{"count": 5, "status":"OK", "data":[{"pols": "[X^4, -320*X^4-832*X^3-640*X^2-224*X-32, 13312*X^4+120832*X^3+212992*X^2+125952*X+26368, 917504*X^4+786432*X^3-6291456*X^2-6881280*X-1900544, -262144*(2*X+1)*(56*X^3+468*X^2+646*X+249), -16777216*(2*X+1)*(4*X+3)*(4*X+5)*(2*X+3)]", "text": "This is operator \"5.14\" from ...", "degz": 5, "h3": "16", "sol": "1 32 2448 273920 38525200 6236600832 1103685859584 207343941083136 40648001362459920 8227704225727500800", "n_discr_factors": "3", "c3": "40", "operator": "4 5 0 0 0 0 1 -32 -224 -640 -832 -320 26368 125952 212992 120832 13312 -1900544 -6881280 -6291456 786432 917504 -65273856 -299892736 -461373440 -260046848 -29360128 -754974720 -3623878656 -6106906624 -4294967296 -1073741824", "new_number": "5.14", "id": 221, "operator_tex": "\\theta^4-2^{5} x\\left(10\\theta^4+26\\theta^3+20\\theta^2+7\\theta+1\\right)+2^{8} x^{2}\\left(52\\theta^4+472\\theta^3+832\\theta^2+492\\theta+103\\right)+2^{16} x^{3}\\left(14\\theta^4+12\\theta^3-96\\theta^2-105\\theta-29\\right)-2^{18} x^{4}(2\\theta+1)(56\\theta^3+468\\theta^2+646\\theta+249)-2^{24} x^{5}(2\\theta+1)(4\\theta+3)(4\\theta+5)(2\\theta+3)", "superseek": "64 23360", "discriminant": "5 1 -320 13312 917504 -29360128 -1073741824", "aesz": "116", "n_sing_complex": "0", "inst_int": "", "c2h": "40", "hash": "0b366ad8c78b6697205c5a7fff270f5b", "dim_h": "6", "inst": " 64 12 23360 654490 53956288 3558145052 286700496448 24007522298674 2129883087617536 196912935173735108", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "-(-1+256z)(32z+1)^2(64z-1)^2", "discr_factors": "-1073741824, -1/256+z, (z+1/32)^2, (z-1/64)^2", "dm_basis": null, "q": "0 1 -96 6816 -493568 32166192 -2164343808 130369476096 -8668096954368 469785092535960", "yuk": "1 64 160 630784 41887520 6744536064 768559962112 98338270281728 12291851458808608 1552684770873814528", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/32","im":"0","approx_re":"-0.03125","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":"1/256","im":"0","approx_re":"0.00390625","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":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/2","3/4","5/4","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[49*X^4, -14*X*(46*X^3+52*X^2+33*X+7), -25088-106680*X-170532*X^2-115392*X^3-29328*X^4, -561568-1780464*X-1927728*X^2-716160*X^3-45760*X^4, -1561088-3332608*X-379392*X^2+3031040*X^3+1141760*X^4, 3112960+17940480*X+32292864*X^2+21626880*X^3+2850816*X^4, 3670016+11010048*X+4718592*X^2-12582912*X^3-11534336*X^4, -33554432*(X+1)^4]", "text": "This is operator \"7.1\" from ...", "degz": 7, "h3": "56", "sol": "1 0 32 288 7776 144000 3552800 82320000 2087125600 52959513600", "n_discr_factors": "4", "c3": "-64", "operator": "4 7 0 0 0 0 49 0 -98 -462 -728 -644 -25088 -106680 -170532 -115392 -29328 -561568 -1780464 -1927728 -716160 -45760 -1561088 -3332608 -379392 3031040 1141760 3112960 17940480 32292864 21626880 2850816 3670016 11010048 4718592 -12582912 -11534336 -33554432 -134217728 -201326592 -134217728 -33554432", "new_number": "7.1", "id": 442, "operator_tex": "7^{2} \\theta^4-2 7 x\\theta(46\\theta^3+52\\theta^2+33\\theta+7)-2^{2} x^{2}\\left(7332\\theta^4+28848\\theta^3+42633\\theta^2+26670\\theta+6272\\right)-2^{4} x^{3}\\left(2860\\theta^4+44760\\theta^3+120483\\theta^2+111279\\theta+35098\\right)+2^{9} x^{4}\\left(2230\\theta^4+5920\\theta^3-741\\theta^2-6509\\theta-3049\\right)+2^{14} x^{5}\\left(174\\theta^4+1320\\theta^3+1971\\theta^2+1095\\theta+190\\right)-2^{19} x^{6}\\left(22\\theta^4+24\\theta^3-9\\theta^2-21\\theta-7\\right)-2^{25} x^{7}\\left((\\theta+1)^4\\right)", "superseek": "10/7 508/7", "discriminant": "7 49 -644 -29328 -45760 1141760 2850816 -11534336 -33554432", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": "80", "hash": "08ab3cb496250adfa30bc3e24ac63c4f", "dim_h": "16", "inst": " 10/7 100/7 508/7 808 59910/7 855864/7 12382494/7 200115472/7 3327848026/7 58373507100/7", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "5", "n_sing": "5", "laurent": null, "discriminant_tex": "-(16z+1)(32z-1)(32z-7)^2(4z+1)^3", "discr_factors": "-33554432, (z+1/4)^3, z-1/32, z+1/16, (z-7/32)^2", "dm_basis": null, "q": "0 1 -2 -71 -236 -580 -16018 -462550 -8253320 -151220156", "yuk": "1 10/7 810/7 13726/7 362794/7 7488760/7 184881150/7 4247195452/7 102459484458/7 2426001224680/7", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/4","im":"0","approx_re":"-0.25","approx_im":"0.0","exponents":["0","1/2","3/2","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/16","im":"0","approx_re":"-0.0625","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":"1/32","im":"0","approx_re":"0.03125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"7/32","im":"0","approx_re":"0.21875","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":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -1152*X^4-192*X^3-256*X^2-160*X-32, 534528*X^4+276480*X^3+333056*X^2+146944*X+23808, -128712704*X^4-130744320*X^3-139182080*X^2-63774720*X-11313152, 17298358272*X^4+27097300992*X^3+28266725376*X^2+13632798720*X+2556952576, -1295603728384*X^4-2650129039360*X^3-2791930068992*X^2-1360447668224*X-255869321216, 50633369452544*X^4+118541097369600*X^3+120502823682048*X^2+54619099103232*X+9540196106240, -869713697570816*X^4-2247401767174144*X^3-2503313098539008*X^2-1379612214951936*X-307863255777280, 3448068464705536*(X+1)^4]", "text": "This is operator \"8.44\" from ...", "degz": 8, "h3": null, "sol": "1 32 2096 172544 15870736 1559276032 160054348544 16950443548672 1837683501894928 202898418734838272", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 1 -32 -160 -256 -192 -1152 23808 146944 333056 276480 534528 -11313152 -63774720 -139182080 -130744320 -128712704 2556952576 13632798720 28266725376 27097300992 17298358272 -255869321216 -1360447668224 -2791930068992 -2650129039360 -1295603728384 9540196106240 54619099103232 120502823682048 118541097369600 50633369452544 -307863255777280 -1379612214951936 -2503313098539008 -2247401767174144 -869713697570816 3448068464705536 13792273858822144 20688410788233216 13792273858822144 3448068464705536", "new_number": "8.44", "id": 490, "operator_tex": "\\theta^4-2^{5} x\\left(36\\theta^4+6\\theta^3+8\\theta^2+5\\theta+1\\right)+2^{8} x^{2}\\left(2088\\theta^4+1080\\theta^3+1301\\theta^2+574\\theta+93\\right)-2^{13} x^{3}\\left(15712\\theta^4+15960\\theta^3+16990\\theta^2+7785\\theta+1381\\right)+2^{18} x^{4}\\left(65988\\theta^4+103368\\theta^3+107829\\theta^2+52005\\theta+9754\\right)-2^{24} x^{5}\\left(77224\\theta^4+157960\\theta^3+166412\\theta^2+81089\\theta+15251\\right)+2^{30} x^{6}\\left(47156\\theta^4+110400\\theta^3+112227\\theta^2+50868\\theta+8885\\right)-2^{38} 7 x^{7}\\left(452\\theta^4+1168\\theta^3+1301\\theta^2+717\\theta+160\\right)+2^{46} 7^{2} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "-64 -131904", "discriminant": "8 1 -1152 534528 -128712704 17298358272 -1295603728384 50633369452544 -869713697570816 3448068464705536", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "2d570a3dc1cbc5b6596272f33b48fc98", "dim_h": null, "inst": " -64 -2084 -131904 -10745878 -1015115456 -105793050452 -11816074995264 -1389140511529039 -169882887296828928 -21436003799740611660", "cleanlist": "True", "n_sing_real": "6", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "6", "laurent": null, "discriminant_tex": "(1-192z+1024z^2)(128z-1)^2(14336z^2-352z+1)^2", "discr_factors": "3448068464705536, (z^2-11/448*z+1/14336)^2, 1/1024-3/16*z+z^2, (z-1/128)^2", "dm_basis": null, "q": "0 1 -32 640 28672 3475888 440300544 57936946176 7820948340736 1078701695219864", "yuk": "1 -64 -16736 -3561472 -687752928 -126889432064 -22851302475776 -4052913723375616 -711239942590620896 -123844624839391849984", "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":"11/896-1/896*65^(1/2)","im":"0","approx_re":"0.003279","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"3/32-1/16*2^(1/2)","im":"0","approx_re":"0.005362","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/128","im":"0","approx_re":"0.0078125","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"11/896+1/896*65^(1/2)","im":"0","approx_re":"0.021275","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"3/32+1/16*2^(1/2)","im":"0","approx_re":"0.182138","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","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -352*X^4-1472*X^3-1024*X^2-288*X-32, -156928*X^4-228352*X^3+7424*X^2+16896*X+1792, -10772480*X^4-8011776*X^3-18374656*X^2-8749056*X-1466368, 248774656*X^4-782761984*X^3-865599488*X^2-411303936*X-82051072, 3523215360*X^4+13136560128*X^3-9361686528*X^2-10821304320*X-2961178624, -47580184576*X^4+95026151424*X^3+78047608832*X^2+4831838208*X-8791261184, -204010946560*X^4+107374182400*X^3+762356695040*X^2+708669603840*X+204010946560, -1717986918400*(X+1)^4]", "text": "This is operator \"8.46\" from ...", "degz": 8, "h3": null, "sol": "1 32 6224 1859072 679223056 278574418432 123145098554624 57372286737276928 27788219971629427984 13867811101033655562752", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 1 -32 -288 -1024 -1472 -352 1792 16896 7424 -228352 -156928 -1466368 -8749056 -18374656 -8011776 -10772480 -82051072 -411303936 -865599488 -782761984 248774656 -2961178624 -10821304320 -9361686528 13136560128 3523215360 -8791261184 4831838208 78047608832 95026151424 -47580184576 204010946560 708669603840 762356695040 107374182400 -204010946560 -1717986918400 -6871947673600 -10307921510400 -6871947673600 -1717986918400", "new_number": "8.46", "id": 492, "operator_tex": "\\theta^4-2^{5} x\\left(11\\theta^4+46\\theta^3+32\\theta^2+9\\theta+1\\right)-2^{8} x^{2}\\left(613\\theta^4+892\\theta^3-29\\theta^2-66\\theta-7\\right)-2^{13} x^{3}\\left(1315\\theta^4+978\\theta^3+2243\\theta^2+1068\\theta+179\\right)+2^{18} x^{4}\\left(949\\theta^4-2986\\theta^3-3302\\theta^2-1569\\theta-313\\right)+2^{23} x^{5}\\left(420\\theta^4+1566\\theta^3-1116\\theta^2-1290\\theta-353\\right)-2^{26} x^{6}\\left(709\\theta^4-1416\\theta^3-1163\\theta^2-72\\theta+131\\right)-2^{31} 5 x^{7}\\left(19\\theta^4-10\\theta^3-71\\theta^2-66\\theta-19\\right)-2^{36} 5^{2} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "192 616896", "discriminant": "8 1 -352 -156928 -10772480 248774656 3523215360 -47580184576 -204010946560 -1717986918400", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "e38642e59fc2f9e3117437fcdbfe450e", "dim_h": null, "inst": " 192 3108 616896 73692781 15330708544 3169207515476 757547413779136 190303924221409951 50710465810985333248 14050572909374827223116", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "7", "laurent": null, "discriminant_tex": "-(16z+1)(16384z^3+2560z^2+624z-1)(-1-128z+2560z^2)^2", "discr_factors": "-1717986918400, z^3+5/32*z^2+39/1024*z-1/16384, (-1/2560-1/20*z+z^2)^2, z+1/16", "dm_basis": null, "q": "0 1 -160 9024 -1007616 -9990480 -21114321920 -3882553055232 -1270290167169024 -355955892124246888", "yuk": "1 192 25056 16656384 4716363040 1916338568192 684548840024064 259838762926243840 97435609206078257952 36967929576208324594176", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/384*(6236+708*177^(1/2))^(1/3)+23/24/(6236+708*177^(1/2))^(1/3)-5/96","im":"-1/32*3^(1/2)*(1/12*(6236+708*177^(1/2))^(1/3)+92/3/(6236+708*177^(1/2))^(1/3))","approx_re":"-0.078921","approx_im":"-0.179189","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/384*(6236+708*177^(1/2))^(1/3)+23/24/(6236+708*177^(1/2))^(1/3)-5/96","im":"1/32*3^(1/2)*(1/12*(6236+708*177^(1/2))^(1/3)+92/3/(6236+708*177^(1/2))^(1/3))","approx_re":"-0.078921","approx_im":"0.179189","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/16","im":"0","approx_re":"-0.0625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/40-1/160*26^(1/2)","im":"0","approx_re":"-0.006869","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*(6236+708*177^(1/2))^(1/3)-23/12/(6236+708*177^(1/2))^(1/3)-5/96","im":"0","approx_re":"0.001592","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/40+1/160*26^(1/2)","im":"0","approx_re":"0.056869","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":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -256*X^4-512*X^3-448*X^2-192*X-32, 256*(2*X+1)*(4*X+3)*(4*X+5)*(2*X+3)]", "text": "This is operator is equivalent to [2.33]. Transformation:.....", "degz": 2, "h3": null, "sol": "1 32 2160 181760 17021200 1698181632 176677611264 18937576120320 2075622689471760 231465995770380800", "n_discr_factors": "1", "c3": null, "operator": "4 2 0 0 0 0 1 -32 -192 -448 -512 -256 11520 55296 93184 65536 16384", "new_number": "2.71", "id": 614, "operator_tex": "\\theta^4-2^{5} x(2\\theta+1)^2(2\\theta^2+2\\theta+1)+2^{8} x^{2}(2\\theta+1)(4\\theta+3)(4\\theta+5)(2\\theta+3)", "superseek": "0 0", "discriminant": "2 1 -256 16384", "aesz": null, "n_sing_complex": "0", "inst_int": null, "c2h": null, "hash": "757b011780c5986bd45a5bf434c76c28", "dim_h": null, "inst": " 0 -20 0 -865 0 -67460 0 -6821070 0 -800369820", "cleanlist": "False", "n_sing_real": "2", "sol_explicit": null, "n_sing_rational": "2", "n_sing": "2", "laurent": null, "discriminant_tex": "(-1+128z)^2", "discr_factors": "16384, (-1/128+z)^2", "dm_basis": null, "q": "0 1 -64 2912 -110592 3772720 -119642112 3598125568 -103922663424 2907171436184", "yuk": "1 0 -160 0 -55520 0 -14571520 0 -3492443360 0", "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":"1/128","im":"0","approx_re":"0.0078125","approx_im":"0.0","exponents":["0","1/4","3/4","1"],"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":[]}]}]}