{"count": 2, "status":"OK", "data":[{"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, -736*X^4-896*X^3-700*X^2-252*X-36, 166656*X^4+463872*X^3+473472*X^2+204672*X+33840, -4460544*X^4-64364544*X^3-99846144*X^2-49600512*X-9061632, -2448949248*X^4-927203328*X^3+8059944960*X^2+6023282688*X+1332412416, 146087608320*X^4+582312001536*X^3-2463105024*X^2-160271695872*X-49304567808, 11529369944064*X^4-10078006542336*X^3-11015685144576*X^2-1638899122176*X+467820085248, -146767085568*(2*X+1)*(1336*X^3+2772*X^2+2234*X+663), -84537841287168*(2*X+1)*(4*X+3)*(4*X+5)*(2*X+3)]", "text": "This is operator \"8.78\" from ...", "degz": 8, "h3": null, "sol": "1 36 3780 555120 95199300 17826144336 3532282505136 728151261963840 154550955916302660 33549072371964349200", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 1 -36 -252 -700 -896 -736 33840 204672 473472 463872 166656 -9061632 -49600512 -99846144 -64364544 -4460544 1332412416 6023282688 8059944960 -927203328 -2448949248 -49304567808 -160271695872 -2463105024 582312001536 146087608320 467820085248 -1638899122176 -11015685144576 -10078006542336 11529369944064 -97306577731584 -522490824622080 -1062593699512320 -1009757548707840 -392161652637696 -3804202857922560 -18260173718028288 -30771774228529152 -21641687369515008 -5410421842378752", "new_number": "8.78", "id": 527, "operator_tex": "\\theta^4-2^{2} x\\left(184\\theta^4+224\\theta^3+175\\theta^2+63\\theta+9\\right)+2^{4} 3 x^{2}\\left(3472\\theta^4+9664\\theta^3+9864\\theta^2+4264\\theta+705\\right)-2^{8} 3^{2} x^{3}\\left(1936\\theta^4+27936\\theta^3+43336\\theta^2+21528\\theta+3933\\right)-2^{16} 3^{3} x^{4}\\left(1384\\theta^4+524\\theta^3-4555\\theta^2-3404\\theta-753\\right)+2^{19} 3^{4} x^{5}\\left(3440\\theta^4+13712\\theta^3-58\\theta^2-3774\\theta-1161\\right)+2^{22} 3^{5} x^{6}\\left(11312\\theta^4-9888\\theta^3-10808\\theta^2-1608\\theta+459\\right)-2^{26} 3^{7} x^{7}(2\\theta+1)(1336\\theta^3+2772\\theta^2+2234\\theta+663)-2^{32} 3^{9} x^{8}(2\\theta+1)(4\\theta+3)(4\\theta+5)(2\\theta+3)", "superseek": "52 48732", "discriminant": "8 1 -736 166656 -4460544 -2448949248 146087608320 11529369944064 -392161652637696 -5410421842378752", "aesz": null, "n_sing_complex": "3", "inst_int": "", "c2h": null, "hash": "2fb524ad6efb19e0117ae7acbd9f67b9", "dim_h": null, "inst": " 52 -399 48732 -992750 98106208 -13164377111/3 346622274844 -20762287104686 1625571068932672 -109698228104560776", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "7", "laurent": null, "discriminant_tex": "-(256z-1)(110592z^3+6912z^2-288z+1)(-1+96z+13824z^2)^2", "discr_factors": "-5410421842378752, z^3+1/16*z^2-1/384*z+1/110592, z-1/256, (-1/13824+1/144*z+z^2)^2", "dm_basis": null, "q": "0 1 -108 7662 -522608 37550709 -2726199720 203058824274 -15495782553792 1207671346097154", "yuk": "1 52 -3140 1315816 -63539140 12263276052 -947833839368 118891440271544 -10630291061138372 1185041309253233704", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/192*(-36+12*I*3^(1/2))^(1/3)-1/16/(-36+12*I*3^(1/2))^(1/3)-1/48+1/96*I*3^(1/2)*(1/2*(-36+12*I*3^(1/2))^(1/3)-6/(-36+12*I*3^(1/2))^(1/3))","im":"0","approx_re":"-0.091906","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/288-1/288*7^(1/2)","im":"0","approx_re":"-0.012659","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":"-1/192*(-36+12*I*3^(1/2))^(1/3)-1/16/(-36+12*I*3^(1/2))^(1/3)-1/48-1/96*I*3^(1/2)*(1/2*(-36+12*I*3^(1/2))^(1/3)-6/(-36+12*I*3^(1/2))^(1/3))","im":"0","approx_re":"0.00385","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":"-1/288+1/288*7^(1/2)","im":"0","approx_re":"0.005714","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/96*(-36+12*I*3^(1/2))^(1/3)+1/8/(-36+12*I*3^(1/2))^(1/3)-1/48","im":"0","approx_re":"0.025556","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","5/4","3/2"],"monodromy":[],"monodromy_dm":[]}]}]}