{"count": 5, "status":"OK", "data":[{"pols": "[X^4, 280*X^4+776*X^3+580*X^2+192*X+24, -6768*X^4+41184*X^3+101328*X^2+57216*X+9888, -41472*X^4+746496*X^3+5446656*X^2+4499712*X+928512, -82944*(3*X+1)*(3*X+2)*(42*X^2+258*X+223), 11943936*(3*X+1)*(3*X+2)*(3*X+4)*(3*X+5)]", "text": "This is operator \"5.101\" from ...", "degz": 5, "h3": "16", "sol": "1 -24 2160 -309120 54608400 -10824637824 2311144932096 -519918637455360 121579349447247120 -29291011307905776000", "n_discr_factors": "2", "c3": "-114", "operator": "4 5 0 0 0 0 1 24 192 580 776 280 9888 57216 101328 41184 -6768 928512 4499712 5446656 746496 -41472 -36993024 -209267712 -366031872 -223948800 -31352832 477757440 2794881024 5267275776 3869835264 967458816", "new_number": "5.101", "id": 183, "operator_tex": "\\theta^4+2^{2} x\\left(70\\theta^4+194\\theta^3+145\\theta^2+48\\theta+6\\right)-2^{4} 3 x^{2}\\left(141\\theta^4-858\\theta^3-2111\\theta^2-1192\\theta-206\\right)-2^{8} 3^{2} x^{3}\\left(18\\theta^4-324\\theta^3-2364\\theta^2-1953\\theta-403\\right)-2^{10} 3^{4} x^{4}(3\\theta+1)(3\\theta+2)(42\\theta^2+258\\theta+223)+2^{14} 3^{6} x^{5}(3\\theta+1)(3\\theta+2)(3\\theta+4)(3\\theta+5)", "superseek": "-52 -44772", "discriminant": "5 1 280 -6768 -41472 -31352832 967458816", "aesz": "348\n", "n_sing_complex": "2", "inst_int": "", "c2h": "40", "hash": "8759f016475d17d0fc88f4b98a374d3f", "dim_h": "6", "inst": " -52 461/2 -44772 3546761/2 -178670332 32517931641/2 -1653102364436 366947580015355/2 -21196688793453600 5118794506088892927/2", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "5", "laurent": null, "discriminant_tex": "(746496z^3+17280z^2+352z+1)(-1+36z)^2", "discr_factors": "967458816, z^3+5/216*z^2+11/23328*z+1/746496, (-1/36+z)^2", "dm_basis": null, "q": "0 1 96 5712 419072 25422576 2011912704 92161450240 10068708114432 59645210003352", "yuk": "1 -52 1792 -1208896 113498144 -22333791552 3511935410176 -567014111001600 93938580597429024 -15452386130428883296", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/2592*(1502+342*57^(1/2))^(1/3)+41/648/(1502+342*57^(1/2))^(1/3)-5/648","im":"-1/16*3^(1/2)*(1/162*(1502+342*57^(1/2))^(1/3)+82/81/(1502+342*57^(1/2))^(1/3))","approx_re":"-0.009925","approx_im":"-0.017537","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/2592*(1502+342*57^(1/2))^(1/3)+41/648/(1502+342*57^(1/2))^(1/3)-5/648","im":"1/16*3^(1/2)*(1/162*(1502+342*57^(1/2))^(1/3)+82/81/(1502+342*57^(1/2))^(1/3))","approx_re":"-0.009925","approx_im":"0.017537","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/1296*(1502+342*57^(1/2))^(1/3)-41/324/(1502+342*57^(1/2))^(1/3)-5/648","im":"0","approx_re":"-0.003299","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":"1/36","im":"0","approx_re":"0.0277777777778","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":["1/3","2/3","4/3","5/3"],"monodromy":[],"monodromy_dm":[]}]}, {"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": "[25*X^4, -8080*X^4-21920*X^3-15460*X^2-4500*X-500, -1070336*X^4-2198528*X^3-1617536*X^2-844800*X-186000, -3840*(2*X+1)*(5672*X^3+9500*X^2+8422*X+2689), -294912*(2*X+1)*(1208*X^3+2892*X^2+2842*X+969), -28311552*(2*X+1)*(6*X+5)*(6*X+7)*(2*X+3)]", "text": "This is operator \"5.37\" from ...", "degz": 5, "h3": "10", "sol": "1 20 2988 618320 156299500 44234633520 13477733161200 4325154502743360 1442412961677873900 495512411116338902000", "n_discr_factors": "3", "c3": "-32", "operator": "4 5 0 0 0 0 25 -500 -4500 -15460 -21920 -8080 -186000 -844800 -1617536 -2198528 -1070336 -10325760 -52992000 -101160960 -94740480 -43560960 -285769728 -1409679360 -2529165312 -2062024704 -712507392 -2972712960 -14042529792 -23328718848 -16307453952 -4076863488", "new_number": "5.37", "id": 246, "operator_tex": "5^{2} \\theta^4-2^{2} 5 x\\left(404\\theta^4+1096\\theta^3+773\\theta^2+225\\theta+25\\right)-2^{4} x^{2}\\left(66896\\theta^4+137408\\theta^3+101096\\theta^2+52800\\theta+11625\\right)-2^{8} 3 5 x^{3}(2\\theta+1)(5672\\theta^3+9500\\theta^2+8422\\theta+2689)-2^{15} 3^{2} x^{4}(2\\theta+1)(1208\\theta^3+2892\\theta^2+2842\\theta+969)-2^{20} 3^{3} x^{5}(2\\theta+1)(6\\theta+5)(6\\theta+7)(2\\theta+3)", "superseek": "492/5 872164/5", "discriminant": "5 25 -8080 -1070336 -43560960 -712507392 -4076863488", "aesz": "221", "n_sing_complex": "0", "inst_int": "", "c2h": "40", "hash": "b7ce7a734c057660ce3d6341a7572078", "dim_h": "5", "inst": " 492/5 10376/5 872164/5 91316176/5 12181916784/5 1850294589528/5 61762450157748 55187365344835504/5 10392704764770167864/5 2039663615626409751968/5", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "-(-1+432z)(16z+1)^2(192z+5)^2", "discr_factors": "-4076863488, (z+5/192)^2, -1/432+z, (z+1/16)^2", "dm_basis": null, "q": "0 1 -100 1574 -102288 -20602367 -2977974168 -588048101710 -116875168258112 -24320631644865004", "yuk": "1 492/5 16700 4709784 5844318764/5 1522739598492/5 399663654969976/5 105922602020538312/5 28255931062400096812/5 7576281773517475921776/5", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/16","im":"0","approx_re":"-0.0625","approx_im":"0.0","exponents":["0","1/4","3/4","1"],"monodromy":[],"monodromy_dm":[]},{"re":"-5/192","im":"0","approx_re":"-0.0260416666667","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":"1/432","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":["1/2","5/6","7/6","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, 288*X^4-768*X^3-528*X^2-144*X-16, -44032*X^4-262144*X^3-64000*X^2-23040*X-5120, -18644992*X^4-33423360*X^3-30851072*X^2-14401536*X-2572288, -3670016*(2*X+1)*(186*X^3+375*X^2+317*X+100), -6576668672*(2*X+1)*(X+1)^2*(2*X+3)]", "text": "This is operator \"5.91\" from ...", "degz": 5, "h3": "16", "sol": "1 16 1488 183040 27611920 4644009216 840155264256 159984411045888 31647762945461520 6447385477360072960", "n_discr_factors": "4", "c3": "68", "operator": "4 5 0 0 0 0 1 -16 -144 -528 -768 288 -5120 -23040 -64000 -262144 -44032 -2572288 -14401536 -30851072 -33423360 -18644992 -367001600 -1897398272 -3703046144 -3435134976 -1365245952 -19730006016 -92073361408 -151263379456 -105226698752 -26306674688", "new_number": "5.91", "id": 306, "operator_tex": "\\theta^4+2^{4} x\\left(18\\theta^4-48\\theta^3-33\\theta^2-9\\theta-1\\right)-2^{9} x^{2}\\left(86\\theta^4+512\\theta^3+125\\theta^2+45\\theta+10\\right)-2^{14} x^{3}\\left(1138\\theta^4+2040\\theta^3+1883\\theta^2+879\\theta+157\\right)-2^{19} 7 x^{4}(2\\theta+1)(186\\theta^3+375\\theta^2+317\\theta+100)-2^{27} 7^{2} x^{5}(2\\theta+1)(\\theta+1)^2(2\\theta+3)", "superseek": "112 186800", "discriminant": "5 1 288 -44032 -18644992 -1365245952 -26306674688", "aesz": "331", "n_sing_complex": "0", "inst_int": "", "c2h": "40", "hash": "a30093d8c1ab2f66122cef8935b79efb", "dim_h": "6", "inst": " 112 -2242 186800 -11675813 1250599376 -109453519578 12996262564592 -1335165142501083 167689997418831488 -18917764674198834614", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "5", "n_sing": "5", "laurent": null, "discriminant_tex": "-(32z+1)(256z-1)(64z+1)(1+224z)^2", "discr_factors": "-26306674688, z-1/256, (1/224+z)^2, z+1/64, z+1/32", "dm_basis": null, "q": "0 1 -80 4224 -353280 32901040 -3889583616 442866134016 -57164706250752 7080975365853336", "yuk": "1 112 -17824 5043712 -747269856 156324922112 -23641955203072 4457718059655168 -683604553707824352 122246008118333198464", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/32","im":"0","approx_re":"-0.03125","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","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/224","im":"0","approx_re":"-0.00446428571429","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":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/2","1","1","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -16*(4*X+1)^2*(4*X+3)^2]", "text": "A-incarnation: X(4,4) in P^5(1,1,1,1,2,2)", "degz": 1, "h3": "4", "sol": "1 144 176400 341510400 811620810000 2167695039654144 6243202569208340736 18955829541661309440000 59844220278907077932490000 194686629373739404697796000000", "n_discr_factors": null, "c3": "-144", "operator": "4 1 0 0 0 0 1 -144 -1536 -5632 -8192 -4096", "new_number": "1.10", "id": 550, "operator_tex": "\\theta^4-2^{4} x(4\\theta+1)^2(4\\theta+3)^2", "superseek": "928 170869536", "discriminant": null, "aesz": "10", "n_sing_complex": null, "inst_int": null, "c2h": "40", "hash": "51f8135aba94201bd0bbe9b2287a92d5", "dim_h": "4", "inst": " 928 245616 170869536 174999877936 221984814405088 322488630778883760 514506002990767360672 879128852394829927420720 1582934400557814144743504640 2970390071697000630704094306000", "cleanlist": "True", "n_sing_real": null, "sol_explicit": null, "n_sing_rational": null, "n_sing": null, "laurent": null, "discriminant_tex": null, "discr_factors": null, "dm_basis": null, "q": "0 1 -960 213600 -160471040 -136981068240 -248123397445632 -445533681536171520 -850742163409138483200 -1692715844493003550786920", "yuk": "1 928 1965856 4613478400 11199994153760 27748101800636928 69657544252854335488 176475559025833204711424 450113972426164122833562400 1153959178006646511522628360960", "gv2": null, "gv0": null, "gv1": null}]}