34423908\\theta^3+65337898\\theta^2+57379329\\theta+19251960\\right)-x^{4}\\left(37610765\\theta^4+220029964\\theta^3+499781264\\theta^2+511393545\\theta+194039928\\right)-2 x^{5}(\\theta+1)(54978121\\theta^3+324737370\\theta^2+665066226\\theta+466789876)-x^{6}(\\theta+1)(\\theta+2)(185181547\\theta^2+915931425\\theta+1176131796)-2^{2} 3 101 x^{7}(\\theta+3)(\\theta+2)(\\theta+1)(138979\\theta+413408)-2^{2} 3^{2} 5^{2} 7 101^{2} x^{8}(\\theta+1)(\\theta+2)(\\theta+3)(\\theta+4)", "superseek": "58/43 1024/43", "discriminant": "8 1849 -6106 -647269 -7200000 -37610765 -109956242 -185181547 -168442548 -64266300", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "85b9064701880ae8e0518e47cff1b030", "dim_h": null, "inst": " 58/43 211/43 1024/43 7544/43 64880/43 642512/43 6932348/43 80121364/43 974406940/43 12346791976/43", "cleanlist": "True", "n_sing_real": "6", "sol_explicit": "", "n_sing_rational": "6", "n_sing": "6", "laurent": null, "discriminant_tex": "-(7z+1)(25z-1)(2z+1)^2(101z+43)^2(3z+1)^2", "discr_factors": "-64266300, (z+1/3)^2, (z+1/2)^2, (z+43/101)^2, z+1/7, z-1/25", "dm_basis": null, "q": "0 1 -3 -32 -33 135 -3440 -63577 -746051 -9406920", "yuk": "1 58/43 1746/43 27706/43 484562/43 188606 138811986/43 2377795422/43 41022622930/43 710342686966/43", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/2","im":"0","approx_re":"-0.5","approx_im":"0.0","exponents":["0","1/3","2/3","1"],"monodromy":[],"monodromy_dm":[]},{"re":"-43/101","im":"0","approx_re":"-0.425742574257","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/3","im":"0","approx_re":"-0.333333333333","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/7","im":"0","approx_re":"-0.142857142857","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":"1/25","im":"0","approx_re":"0.04","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","4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[25*X^4, -3380*X^4-4120*X^3-3710*X^2-1650*X-300, 185584*X^4+413632*X^3+501164*X^2+305480*X+76320, -5544384*X^4-17179008*X^3-25159152*X^2-18009840*X-5113440, 99910656*X^4+385357824*X^3+644136192*X^2+508886784*X+154972224, -1120960512*X^4-5065998336*X^3-9322573824*X^2-7852363776*X-2491250688, 7686586368*X^4+39154876416*X^3+77370163200*X^2+67974266880*X+22084337664, -509607936*(X+1)^2*(58*X^2+208*X+201), 48922361856*(X+1)^2*(X+2)^2]", "text": "This is operator \"8.79\" from ...", "degz": 8, "h3": null, "sol": "1 12 204 4368 112140 3300912 107091024 3718116288 135443387916 5110962695760", "n_discr_factors": "4", "c3": null, "operator": "4 8 0 0 0 0 25 -300 -1650 -3710 -4120 -3380 76320 305480 501164 413632 185584 -5113440 -18009840 -25159152 -17179008 -5544384 154972224 508886784 644136192 385357824 99910656 -2491250688 -7852363776 -9322573824 -5065998336 -1120960512 22084337664 67974266880 77370163200 39154876416 7686586368 -102431195136 -310860840960 -343985356800 -165112971264 -29557260288 195689447424 587068342272 635990704128 293534171136 48922361856", "new_number": "8.79", "id": 528, "operator_tex": "5^{2} \\theta^4-2 5 x\\left(338\\theta^4+412\\theta^3+371\\theta^2+165\\theta+30\\right)+2^{2} x^{2}\\left(46396\\theta^4+103408\\theta^3+125291\\theta^2+76370\\theta+19080\\right)-2^{4} 3 x^{3}\\left(115508\\theta^4+357896\\theta^3+524149\\theta^2+375205\\theta+106530\\right)+2^{6} 3^{2} x^{4}\\left(173456\\theta^4+669024\\theta^3+1118292\\theta^2+883484\\theta+269049\\right)-2^{11} 3^{3} x^{5}\\left(20272\\theta^4+91616\\theta^3+168594\\theta^2+142006\\theta+45053\\right)+2^{14} 3^{4} x^{6}\\left(5792\\theta^4+29504\\theta^3+58300\\theta^2+51220\\theta+16641\\right)-2^{21} 3^{5} x^{7}(\\theta+1)^2(58\\theta^2+208\\theta+201)+2^{26} 3^{6} x^{8}(\\theta+1)^2(\\theta+2)^2", "superseek": "22/5 68", "discriminant": "8 25 -3380 185584 -5544384 99910656 -1120960512 7686586368 -29557260288 48922361856", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "064e5b590dd8b6a4daa1e905fbe693c2", "dim_h": null, "inst": " 22/5 8 68 3292/5 38826/5 1517408/15 7418706/5 115188852/5 1132445042/3 32217796776/5", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "5", "n_sing": "5", "laurent": null, "discriminant_tex": "(-1+48z)(16z-1)^2(48z-5)^2(12z-1)^3", "discr_factors": "48922361856, (z-1/12)^3, (z-1/16)^2, -1/48+z, (z-5/48)^2", "dm_basis": null, "q": "0 1 -18 233 -2988 33412 -382914 3792338 -42902088 352614016", "yuk": "1 22/5 342/5 9202/5 42206 4853272/5 109262898/5 508923236 58976903254/5 1375920735232/5", "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":"1/48","im":"0","approx_re":"0.0208333333333","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":"1/12","im":"0","approx_re":"0.0833333333333","approx_im":"0.0","exponents":["0","1/2","3/2","2"],"monodromy":[],"monodromy_dm":[]},{"re":"5/48","im":"0","approx_re":"0.104166666667","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","2","2"],"monodromy":[],"monodromy_dm":[]}]}]}