{"count": 13, "status":"OK", "data":[{"pols": "[X^4, -4*(2*X+1)^2*(17*X^2+17*X+6), 1152*(2*X+1)^2*(2*X+3)^2]", "text": "Hadamard product $A \\ast g$.", "degz": 2, "h3": "48", "sol": "1 24 1512 124800 11730600 1191081024 127328737536 14125302816768 1611627491845800 187994423786769600", "n_discr_factors": "2", "c3": "-16", "operator": "4 2 0 0 0 0 1 -24 -164 -436 -544 -272 10368 55296 101376 73728 18432", "new_number": "2.24", "id": 16, "operator_tex": "\\theta^4-2^{2} x(2\\theta+1)^2(17\\theta^2+17\\theta+6)+2^{7} 3^{2} x^{2}(2\\theta+1)^2(2\\theta+3)^2", "superseek": "20 1684/3", "discriminant": "2 1 -272 18432", "aesz": "137", "n_sing_complex": "0", "inst_int": "", "c2h": "96", "hash": "198d6c822d6c46225ac2553d60df6539", "dim_h": "16", "inst": " 20 2 1684/3 7602 173472 16800962/3 170592988 5706758282 581797416016/3 6746210337168", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "A_{n}=\\dbinom{2n}{n}^2\\sum_{j,k}^{n}(-1)^{j}8^{n-j}\\dbinom{n}{j}\\dbinom{j}{k}^3", 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{"pols": "[X^4, -2*(2*X+1)^2*(7*X^2+7*X+3), 324*(2*X+1)*(X+1)^2*(2*X+3)]", "text": "Hadamard product $I \\ast \\delta$", "degz": 2, "h3": null, "sol": "1 6 54 60 -19530 -755244 -17954244 -226007496 3762274230 350186668260", "n_discr_factors": "1", "c3": null, "operator": "4 2 0 0 0 0 1 -6 -38 -94 -112 -56 972 4536 7452 5184 1296", "new_number": "2.54", "id": 49, "operator_tex": "\\theta^4-2 x(2\\theta+1)^2(7\\theta^2+7\\theta+3)+2^{2} 3^{4} x^{2}(2\\theta+1)(\\theta+1)^2(2\\theta+3)", "superseek": "2 -104", "discriminant": "2 1 -56 1296", "aesz": "41", "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "a9ddeed4299f59fb9ac9f6f248383b8f", "dim_h": null, "inst": " 2 -7 -104 -588 3300 128384 1336396 -5019718 -393656474 -5619028410", "cleanlist": "True", "n_sing_real": "1", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "3", "laurent": null, "discriminant_tex": "1-56z+1296z^2", "discr_factors": "1296, 1/1296-7/162*z+z^2", "dm_basis": ["1-872284041/1000000000*I", "24", 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{"pols": "[X^4, -2*(2*X+1)^2*(11*X^2+11*X+5), 500*(2*X+1)*(X+1)^2*(2*X+3)]", "text": "Hadamard product $I \\ast \\eta$", "degz": 2, "h3": null, "sol": "1 10 210 5500 159250 4852260 151466700 4755808200 147797471250 4462410452500", "n_discr_factors": "1", "c3": null, "operator": "4 2 0 0 0 0 1 -10 -62 -150 -176 -88 1500 7000 11500 8000 2000", "new_number": "2.57", "id": 52, "operator_tex": "\\theta^4-2 x(2\\theta+1)^2(11\\theta^2+11\\theta+5)+2^{2} 5^{3} x^{2}(2\\theta+1)(\\theta+1)^2(2\\theta+3)", "superseek": "2 -8", "discriminant": "2 1 -88 2000", "aesz": "184\n", "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "ee8bb517b329e58eeb4352dc3cdc3f81", "dim_h": null, "inst": " 2 4 -8 -194 -2820 -30344 -270492 -1455330 8797602 438054080", "cleanlist": "True", "n_sing_real": "1", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "1-88z+2000z^2", "discr_factors": "2000, 1/2000-11/250*z+z^2", "dm_basis": ["5/6-96920449/100000000*I", "85/3", "11/10", "1", "-20/3", "-60", "-1", "0", "10", "100", "0", "0", "-100", "0", "0", "0"], "q": "0 1 -22 359 -4892 61955 -725338 8256993 -90306968 961834366", "yuk": "1 2 34 -214 -12382 -352498 -6554486 -92778754 -745141342 6413451644", "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","100","1","0","0","0","1","1"]},{"re":"11/500","im":"-1/250","approx_re":"0.022","approx_im":"-0.004","exponents":["0","1","1","2"],"monodromy":[".16666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666667+.969204490*I","-1/12+20*lambda","-1/18+40/3*lambda",".2449129e-2+10/3*lambda","20/3","5/3","4/9","1/18-40/3*lambda","-10","-1","1/3","-1/12+20*lambda","100","10","20/3","1.8333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333-.969204490*I"],"monodromy_dm":["1","-29","-1","-1","0","1","0","0","0","0","1","0","0","0","0","1"]},{"re":"11/500","im":"1/250","approx_re":"0.022","approx_im":"0.004","exponents":["0","1","1","2"],"monodromy":["1.8333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333+.969204490*I","-1/12-20*lambda","1/18+40/3*lambda",".2449129e-2-10/3*lambda","20/3","1/3","4/9","-1/18-40/3*lambda","10","-1","5/3","-1/12-20*lambda","100","-10","20/3",".16666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666667-.969204490*I"],"monodromy_dm":["-2","-41","-6/5","-1","3/5","46/5","6/25","1/5","-36","-492","-67/5","-12","138/5","1886/5","276/25","51/5"]},{"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, -35*X^4-70*X^3-63*X^2-28*X-5, (X+1)^2*(259*X^2+518*X+285), -225*(X+1)^2*(X+2)^2]", "text": "", "degz": 3, "h3": "120", "sol": "1 5 45 545 7885 127905 2241225 41467725 798562125 15855173825", "n_discr_factors": "3", "c3": "-80", "operator": "4 3 0 0 0 0 1 -5 -28 -63 -70 -35 285 1088 1580 1036 259 -900 -2700 -2925 -1350 -225", "new_number": "3.1", "id": 79, "operator_tex": "\\theta^4-x\\left(35\\theta^4+70\\theta^3+63\\theta^2+28\\theta+5\\right)+x^{2}(\\theta+1)^2(259\\theta^2+518\\theta+285)-3^{2} 5^{2} x^{3}(\\theta+1)^2(\\theta+2)^2", "superseek": "1 28/3", "discriminant": "3 1 -35 259 -225", "aesz": "34", "n_sing_complex": "0", "inst_int": "", "c2h": "120", "hash": "e5461c5f5ae4d929328f66b8955a31f5", "dim_h": "30", "inst": " 1 2 28/3 52 350 7852/3 21514 189154 5252815/3 16877300", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "-(z-1)(25z-1)(9z-1)", "discr_factors": "-225, z-1/25, z-1/9, z-1", "dm_basis": ["-80*lambda", "25", "1", "1", "-5", "-60", "-1", "0", "0", "120", "0", "0", "-120", "0", "0", "0"], "q": "0 1 -8 36 -168 514 -2760 1676 -83336 -498969", "yuk": "1 1 17 253 3345 43751 565613 7379303 96850193 1276434298", "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":"1/25","im":"0","approx_re":"0.04","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/9","im":"0","approx_re":"0.111111111111","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1","im":"0","approx_re":"1.0","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","2","2"],"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, -321*X^4-258*X^3-258*X^2-129*X-26, 74028*X^3+14112+55150*X+89219*X^2+46467*X^4, -2763616-9502728*X-3994080*X^4-9477984*X^3-13326472*X^2, 225727920*X^4+710675040*X^3+1140231264*X^2+905625648*X+286997664, -34390390656*X^3-18170011648-53733114688*X-61977989504*X^2-8763336000*X^4, 742436462336+2082580125696*X+236647498944*X^4+1113707956224*X^3+2228596709440*X^2, -4388517983232*X^4-24133481490432*X^3-53161009356288*X^2-53101508209152*X-19806669712384, 337377634074624*X^3+335043229626368+862910484692992*X+812804507672576*X^2+53476447629312*X^4, -8978432*(2*X+3)*(21527774*X^3+121431015*X^2+220937755*X+121634574), 314635717705728*(X+1)*(2*X+5)*(2*X+3)*(X+3)]", "text": "This is operator \"10.3\" from ...", "degz": 10, "h3": null, "sol": "1 26 730 21320 638506 19464236 601160176 18749438720 588987246250 18594853518356", "n_discr_factors": "4", "c3": null, "operator": "4 10 0 0 0 0 1 -26 -129 -258 -258 -321 14112 55150 89219 74028 46467 -2763616 -9502728 -13326472 -9477984 -3994080 286997664 905625648 1140231264 710675040 225727920 -18170011648 -53733114688 -61977989504 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x^{6}\\left(3697617171\\theta^4+17401686816\\theta^3+34821823585\\theta^2+32540314464\\theta+11600569724\\right)-2^{9} x^{7}\\left(8571324186\\theta^4+47135706036\\theta^3+103830096399\\theta^2+103713883221\\theta+38684901782\\right)+2^{12} x^{8}\\left(13055773347\\theta^4+82367586444\\theta^3+198438600506\\theta^2+210671505052\\theta+81797663483\\right)-2^{16} 137 x^{9}(2\\theta+3)(21527774\\theta^3+121431015\\theta^2+220937755\\theta+121634574)+2^{20} 3 73^{2} 137^{2} x^{10}(\\theta+1)(2\\theta+5)(2\\theta+3)(\\theta+3)", "superseek": "2 421/9", "discriminant": "10 1 -321 46467 -3994080 225727920 -8763336000 236647498944 -4388517983232 53476447629312 -386571309940736 1258542870822912", "aesz": null, "n_sing_complex": "4", "inst_int": "", "c2h": null, "hash": "5219414e025733d8e128028821370b4b", "dim_h": null, "inst": " 2 -3/2 421/9 -519/2 285 -77417/6 98268 -807195/2 20513023/3 -58806463", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "8", "laurent": null, "discriminant_tex": "(24z-1)(42632z^3-3675z^2+105z-1)(32z-1)^2(1096z^2-64z+1)^2", "discr_factors": "1258542870822912, z-1/24, z^3-3675/42632*z^2+105/42632*z-1/42632, (z^2-8/137*z+1/1096)^2, (z-1/32)^2", "dm_basis": null, "q": "0 1 -25 552 -11513 232073 -4559826 87946426 -1672297261 31438664415", "yuk": "1 2 -10 1265 -16618 35627 -2785759 33705926 -206658538 4984665854", "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":"-105/85264*3^(2/3)-27/85264*3^(1/3)+1225/42632","im":"-1/2*3^(1/2)*(105/42632*3^(2/3)-27/42632*3^(1/3))","approx_re":"0.025716","approx_im":"-0.003646","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-105/85264*3^(2/3)-27/85264*3^(1/3)+1225/42632","im":"1/2*3^(1/2)*(105/42632*3^(2/3)-27/42632*3^(1/3))","approx_re":"0.025716","approx_im":"0.003646","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"4/137","im":"-3/548*2^(1/2)","approx_re":"0.029197080292","approx_im":"-0.007742","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"4/137","im":"3/548*2^(1/2)","approx_re":"0.029197080292","approx_im":"0.007742","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/32","im":"0","approx_re":"0.03125","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"105/42632*3^(2/3)+27/42632*3^(1/3)+1225/42632","im":"0","approx_re":"0.034771","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/24","im":"0","approx_re":"0.0416666666667","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","3/2","5/2","3"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -217*X^4-178*X^3-178*X^2-89*X-18, 6192+24334*X+39795*X^2+33324*X^3+20643*X^4, -1114456*X^4-2668464*X^3-3660480*X^2-2524040*X-713952, 36536560*X^4+116144992*X^3+177648928*X^2+131081136*X+38709792, -697005504*X^4-2793831552*X^3-4599245184*X^2-3383810496*X-951160320, -1056312576+18392859648*X+42714847296*X^2+27747606528*X^3+5402526912*X^4, 61703493120*X^4+287137944576*X^3+857573111808*X^2+1328270068224*X+678366544896, -1748457529344*X^4-10559291424768*X^3-27646051700736*X^2-35365777514496*X-16291812372480, 9300074102784*X^4+69953722122240*X^3+191597765492736*X^2+246689600274432*X+114446794752000, 15479341056*(X+1)*(6759*X^3+40481*X^2+97855*X+79397), -41278242816*(X+1)*(X+2)*(29107*X^2+160713*X+251822), -71328803586048*(X+3)*(X+2)*(X+1)*(17*X+4), 38517553936465920*(X+1)*(X+2)*(X+3)*(X+4)]", "text": "This is operator \"13.6\" from ...", "degz": 13, "h3": null, "sol": "1 18 378 8280 187434 4330908 101527344 2402089344 57112491690 1359099894852", "n_discr_factors": "5", "c3": null, "operator": "4 13 0 0 0 0 1 -18 -89 -178 -178 -217 6192 24334 39795 33324 20643 -713952 -2524040 -3660480 -2668464 -1114456 38709792 131081136 177648928 116144992 36536560 -951160320 -3383810496 -4599245184 -2793831552 -697005504 -1056312576 18392859648 42714847296 27747606528 5402526912 678366544896 1328270068224 857573111808 287137944576 61703493120 -16291812372480 -35365777514496 -27646051700736 -10559291424768 -1748457529344 114446794752000 246689600274432 191597765492736 69953722122240 9300074102784 1229013241823232 2743744160858112 2141350124322816 731244071485440 104624866197504 -20789539324821504 -44452209462607872 -32699592002764800 -10238407678623744 -1201485813645312 -1711891286065152 -10414005323563008 -15050377556656128 -7560853180121088 -1212589660962816 924421294475182080 1925877696823296000 1348114387776307200 385175539364659200 38517553936465920", "new_number": "13.6", "id": 374, "operator_tex": "\\theta^4-x\\left(217\\theta^4+178\\theta^3+178\\theta^2+89\\theta+18\\right)+x^{2}\\left(6192+24334\\theta+39795\\theta^2+33324\\theta^3+20643\\theta^4\\right)-2^{3} x^{3}\\left(139307\\theta^4+333558\\theta^3+457560\\theta^2+315505\\theta+89244\\right)+2^{4} x^{4}\\left(2283535\\theta^4+7259062\\theta^3+11103058\\theta^2+8192571\\theta+2419362\\right)-2^{6} 3 x^{5}\\left(3630237\\theta^4+14551206\\theta^3+23954402\\theta^2+17624013\\theta+4953960\\right)+2^{6} 3^{2} x^{6}\\left(9379387\\theta^4+48172928\\theta^3+74157721\\theta^2+31932048\\theta-1833876\\right)+2^{9} 3^{5} x^{7}\\left(495945\\theta^4+2307886\\theta^3+6892788\\theta^2+10676039\\theta+5452406\\right)-2^{12} 3^{4} x^{8}\\left(5269994\\theta^4+31826568\\theta^3+83327461\\theta^2+106595346\\theta+49104855\\right)+2^{15} 3^{7} x^{9}\\left(129774\\theta^4+976140\\theta^3+2673571\\theta^2+3442327\\theta+1597000\\right)+2^{18} 3^{10} x^{10}(\\theta+1)(6759\\theta^3+40481\\theta^2+97855\\theta+79397)-2^{21} 3^{9} x^{11}(\\theta+1)(\\theta+2)(29107\\theta^2+160713\\theta+251822)-2^{27} 3^{12} x^{12}(\\theta+3)(\\theta+2)(\\theta+1)(17\\theta+4)+2^{29} 3^{15} 5 x^{13}(\\theta+1)(\\theta+2)(\\theta+3)(\\theta+4)", "superseek": "2 421/9", "discriminant": "13 1 -217 20643 -1114456 36536560 -697005504 5402526912 61703493120 -1748457529344 9300074102784 104624866197504 -1201485813645312 -1212589660962816 38517553936465920", "aesz": null, "n_sing_complex": "4", "inst_int": "", "c2h": null, "hash": "679aa37a05aafe03e8d68785d566fcfb", "dim_h": null, "inst": " 2 -3/2 421/9 -519/2 285 -77417/6 98268 -807195/2 20513023/3 -58806463", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "9", "laurent": null, "discriminant_tex": "(16z-1)(19440z^3-2187z^2+81z-1)(24z-1)^2(648z^2-48z+1)^2(8z+1)^3", "discr_factors": "38517553936465920, (z-1/24)^2, z^3-9/80*z^2+1/240*z-1/19440, z-1/16, (z^2-2/27*z+1/648)^2, (z+1/8)^3", "dm_basis": null, "q": "0 1 -17 216 -1969 5945 257742 -7810742 146004187 -2114608545", "yuk": "1 2 -10 1265 -16618 35627 -2785759 33705926 -206658538 4984665854", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/8","im":"0","approx_re":"-0.125","approx_im":"0.0","exponents":["0","1/2","3/2","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":"-1/480*3^(2/3)-1/1440*3^(1/3)+3/80","im":"-1/6*3^(1/2)*(1/80*3^(2/3)-1/240*3^(1/3))","approx_re":"0.032165","approx_im":"-0.005771","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/480*3^(2/3)-1/1440*3^(1/3)+3/80","im":"1/6*3^(1/2)*(1/80*3^(2/3)-1/240*3^(1/3))","approx_re":"0.032165","approx_im":"0.005771","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/27","im":"-1/108*2^(1/2)","approx_re":"0.037037037037","approx_im":"-0.013095","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/27","im":"1/108*2^(1/2)","approx_re":"0.037037037037","approx_im":"0.013095","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/24","im":"0","approx_re":"0.0416666666667","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"1/240*3^(2/3)+1/720*3^(1/3)+3/80","im":"0","approx_re":"0.04817","approx_im":"0.0","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":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","2","3","4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, 16+70*X+118*X^2+96*X^3+144*X^4, 3968+13064*X+18292*X^2+13008*X^3+9108*X^4, 384352+1051584*X+1238000*X^2+762144*X^3+334512*X^4, 20030464+47545600*X+48121088*X^2+25534976*X^3+7957888*X^4, 640318976+1346663424*X+1191714816*X^2+546017280*X^3+129690624*X^4, 13412447232+25299763200*X+19808776192*X^2+7882752000*X^3+1494462464*X^4, 190799466496+325567234048*X+227550035968*X^2+79250423808*X^3+12387532800*X^4, 1877723480064+2918001410048*X+1833709076480*X^2+563327008768*X^3+74335780864*X^4, 12850565480448+18291291586560*X+10397339877376*X^2+2838151299072*X^3+321845723136*X^4, 60646329679872+79470283194368*X+41080682708992*X^2+10030761902080*X^3+991013371904*X^4, 192324546068480+233163624284160*X+110170390659072*X^2+24213146566656*X^3+2107084111872*X^4, 388342050979840+437965868236800*X+190187325882368*X^2+37855841746944*X^3+2928093954048*X^4, 446692704911360+471936375193600*X+189595962572800*X^2+34402688040960*X^3+2383706849280*X^4, 858993459200*(X+4)^4]", "text": "This is operator \"14.10\" from ...", "degz": 14, "h3": null, "sol": "1 -16 196 -2352 29920 -412288 6126592 -96801792 1602339600 -27454700544", "n_discr_factors": "5", "c3": null, "operator": "4 14 0 0 0 0 1 16 70 118 96 144 3968 13064 18292 13008 9108 384352 1051584 1238000 762144 334512 20030464 47545600 48121088 25534976 7957888 640318976 1346663424 1191714816 546017280 129690624 13412447232 25299763200 19808776192 7882752000 1494462464 190799466496 325567234048 227550035968 79250423808 12387532800 1877723480064 2918001410048 1833709076480 563327008768 74335780864 12850565480448 18291291586560 10397339877376 2838151299072 321845723136 60646329679872 79470283194368 41080682708992 10030761902080 991013371904 192324546068480 233163624284160 110170390659072 24213146566656 2107084111872 388342050979840 437965868236800 190187325882368 37855841746944 2928093954048 446692704911360 471936375193600 189595962572800 34402688040960 2383706849280 219902325555200 219902325555200 82463372083200 13743895347200 858993459200", "new_number": "14.10", "id": 378, "operator_tex": "\\theta^4+2 x\\left(72\\theta^4+48\\theta^3+59\\theta^2+35\\theta+8\\right)+2^{2} x^{2}\\left(2277\\theta^4+3252\\theta^3+4573\\theta^2+3266\\theta+992\\right)+2^{4} x^{3}\\left(20907\\theta^4+47634\\theta^3+77375\\theta^2+65724\\theta+24022\\right)+2^{7} x^{4}\\left(62171\\theta^4+199492\\theta^3+375946\\theta^2+371450\\theta+156488\\right)+2^{9} x^{5}\\left(253302\\theta^4+1066440\\theta^3+2327568\\theta^2+2630202\\theta+1250623\\right)+2^{10} x^{6}\\left(1459436\\theta^4+7698000\\theta^3+19344508\\theta^2+24706800\\theta+13098093\\right)+2^{12} x^{7}\\left(3024300\\theta^4+19348248\\theta^3+55554208\\theta^2+79484188\\theta+46581901\\right)+2^{15} x^{8}\\left(2268548\\theta^4+17191376\\theta^3+55960360\\theta^2+89050336\\theta+57303573\\right)+2^{18} x^{9}\\left(1227744\\theta^4+10826688\\theta^3+39662704\\theta^2+69775740\\theta+49021017\\right)+2^{20} x^{10}\\left(945104\\theta^4+9566080\\theta^3+39177592\\theta^2+75788768\\theta+57836847\\right)+2^{22} x^{11}\\left(502368\\theta^4+5772864\\theta^3+26266668\\theta^2+55590540\\theta+45853745\\right)+2^{25} x^{12}\\left(87264\\theta^4+1128192\\theta^3+5668024\\theta^2+13052400\\theta+11573495\\right)+2^{30} 5 x^{13}\\left(444\\theta^4+6408\\theta^3+35315\\theta^2+87905\\theta+83203\\right)+2^{35} 5^{2} x^{14}\\left((\\theta+4)^4\\right)", "superseek": "2 38", "discriminant": "14 1 144 9108 334512 7957888 129690624 1494462464 12387532800 74335780864 321845723136 991013371904 2107084111872 2928093954048 2383706849280 858993459200", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "364dddcd3359111a8e01be8efc1de60c", "dim_h": null, "inst": " 2 -29/4 38 -2077/8 2034 -69631/4 158858 -12172903/8 15129336 -619853933/4", "cleanlist": "True", "n_sing_real": "8", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "8", "laurent": null, "discriminant_tex": "(4z+1)(2z+1)^2(64z^2+24z+1)^2(160z^2+32z+1)^2(8z+1)^3", "discr_factors": "858993459200, z+1/4, (z+1/8)^3, (z^2+3/8*z+1/64)^2, (z^2+1/5*z+1/160)^2, (z+1/2)^2", "dm_basis": null, "q": "0 1 6 22 96 190 1472 -3540 55296 -451314", "yuk": "1 2 -56 1028 -16672 254252 -3759104 54488296 -779082464 11029286972", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/2","im":"0","approx_re":"-0.5","approx_im":"0.0","exponents":["0","1","-2","3"],"monodromy":[],"monodromy_dm":[]},{"re":"-3/16-1/16*5^(1/2)","im":"0","approx_re":"-0.327254","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/4","im":"0","approx_re":"-0.25","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/10-1/40*6^(1/2)","im":"0","approx_re":"-0.161237","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/8","im":"0","approx_re":"-0.125","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"-3/16+1/16*5^(1/2)","im":"0","approx_re":"-0.047746","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/10+1/40*6^(1/2)","im":"0","approx_re":"-0.038763","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":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["4","4","4","4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, 12+54*X+94*X^2+80*X^3+146*X^4, 2456+9092*X+14064*X^2+10896*X^3+9396*X^4, 210848+676592*X+920344*X^2+642432*X^3+352728*X^4, 9914944+28603392*X+34693728*X^2+21707072*X^3+8626912*X^4, 286847488+760763904*X+836176384*X^2+469761024*X^3+145606400*X^4, 5430845440+13443704832*X+13582102528*X^2+6899736576*X^3+1753843712*X^4, 69713803264+163008135168*X+153273556992*X^2+71104528384*X^3+15376457728*X^4, 619062042624+1381508808704*X+1222573686784*X^2+523627331584*X^3+99110846464*X^4, 3835533262848+8246965305344*X+6940439085056*X^2+2775432822784*X^3+470517284864*X^4, 16544582598656+34586228686848*X+27958274162688*X^2+10557532930048*X^3+1634704818176*X^4, 49013967552512+100486178930688*X+78794027171840*X^2+28418456420352*X^3+4089110855680*X^4, 96980135051264+196496062414848*X+150874785579008*X^2+52568789090304*X^3+7142262177792*X^4, 121818627178496+245231895183360*X+185897458860032*X^2+63264868270080*X^3+8239894757376*X^4, 87756919275520+175803748843520*X+132317204971520*X^2+44409961840640*X^3+5626407157760*X^4, 1717986918400*(X+2)^4]", "text": "This is operator \"15.2\" from ...", "degz": 15, "h3": null, "sol": "1 -12 136 -1632 21296 -302016 4597120 -73944576 1239638800 -21432549312", "n_discr_factors": "5", "c3": null, "operator": "4 15 0 0 0 0 1 12 54 94 80 146 2456 9092 14064 10896 9396 210848 676592 920344 642432 352728 9914944 28603392 34693728 21707072 8626912 286847488 760763904 836176384 469761024 145606400 5430845440 13443704832 13582102528 6899736576 1753843712 69713803264 163008135168 153273556992 71104528384 15376457728 619062042624 1381508808704 1222573686784 523627331584 99110846464 3835533262848 8246965305344 6940439085056 2775432822784 470517284864 16544582598656 34586228686848 27958274162688 10557532930048 1634704818176 49013967552512 100486178930688 78794027171840 28418456420352 4089110855680 96980135051264 196496062414848 150874785579008 52568789090304 7142262177792 121818627178496 245231895183360 185897458860032 63264868270080 8239894757376 87756919275520 175803748843520 132317204971520 44409961840640 5626407157760 27487790694400 54975581388800 41231686041600 13743895347200 1717986918400", "new_number": "15.2", "id": 390, "operator_tex": "\\theta^4+2 x\\left(73\\theta^4+40\\theta^3+47\\theta^2+27\\theta+6\\right)+2^{2} x^{2}\\left(2349\\theta^4+2724\\theta^3+3516\\theta^2+2273\\theta+614\\right)+2^{3} x^{3}\\left(44091\\theta^4+80304\\theta^3+115043\\theta^2+84574\\theta+26356\\right)+2^{5} x^{4}\\left(269591\\theta^4+678346\\theta^3+1084179\\theta^2+893856\\theta+309842\\right)+2^{8} x^{5}\\left(568775\\theta^4+1835004\\theta^3+3266314\\theta^2+2971734\\theta+1120498\\right)+2^{11} x^{6}\\left(856369\\theta^4+3369012\\theta^3+6631886\\theta^2+6564309\\theta+2651780\\right)+2^{11} x^{7}\\left(7508036\\theta^4+34719008\\theta^3+74840604\\theta^2+79593816\\theta+34039943\\right)+2^{13} x^{8}\\left(12098492\\theta^4+63919352\\theta^3+149239952\\theta^2+168641212\\theta+75569097\\right)+2^{16} x^{9}\\left(7179524\\theta^4+42349744\\theta^3+105902696\\theta^2+125838704\\theta+58525593\\right)+2^{19} x^{10}\\left(3117952\\theta^4+20136896\\theta^3+53326176\\theta^2+65967996\\theta+31556287\\right)+2^{21} x^{11}\\left(1949840\\theta^4+13550976\\theta^3+37571920\\theta^2+47915544\\theta+23371681\\right)+2^{23} x^{12}\\left(851424\\theta^4+6266688\\theta^3+17985676\\theta^2+23424156\\theta+11560933\\right)+2^{26} x^{13}\\left(122784\\theta^4+942720\\theta^3+2770088\\theta^2+3654240\\theta+1815239\\right)+2^{31} 5 x^{14}\\left(524\\theta^4+4136\\theta^3+12323\\theta^2+16373\\theta+8173\\right)+2^{36} 5^{2} x^{15}\\left((\\theta+2)^4\\right)", "superseek": "2 38", "discriminant": "15 1 146 9396 352728 8626912 145606400 1753843712 15376457728 99110846464 470517284864 1634704818176 4089110855680 7142262177792 8239894757376 5626407157760 1717986918400", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "76d5c5e186c39f14d8f32dfa0f13e22a", "dim_h": null, "inst": " 2 -29/4 38 -2077/8 2034 -69631/4 158858 -12172903/8 15129336 -619853933/4", "cleanlist": "True", "n_sing_real": "8", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "8", "laurent": null, "discriminant_tex": "(4z+1)(64z^2+24z+1)^2(160z^2+32z+1)^2(2z+1)^3(8z+1)^3", "discr_factors": "1717986918400, z+1/4, (z+1/8)^3, (z+1/2)^3, (z^2+3/8*z+1/64)^2, (z^2+1/5*z+1/160)^2", "dm_basis": null, "q": "0 1 6 22 96 190 1472 -3540 55296 -451314", "yuk": "1 2 -56 1028 -16672 254252 -3759104 54488296 -779082464 11029286972", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/2","im":"0","approx_re":"-0.5","approx_im":"0.0","exponents":["0","2","3","5"],"monodromy":[],"monodromy_dm":[]},{"re":"-3/16-1/16*5^(1/2)","im":"0","approx_re":"-0.327254","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/4","im":"0","approx_re":"-0.25","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/10-1/40*6^(1/2)","im":"0","approx_re":"-0.161237","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/8","im":"0","approx_re":"-0.125","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"-3/16+1/16*5^(1/2)","im":"0","approx_re":"-0.047746","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/10+1/40*6^(1/2)","im":"0","approx_re":"-0.038763","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":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["2","2","2","2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -14-73*X-154*X^2-162*X^3-81*X^4, 3256+11390*X+15571*X^2+9876*X^3+2469*X^4, -162708-457536*X-476503*X^2-215994*X^3-35999*X^4, 2949480+7097160*X+6016050*X^2+2120880*X^3+265110*X^4, -6300*(X+4)*(X+1)*(151*X^2+755*X+850), 1323000*(X+5)*(X+4)*(X+2)*(X+1)]", "text": "This is operator \"6.17\" from ...", "degz": 6, "h3": null, "sol": "1 14 220 3800 70840 1404944 29317456 638193920 14393845480 334501958000", "n_discr_factors": "5", "c3": null, "operator": "4 6 0 0 0 0 1 -14 -73 -154 -162 -81 3256 11390 15571 9876 2469 -162708 -457536 -476503 -215994 -35999 2949480 7097160 6016050 2120880 265110 -21420000 -45801000 -32942700 -9513000 -951300 52920000 103194000 64827000 15876000 1323000", "new_number": "6.17", "id": 400, "operator_tex": "\\theta^4-x\\left(14+73\\theta+154\\theta^2+162\\theta^3+81\\theta^4\\right)+x^{2}\\left(3256+11390\\theta+15571\\theta^2+9876\\theta^3+2469\\theta^4\\right)-x^{3}\\left(162708+457536\\theta+476503\\theta^2+215994\\theta^3+35999\\theta^4\\right)+2 3 5 x^{4}\\left(8837\\theta^4+70696\\theta^3+200535\\theta^2+236572\\theta+98316\\right)-2^{2} 3^{2} 5^{2} 7 x^{5}(\\theta+4)(\\theta+1)(151\\theta^2+755\\theta+850)+2^{3} 3^{3} 5^{3} 7^{2} x^{6}(\\theta+5)(\\theta+4)(\\theta+2)(\\theta+1)", "superseek": "2 224/9", "discriminant": "6 1 -81 2469 -35999 265110 -951300 1323000", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "bbcabbebf6c04783d4ec5d0a5664f174", "dim_h": null, "inst": " 2 -4 224/9 -112 4446/5 -49628/9 46974 -341400 9101936/3 -121028712/5", "cleanlist": "True", "n_sing_real": "6", "sol_explicit": "", "n_sing_rational": "6", "n_sing": "6", "laurent": null, "discriminant_tex": "(6z-1)(14z-1)(30z-1)(21z-1)(-1+5z)^2", "discr_factors": "1323000, z-1/6, z-1/21, z-1/14, z-1/30, (-1/5+z)^2", "dm_basis": null, "q": "0 1 -17 267 -4189 65570 -1027203 16092382 -252180497 3952190541", "yuk": "1 2 -30 674 -7198 111152 -1190430 16112084 -174803998 2211771122", "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":"1/30","im":"0","approx_re":"0.0333333333333","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/21","im":"0","approx_re":"0.047619047619","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/14","im":"0","approx_re":"0.0714285714286","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/6","im":"0","approx_re":"0.166666666667","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/5","im":"0","approx_re":"0.2","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","4","5"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -168*X^4-598*X^2-528*X^3-334*X-74, 89772*X^2+75800*X+42560*X^3+24284+1040*X^4, 937856*X^2+2065920*X^3-1046784*X-830080+582400*X^4, -117092352*X^2-41107456+3829760*X^4-119742464*X-35471360*X^3, -3860594688*X-4028891136*X^2-1394343936-1875640320*X^3-325582848*X^4, -37748736*(3*X+5)^2*(3*X+4)^2]", "text": "This is operator \"6.38\" from ...", "degz": 6, "h3": null, "sol": "1 74 6354 585020 55958290 5480448804 545384635596 54901271764296 5574757048469010 569912441021078420", "n_discr_factors": "3", "c3": null, "operator": "4 6 0 0 0 0 1 -74 -334 -598 -528 -168 24284 75800 89772 42560 1040 -830080 -1046784 937856 2065920 582400 -41107456 -119742464 -117092352 -35471360 3829760 -1394343936 -3860594688 -4028891136 -1875640320 -325582848 -15099494400 -40768634880 -41108373504 -18345885696 -3057647616", "new_number": "6.38", "id": 423, "operator_tex": "\\theta^4-2 x\\left(84\\theta^4+264\\theta^3+299\\theta^2+167\\theta+37\\right)+2^{2} x^{2}\\left(260\\theta^4+10640\\theta^3+22443\\theta^2+18950\\theta+6071\\right)+2^{7} x^{3}\\left(4550\\theta^4+16140\\theta^3+7327\\theta^2-8178\\theta-6485\\right)+2^{12} x^{4}\\left(935\\theta^4-8660\\theta^3-28587\\theta^2-29234\\theta-10036\\right)-2^{18} 3 x^{5}\\left(414\\theta^4+2385\\theta^3+5123\\theta^2+4909\\theta+1773\\right)-2^{22} 3^{2} x^{6}(3\\theta+5)^2(3\\theta+4)^2", "superseek": "2 952", "discriminant": "6 1 -168 1040 582400 3829760 -325582848 -3057647616", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "ab13475ec61ba4278f6e59d858b5c527", "dim_h": null, "inst": " 2 -172 952 -45148 17303644/25 -26019072 600090980 -21048155292 596535616354 -515471219056408/25", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "-(-1+16z+256z^2)(32z+1)^2(108z-1)^2", "discr_factors": "-3057647616, (z-1/108)^2, (z+1/32)^2, -1/256+1/16*z+z^2", "dm_basis": null, "q": "0 1 -38 871 -23804 626435 -18458314 559674337 -18113570392 599615908222", "yuk": "1 2 -1374 25706 -2890846 86518222 -5620095222 205831206142 -10776658400350 434874464347772", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/32-1/32*5^(1/2)","im":"0","approx_re":"-0.101127","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"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":"1/108","im":"0","approx_re":"0.00925925925926","approx_im":"0.0","exponents":["0","-1/2","1","3/2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/32+1/32*5^(1/2)","im":"0","approx_re":"0.038627","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":["4/3","4/3","5/3","5/3"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, X*(3*X^3-6*X^2-4*X-1), -211*X^4-856*X^3-1433*X^2-1184*X-384, -1522*X^4-6576*X^3-12954*X^2-13308*X-5400, 4*(X+1)*(2013*X^3+17379*X^2+40726*X+28548), 8*(X+1)*(15719*X^3+126105*X^2+325408*X+269508), 288*(X+1)*(X+2)*(1817*X^2+11967*X+19631), 10368*(X+3)*(X+2)*(X+1)*(89*X+350), 594432*(X+1)*(X+2)*(X+3)*(X+4)]", "text": "This is operator \"8.54\" from ...", "degz": 8, "h3": null, "sol": "1 0 24 72 1296 8640 103560 932400 10135440 102291840", "n_discr_factors": "5", "c3": null, "operator": "4 8 0 0 0 0 1 0 -1 -4 -6 3 -384 -1184 -1433 -856 -211 -5400 -13308 -12954 -6576 -1522 114192 277096 232420 77568 8052 2156064 4759328 3612104 1134592 125752 11307456 23854176 17039808 5016384 523296 21772800 45453312 31923072 9165312 922752 14266368 29721600 20805120 5944320 594432", "new_number": "8.54", "id": 501, "operator_tex": "\\theta^4+x\\theta(3\\theta^3-6\\theta^2-4\\theta-1)-x^{2}\\left(211\\theta^4+856\\theta^3+1433\\theta^2+1184\\theta+384\\right)-2 x^{3}\\left(761\\theta^4+3288\\theta^3+6477\\theta^2+6654\\theta+2700\\right)+2^{2} x^{4}(\\theta+1)(2013\\theta^3+17379\\theta^2+40726\\theta+28548)+2^{3} x^{5}(\\theta+1)(15719\\theta^3+126105\\theta^2+325408\\theta+269508)+2^{5} 3^{2} x^{6}(\\theta+1)(\\theta+2)(1817\\theta^2+11967\\theta+19631)+2^{7} 3^{4} x^{7}(\\theta+3)(\\theta+2)(\\theta+1)(89\\theta+350)+2^{9} 3^{3} 43 x^{8}(\\theta+1)(\\theta+2)(\\theta+3)(\\theta+4)", "superseek": "0 1/3", "discriminant": "8 1 3 -211 -1522 8052 125752 523296 922752 594432", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "bb80872017d0578a4ae56172666b807c", "dim_h": null, "inst": " 0 1/2 1/3 -1 2 493/36 69/7 -62 737/3 1463", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "5", "n_sing": "7", "laurent": null, "discriminant_tex": "(4z+1)(6z+1)(43z^2+13z+1)(2z+1)^2(12z-1)^2", "discr_factors": "594432, z+1/6, z^2+13/43*z+1/43, (z-1/12)^2, z+1/4, (z+1/2)^2", "dm_basis": null, "q": "0 1 -1 -25 5 730 631 -20569 -40309 559198", "yuk": "1 0 4 9 -60 250 2971 3381 -31804 179100", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/2","im":"0","approx_re":"-0.5","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/4","im":"0","approx_re":"-0.25","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/6","im":"0","approx_re":"-0.166666666667","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-13/86","im":"-1/86*3^(1/2)","approx_re":"-0.151162790698","approx_im":"-0.02014","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-13/86","im":"1/86*3^(1/2)","approx_re":"-0.151162790698","approx_im":"0.02014","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":"1/12","im":"0","approx_re":"0.0833333333333","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"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -9-48*X-104*X^2-112*X^3-41*X^4, 1146+3980*X+5186*X^2+2716*X^3+334*X^4, -18018-44376*X-32478*X^2-1644*X^3+2546*X^4, -32670-166800*X-259390*X^2-148700*X^3-19615*X^4, -25*(X+1)*(2929*X^3+4467*X^2-1969*X-4047), 22500*(X+2)*(X+1)*(2*X+3)^2]", "text": "This is operator \"6.35\" from ...", "degz": 6, "h3": null, "sol": "1 9 105 1425 21465 349569 6049761 109894185 2075840505 40482257025", "n_discr_factors": null, "c3": null, "operator": "4 6 0 0 0 0 1 -9 -48 -104 -112 -41 1146 3980 5186 2716 334 -18018 -44376 -32478 -1644 2546 -32670 -166800 -259390 -148700 -19615 101175 150400 -62450 -184900 -73225 405000 1147500 1192500 540000 90000", "new_number": "6.35", "id": 584, "operator_tex": "\\theta^4-x\\left(9+48\\theta+104\\theta^2+112\\theta^3+41\\theta^4\\right)+2 x^{2}\\left(167\\theta^4+1358\\theta^3+2593\\theta^2+1990\\theta+573\\right)+2 x^{3}\\left(1273\\theta^4-822\\theta^3-16239\\theta^2-22188\\theta-9009\\right)-5 x^{4}\\left(3923\\theta^4+29740\\theta^3+51878\\theta^2+33360\\theta+6534\\right)-5^{2} x^{5}(\\theta+1)(2929\\theta^3+4467\\theta^2-1969\\theta-4047)+2^{2} 3^{2} 5^{4} x^{6}(\\theta+2)(\\theta+1)(2\\theta+3)^2", "superseek": "2 224/9", "discriminant": null, "aesz": null, "n_sing_complex": null, "inst_int": null, "c2h": null, "hash": "31d226ff68f616edaab012f85462b8e9", "dim_h": null, "inst": " 2 -4 224/9 -112 4446/5 -49628/9 46974 -341400 9101936/3 -121028712/5", "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 -12 122 -1224 12115 -120528 1200422 -12031512 121015921", "yuk": "1 2 -30 674 -7198 111152 -1190430 16112084 -174803998 2211771122", "gv2": null, "gv0": null, "gv1": null}]}