{"count": 17, "status":"OK", "data":[{"pols": "[X^4, -2752*X^4-4928*X^3-3608*X^2-1144*X-132, 144*(4*X+3)*(3776*X^3+10096*X^2+8268*X+1515), -2073600*(4*X+1)*(4*X+3)*(4*X+7)*(4*X+9)]", "text": "Operator equivalent to AESZ 229", "degz": 3, "h3": "6", "sol": "1 132 62748 43686384 37830871260 37683925559280 41191522867207440 47982923045768093760 58486865023796076988380 73734263514698203059442800", "n_discr_factors": "2", "c3": "-56", "operator": "4 3 0 0 0 0 1 -132 -1144 -3608 -4928 -2752 654480 4444416 9123840 7446528 2174976 -391910400 -2488320000 -4313088000 -2654208000 -530841600", "new_number": "3.13", "id": 73, "operator_tex": "\\theta^4-2^{2} x\\left(688\\theta^4+1232\\theta^3+902\\theta^2+286\\theta+33\\right)+2^{4} 3^{2} x^{2}(4\\theta+3)(3776\\theta^3+10096\\theta^2+8268\\theta+1515)-2^{10} 3^{4} 5^{2} x^{3}(4\\theta+1)(4\\theta+3)(4\\theta+7)(4\\theta+9)", "superseek": "352 15001120/3", "discriminant": "3 1 -2752 2174976 -530841600", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": "36", "hash": "b5a6f76d274395537de2c3169fdac9bf", "dim_h": "4", "inst": " 352 18676 15001120/3 1489325052 586526654304 260434681338932 127392396596397408 66690501977249294972 110384391853499640630304/3 21156326782570025111421748", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "-(1600z-1)(-1+576z)^2", "discr_factors": "-530841600, (-1/576+z)^2, z-1/1600", "dm_basis": ["-56*lambda", "5/2", "1", "1", "-3/2", "-3", "-1", "0", "0", "6", "0", "0", "-6", "0", "0", "0"], "q": "0 1 -616 288300 -133696960 56027836110 -23998676441568 9384113509972152 -3959114636186356224 1432881233200427758821", "yuk": "1 352 149760 135010432 95316953088 73315831788352 56253891304369152 43695592032564311296 34145537012446955978752 26823407220400412808174304", "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":"1/1600","im":"0","approx_re":"0.000625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/576","im":"0","approx_re":"0.00173611111111","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":["1/4","3/4","7/4","9/4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -1808*X^4-3680*X^3-2532*X^2-692*X-68, -16*(4*X+3)*(3808*X^3+10504*X^2+8884*X+1635), -30976*(4*X+1)*(4*X+3)*(4*X+7)*(4*X+9)]", "text": "This is operator Pi = 3.14 (approx.), equivalent to AESZ 238.", "degz": 3, "h3": "5", "sol": "1 68 42220 38866320 43812369900 55414549043568 75528977653335024 108483998232210868800 161980690467592131864300 249190451217633428740094000", "n_discr_factors": "2", "c3": "-100", "operator": "4 3 0 0 0 0 1 -68 -692 -2532 -3680 -1808 -78480 -531072 -1072768 -855040 -243712 -5854464 -37171200 -64430080 -39649280 -7929856", "new_number": "3.14", "id": 74, "operator_tex": "\\theta^4-2^{2} x\\left(452\\theta^4+920\\theta^3+633\\theta^2+173\\theta+17\\right)-2^{4} x^{2}(4\\theta+3)(3808\\theta^3+10504\\theta^2+8884\\theta+1635)-2^{8} 11^{2} x^{3}(4\\theta+1)(4\\theta+3)(4\\theta+7)(4\\theta+9)", "superseek": "444 19050964", "discriminant": "3 1 -1808 -243712 -7929856", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": "38", "hash": "dc96aa2da269d989ee90c49dab6a9c5a", "dim_h": "4", "inst": " 444 57104 19050964 9432910668 5781274591408 4058389108418096 3128917495561043956 2583677026445362637052 2248245582621571943692888 2038917173314965930447657536", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "-(1936z-1)(1+64z)^2", "discr_factors": "-7929856, (1/64+z)^2, z-1/1936", "dm_basis": ["-100*lambda", "29/12", "1", "1", "-19/12", "-5/2", "-1", "0", "0", "5", "0", "0", "-5", "0", "0", "0"], "q": "0 1 -420 11814 -8013968 -9634342911 -6823847203608 -6014006082869582 -5551278928382532672 -5331789302913401246700", "yuk": "1 444 457276 514376472 603706740028 722659323926444 876612047933142040 1073218700977438077352 1322842637540629376910652 1638971029731125947466491824", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/64","im":"0","approx_re":"-0.015625","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":"1/1936","im":"0","approx_re":"0.00051652892562","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":["1/4","3/4","7/4","9/4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -912*X^4-1824*X^3-1540*X^2-628*X-104, 2048*(X+1)^2*(132*X^2+264*X+109), -6553600*(X+1)*(X+2)*(2*X+1)*(2*X+5)]", "text": "This is operator \"3.17\" from ...", "degz": 3, "h3": "12", "sol": "1 104 18600 3925760 906368680 222749440704 57562268096256 15541087025418240 4366013175750231720 1272142436194984228160", "n_discr_factors": "2", "c3": "80", "operator": "4 3 0 0 0 0 1 -104 -628 -1540 -1824 -912 223232 987136 1574912 1081344 270336 -65536000 -255590400 -321126400 -157286400 -26214400", "new_number": "3.17", "id": 77, "operator_tex": "\\theta^4-2^{2} x\\left(228\\theta^4+456\\theta^3+385\\theta^2+157\\theta+26\\right)+2^{11} x^{2}(\\theta+1)^2(132\\theta^2+264\\theta+109)-2^{18} 5^{2} x^{3}(\\theta+1)(\\theta+2)(2\\theta+1)(2\\theta+5)", "superseek": "68 125636/3", "discriminant": "3 1 -912 270336 -26214400", "aesz": "387", "n_sing_complex": "0", "inst_int": "", "c2h": "24", "hash": "06864aab02693f4b84eb494138bb3428", "dim_h": "4", "inst": " 68 204 125636/3 841384 123715360 6684183300 733643578092 60209440521080 18981546511013648/3 622264120727284960", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "-(400z-1)(-1+256z)^2", "discr_factors": "-26214400, z-1/400, (-1/256+z)^2", "dm_basis": ["80*lambda", "3", "1", "1", "-1", "-6", "-1", "0", "0", "12", "0", "0", "-12", "0", "0", "0"], "q": "0 1 -212 38622 -6606224 1078429485 -171109302936 26547238818834 -4053702590226240 610863748603039494", "yuk": "1 68 1700 1130792 53850276 15464420068 1443784725224 251639747285624 30827233600643236 4612515802177447256", "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":"1/400","im":"0","approx_re":"0.0025","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/256","im":"0","approx_re":"0.00390625","approx_im":"0.0","exponents":["0","0","1","1"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/2","1","2","5/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -1164*X^4-2328*X^3-1630*X^2-466*X-50, 4*(X+1)^2*(2316*X^2+4632*X+1907), -4624*(X+1)*(X+2)*(2*X+1)*(2*X+5)]", "text": "This is operator \"3.18\" from ...", "degz": 3, "h3": "6", "sol": "1 50 17142 9383540 6301530550 4753716061500 3866146815507900 3314249802229852200 2953892031977184333750 2712752476588987111093100", "n_discr_factors": "2", "c3": "-64", "operator": "4 3 0 0 0 0 1 -50 -466 -1630 -2328 -1164 7628 33784 53948 37056 9264 -46240 -180336 -226576 -110976 -18496", "new_number": "3.18", "id": 78, "operator_tex": "\\theta^4-2 x\\left(582\\theta^4+1164\\theta^3+815\\theta^2+233\\theta+25\\right)+2^{2} x^{2}(\\theta+1)^2(2316\\theta^2+4632\\theta+1907)-2^{4} 17^{2} x^{3}(\\theta+1)(\\theta+2)(2\\theta+1)(2\\theta+5)", "superseek": "266 11433160/3", "discriminant": "3 1 -1164 9264 -18496", "aesz": "388", "n_sing_complex": "0", "inst_int": "", "c2h": "36", "hash": "7e11db69c1b7bd8781e54a5eadb0e307", "dim_h": "4", "inst": " 266 19320 11433160/3 1106069392 397606861972 163708396964448 74029950842252412 35855597962756080032 54903164177222802846682/3 9735374577114117165638320", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "-(1156z-1)(4z-1)^2", "discr_factors": "-18496, (z-1/4)^2, z-1/1156", "dm_basis": ["-64*lambda", "5/2", "1", "1", "-3/2", "-3", "-1", "0", "0", "6", "0", "0", "-6", "0", "0", "0"], "q": "0 1 -266 14079 -3405860 -924112185 -466501974198 -237121195584531 -128307385503252456 -72331818578975524608", "yuk": "1 266 154826 102898706 70788595914 49700857746766 35361013847374034 25392273138892577582 18358066157001901572298 13341468895065141194642432", "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":"1/1156","im":"0","approx_re":"0.000865051903114","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/4","im":"0","approx_re":"0.25","approx_im":"0.0","exponents":["0","0","1","1"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/2","1","2","5/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -460*X^4-992*X^3-646*X^2-150*X-12, -12*(6*X+5)*(1866*X^3+5341*X^2+4760*X+1084), -24336*(6*X+5)*(6*X+11)*(3*X+1)*(3*X+7)]", "text": "This is operator \"3.22\" from ...", "degz": 3, "h3": "7", "sol": "1 12 5760 1664544 681014880 301062617856 144001775971872 72412616435777280 37833106664287101024 20355129524032767235200", "n_discr_factors": "2", "c3": "-36", "operator": "4 3 0 0 0 0 1 -12 -150 -646 -992 -460 -65040 -363648 -663180 -496512 -134352 -9369360 -48477312 -74249136 -42052608 -7884864", "new_number": "3.22", "id": 81, "operator_tex": "\\theta^4-2 x\\left(230\\theta^4+496\\theta^3+323\\theta^2+75\\theta+6\\right)-2^{2} 3 x^{2}(6\\theta+5)(1866\\theta^3+5341\\theta^2+4760\\theta+1084)-2^{4} 3^{2} 13^{2} x^{3}(6\\theta+5)(6\\theta+11)(3\\theta+1)(3\\theta+7)", "superseek": "166 1016100", "discriminant": "3 1 -460 -134352 -7884864", "aesz": "392", "n_sing_complex": "0", "inst_int": "", "c2h": "34", "hash": "5862be5cc4d3ec1686e6b9a6ec08f7e7", "dim_h": "4", "inst": " 166 8076 1016100 189329096 43879949258 11641348524744 23747294280862622/7 1058922686246549520 348334789616884018134 119425507449141363609236", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "-(676z-1)(1+108z)^2", "discr_factors": "-7884864, z-1/676, (1/108+z)^2", "dm_basis": ["-36*lambda", "31/12", "1", "1", "-17/12", "-7/2", "-1", "0", "0", "7", "0", "0", "-7", "0", "0", "0"], "q": "0 1 -102 -13479 -20644 -146630244 -70456962006 -21654760723062 -7360483846618200 -2679511387128156252", "yuk": "1 166 64774 27434866 12117126918 5484993657416 2514531308844178 1163617419762268644 542168415370350481158 253936061630708476654552", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/108","im":"0","approx_re":"-0.00925925925926","approx_im":"0.0","exponents":["0","1/3","1","4/3"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/676","im":"0","approx_re":"0.00147928994083","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","5/6","11/6","7/3"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -13840*X^4-23072*X^3-17540*X^2-6004*X-744, 9216*(4*X+3)*(1732*X^3+4475*X^2+3531*X+645), -383533056*(4*X+1)*(4*X+3)*(4*X+7)*(4*X+9)]", "text": "This is operator \"3.21\" from ...", "degz": 3, "h3": "12", "sol": "1 744 1731240 5192436480 17479541356200 62877279372836544 236149304275868772096 914205285330005286604800 3619629292068932238660306600 14581977636437185166407440456000", "n_discr_factors": "2", "c3": "304", "operator": "4 3 0 0 0 0 1 -744 -6004 -17540 -23072 -13840 17832960 121402368 253891584 212852736 63848448 -72487747584 -460239667200 -797748756480 -490922311680 -98184462336", "new_number": "3.21", "id": 84, "operator_tex": "\\theta^4-2^{2} x\\left(3460\\theta^4+5768\\theta^3+4385\\theta^2+1501\\theta+186\\right)+2^{10} 3^{2} x^{2}(4\\theta+3)(1732\\theta^3+4475\\theta^2+3531\\theta+645)-2^{14} 3^{4} 17^{2} x^{3}(4\\theta+1)(4\\theta+3)(4\\theta+7)(4\\theta+9)", "superseek": "964 85888580/3", "discriminant": "3 1 -13840 63848448 -98184462336", "aesz": "391", "n_sing_complex": "0", "inst_int": "", "c2h": "24", "hash": "907f1fbd0b6f7c89689fb136ee18482a", "dim_h": "4", "inst": " 964 -111140 85888580/3 -9197858184 3544241969952 -1482429836810060 669439235043160428 -316380104334379890616 467260149286033920341264/3 -78935289037962694175130272", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "-(4624z-1)(-1+4608z)^2", "discr_factors": "-98184462336, (-1/4608+z)^2, z-1/4624", "dm_basis": null, "q": "0 1 -3028 7770846 -18332138896 41122301488941 -89207047616754840 188952479870365464594 -393131883281872291307328 806652364184876012063782662", "yuk": "1 964 -888156 772998184 -588663811932 443030246244964 -320204843978863896 229617657619804027768 -161986613419791167807324 113544216276506243415925336", "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":"1/4624","im":"0","approx_re":"0.000216262975779","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/4608","im":"0","approx_re":"0.000217013888889","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":["1/4","3/4","7/4","9/4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, 240*X^4-32*X^3+124*X^2+140*X+24, -1024*(4*X+3)*(132*X^3+395*X^2+363*X+69), -802816*(4*X+1)*(4*X+3)*(4*X+7)*(4*X+9)]", "text": "Operator AESZ 33 is replaced by this equivalent operator.", "degz": 3, "h3": "6", "sol": "1 -24 13992 -920832 1808021160 87171860160 387667754960640 86477726324183040 112077004497429038760 44221649198354799124800", "n_discr_factors": "2", "c3": "-72", "operator": "4 3 0 0 0 0 1 24 140 124 -32 240 -211968 -1397760 -2700288 -2023424 -540672 -151732224 -963379200 -1669857280 -1027604480 -205520896", "new_number": "3.6", "id": 101, "operator_tex": "\\theta^4+2^{2} x\\left(60\\theta^4-8\\theta^3+31\\theta^2+35\\theta+6\\right)-2^{10} x^{2}(4\\theta+3)(132\\theta^3+395\\theta^2+363\\theta+69)-2^{14} 7^{2} x^{3}(4\\theta+1)(4\\theta+3)(4\\theta+7)(4\\theta+9)", "superseek": "196 2993772", "discriminant": "3 1 240 -540672 -205520896", "aesz": "~33", "n_sing_complex": "0", "inst_int": "", "c2h": "36", "hash": "29aeacb8c7e91c8c2838e65ce2750b5a", "dim_h": "4", "inst": " 196 17212 2993772 789858520 260782261024 98690449514452 41025582428172396 18268297351138829992 8573113961387638222256 4193246127394751256758368", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "-(784z-1)(1+512z)^2", "discr_factors": "-205520896, (1/512+z)^2, z-1/784", "dm_basis": null, "q": "0 1 44 -58658 -12875152 -850960595 -247297178776 -258815479238638 -146967407776333632 -73089849806203869434", "yuk": "1 196 137892 80832040 50551083172 32597782628196 21317137176091368 14071774772863132024 9353368243833632039076 6249800077851588344856664", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/512","im":"0","approx_re":"-0.001953125","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":"1/784","im":"0","approx_re":"0.00127551020408","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":["1/4","3/4","7/4","9/4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -108*X^4-216*X^3-54*X^2+54*X+18, -2916*(X+1)^2*(20*X^2+40*X+17), -944784*(X+1)*(X+2)*(2*X+1)*(2*X+5)]", "text": "Operator equivalent to AESZ 73", "degz": 3, "h3": "9", "sol": "1 -18 2754 37620 43789410 6088103532 1715335241004 385807115999448 99807709568908770 25528366039107763260", "n_discr_factors": "2", "c3": "12", "operator": "4 3 0 0 0 0 1 18 54 -54 -216 -108 -49572 -215784 -341172 -233280 -58320 -9447840 -36846576 -46294416 -22674816 -3779136", "new_number": "3.7", "id": 102, "operator_tex": "\\theta^4-2 3^{2} x\\left(6\\theta^4+12\\theta^3+3\\theta^2-3\\theta-1\\right)-2^{2} 3^{6} x^{2}(\\theta+1)^2(20\\theta^2+40\\theta+17)-2^{4} 3^{10} x^{3}(\\theta+1)(\\theta+2)(2\\theta+1)(2\\theta+5)", "superseek": "90 151648", "discriminant": "3 1 -108 -58320 -3779136", "aesz": "~73", "n_sing_complex": "0", "inst_int": "", "c2h": "30", "hash": "9f672e1168859bdcc8ddc7a201c57968", "dim_h": "4", "inst": " 90 2196 151648 14813388 1820806056 256288477264 39613204229256 6558770323351260 1144477326915177220 208148451286833099936", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "-(324z-1)(1+108z)^2", "discr_factors": "-3779136, z-1/324, (1/108+z)^2", "dm_basis": null, "q": "0 1 -18 -6885 -284964 -3892887 -2544634278 -635787930573 -114092490856392 -21147227686705293", "yuk": "1 90 17658 4094586 948074490 227600757090 55358315201178 13587329050634898 3358090406503919610 834323971321168287966", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/108","im":"0","approx_re":"-0.00925925925926","approx_im":"0.0","exponents":["0","0","1","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":"1/324","im":"0","approx_re":"0.00308641975309","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","2","5/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -320*X^4-896*X^3-608*X^2-160*X-16, -86016*X^4-245760*X^3-267264*X^2-137216*X-25600, -65536*(2*X+1)^2*(23*X^2+55*X+39), -8388608*(2*X+1)^2*(2*X+3)^2]", "text": "Sporadic Operator.\nReducible to 3.32, so not a primary operator.\nB-Incarnation: 81111- x 82--11\n", "degz": 4, "h3": "8", "sol": "1 16 3600 851200 257328400 86333942016 31204775137536 11874454884864000 4695209743316835600 1912190218793129017600", "n_discr_factors": "2", "c3": "-8", "operator": "4 4 0 0 0 0 1 -16 -160 -608 -896 -320 -25600 -137216 -267264 -245760 -86016 -2555904 -13828096 -26148864 -20447232 -6029312 -75497472 -402653184 -738197504 -536870912 -134217728", "new_number": "4.41", "id": 139, "operator_tex": "\\theta^4-2^{4} x\\left(20\\theta^4+56\\theta^3+38\\theta^2+10\\theta+1\\right)-2^{10} x^{2}\\left(84\\theta^4+240\\theta^3+261\\theta^2+134\\theta+25\\right)-2^{16} x^{3}(2\\theta+1)^2(23\\theta^2+55\\theta+39)-2^{23} x^{4}(2\\theta+1)^2(2\\theta+3)^2", "superseek": "128 382592", "discriminant": "4 1 -320 -86016 -6029312 -134217728", "aesz": "220", "n_sing_complex": "0", "inst_int": "", "c2h": "32", "hash": "671a1aa788ead53985e13ad6774d0189", "dim_h": "4", "inst": " 128 4084 382592 51510860 8644861312 1659459740132 349956800171136 79045292244127852 18815837160365104128 4668098318162928620860", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "-(512z-1)(64z+1)^3", "discr_factors": "-134217728, (z+1/64)^3, z-1/512", "dm_basis": null, "q": "0 1 -96 -3360 47104 -59645904 -11999339520 -2746669569536 -697657825099776 -183142363318091112", "yuk": "1 128 32800 10330112 3296727840 1080607664128 358443314231296 120035182458699776 40471189632290188064 13716745289906171239424", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/64","im":"0","approx_re":"-0.015625","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":"1/512","im":"0","approx_re":"0.001953125","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","1/2","3/2","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -80-704*X-2496*X^2-3584*X^3-256*X^4, 180224+1081344*X+1966080*X^2-786432*X^3-786432*X^4, 20971520+201326592*X+654311424*X^2+805306368*X^3-67108864*X^4, 4294967296*(2*X+1)^4]", "text": "Sporadic Operator.", "degz": 4, "h3": "8", "sol": "1 80 24336 11398400 6632189200 4375826945280 3128385870086400 2363772411985121280 1859710567888951549200 1508986129076374769849600", "n_discr_factors": "3", "c3": "48", "operator": "4 4 0 0 0 0 1 -80 -704 -2496 -3584 -256 180224 1081344 1966080 -786432 -786432 20971520 201326592 654311424 805306368 -67108864 4294967296 34359738368 103079215104 137438953472 68719476736", "new_number": "4.52", "id": 151, "operator_tex": "\\theta^4-2^{4} x\\left(16\\theta^4+224\\theta^3+156\\theta^2+44\\theta+5\\right)-2^{14} x^{2}\\left(48\\theta^4+48\\theta^3-120\\theta^2-66\\theta-11\\right)-2^{22} x^{3}\\left(16\\theta^4-192\\theta^3-156\\theta^2-48\\theta-5\\right)+2^{32} x^{4}\\left((2\\theta+1)^4\\right)", "superseek": "480 4215904", "discriminant": "4 1 -256 -786432 -67108864 68719476736", "aesz": "258", "n_sing_complex": "0", "inst_int": "", "c2h": "32", "hash": "bfb9f01124fd9980817cbf1b50f789c3", "dim_h": "4", "inst": " 480 -16536 4215904 -242723592 151800032928 -1451841658552 9691266849668832 875056266892499832 896019960722254141696 184580570409555186384120", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "(1024z-1)(256z-1)(1+512z)^2", "discr_factors": "68719476736, (1/512+z)^2, z-1/256, z-1/1024", "dm_basis": null, "q": "0 1 -384 109920 -32946176 9269408304 -2759387652096 772834218570240 -235800183728504832 65119631126813469336", "yuk": "1 480 -131808 113829888 -15534441696 18975004116480 -313597684549632 3324104529436409856 448028808633425472288 653198551366523383126272", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/512","im":"0","approx_re":"-0.001953125","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":"1/1024","im":"0","approx_re":"0.0009765625","approx_im":"0.0","exponents":["0","1","1","2"],"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","1/2","1/2","1/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -1408*X^4-512*X^3-528*X^2-272*X-48, 770048*X^4+720896*X^3+735232*X^2+305152*X+47616, -203423744*X^4-352321536*X^3-362020864*X^2-170655744*X-30670848, 25165824*(2*X+1)*(512*X^3+1152*X^2+1054*X+339), -19327352832*(2*X+1)*(4*X+3)*(4*X+5)*(2*X+3)]", "text": "This is operator \"5.13\" from ...", "degz": 5, "h3": "32", "sol": "1 48 5328 779520 131619600 24257173248 4739368322304 965015828434944 202584554505899280 43534711014765484800", "n_discr_factors": "3", "c3": "360", "operator": "4 5 0 0 0 0 1 -48 -272 -528 -512 -1408 47616 305152 735232 720896 770048 -30670848 -170655744 -362020864 -352321536 -203423744 8531214336 43587207168 82040586240 70866960384 25769803776 -869730877440 -4174708211712 -7035156430848 -4947802324992 -1236950581248", "new_number": "5.13", "id": 220, "operator_tex": "\\theta^4-2^{4} x\\left(88\\theta^4+32\\theta^3+33\\theta^2+17\\theta+3\\right)+2^{9} x^{2}\\left(1504\\theta^4+1408\\theta^3+1436\\theta^2+596\\theta+93\\right)-2^{18} x^{3}\\left(776\\theta^4+1344\\theta^3+1381\\theta^2+651\\theta+117\\right)+2^{23} 3 x^{4}(2\\theta+1)(512\\theta^3+1152\\theta^2+1054\\theta+339)-2^{31} 3^{2} x^{5}(2\\theta+1)(4\\theta+3)(4\\theta+5)(2\\theta+3)", "superseek": "-80 -174096", "discriminant": "5 1 -1408 770048 -203423744 25769803776 -1236950581248", "aesz": "83", "n_sing_complex": "0", "inst_int": "", "c2h": "-16", "hash": "171e1251d8e4f7de878d0d07de6f58ab", "dim_h": "4", "inst": " -80 -2954 -174096 -13270953 -1179175536 -115795446786 -12188186517456 -1349830285576015 -155427513115593600 -18456445525841201614", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "-(128z-1)(384z-1)^2(256z-1)^2", "discr_factors": "-1236950581248, (z-1/384)^2, z-1/128, (z-1/256)^2", "dm_basis": null, "q": "0 1 -80 3840 -181248 5466544 -307951104 46314496 -945821483008 -60856937695080", "yuk": "1 -80 -23712 -4700672 -849364704 -147396942080 -25011821230080 -4180547975487488 -691113107064284384 -113306657061272435072", "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":"1/384","im":"0","approx_re":"0.00260416666667","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/256","im":"0","approx_re":"0.00390625","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"1/128","im":"0","approx_re":"0.0078125","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","5/4","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[81*X^4, -17937*X^4-28962*X^3-21933*X^2-7452*X-972, 559552*X^4+805888*X^3+391648*X^2+89280*X+9504, -6046720*X^4-8902656*X^3-7399680*X^2-3186432*X-539136, 32768*(2*X+1)*(340*X^3+618*X^2+455*X+129), -4194304*(2*X+1)*(X+1)^2*(2*X+3)]", "text": "This is operator \"5.75\" from ...", "degz": 5, "h3": "18", "sol": "1 12 708 63840 6989220 855982512 112786041984 15645580194816 2254801269803940 334669706566543920", "n_discr_factors": "3", "c3": "-92", "operator": "4 5 0 0 0 0 81 -972 -7452 -21933 -28962 -17937 9504 89280 391648 805888 559552 -539136 -3186432 -7399680 -8902656 -6046720 4227072 23363584 50069504 51642368 22282240 -12582912 -58720256 -96468992 -67108864 -16777216", "new_number": "5.75", "id": 288, "operator_tex": "3^{4} \\theta^4-3^{2} x\\left(1993\\theta^4+3218\\theta^3+2437\\theta^2+828\\theta+108\\right)+2^{5} x^{2}\\left(17486\\theta^4+25184\\theta^3+12239\\theta^2+2790\\theta+297\\right)-2^{8} x^{3}\\left(23620\\theta^4+34776\\theta^3+28905\\theta^2+12447\\theta+2106\\right)+2^{15} x^{4}(2\\theta+1)(340\\theta^3+618\\theta^2+455\\theta+129)-2^{22} x^{5}(2\\theta+1)(\\theta+1)^2(2\\theta+3)", "superseek": "205/9 97622/9", "discriminant": "5 81 -17937 559552 -6046720 22282240 -16777216", "aesz": "298", "n_sing_complex": "0", "inst_int": "", "c2h": "12", "hash": "e52d50673ec5c795512e2bc3e1017b12", "dim_h": "4", "inst": " 205/9 3206/9 97622/9 496806 254037095/9 16476340418/9 1172722066057/9 9930597861190 7176881517850505/9 200193418895368288/3", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "-(z-1)(1024z^2-192z+1)(-9+128z)^2", "discr_factors": "-16777216, (-9/128+z)^2, z^2-3/16*z+1/1024, z-1", "dm_basis": null, "q": "0 1 -44 350 -10696 -567579 -43127416 -3457085002 -294469950256 -26124408525758", "yuk": "1 205/9 25853/9 2635999/9 286186109/9 31754637080/9 3558892191935/9 402243668657756/9 45760195230549629/9 5231946626515654144/9", "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":"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":"9/128","im":"0","approx_re":"0.0703125","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":"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":["1/2","1","1","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, 1792*X^4-1024*X^3-512*X^2+16, 917504*X^4-1048576*X^3+49152*X^2-163840*X-65536, 33554432*X^4-402653184*X^3-457179136*X^2-276824064*X-57671680, -1610612736*(2*X+1)*(10*X+7)*(2*X^2+4*X+3), -2473901162496*(2*X+1)*(X+1)^2*(2*X+3)]", "text": "B-Incarnation as double octic D.O.20\n", "degz": 5, "h3": "16", "sol": "1 -16 4368 -344320 107445520 -12148367616 3860075847936 -516712812515328 164039018022182160 -24277289247356104960", "n_discr_factors": "3", "c3": "320", "operator": "4 5 0 0 0 0 1 16 0 -512 -1024 1792 -65536 -163840 49152 -1048576 917504 -57671680 -276824064 -457179136 -402653184 33554432 -33822867456 -161061273600 -273804165120 -206158430208 -64424509440 -7421703487488 -34634616274944 -56899726737408 -39582418599936 -9895604649984", "new_number": "5.90", "id": 305, "operator_tex": "\\theta^4+2^{4} x\\left(112\\theta^4-64\\theta^3-32\\theta^2+1\\right)+2^{14} x^{2}\\left(56\\theta^4-64\\theta^3+3\\theta^2-10\\theta-4\\right)+2^{20} x^{3}\\left(32\\theta^4-384\\theta^3-436\\theta^2-264\\theta-55\\right)-2^{29} 3 x^{4}(2\\theta+1)(10\\theta+7)(2\\theta^2+4\\theta+3)-2^{38} 3^{2} x^{5}(2\\theta+1)(\\theta+1)^2(2\\theta+3)", "superseek": "352 3284448", "discriminant": "5 1 1792 917504 33554432 -64424509440 -9895604649984", "aesz": "330", "n_sing_complex": "0", "inst_int": "", "c2h": "16", "hash": "ba5b66d5fe92237e6416a117563571e9", "dim_h": "4", "inst": " 352 -23368 3284448 -578330224 120252731680 -27415759432616 6701726151914080 -1720803298688523376 459238567520109337856 -126317379213699482253720", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "-(-1+256z)(256z+1)^2(768z+1)^2", "discr_factors": "-9895604649984, (z+1/256)^2, (z+1/768)^2, -1/256+z", "dm_basis": null, "q": "0 1 -64 1632 -436224 141710896 -43304871936 12756718699008 -3828584306835456 1163560985061276312", "yuk": "1 352 -186592 88680448 -37013320928 15031591460352 -5921803948951552 2298692070106529792 -881051288965537289440 334784915722159795977472", "gv2": null, "gv0": null, "gv1": null, 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