{"count": 6, "status":"OK", "data":[{"pols": "[X^4, -5832*X^4-11664*X^3-13770*X^2-7938*X-1746, 236196*(X+1)^2*(6*X+5)*(6*X+7)]", "text": "Operator equivalent to $\\hat{4}$", "degz": 2, "h3": null, "sol": "1 1746 3951990 9740271348 25043989159350 66042700202991996 177115354806794088636 480730042522583271956520 1316595143051828406693466038 3631103407214519008442157554220", "n_discr_factors": "1", "c3": null, "operator": "4 2 0 0 0 0 1 -1746 -7938 -13770 -11664 -5832 8266860 33539832 50782140 34012224 8503056", "new_number": "2.41", "id": 35, "operator_tex": "\\theta^4-2 3^{2} x\\left(324\\theta^4+648\\theta^3+765\\theta^2+441\\theta+97\\right)+2^{2} 3^{10} x^{2}(\\theta+1)^2(6\\theta+5)(6\\theta+7)", "superseek": "-522 -9879192", "discriminant": "2 1 -5832 8503056", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "73d9f98b2c49f1c35df531f020cf1721", "dim_h": null, "inst": " -522 -105291/2 -9879192 -2420127936 -689420749716 -216357353050266 -72634690919277180 -25626633195551666544 -9392840331059964324510 -3548231463433108407572043", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "2", "laurent": null, "discriminant_tex": "(2916z-1)^2", "discr_factors": "8503056, (z-1/2916)^2", "dm_basis": ["cy[DM_basis]"], "q": "0 1 -954 353727 -76415556 11655125127 -1450031521158 134882141008365 -18262721155776552 -1103456195305136640", "yuk": "1 -522 -421686 -266738706 -154888609590 -86177593715022 -46733188526017326 -24913698985312073262 -13120836196277341880118 -6847380601342714259306496", "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":["1","-1","1/2","-1/6","0","1","-1","1/2","0","0","1","-1","0","0","0","1"],"monodromy_dm":["cy[T_DM][1]"]},{"re":"1/2916","im":"0","approx_re":"0.000342935528121","approx_im":"0.0","exponents":["0","-1/2","1","3/2"],"monodromy":["7/8","-108*lambda","5/64","0","0","-7/8","0","5/64","3","0","-7/8","108*lambda","0","3","0","7/8"],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["5/6","1","1","7/6"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -43*X^4-86*X^3-77*X^2-34*X-6, 12*(X+1)^2*(6*X+5)*(6*X+7)]", "text": "This is operator \"2.64\" from ...", "degz": 2, "h3": "132", "sol": "1 6 66 924 14850 261756 4933236 97806456 2017042434 42917560620", "n_discr_factors": "2", "c3": "-96", "operator": "4 2 0 0 0 0 1 -6 -34 -77 -86 -43 420 1704 2580 1728 432", "new_number": "2.64", "id": 60, "operator_tex": "\\theta^4-x\\left(43\\theta^4+86\\theta^3+77\\theta^2+34\\theta+6\\right)+2^{2} 3 x^{2}(\\theta+1)^2(6\\theta+5)(6\\theta+7)", "superseek": "1 7", "discriminant": "2 1 -43 432", "aesz": "182", "n_sing_complex": "0", "inst_int": "", "c2h": "132", "hash": "89ba4729efa82413b33fe6928ff8d2c9", "dim_h": "33", "inst": " 1 7/4 7 40 270 7913/4 15618 131512 1168395 21654889/2", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "(27z-1)(16z-1)", "discr_factors": "432, z-1/16, z-1/27", "dm_basis": ["-96*lambda", "55/2", "1", "1", "-11/2", "-66", "-1", "0", "0", "132", "0", "0", "-132", "0", "0", "0"], "q": "0 1 -10 63 -336 1399 -6150 17483 -103744 -85626", "yuk": "1 1 15 190 2575 33751 427506 5356975 67336719 851760145", "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":["1","-1","1/2","-1/6","0","1","-1","1/2","0","0","1","-1","0","0","0","1"],"monodromy_dm":["1","0","0","0","1","1","0","0","0","132","1","0","0","0","1","1"]},{"re":"1/27","im":"0","approx_re":"0.037037037037","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["1+96*lambda","0","4*lambda",".1639606e-2","11/2","1","11/48","-4*lambda","0","0","1","0","132","0","11/2","1-96*lambda"],"monodromy_dm":["1","-33","-1","-1","0","1","0","0","0","0","1","0","0","0","0","1"]},{"re":"1/16","im":"0","approx_re":"0.0625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["17/4+288*lambda","-13/24-48*lambda","13/96+12*lambda","-.21754163e-1-52/11*lambda","33/2","-7/4","11/16","-13/96-12*lambda","66","-11","15/4","-13/24-48*lambda","396","-66","33/2","-9/4-288*lambda"],"monodromy_dm":["-5","-132","-7/2","-3","1","23","583333/1000000","1/2","-66","-1452","-75/2","-33","45","990","105/4","47/2"]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["5/6","1","1","7/6"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -120*X^4-180*X^3-136*X^2-46*X-6, 1252*X^4-1592*X^3-5668*X^2-4132*X-1008, 5232*X^4+40512*X^3+28592*X^2+1032*X-3240, -50240*X^4+3200*X^3+135920*X^2+132880*X+38400, -4800*(X+1)^2*(6*X+5)*(6*X+7)]", "text": "This is operator \"5.111\" from ...", "degz": 5, "h3": null, "sol": "1 6 246 13020 832950 59364756 4543863996 365802101496 30576859664310 2631271897080420", "n_discr_factors": "3", "c3": null, "operator": "4 5 0 0 0 0 1 -6 -46 -136 -180 -120 -1008 -4132 -5668 -1592 1252 -3240 1032 28592 40512 5232 38400 132880 135920 3200 -50240 -168000 -681600 -1032000 -691200 -172800", "new_number": "5.111", "id": 194, "operator_tex": "\\theta^4-2 x\\left(60\\theta^4+90\\theta^3+68\\theta^2+23\\theta+3\\right)+2^{2} x^{2}\\left(313\\theta^4-398\\theta^3-1417\\theta^2-1033\\theta-252\\right)+2^{3} x^{3}\\left(654\\theta^4+5064\\theta^3+3574\\theta^2+129\\theta-405\\right)-2^{4} 5 x^{4}\\left(628\\theta^4-40\\theta^3-1699\\theta^2-1661\\theta-480\\right)-2^{6} 3 5^{2} x^{5}(\\theta+1)^2(6\\theta+5)(6\\theta+7)", "superseek": "12 2320", "discriminant": "5 1 -120 1252 5232 -50240 -172800", "aesz": "380", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "85214e3836a67470a05358a4d38fb124", "dim_h": null, "inst": " 12 511/4 2320 63507 2180312 85468145 3674561480 169146821452 8204014122468 829356661449007/2", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "-(108z-1)(4z+1)^2(10z-1)^2", "discr_factors": "-172800, (z+1/4)^2, (z-1/10)^2, z-1/108", "dm_basis": null, "q": "0 1 -22 -81 -316 -83913 -3983850 -187254163 -9590018392 -513687167424", "yuk": "1 12 1034 62652 4065482 272539012 18461182994 1260374587652 86603176648906 5980726295341824", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/4","im":"0","approx_re":"-0.25","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"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","im":"0","approx_re":"0.00925925925926","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/10","im":"0","approx_re":"0.1","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":["5/6","1","1","7/6"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[49*X^4, -98-588*X-1407*X^2-1638*X^3-273*X^4, -15512-68656*X-114922*X^2-86444*X^3-24146*X^4, 128128+323904*X+133572*X^2-193704*X^3-115692*X^4, 428896+1641536*X+2163720*X^2+1018160*X^3+37336*X^4, 16224*(X+1)^2*(6*X+5)*(6*X+7)]", "text": "This is operator \"5.81\" from ...", "degz": 5, "h3": "84", "sol": "1 2 30 308 5950 96252 1973244 38397480 823170366 17515057340", "n_discr_factors": "4", "c3": "-108", "operator": "4 5 0 0 0 0 49 -98 -588 -1407 -1638 -273 -15512 -68656 -114922 -86444 -24146 128128 323904 133572 -193704 -115692 428896 1641536 2163720 1018160 37336 567840 2303808 3488160 2336256 584064", "new_number": "5.81", "id": 295, "operator_tex": "7^{2} \\theta^4-7 x\\left(39\\theta^4+234\\theta^3+201\\theta^2+84\\theta+14\\right)-2 x^{2}\\left(12073\\theta^4+43222\\theta^3+57461\\theta^2+34328\\theta+7756\\right)-2^{2} x^{3}\\left(28923\\theta^4+48426\\theta^3-33393\\theta^2-80976\\theta-32032\\right)+2^{3} 13 x^{4}\\left(359\\theta^4+9790\\theta^3+20805\\theta^2+15784\\theta+4124\\right)+2^{5} 3 13^{2} x^{5}(\\theta+1)^2(6\\theta+5)(6\\theta+7)", "superseek": "5/7 48/7", "discriminant": "5 49 -273 -24146 -115692 37336 584064", "aesz": "312", "n_sing_complex": "0", "inst_int": "", "c2h": "108", "hash": "767262575f8b1458839c1e9a8beacf0a", "dim_h": "23", "inst": " 5/7 239/28 48/7 4451/14 5888/7 177307/7 124308 21455179/7 21345700 3274689851/7", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "5", "n_sing": "5", "laurent": null, "discriminant_tex": "(16z+1)(2z-1)(27z-1)(7+26z)^2", "discr_factors": "584064, z-1/2, z-1/27, (7/26+z)^2, z+1/16", "dm_basis": null, "q": "0 1 -4 -40 248 -1488 -864 -90452 -266448 -17360416", "yuk": "1 5/7 69 1301/7 142915/7 736005/7 38300091/7 298463513/7 1569313509 108927108401/7", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-7/26","im":"0","approx_re":"-0.269230769231","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/16","im":"0","approx_re":"-0.0625","approx_im":"0.0","exponents":["0","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":"1/27","im":"0","approx_re":"0.037037037037","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/2","im":"0","approx_re":"0.5","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["5/6","1","1","7/6"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, 30+174*X+417*X^2+486*X^3+297*X^4, 18792+83916*X+153090*X^2+119556*X^3+21870*X^4, 3551688+13060764*X+17583480*X^2+6456024*X^3-1023516*X^4, 214465968+599465448*X+424208016*X^2-365631408*X^3-157306536*X^4, 561201696-8851681296*X-30075309072*X^2-31223221632*X^3-1377495072*X^4, -146014477632-494520730848*X-450440888544*X^2+99179645184*X^3+247949112960*X^4, 148769467776*(X+1)^2*(6*X+5)*(6*X+7)]", "text": "This is operator \"7.12\" from ...", "degz": 7, "h3": null, "sol": "1 -30 1458 -89076 6250050 -480036780 39218993100 -3347929943640 295182414161730 -26673786677257500", "n_discr_factors": "4", "c3": null, "operator": "4 7 0 0 0 0 1 30 174 417 486 297 18792 83916 153090 119556 21870 3551688 13060764 17583480 6456024 -1023516 214465968 599465448 424208016 -365631408 -157306536 561201696 -8851681296 -30075309072 -31223221632 -1377495072 -146014477632 -494520730848 -450440888544 99179645184 247949112960 5206931372160 21125264424192 31985435571840 21422803359744 5355700839936", "new_number": "7.12", "id": 434, "operator_tex": "\\theta^4+3 x\\left(99\\theta^4+162\\theta^3+139\\theta^2+58\\theta+10\\right)+2 3^{4} x^{2}\\left(135\\theta^4+738\\theta^3+945\\theta^2+518\\theta+116\\right)-2^{2} 3^{7} x^{3}\\left(117\\theta^4-738\\theta^3-2010\\theta^2-1493\\theta-406\\right)-2^{3} 3^{10} x^{4}\\left(333\\theta^4+774\\theta^3-898\\theta^2-1269\\theta-454\\right)-2^{4} 3^{13} x^{5}\\left(54\\theta^4+1224\\theta^3+1179\\theta^2+347\\theta-22\\right)+2^{5} 3^{16} x^{6}\\left(180\\theta^4+72\\theta^3-327\\theta^2-359\\theta-106\\right)+2^{7} 3^{19} x^{7}(\\theta+1)^2(6\\theta+5)(6\\theta+7)", "superseek": "-21 -7941", "discriminant": "7 1 297 21870 -1023516 -157306536 -1377495072 247949112960 5355700839936", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "0841b278bc566a089b643bbe2460fe8b", "dim_h": null, "inst": " -21 -399 -7941 -986355/4 -8179455 -306790500 -12151571244 -1015240586355/2 -21975670374150 -980756726018385", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "5", "n_sing": "5", "laurent": null, "discriminant_tex": "(27z+1)(54z+1)(54z-1)^2(108z+1)^3", "discr_factors": "5355700839936, (z+1/108)^3, z+1/54, (z-1/54)^2, z+1/27", "dm_basis": null, "q": "0 1 54 2565 125676 6195150 310093758 15690242988 802117062504 41365068279705", "yuk": "1 -21 -3213 -214428 -15784893 -1022431896 -66266965620 -4167988936713 -259901605891773 -16020263702969778", "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":"-1/54","im":"0","approx_re":"-0.0185185185185","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/108","im":"0","approx_re":"-0.00925925925926","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":"1/54","im":"0","approx_re":"0.0185185185185","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":["5/6","1","1","7/6"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, 333*X^4+558*X^3+507*X^2+228*X+42, 45522*X^4+124740*X^3+170694*X^2+109728*X+27144, 3682908*X^4+10655064*X^3+15441192*X^2+11696076*X+3267216, 215883144*X^4+584821296*X^3+604346832*X^2+326737800*X+67546224, 9183300480*X^4+25407131328*X^3+26736442416*X^2+8585252208*X-178879104, 275499014400*X^4+694257516288*X^3+918176992992*X^2+529417272672*X+111866204736, 5950778711040*X^4+15472024648704*X^3+17455617552384*X^2+9670015405440*X+2165422253184, 1785233613312*(X+1)^2*(6*X+5)*(6*X+7)]", "text": "This is operator \"8.71\" from ...", "degz": 8, "h3": null, "sol": "1 -42 2682 -200436 16310250 -1400554692 124801086564 -11424723191784 1067465530790442 -101347492002866340", "n_discr_factors": "4", "c3": null, "operator": "4 8 0 0 0 0 1 42 228 507 558 333 27144 109728 170694 124740 45522 3267216 11696076 15441192 10655064 3682908 67546224 326737800 604346832 584821296 215883144 -178879104 8585252208 26736442416 25407131328 9183300480 111866204736 529417272672 918176992992 694257516288 275499014400 2165422253184 9670015405440 17455617552384 15472024648704 5950778711040 62483176465920 253503173090304 383825226862080 257073640316928 64268410079232", "new_number": "8.71", "id": 520, "operator_tex": "\\theta^4+3 x\\left(111\\theta^4+186\\theta^3+169\\theta^2+76\\theta+14\\right)+2 3^{2} x^{2}\\left(2529\\theta^4+6930\\theta^3+9483\\theta^2+6096\\theta+1508\\right)+2^{2} 3^{4} x^{3}\\left(11367\\theta^4+32886\\theta^3+47658\\theta^2+36099\\theta+10084\\right)+2^{3} 3^{6} x^{4}\\left(37017\\theta^4+100278\\theta^3+103626\\theta^2+56025\\theta+11582\\right)+2^{4} 3^{9} x^{5}\\left(29160\\theta^4+80676\\theta^3+84897\\theta^2+27261\\theta-568\\right)+2^{5} 3^{12} x^{6}\\left(16200\\theta^4+40824\\theta^3+53991\\theta^2+31131\\theta+6578\\right)+2^{7} 3^{17} x^{7}\\left(360\\theta^4+936\\theta^3+1056\\theta^2+585\\theta+131\\right)+2^{9} 3^{20} x^{8}(\\theta+1)^2(6\\theta+5)(6\\theta+7)", "superseek": "-15 14044/3", "discriminant": "8 1 333 45522 3682908 215883144 9183300480 275499014400 5950778711040 64268410079232", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "de469dbb89801caa07ec523e3b0e4772", "dim_h": null, "inst": " -15 39 14044/3 213069/2 462576 -197919131/3 -2791067118 -39839884932 4406567889568/3 105941893357989", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "6", "laurent": null, "discriminant_tex": "(27z+1)(54z+1)(108z+1)^2(1944z^2+18z+1)^2", "discr_factors": "64268410079232, z+1/54, (z+1/108)^2, (z^2+1/108*z+1/1944)^2, z+1/27", "dm_basis": null, "q": "0 1 60 2736 102260 3082884 68872896 803338082 -12653698056 -754545356694", "yuk": "1 -15 297 126381 6818505 57821985 -14250050739 -957336021489 -20398014266679 1070795997291405", "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":"-1/54","im":"0","approx_re":"-0.0185185185185","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/108","im":"0","approx_re":"-0.00925925925926","approx_im":"0.0","exponents":["0","1/6","5/6","1"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/216","im":"-1/216*23^(1/2)","approx_re":"-0.00462962962963","approx_im":"-0.022203","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/216","im":"1/216*23^(1/2)","approx_re":"-0.00462962962963","approx_im":"0.022203","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["5/6","1","1","7/6"],"monodromy":[],"monodromy_dm":[]}]}]}