{"count": 2, "status":"OK", "data":[{"pols": "[X^4, -12*(3*X+1)*(3*X+2)*(8*X^2+8*X+3), 2304*(3*X+1)*(3*X+2)*(3*X+4)*(3*X+5)]", "text": "", "degz": 2, "h3": null, "sol": "1 72 14760 3951360 1198751400 391176257472 133901221918464 47411323466158080 17215474536402765480 6374166727892926248000", "n_discr_factors": "1", "c3": null, "operator": "4 2 0 0 0 0 1 -72 -516 -1380 -1728 -864 92160 539136 1016064 746496 186624", "new_number": "2.18", "id": 9, "operator_tex": "\\theta^4-2^{2} 3 x(3\\theta+1)(3\\theta+2)(8\\theta^2+8\\theta+3)+2^{8} 3^{2} x^{2}(3\\theta+1)(3\\theta+2)(3\\theta+4)(3\\theta+5)", "superseek": "36 8076", "discriminant": "2 1 -864 186624", "aesz": "110", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "5060b638cac581d5f0f9dd7f40d90e6c", "dim_h": null, "inst": " 36 -144 8076 -57996 6960672 -12143856 10041274764 98875091268 19944340019760 482716439753472", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "A_{n}=\\dbinom{2n}{n}\\dbinom{3n}{n}\\sum_{k=0}^{n}4^{n-k}\\dbinom{2k}{k}^2\\dbinom{2n-2k}{n-k}", "n_sing_rational": "2", "n_sing": "2", "laurent": null, "discriminant_tex": "(432z-1)^2", "discr_factors": "186624, (z-1/432)^2", "dm_basis": ["3/2-24*lambda", "0", "1/2", "1", "1", "0", "-1", "0", "6", "-12", "0", "0", "12", "0", "0", "0"], "q": "0 1 -228 39006 -5773648 784430637 -100616704632 12381829002386 -1476632870320704 171818463840250374", "yuk": "1 36 -1116 218088 -3712860 870084036 -2622855960 3444157244088 50624043016356 14539423874623128", "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","-12","1","0","0","0","1","1"]},{"re":"1/432","im":"0","approx_re":"0.00231481481481","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":["-1/2+24*lambda","12*lambda","-1/8+2*lambda","-.1127229e-2","-1","1/2","-1/12","-1/8-2*lambda","-6","0","1/2","-12*lambda","-12","-6","-1","-1/2-24*lambda"],"monodromy_dm":["-3","1","0","-1","-1","1","1/4","0","0","0","1","0","3","0","-3/4","1"]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/3","2/3","4/3","5/3"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -460*X^4-992*X^3-646*X^2-150*X-12, -12*(6*X+5)*(1866*X^3+5341*X^2+4760*X+1084), -24336*(6*X+5)*(6*X+11)*(3*X+1)*(3*X+7)]", "text": "This is operator \"3.22\" from ...", "degz": 3, "h3": "7", "sol": "1 12 5760 1664544 681014880 301062617856 144001775971872 72412616435777280 37833106664287101024 20355129524032767235200", "n_discr_factors": "2", "c3": "-36", "operator": "4 3 0 0 0 0 1 -12 -150 -646 -992 -460 -65040 -363648 -663180 -496512 -134352 -9369360 -48477312 -74249136 -42052608 -7884864", "new_number": "3.22", "id": 81, "operator_tex": "\\theta^4-2 x\\left(230\\theta^4+496\\theta^3+323\\theta^2+75\\theta+6\\right)-2^{2} 3 x^{2}(6\\theta+5)(1866\\theta^3+5341\\theta^2+4760\\theta+1084)-2^{4} 3^{2} 13^{2} x^{3}(6\\theta+5)(6\\theta+11)(3\\theta+1)(3\\theta+7)", "superseek": "166 1016100", "discriminant": "3 1 -460 -134352 -7884864", "aesz": "392", "n_sing_complex": "0", "inst_int": "", "c2h": "34", "hash": "5862be5cc4d3ec1686e6b9a6ec08f7e7", "dim_h": "4", "inst": " 166 8076 1016100 189329096 43879949258 11641348524744 23747294280862622/7 1058922686246549520 348334789616884018134 119425507449141363609236", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "-(676z-1)(1+108z)^2", "discr_factors": "-7884864, z-1/676, (1/108+z)^2", "dm_basis": ["-36*lambda", "31/12", "1", "1", "-17/12", "-7/2", "-1", "0", "0", "7", "0", "0", "-7", "0", "0", "0"], "q": "0 1 -102 -13479 -20644 -146630244 -70456962006 -21654760723062 -7360483846618200 -2679511387128156252", "yuk": "1 166 64774 27434866 12117126918 5484993657416 2514531308844178 1163617419762268644 542168415370350481158 253936061630708476654552", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/108","im":"0","approx_re":"-0.00925925925926","approx_im":"0.0","exponents":["0","1/3","1","4/3"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/676","im":"0","approx_re":"0.00147928994083","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":["1/3","5/6","11/6","7/3"],"monodromy":[],"monodromy_dm":[]}]}]}