{"count": 4, "status":"OK", "data":[{"pols": "[X^4, -4*(2*X+1)^2*(11*X^2+11*X+3), -16*(2*X+1)^2*(2*X+3)^2]", "text": "Hadamard product $A\\ast b$\n\nA-incarnation: X(1,2,2) in G(2,5)", "degz": 2, "h3": "20", "sol": "1 12 684 58800 6129900 714610512 89611475184 11829354533568 1622229744177900 229106666659213200", "n_discr_factors": "1", "c3": "-120", "operator": "4 2 0 0 0 0 1 -12 -92 -268 -352 -176 -144 -768 -1408 -1024 -256", "new_number": "2.5", "id": 55, "operator_tex": "\\theta^4-2^{2} x(2\\theta+1)^2(11\\theta^2+11\\theta+3)-2^{4} x^{2}(2\\theta+1)^2(2\\theta+3)^2", "superseek": "20 8220", "discriminant": "2 1 -176 -256", "aesz": "25", "n_sing_complex": "0", "inst_int": "", "c2h": "68", "hash": "93279abcbeeade30c29508de7784e582", "dim_h": "9", "inst": " 20 277 8220 352994 18651536 1126617687 74667602300 5297682428242 395996602125000 30845267770384740", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "A_{n}=\\dbinom{2n}{n}^2\\sum_{k=0}^{n}\\dbinom{n}{k}^2\\dbinom{n+k}{n}", "n_sing_rational": "1", "n_sing": "3", "laurent": null, "discriminant_tex": "1-176z-256z^2", "discr_factors": "-256, -1/256+11/16*z+z^2", "dm_basis": ["-120*lambda", "37/6", "1", "1", "-17/6", "-10", "-1", "0", "0", "20", "0", "0", "-20", "0", "0", "0"], "q": "0 1 -44 486 -11184 -390527 -28173000 -2131044622 -168764951744 -13946975993196", "yuk": "1 20 2236 221960 22593852 2331442020 243349644568 25610987588920 2712413425853756 288681522949346960", "gv2": null, "gv0": "400 5540 164400 7059880 373030720 22532353740 1493352046000 105953648564840 7919932042500000 616905355407694800", "gv1": "0 0 0 1537 882496 214941640 37001766880 5388182343297 715201587952800 89732472170109248 10853707837547302400 1280463172653164106787 148416320937642960627520 16982448267723313699121648 1924600069649944296621370400 216520674412430601976469772097 24221257332526265388744193723840 2697512504678650518375575027208704 299363543965147494551366272473595840", "spectrum":[{"re":"-11/32-5/32*5^(1/2)","im":"0","approx_re":"-0.693136","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["16/3+480*lambda","-13/6-240*lambda","299/360+92*lambda","-.167088493-52*lambda","46/3","-20/3","529/180","-299/360-92*lambda","40","-20","26/3","-13/6-240*lambda","80","-40","46/3","-10/3-480*lambda"],"monodromy_dm":["-9","-60","-6","-4","5","31","3","2","-60","-360","-35","-24","40","240","24","17"]},{"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","20","1","0","0","0","1","1"]},{"re":"-11/32+5/32*5^(1/2)","im":"0","approx_re":"0.005636","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["1+120*lambda","0","17*lambda",".16908432e-1","17/6","1","289/720","-17*lambda","0","0","1","0","20","0","17/6","1-120*lambda"],"monodromy_dm":["1","-9","-1","-1","0","1","0","0","0","0","1","0","0","0","0","1"]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/2","1/2","3/2","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[25*X^4, 2960*X^4+7840*X^3+6820*X^2+2900*X+500, 65536*X^4+514048*X^3+912256*X^2+606720*X+146800, -1703936*X^4-1966080*X^3+9461760*X^2+12779520*X+4348160, -16777216*X^4-159383552*X^3-299368448*X^2-211812352*X-52002816, 1048576*(4*X+5)^2*(4*X+3)^2]", "text": "This is operator \"5.50\" from ...", "degz": 5, "h3": null, "sol": "1 -20 684 -28496 1317100 -64879920 3335900400 -176877737280 9598031287020 -530304938966000", "n_discr_factors": "3", "c3": null, "operator": "4 5 0 0 0 0 25 500 2900 6820 7840 2960 146800 606720 912256 514048 65536 4348160 12779520 9461760 -1966080 -1703936 -52002816 -211812352 -299368448 -159383552 -16777216 235929600 1006632960 1577058304 1073741824 268435456", "new_number": "5.50", "id": 261, "operator_tex": "5^{2} \\theta^4+2^{2} 5 x\\left(148\\theta^4+392\\theta^3+341\\theta^2+145\\theta+25\\right)+2^{4} x^{2}\\left(4096\\theta^4+32128\\theta^3+57016\\theta^2+37920\\theta+9175\\right)-2^{8} x^{3}\\left(6656\\theta^4+7680\\theta^3-36960\\theta^2-49920\\theta-16985\\right)-2^{15} x^{4}\\left(512\\theta^4+4864\\theta^3+9136\\theta^2+6464\\theta+1587\\right)+2^{20} x^{5}(4\\theta+5)^2(4\\theta+3)^2", "superseek": "-44/5 -596", "discriminant": "5 25 2960 65536 -1703936 -16777216 268435456", "aesz": "249", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "85592af20bbb190e37428e945664c2f3", "dim_h": null, "inst": " -44/5 -277/5 -596 -7236 -502128/5 -7562487/5 -122037828/5 -2070073956/5 -36496996024/5 -662519510308/5", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "(1+16z)(64z+1)^2(64z-5)^2", "discr_factors": "268435456, (z+1/64)^2, 1/16+z, (z-5/64)^2", "dm_basis": null, "q": "0 1 36 1062 29328 785409 20599320 531771570 13558154304 342274846740", "yuk": "1 -44/5 -452 -80504/5 -463556 -62766044/5 -1633579912/5 -41858975048/5 -1059880183252/5 -5321262036400", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/16","im":"0","approx_re":"-0.0625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/64","im":"0","approx_re":"-0.015625","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":"5/64","im":"0","approx_re":"0.078125","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":["3/4","3/4","5/4","5/4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[25*X^4, -720*X^4+12720*X^3+9760*X^2+3400*X+500, -340816*X^4-434368*X^3+1390224*X^2+1009760*X+239600, 5000960*X^4-75344640*X^3-32364800*X^2+13923840*X+9153280, 663428096*X^4-1805109248*X^3-5426021376*X^2-4251594752*X-1072927744, 342196224*(4*X+5)*(3*X+2)*(3*X+4)*(4*X+3)]", "text": "This is operator \"5.52\" from ...", "degz": 5, "h3": null, "sol": "1 -20 684 -32240 1969900 -140379120 10801148400 -869448127680 72451088433900 -6214905203078000", "n_discr_factors": "3", "c3": null, "operator": "4 5 0 0 0 0 25 500 3400 9760 12720 -720 239600 1009760 1390224 -434368 -340816 9153280 13923840 -32364800 -75344640 5000960 -1072927744 -4251594752 -5426021376 -1805109248 663428096 41063546880 179995213824 287102631936 197105025024 49276256256", "new_number": "5.52", "id": 263, "operator_tex": "5^{2} \\theta^4-2^{2} 5 x\\left(36\\theta^4-636\\theta^3-488\\theta^2-170\\theta-25\\right)-2^{4} x^{2}\\left(21301\\theta^4+27148\\theta^3-86889\\theta^2-63110\\theta-14975\\right)+2^{8} 5 x^{3}\\left(3907\\theta^4-58863\\theta^3-25285\\theta^2+10878\\theta+7151\\right)+2^{10} 59 x^{4}\\left(10981\\theta^4-29878\\theta^3-89811\\theta^2-70372\\theta-17759\\right)+2^{15} 3 59^{2} x^{5}(4\\theta+5)(3\\theta+2)(3\\theta+4)(4\\theta+3)", "superseek": "-232/5 -122168/5", "discriminant": "5 25 -720 -340816 5000960 663428096 49276256256", "aesz": "252", "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "cae57e93a6afb98313f62899d1f75e2e", "dim_h": null, "inst": " -232/5 -7499/10 -122168/5 -4503443/5 -200467616/5 -19296162041/10 -502767574136/5 -54775768970643/10 -310784583462160 -90689567211431134/5", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "(108z+1)(2048z^2+52z+1)(-5+472z)^2", "discr_factors": "49276256256, z^2+13/512*z+1/2048, z+1/108, (-5/472+z)^2", "dm_basis": null, "q": "0 1 56 3214 201824 12937265 844771024 55869094922 3739124425088 252649090928836", "yuk": "1 -232/5 -30228/5 -3298768/5 -57650116 -25058452232/5 -2083988829192/5 -34489855585776 -14022597144735188/5 -1132809806722871968/5", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-13/1024","im":"-7/1024*7^(1/2)","approx_re":"-0.0126953125","approx_im":"-0.018086","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-13/1024","im":"7/1024*7^(1/2)","approx_re":"-0.0126953125","approx_im":"0.018086","exponents":["0","1","1","2"],"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":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"5/472","im":"0","approx_re":"0.010593220339","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":["2/3","3/4","5/4","4/3"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[25*X^4, -79920*X^4-211680*X^3-197340*X^2-91500*X-17100, 47775744*X^4+374740992*X^3+652800384*X^2+431516160*X+104315760, 33538572288*X^4+38698352640*X^3-188170739712*X^2-249389383680*X-81864794880, -8916100448256*X^4-84702954258432*X^3-158229824274432*X^2-109841404133376*X-25973259337728, -185752092672*(12*X+7)*(12*X+11)*(12*X+13)*(12*X+17)]", "text": "This is operator \"5.64\" from ...", "degz": 5, "h3": null, "sol": "1 684 761004 985011120 1373164693740 2000308394975184 2999737945992631536 4592165354561372296896 7138856745753215194714860 11230855067389469877341467920", "n_discr_factors": "3", "c3": null, "operator": "4 5 0 0 0 0 25 -17100 -91500 -197340 -211680 -79920 104315760 431516160 652800384 374740992 47775744 -81864794880 -249389383680 -188170739712 38698352640 33538572288 -25973259337728 -109841404133376 -158229824274432 -84702954258432 -8916100448256 -3160943360999424 -14016109904658432 -22415076526915584 -15407021574586368 -3851755393646592", "new_number": "5.64", "id": 276, "operator_tex": "5^{2} \\theta^4-2^{2} 3 5 x\\left(1332\\theta^4+3528\\theta^3+3289\\theta^2+1525\\theta+285\\right)+2^{4} 3^{2} x^{2}\\left(331776\\theta^4+2602368\\theta^3+4533336\\theta^2+2996640\\theta+724415\\right)+2^{8} 3^{5} x^{3}\\left(539136\\theta^4+622080\\theta^3-3024864\\theta^2-4008960\\theta-1315985\\right)-2^{15} 3^{8} x^{4}\\left(41472\\theta^4+393984\\theta^3+735984\\theta^2+510912\\theta+120811\\right)-2^{20} 3^{11} x^{5}(12\\theta+7)(12\\theta+11)(12\\theta+13)(12\\theta+17)", "superseek": "468/5 11885484", "discriminant": "5 25 -79920 47775744 33538572288 -8916100448256 -3851755393646592", "aesz": "272", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "467bb784f4bd6e978748e98f6ea4a573", "dim_h": null, "inst": " 468/5 -315477/5 11885484 -14354122356/5 808514230608 -1258871905551543/5 444331666288762812/5 -169531638476468437764/5 13514603472770718331560 -5523207855313637518334676", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "-(-1+432z)(1728z+5)^2(1728z-1)^2", "discr_factors": "-3851755393646592, (z-1/1728)^2, -1/432+z, (z+5/1728)^2", "dm_basis": null, "q": "0 1 -924 669222 -445396592 285409255425 -178021670149224 108757332969381554 -65384540320368271296 38818215719959795717140", "yuk": "1 468/5 -2523348/5 1604540808/5 -918666354132/5 505321394130468/5 -271916329997116296/5 152405761537045644984/5 -17360039780174101297860 49260729658249269923077008/5", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-5/1728","im":"0","approx_re":"-0.00289351851852","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":"1/1728","im":"0","approx_re":"0.000578703703704","approx_im":"0.0","exponents":["0","-1/6","1","7/6"],"monodromy":[],"monodromy_dm":[]},{"re":"1/432","im":"0","approx_re":"0.00231481481481","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":["7/12","11/12","13/12","17/12"],"monodromy":[],"monodromy_dm":[]}]}]}