{"count": 6, "status":"OK", "data":[{"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, 15*X^4+30*X^3+35*X^2+20*X+4, -32*(X+1)^2*(66*X^2+132*X+53), -12544*(X+1)*(X+2)*(2*X+1)*(2*X+5)]", "text": "Operator equivalent to AESZ 100= $ a \\ast a$", "degz": 3, "h3": "36", "sol": "1 -4 132 -1120 72100 -265104 59047296 350118912 63064312740 1096066914800", "n_discr_factors": "2", "c3": "-72", "operator": "4 3 0 0 0 0 1 4 20 35 30 15 -1696 -7616 -12256 -8448 -2112 -125440 -489216 -614656 -301056 -50176", "new_number": "3.8", "id": 103, "operator_tex": "\\theta^4+x\\left(15\\theta^4+30\\theta^3+35\\theta^2+20\\theta+4\\right)-2^{5} x^{2}(\\theta+1)^2(66\\theta^2+132\\theta+53)-2^{8} 7^{2} x^{3}(\\theta+1)(\\theta+2)(2\\theta+1)(2\\theta+5)", "superseek": "5 454", "discriminant": "3 1 15 -2112 -50176", "aesz": "~100", "n_sing_complex": "0", "inst_int": "", "c2h": "72", "hash": "82a1ac6ac6fb9ab2e4d6b5d5790d1d9b", "dim_h": "12", "inst": " 5 42 454 7498 154351 3652254 94572705 2621325434 76541504257 2329054186336", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "-(49z-1)(1+32z)^2", "discr_factors": "-50176, (1/32+z)^2, z-1/49", "dm_basis": null, "q": "0 1 4 -258 -4616 -15963 203304 -9506154 -568626864 -17941215870", "yuk": "1 5 341 12263 480213 19293880 788899463 32438437820 1342119102421 55798756615616", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/32","im":"0","approx_re":"-0.03125","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/49","im":"0","approx_re":"0.0204081632653","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, -48-384*X-1136*X^2-1504*X^3-1328*X^4, 61440+436224*X+1069056*X^2+1173504*X^3+620544*X^4, -6488064-60162048*X-196411392*X^2-254803968*X^3-119734272*X^4, 226492416*(3*X+1)*(2*X+1)^2*(3*X+2)]", "text": "Sporadic Operator.", "degz": 4, "h3": "16", "sol": "1 48 9360 2553600 813027600 283184149248 104664044669184 40361741131345920 16073129967819210000 6564949660340509152000", "n_discr_factors": "3", "c3": "-72", "operator": "4 4 0 0 0 0 1 -48 -384 -1136 -1504 -1328 61440 436224 1069056 1173504 620544 -6488064 -60162048 -196411392 -254803968 -119734272 452984832 3850371072 12004098048 16307453952 8153726976", "new_number": "4.45", "id": 143, "operator_tex": "\\theta^4-2^{4} x\\left(83\\theta^4+94\\theta^3+71\\theta^2+24\\theta+3\\right)+2^{11} 3 x^{2}\\left(101\\theta^4+191\\theta^3+174\\theta^2+71\\theta+10\\right)-2^{16} 3^{2} x^{3}\\left(203\\theta^4+432\\theta^3+333\\theta^2+102\\theta+11\\right)+2^{23} 3^{3} x^{4}(3\\theta+1)(2\\theta+1)^2(3\\theta+2)", "superseek": "80 104976", "discriminant": "4 1 -1328 620544 -119734272 8153726976", "aesz": "233", "n_sing_complex": "0", "inst_int": "", "c2h": "64", "hash": "03f67459f6d678669f766c99281b1e79", "dim_h": "8", "inst": " 80 2794 104976 5367454 508265072 71026691490 10979503341520 1741443998259494 281028365633566080 46168051267005890030", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "(512z-1)(432z-1)(-1+192z)^2", "discr_factors": "8153726976, z-1/432, z-1/512, (-1/192+z)^2", "dm_basis": null, "q": "0 1 -192 20256 -1451008 76300080 -3901906944 74979753472 -15535962980352 -1686551922782568", "yuk": "1 80 22432 2834432 343539488 63533134080 15341768218624 3765969646141440 891619327452400416 204869678546872506752", "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":"1/512","im":"0","approx_re":"0.001953125","approx_im":"0.0","exponents":["0","1","1","2"],"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":"1/192","im":"0","approx_re":"0.00520833333333","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","1/2","1/2","2/3"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[25*X^4, -200-1450*X-4095*X^2-5290*X^3-5285*X^4, 5760+48320*X+186816*X^2+365408*X^3+323936*X^4, -1305600-6528000*X-12342016*X^2-11919360*X^3-7931136*X^4, 180224*(2*X+1)*(234*X^3+591*X^2+581*X+202), -126877696*(2*X+1)*(X+1)^2*(2*X+3)]", "text": "This is operator \"5.39\" from ...", "degz": 5, "h3": "20", "sol": "1 8 312 19520 1475320 124363008 11265866304 1073852921856 106307436601080 10836331719836480", "n_discr_factors": "3", "c3": "-72", "operator": "4 5 0 0 0 0 25 -200 -1450 -4095 -5290 -5285 5760 48320 186816 365408 323936 -1305600 -6528000 -12342016 -11919360 -7931136 36405248 177520640 315932672 255197184 84344832 -380633088 -1776287744 -2918187008 -2030043136 -507510784", "new_number": "5.39", "id": 248, "operator_tex": "5^{2} \\theta^4-5 x\\left(1057\\theta^4+1058\\theta^3+819\\theta^2+290\\theta+40\\right)+2^{5} x^{2}\\left(10123\\theta^4+11419\\theta^3+5838\\theta^2+1510\\theta+180\\right)-2^{8} x^{3}\\left(30981\\theta^4+46560\\theta^3+48211\\theta^2+25500\\theta+5100\\right)+2^{14} 11 x^{4}(2\\theta+1)(234\\theta^3+591\\theta^2+581\\theta+202)-2^{20} 11^{2} x^{5}(2\\theta+1)(\\theta+1)^2(2\\theta+3)", "superseek": "59/5 22503/5", "discriminant": "5 25 -5285 323936 -7931136 84344832 -507510784", "aesz": "224", "n_sing_complex": "2", "inst_int": "", "c2h": "56", "hash": "ba17e8cb074bba75e7a27206be530698", "dim_h": "8", "inst": " 59/5 186 22503/5 718052/5 29091017/5 1367927712/5 14151915978 3919628383228/5 228793583855178/5 13919107695848262/5", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "-(128z-1)(128z^2-13z+1)(-5+176z)^2", "discr_factors": "-507510784, (-5/176+z)^2, z-1/128, z^2-13/128*z+1/128", "dm_basis": null, "q": "0 1 -26 -27 -5160 -163922 -10140210 -599548870 -37048333664 -2381226834885", "yuk": "1 59/5 7499/5 121528 45962827/5 3636377184/5 295473000872/5 24270535902329/5 2006849778175563/5 166790522631032402/5", "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","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"5/176","im":"0","approx_re":"0.0284090909091","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"13/256","im":"-7/256*7^(1/2)","approx_re":"0.05078125","approx_im":"-0.072345","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"13/256","im":"7/256*7^(1/2)","approx_re":"0.05078125","approx_im":"0.072345","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": "[169*X^4, -2028-14534*X-40859*X^2-52650*X^3-18837*X^4, 281424+1317056*X+1936736*X^2+433792*X^3-364160*X^4, -5001984-16253952*X-8778752*X^2+10223616*X^3+978944*X^4, -196608*(2*X+1)*(40*X^3+684*X^2+1013*X+399), -9437184*(2*X+1)*(4*X+3)*(4*X+5)*(2*X+3)]", "text": "This is operator \"5.44\" from ...", "degz": 5, "h3": "26", "sol": "1 12 468 28560 2135700 179060112 16166559024 1537448717376 151947395002260 15468902712634800", "n_discr_factors": "3", "c3": "-72", "operator": "4 5 0 0 0 0 169 -2028 -14534 -40859 -52650 -18837 281424 1317056 1936736 433792 -364160 -5001984 -16253952 -8778752 10223616 978944 -78446592 -356057088 -532807680 -276824064 -15728640 -424673280 -2038431744 -3435134976 -2415919104 -603979776", "new_number": "5.44", "id": 254, "operator_tex": "13^{2} \\theta^4-13 x\\left(1449\\theta^4+4050\\theta^3+3143\\theta^2+1118\\theta+156\\right)-2^{4} x^{2}\\left(22760\\theta^4-27112\\theta^3-121046\\theta^2-82316\\theta-17589\\right)+2^{8} x^{3}\\left(3824\\theta^4+39936\\theta^3-34292\\theta^2-63492\\theta-19539\\right)-2^{16} 3 x^{4}(2\\theta+1)(40\\theta^3+684\\theta^2+1013\\theta+399)-2^{20} 3^{2} x^{5}(2\\theta+1)(4\\theta+3)(4\\theta+5)(2\\theta+3)", "superseek": "231/13 38037/13", "discriminant": "5 169 -18837 -364160 978944 -15728640 -603979776", "aesz": "240", "n_sing_complex": "2", "inst_int": "", "c2h": "68", "hash": "8f46cd6968b3b676e251a9d8635637fc", "dim_h": "10", "inst": " 231/13 826/13 38037/13 786076/13 32662752/13 1251531252/13 56830429026/13 2686705844700/13 135076469305428/13 7052986465933572/13", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "-(128z-1)(128z^2-13z+1)(13+192z)^2", "discr_factors": "-603979776, z-1/128, (13/192+z)^2, z^2-13/128*z+1/128", "dm_basis": null, "q": "0 1 -38 771 -20752 393365 -14552562 106677773 -15365058336 -334070060625", "yuk": "1 231/13 6839/13 1027230/13 50315703/13 4082844231/13 270331784270/13 19492837156149/13 1375593442802103/13 98470746124684242/13", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-13/192","im":"0","approx_re":"-0.0677083333333","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":"1/128","im":"0","approx_re":"0.0078125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"13/256","im":"-7/256*7^(1/2)","approx_re":"0.05078125","approx_im":"-0.072345","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"13/256","im":"7/256*7^(1/2)","approx_re":"0.05078125","approx_im":"0.072345","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": "[X^4, -216*X^4-264*X^3-196*X^2-64*X-8, 6672*X^4-4896*X^3-19504*X^2-12416*X-2464, 42496*X^4+491520*X^3+406784*X^2+110592*X+5888, -28672*(2*X+1)*(38*X^3+45*X^2+12*X-2), -802816*(2*X+1)*(X+1)^2*(2*X+3)]", "text": "This is operator \"5.73\" from ...", "degz": 5, "h3": "16", "sol": "1 8 528 45440 4763920 556795008 69938905344 9243039995904 1268613972671760 179279670581348480", "n_discr_factors": "3", "c3": "-72", "operator": "4 5 0 0 0 0 1 -8 -64 -196 -264 -216 -2464 -12416 -19504 -4896 6672 5888 110592 406784 491520 42496 57344 -229376 -1978368 -3670016 -2179072 -2408448 -11239424 -18464768 -12845056 -3211264", "new_number": "5.73", "id": 286, "operator_tex": "\\theta^4-2^{2} x\\left(54\\theta^4+66\\theta^3+49\\theta^2+16\\theta+2\\right)+2^{4} x^{2}\\left(417\\theta^4-306\\theta^3-1219\\theta^2-776\\theta-154\\right)+2^{8} x^{3}\\left(166\\theta^4+1920\\theta^3+1589\\theta^2+432\\theta+23\\right)-2^{12} 7 x^{4}(2\\theta+1)(38\\theta^3+45\\theta^2+12\\theta-2)-2^{14} 7^{2} x^{5}(2\\theta+1)(\\theta+1)^2(2\\theta+3)", "superseek": "20 13188", "discriminant": "5 1 -216 6672 42496 -2179072 -3211264", "aesz": "293\n", "n_sing_complex": "0", "inst_int": "", "c2h": "52", "hash": "f19eeaee48396d15d7cf7be47d7d48a7", "dim_h": "7", "inst": " 20 867/2 13188 609734 35512476 4757494887/2 174895402996 13771251674214 1142718645352032 197654872436043985/2", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "-(16z+1)(256z^2+176z-1)(-1+28z)^2", "discr_factors": "-3211264, z^2+11/16*z-1/256, z+1/16, (-1/28+z)^2", "dm_basis": null, "q": "0 1 -32 -480 -4352 -721104 -62992896 -5185868288 -452386127872 -41357676687720", "yuk": "1 20 3488 356096 39026464 4439059520 513809807360 59989123227648 7050880896224032 833041892461987424", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-11/32-5/32*5^(1/2)","im":"0","approx_re":"-0.693136","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"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":"-11/32+5/32*5^(1/2)","im":"0","approx_re":"0.005636","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/28","im":"0","approx_re":"0.0357142857143","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":["1/2","1","1","3/2"],"monodromy":[],"monodromy_dm":[]}]}]}