{"count": 3, "status":"OK", "data":[{"pols": "[X^4, -128*X^4-256*X^3-252*X^2-124*X-24, 256*(4*X+3)*(X+1)^2*(4*X+5)]", "text": "This is operator \"2.63\" from ...", "degz": 2, "h3": null, "sol": "1 24 936 43008 2145960 112521024 6098593536 338463166464 19121128195752 1095276775623360", "n_discr_factors": "1", "c3": null, "operator": "4 2 0 0 0 0 1 -24 -124 -252 -256 -128 3840 15872 24320 16384 4096", "new_number": "2.63", "id": 59, "operator_tex": "\\theta^4-2^{2} x\\left(32\\theta^4+64\\theta^3+63\\theta^2+31\\theta+6\\right)+2^{8} x^{2}(4\\theta+3)(\\theta+1)^2(4\\theta+5)", "superseek": "-4 -44", "discriminant": "2 1 -128 4096", "aesz": "84", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "908b978c0c447d3643c3018c40e7f5d1", "dim_h": null, "inst": " -4 -11 -44 -156 -288 3207 55764 578820 4717904 29814248", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "2", "laurent": null, "discriminant_tex": "(64z-1)^2", "discr_factors": "4096, (z-1/64)^2", "dm_basis": ["-96*lambda", "-6", "1", "1", "-2", "24", "-1", "0", "0", "-48", "0", "0", "48", "0", "0", "0"], "q": "0 1 -28 478 -6064 64813 -610696 5253394 -42301888 320357638", "yuk": "1 -4 -92 -1192 -10076 -36004 691432 19127048 296345764 3439350824", "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","-48","1","0","0","0","1","1"]},{"re":"1/64","im":"0","approx_re":"0.015625","approx_im":"0.0","exponents":["0","0","1","1"],"monodromy":["1+96*lambda","1/4","-4*lambda",".5907751e-2","2","1","-1/12","4*lambda","0","6","1","1/4","-48","0","2","1-96*lambda"],"monodromy_dm":["1","4","-1","-1","0","-2","1/8","0","0","-72","4","0","0","60","-5/2","1"]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["3/4","1","1","5/4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, 264*X^4+528*X^3+586*X^2+322*X+70, 100*(X+1)^2*(228*X^2+456*X+335), 40000*(X+1)*(X+2)*(4*X+5)*(4*X+7)]", "text": "This is operator \"3.26\" from ...", "degz": 3, "h3": null, "sol": "1 -70 5650 -484900 43071250 -3910845820 360556161100 -33614244139000 3160609857375250 -299175771274607500", "n_discr_factors": "2", "c3": null, "operator": "4 3 0 0 0 0 1 70 322 586 528 264 33500 112600 147500 91200 22800 2800000 8040000 8440000 3840000 640000", "new_number": "3.26", "id": 88, "operator_tex": "\\theta^4+2 x\\left(132\\theta^4+264\\theta^3+293\\theta^2+161\\theta+35\\right)+2^{2} 5^{2} x^{2}(\\theta+1)^2(228\\theta^2+456\\theta+335)+2^{6} 5^{4} x^{3}(\\theta+1)(\\theta+2)(4\\theta+5)(4\\theta+7)", "superseek": "2 440", "discriminant": "3 1 264 22800 640000", "aesz": "407", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "c46d32ba4b3738ba34fe1e6c16e6f242", "dim_h": null, "inst": " 2 -44 440 -4844 46268 -452800 5683556 -112203980 2492707170 -48960763800", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "(64z+1)(1+100z)^2", "discr_factors": "640000, z+1/64, (1/100+z)^2", "dm_basis": null, "q": "0 1 42 1191 29348 631875 12955494 248209377 4613546472 82700284542", "yuk": "1 2 -350 11882 -310366 5783502 -97793270 1949459710 -57448748126 1817183538812", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/64","im":"0","approx_re":"-0.015625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/100","im":"0","approx_re":"-0.01","approx_im":"0.0","exponents":["0","-1/2","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","5/4","7/4","2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -280*(X+1/2)^4-266*(X+1/2)^2-9, 27888*(X+1)^4+31638*(X+1)^2+3063, -1189120*(X+3/2)^4-1276704*(X+3/2)^2-75906, 21204736*(X+2)^4+11869760*(X+2)^2+941769, -1800*(4*X+9)*(4*X+11)*(4144*(X+5/2)^2+2435), 810000*(4*X+9)*(4*X+11)*(4*X+13)*(4*X+15)]", "text": "This is operator \"6.2\" from ...", "degz": 6, "h3": null, "sol": "1 93 15717/2 1345795/2 473123715/8 42544773243/8 7787361167553/16 722151543940371/16 541102909100896035/128 51071315492859914335/128", "n_discr_factors": "3", "c3": null, "operator": "4 6 0 0 0 0 1 -93 -406 -686 -560 -280 62589 174828 198966 111552 27888 -8968410 -19883232 -17329824 -7134720 -1189120 387696585 726030592 520783424 169637888 21204736 -5049297000 -7772544000 -4538188800 -1193472000 -119347200 15637050000 21617280000 11067840000 2488320000 207360000", "new_number": "6.2", "id": 414, "operator_tex": "\\theta^4-x\\left(280\\theta^4+560\\theta^3+686\\theta^2+406\\theta+93\\right)+3 x^{2}\\left(9296\\theta^4+37184\\theta^3+66322\\theta^2+58276\\theta+20863\\right)-2 x^{3}\\left(594560\\theta^4+3567360\\theta^3+8664912\\theta^2+9941616\\theta+4484205\\right)+x^{4}\\left(21204736\\theta^4+169637888\\theta^3+520783424\\theta^2+726030592\\theta+387696585\\right)-2^{3} 3^{2} 5^{2} x^{5}(4\\theta+9)(4\\theta+11)(4144\\theta^2+20720\\theta+28335)+2^{4} 3^{4} 5^{4} x^{6}(4\\theta+9)(4\\theta+11)(4\\theta+13)(4\\theta+15)", "superseek": "-8 -1552/3", "discriminant": "6 1 -280 27888 -1189120 21204736 -119347200 207360000", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "fd7b14f2d0f2a78723588771a9b1a984", "dim_h": null, "inst": " -8 -44 -1552/3 -8044 -138528 -7377560/3 -46370768 -923702508 -57511308400/3 -409728263024", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "(100z-1)^2(4z-1)^2(36z-1)^2", "discr_factors": "207360000, (z-1/36)^2, (z-1/100)^2, (z-1/4)^2", "dm_basis": null, "q": "0 1 -34 627 -12164 173165 -3028038 42010079 -741949320 9120226173", "yuk": "1 -8 -360 -13976 -515176 -17316008 -531198648 -15905173432 -472936199272 -13975247955176", "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":"1/100","im":"0","approx_re":"0.01","approx_im":"0.0","exponents":["0","-1/2","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/36","im":"0","approx_re":"0.0277777777778","approx_im":"0.0","exponents":["0","-1/2","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/4","im":"0","approx_re":"0.25","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":["9/4","11/4","13/4","15/4"],"monodromy":[],"monodromy_dm":[]}]}]}