{"count": 3, "status":"OK", "data":[{"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": "[25*X^4, -4995*X^4-13230*X^3-11715*X^2-5100*X-900, 186624*X^4+1463832*X^3+2585844*X^2+1717200*X+415440, 8188128*X^4+9447840*X^3-45585828*X^2-61279740*X-20664720, -136048896*X^4-1292464512*X^3-2424315744*X^2-1707224688*X-415285056, -11337408*(3*X+2)*(3*X+4)*(6*X+5)*(6*X+7)]", "text": "This is operator \"5.65\" from ...", "degz": 5, "h3": null, "sol": "1 36 2196 161280 13032900 1115973936 99328836096 9088750224576 849053816612100 80605604422371600", "n_discr_factors": "3", "c3": null, "operator": "4 5 0 0 0 0 25 -900 -5100 -11715 -13230 -4995 415440 1717200 2585844 1463832 186624 -20664720 -61279740 -45585828 9447840 8188128 -415285056 -1707224688 -2424315744 -1292464512 -136048896 -3174474240 -13672914048 -21529737792 -14693280768 -3673320192", "new_number": "5.65", "id": 277, "operator_tex": "5^{2} \\theta^4-3 5 x\\left(333\\theta^4+882\\theta^3+781\\theta^2+340\\theta+60\\right)+2^{2} 3^{2} x^{2}\\left(5184\\theta^4+40662\\theta^3+71829\\theta^2+47700\\theta+11540\\right)+2^{2} 3^{5} x^{3}\\left(8424\\theta^4+9720\\theta^3-46899\\theta^2-63045\\theta-21260\\right)-2^{4} 3^{8} x^{4}\\left(1296\\theta^4+12312\\theta^3+23094\\theta^2+16263\\theta+3956\\right)-2^{6} 3^{11} x^{5}(3\\theta+2)(3\\theta+4)(6\\theta+5)(6\\theta+7)", "superseek": "63/5 14016/5", "discriminant": "5 25 -4995 186624 8188128 -136048896 -3673320192", "aesz": "273", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "cf49bc645cb0404ce7bc9ca1d41d3152", "dim_h": null, "inst": " 63/5 -747/4 14016/5 -55584 6071598/5 -29280858 3789513648/5 -103572330372/5 2946639866493/5 -172753730633619/10", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "-(-1+27z)(108z+5)^2(108z-1)^2", "discr_factors": "-3673320192, (z+5/108)^2, (z-1/108)^2, -1/27+z", "dm_basis": null, "q": "0 1 -60 2916 -132140 5799354 -248943456 10506838262 -437619310824 18036699887331", "yuk": "1 63/5 -7407/5 75699 -17794287/5 758949813/5 -6324591123 1299803181327/5 -53029050944751/5 2148100463051892/5", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-5/108","im":"0","approx_re":"-0.0462962962963","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","im":"0","approx_re":"0.00925925925926","approx_im":"0.0","exponents":["0","1/6","5/6","1"],"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":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["2/3","5/6","7/6","4/3"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -3*X*(-2-11*X-18*X^2+27*X^3), -1152-4968*X-8532*X^2-8640*X^3-702*X^4, 225504*X^4+746496*X^3+1139832*X^2+719280*X+168480, -10295424-39937536*X-55281528*X^2-30932928*X^3-6648480*X^4, 39366000*X^4+439009632*X^3+1087866288*X^2+925468416*X+261740160, -1698091776-4500950976*X-2127653568*X^2+2040733440*X^3+878649120*X^4, -7958860416*X^4-59997563136*X^3-108090847872*X^2-75030966144*X-18139852800, -204073344*(3*X+2)*(3*X+4)*(6*X+5)*(6*X+7)]", "text": "This is operator \"8.21\" from ...", "degz": 8, "h3": null, "sol": "1 0 72 -1440 48600 -1814400 68090400 -2794176000 116735434200 -5045645404800", "n_discr_factors": "4", "c3": null, "operator": "4 8 0 0 0 0 1 0 6 33 54 -81 -1152 -4968 -8532 -8640 -702 168480 719280 1139832 746496 225504 -10295424 -39937536 -55281528 -30932928 -6648480 261740160 925468416 1087866288 439009632 39366000 -1698091776 -4500950976 -2127653568 2040733440 878649120 -18139852800 -75030966144 -108090847872 -59997563136 -7958860416 -57140536320 -246112452864 -387535280256 -264479053824 -66119763456", "new_number": "8.21", "id": 465, "operator_tex": "\\theta^4-3 x\\theta(-2-11\\theta-18\\theta^2+27\\theta^3)-2 3^{2} x^{2}\\left(39\\theta^4+480\\theta^3+474\\theta^2+276\\theta+64\\right)+2^{3} 3^{4} x^{3}\\left(348\\theta^4+1152\\theta^3+1759\\theta^2+1110\\theta+260\\right)-2^{3} 3^{5} x^{4}\\left(3420\\theta^4+15912\\theta^3+28437\\theta^2+20544\\theta+5296\\right)+2^{4} 3^{7} x^{5}\\left(1125\\theta^4+12546\\theta^3+31089\\theta^2+26448\\theta+7480\\right)+2^{5} 3^{9} x^{6}\\left(1395\\theta^4+3240\\theta^3-3378\\theta^2-7146\\theta-2696\\right)-2^{7} 3^{11} x^{7}\\left(351\\theta^4+2646\\theta^3+4767\\theta^2+3309\\theta+800\\right)-2^{7} 3^{13} x^{8}(3\\theta+2)(3\\theta+4)(6\\theta+5)(6\\theta+7)", "superseek": "-9 -3145/3", "discriminant": "8 1 -81 -702 225504 -6648480 39366000 878649120 -7958860416 -66119763456", "aesz": "251", "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "dd2b60d18804c72129ba319fc8b50023", "dim_h": null, "inst": " -9 -27/4 -3145/3 -20907/4 -327348 -24524575/12 -161490492 -861171237 -101393558686 -315735960033", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "7", "laurent": null, "discriminant_tex": "-(54z+1)(27z-1)(432z^2-36z+1)(-1+36z+324z^2)^2", "discr_factors": "-66119763456, z^2-1/12*z+1/432, z+1/54, z-1/27, (-1/324+1/9*z+z^2)^2", "dm_basis": null, "q": "0 1 6 -117 1652 16017 625266 2524463 500650824 624838131", "yuk": "1 -9 -63 -28314 -334575 -40918509 -441470718 -55391238765 -440920007919 -73915904310408", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/18-1/18*2^(1/2)","im":"0","approx_re":"-0.134123","approx_im":"0.0","exponents":["0","1","3","4"],"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":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/18+1/18*2^(1/2)","im":"0","approx_re":"0.023012","approx_im":"0.0","exponents":["0","1","3","4"],"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":"1/24","im":"-1/72*3^(1/2)","approx_re":"0.0416666666667","approx_im":"-0.024056","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/24","im":"1/72*3^(1/2)","approx_re":"0.0416666666667","approx_im":"0.024056","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":[]}]}]}