{"count": 8, "status":"OK", "data":[{"pols": "[X^4, -12*(2*X+1)^2*(3*X^2+3*X+1), 432*(2*X+1)^2*(2*X+3)^2]", "text": "Hadamard product A*f\nExplicit solution not yet verified", "degz": 2, "h3": null, "sol": "1 12 324 8400 44100 -18860688 -2066991696 -152332944192 -8680533018300 -343458761989200", "n_discr_factors": "1", "c3": null, "operator": "4 2 0 0 0 0 1 -12 -84 -228 -288 -144 3888 20736 38016 27648 6912", "new_number": "2.20", "id": 12, "operator_tex": "\\theta^4-2^{2} 3 x(2\\theta+1)^2(3\\theta^2+3\\theta+1)+2^{4} 3^{3} x^{2}(2\\theta+1)^2(2\\theta+3)^2", "superseek": "12 -3284/3", "discriminant": "2 1 -144 6912", "aesz": "133", "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "4c9628f7dd48f4e9e6ec75303e557389", "dim_h": null, "inst": " 12 -42 -3284/3 -20538 -103776 28249414/3 427369380 8149884534 -318803512000/3 -13871427417456", "cleanlist": "True", "n_sing_real": "1", "sol_explicit": "A_{n}=\\dbinom{2n}{n}^2\\sum_{k=0}^{n}(-1)^{k}3^{n-3k}\\dbinom{n}{3k}\\frac{(3k)!}{k!^3}", "n_sing_rational": "1", "n_sing": "3", "laurent": null, "discriminant_tex": "1-144z+6912z^2", "discr_factors": "6912, 1/6912-1/48*z+z^2", "dm_basis": ["5/6-120*lambda", "78000000031/6000000000+71/3000000000*I", "302400000483599999147/259200000446400001090+1124400000899/259200000446400001090*I", "1", "-4-7/1000000000*I", "-48000000031/2000000000-89/2000000000*I", "-648000001115999998236/648000001116000002725-2412000002077/648000001116000002725*I", "0", "6+11/1000000000*I", "36000000031/1000000000+67/1000000000*I", "0", "0", "-36000000031/1000000000-67/1000000000*I", "0", "0", "0"], "q": "0 1 -36 1134 -24912 564597 -11502648 173126610 -4303513152 65913697026", "yuk": "1 12 -324 -29544 -1314756 -12971988 2033927928 146587697352 4172739566652 -77469253445544", "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","36","1","0","0","0","1","1"]},{"re":"1/96","im":"-1/288*3^(1/2)","approx_re":"0.0104166666667","approx_im":"-0.006014","exponents":["0","1","1","2"],"monodromy":["1/6+120*lambda","-5/36+20*lambda","-5/54+40/3*lambda","-.9896550e-2+50/9*lambda","4+7/1000000000*I","5/3-1/500000000*I","4/9-1/500000000*I","5/54-40/3*lambda","-6.-.11e-7*I","-1+3/1000000000*I","1/3+3/1000000000*I","-5/36+20*lambda","36.000000031+.67e-7*I","-24*I*3^(19/41)*lambda*Pi^3-1/62500000*I","4-9/500000000*I","11/6-120*lambda"],"monodromy_dm":["1","-13","-1","-1","0","1","0","0","0","0","1","0","0","0","0","1"]},{"re":"1/96","im":"1/288*3^(1/2)","approx_re":"0.0104166666667","approx_im":"0.006014","exponents":["0","1","1","2"],"monodromy":["11/6+120*lambda","-5/36-20*lambda","5/54+40/3*lambda","-.9896550e-2-50/9*lambda","4","1/3","4/9","-5/54-40/3*lambda","6","-1","5/3","-5/36-20*lambda","36","-6","4","1/6-120*lambda"],"monodromy_dm":["-2","-21","-1333333/1000000","-1","1","8","111111/250000","333333/1000000","-24","-168","-9666667/1000000","-8","20","140","8888889/1000000","7666667/1000000"]},{"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, 4*(2*X+1)^2*(7*X^2+7*X+3), 48*(2*X+1)*(4*X+3)*(4*X+5)*(2*X+3)]", "text": "This is operator \"2.65\" from ...", "degz": 2, "h3": null, "sol": "1 -12 324 -11280 447300 -19241712 876207024 -41638753728 2046133011780 -103313778625200", "n_discr_factors": "2", "c3": null, "operator": "4 2 0 0 0 0 1 12 76 188 224 112 2160 10368 17472 12288 3072", "new_number": "2.65", "id": 61, "operator_tex": "\\theta^4+2^{2} x(2\\theta+1)^2(7\\theta^2+7\\theta+3)+2^{4} 3 x^{2}(2\\theta+1)(4\\theta+3)(4\\theta+5)(2\\theta+3)", "superseek": "-4 -556/9", "discriminant": "2 1 112 3072", "aesz": "183", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "04a3788c3f9ed53281ae824deb33d833", "dim_h": null, "inst": " -4 8 -556/9 624 -8928 1199704/9 -2132876 35762384 -5668837952/9 11571895488", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "A_{n}=\\binom{2n}{n}\\sum_{j,k=0}^{n}(-4)^{n-j}\\binom{n}{j}\\binom{n}{k}\\binom{j}{k}\\binom{2j}{j}\\binom{2n-3k}{n}", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "(48z+1)(64z+1)", "discr_factors": "3072, z+1/64, z+1/48", "dm_basis": ["-4-310145437/500000000*I", "8", "1/2", "1", "-14", "0", "-1", "0", "-36", "72", "0", "0", "-72", "0", "0", "0"], "q": "0 1 28 558 9520 144885 2085960 28114706 372061120 4641274242", "yuk": "1 -4 60 -1672 39996 -1116004 28791288 -731576472 18310380604 -459175875784", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/48","im":"0","approx_re":"-0.0208333333333","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["3.666666992+1.240581667*I","-.888889273-.413527825*I",".296296213+.137842738*I","-.38694844e-1-.45947515e-1*I","16.000002509-.2845e-5*I","-4.333336913-.1390e-5*I","1.777778225+.1587e-5*I","-.296296073-.137842774*I","48.000008758-.8909e-5*I","-16.000011149-.4045e-5*I","6.333334810+.4721e-5*I","-.888888245-.413528325*I","144.000033661-.28975e-4*I","-48.000035910-.11385e-4*I","16.000005252+.13912e-4*I","-1.666664890-1.240584998*I"],"monodromy_dm":["5","-32000009/1000000-11/1000000*I","-1666667/1000000","-2","666667/1000000","-866667/200000-1/500000*I","-138889/500000","-333333/1000000","-24","96000037/500000+29/500000*I","2200001/200000","3000001/250000-3/1000000*I","17333333/1000000","-866667/6250-21/500000*I","-3611113/500000","-766667/100000+1/500000*I"]},{"re":"-1/64","im":"0","approx_re":"-0.015625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["5.+.620290874*I","-2-64*lambda","7/9+224/9*lambda","-.216878323-.68921208e-1*I","14","-6","49/18","-7/9-224/9*lambda","36","-18","8","-2-64*lambda","72","-36","14","-3.-.620290874*I"],"monodromy_dm":["1","-22","-1","-1","0","1","0","0","0","0","1","0","0","0","0","1"]},{"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","72","1","0","0","0","1","1"]},{"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, -12-68*X-148*X^2-160*X^3-208*X^4, 1968+11008*X+24192*X^2+24576*X^3+15360*X^4, -152832-720896*X-1327104*X^2-1179648*X^3-458752*X^4, 16384*(4*X+5)^2*(4*X+3)^2]", "text": "Sporadic Operator, reducible to 3.33, so not a primary operator.", "degz": 4, "h3": null, "sol": "1 12 324 11856 504900 23475312 1155060144 59120134848 3115322063172 167873343726000", "n_discr_factors": "2", "c3": null, "operator": "4 4 0 0 0 0 1 -12 -68 -148 -160 -208 1968 11008 24192 24576 15360 -152832 -720896 -1327104 -1179648 -458752 3686400 15728640 24641536 16777216 4194304", "new_number": "4.71", "id": 172, "operator_tex": "\\theta^4-2^{2} x\\left(52\\theta^4+40\\theta^3+37\\theta^2+17\\theta+3\\right)+2^{4} x^{2}\\left(960\\theta^4+1536\\theta^3+1512\\theta^2+688\\theta+123\\right)-2^{8} x^{3}\\left(1792\\theta^4+4608\\theta^3+5184\\theta^2+2816\\theta+597\\right)+2^{14} x^{4}(4\\theta+5)^2(4\\theta+3)^2", "superseek": "-4 -1580/9", "discriminant": "4 1 -208 15360 -458752 4194304", "aesz": "353", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "33845d8200fe810109063e352fbfc8b1", "dim_h": null, "inst": " -4 -24 -1580/9 -1580 -17120 -621272/3 -2660236 -35601596 -493759552 -7061891648", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "(16z-1)(64z-1)^3", "discr_factors": "4194304, z-1/16, (z-1/64)^3", "dm_basis": null, "q": "0 1 -20 174 -1808 10485 -97368 267922 -6478144 -38096766", "yuk": "1 -4 -196 -4744 -101316 -2140004 -44736520 -912460952 -18228118468 -359950718152", "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":"1/64","im":"0","approx_re":"0.015625","approx_im":"0.0","exponents":["0","1/2","3/2","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/16","im":"0","approx_re":"0.0625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["3/4","3/4","5/4","5/4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -12-92*X-268*X^2-352*X^3-320*X^4, 7344+46656*X+104448*X^2+99840*X^3+44544*X^4, -165888-1492992*X-4709376*X^2-5971968*X^3-2506752*X^4, 2985984*(2*X+1)^4]", "text": "Sporadic Operator. There is a second MUM-point hiding at infinity, corresponding to Operator AESZ 362/4.73", "degz": 4, "h3": null, "sol": "1 12 324 -6000 -2778300 -361782288 -30344052816 -1087320117312 175645509682500 45289843467726000", "n_discr_factors": "2", "c3": null, "operator": "4 4 0 0 0 0 1 -12 -92 -268 -352 -320 7344 46656 104448 99840 44544 -165888 -1492992 -4709376 -5971968 -2506752 2985984 23887872 71663616 95551488 47775744", "new_number": "4.72", "id": 173, "operator_tex": "\\theta^4-2^{2} x\\left(80\\theta^4+88\\theta^3+67\\theta^2+23\\theta+3\\right)+2^{4} 3 x^{2}\\left(928\\theta^4+2080\\theta^3+2176\\theta^2+972\\theta+153\\right)-2^{10} 3^{2} x^{3}\\left(272\\theta^4+648\\theta^3+511\\theta^2+162\\theta+18\\right)+2^{12} 3^{6} x^{4}\\left((2\\theta+1)^4\\right)", "superseek": "20 -119332/9", "discriminant": "4 1 -320 44544 -2506752 47775744", "aesz": "361", "n_sing_complex": "1", "inst_int": "", "c2h": null, "hash": "f55eaa640956f064f5230c04d8173d60", "dim_h": null, "inst": " 20 -139 -119332/9 -462222 -2113440 9744926503/9 86597298876 2523690015938 -1608859520322496/9 -27901291082883368", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "3", "laurent": null, "discriminant_tex": "(20736z^2-224z+1)(-1+48z)^2", "discr_factors": "47775744, z^2-7/648*z+1/20736, (-1/48+z)^2", "dm_basis": null, "q": "0 1 -44 1902 -14192 942453 -28814376 -3593659182 -207641592000 1037108780802", "yuk": "1 20 -1092 -357976 -29583300 -264179980 233877876984 29702873514488 1292129258576956 -130317621146480152", "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":"s_1","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"s_2","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"7/1296","im":"-1/324*2^(1/2)","approx_re":"0.0054012345679","approx_im":"-0.004365","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"7/1296","im":"1/324*2^(1/2)","approx_re":"0.0054012345679","approx_im":"0.004365","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/48","im":"0","approx_re":"0.0208333333333","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","1/2","1/2","1/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[529*X^4, -75233*X^4-116794*X^3-89608*X^2-31211*X-4232, 1357863*X^4+999924*X^3-787393*X^2-850862*X-205712, -6206392*X^4+2179848*X^3+1750568*X^2-1413672*X-801872, -980880*X^4+15278304*X^3+35445392*X^2+27267488*X+7128704, -1905152*(4*X+3)*(X+1)^2*(4*X+5)]", "text": "This is operator \"5.51\" from ...", "degz": 5, "h3": "23", "sol": "1 8 324 19304 1388260 111469008 9620458344 873705161232 82410223605732 8003897628341120", "n_discr_factors": "2", "c3": "-74", "operator": "4 5 0 0 0 0 529 -4232 -31211 -89608 -116794 -75233 -205712 -850862 -787393 999924 1357863 -801872 -1413672 1750568 2179848 -6206392 7128704 27267488 35445392 15278304 -980880 -28577280 -118119424 -180989440 -121929728 -30482432", "new_number": "5.51", "id": 262, "operator_tex": "23^{2} \\theta^4-23 x\\left(3271\\theta^4+5078\\theta^3+3896\\theta^2+1357\\theta+184\\right)+x^{2}\\left(1357863\\theta^4+999924\\theta^3-787393\\theta^2-850862\\theta-205712\\right)-2^{3} x^{3}\\left(775799\\theta^4-272481\\theta^3-218821\\theta^2+176709\\theta+100234\\right)-2^{4} 61 x^{4}\\left(1005\\theta^4-15654\\theta^3-36317\\theta^2-27938\\theta-7304\\right)-2^{9} 61^{2} x^{5}(4\\theta+3)(\\theta+1)^2(4\\theta+5)", "superseek": "308/23 70799/23", "discriminant": "5 529 -75233 1357863 -6206392 -980880 -30482432", "aesz": "250", "n_sing_complex": "2", "inst_int": "", "c2h": "62", "hash": "9c19794a84073d1c6dfd11c8a7c9a740", "dim_h": "9", "inst": " 308/23 3526/23 70799/23 2148684/23 81402822/23 3517706942/23 166755728017/23 8463817366930/23 452628943972573/23 25225062363800138/23", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "5", "laurent": null, "discriminant_tex": "-(512z^3+113z^2+121z-1)(-23+244z)^2", "discr_factors": "-30482432, (-23/244+z)^2, z^3+113/512*z^2+121/512*z-1/512", "dm_basis": null, "q": "0 1 -27 31 -1565 -122872 -6002087 -316779981 -17953605095 -1060383625879", "yuk": "1 308/23 28516/23 1911881/23 137544292/23 10175353058/23 759826639561/23 57197214710139/23 4333474629412452/23 329966500157917598/23", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/3072*(33598639+5035776*249^(1/2))^(1/3)+173087/3072/(33598639+5035776*249^(1/2))^(1/3)-113/1536","im":"-1/2*3^(1/2)*(1/1536*(33598639+5035776*249^(1/2))^(1/3)+173087/1536/(33598639+5035776*249^(1/2))^(1/3))","approx_re":"-0.114451","approx_im":"-0.474453","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/3072*(33598639+5035776*249^(1/2))^(1/3)+173087/3072/(33598639+5035776*249^(1/2))^(1/3)-113/1536","im":"1/2*3^(1/2)*(1/1536*(33598639+5035776*249^(1/2))^(1/3)+173087/1536/(33598639+5035776*249^(1/2))^(1/3))","approx_re":"-0.114451","approx_im":"0.474453","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":"1/1536*(33598639+5035776*249^(1/2))^(1/3)-173087/1536/(33598639+5035776*249^(1/2))^(1/3)-113/1536","im":"0","approx_re":"0.008199","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"23/244","im":"0","approx_re":"0.094262295082","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":["3/4","1","1","5/4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[25*X^4, -3785*X^4-6490*X^3-5245*X^2-2000*X-300, 196416*X^4+629928*X^3+796356*X^2+429840*X+84240, -4901472*X^4-22044960*X^3-36343404*X^2-23925780*X-5307120, 104976*(2*X+1)*(216*X^3+864*X^2+1015*X+356), -3779136*(2*X+1)*(3*X+2)*(3*X+4)*(2*X+3)]", "text": "This is operator \"5.66\" from ...", "degz": 5, "h3": null, "sol": "1 12 324 12000 548100 28767312 1645769664 99394371648 6230457476100 401731786513200", "n_discr_factors": "3", "c3": null, "operator": "4 5 0 0 0 0 25 -300 -2000 -5245 -6490 -3785 84240 429840 796356 629928 196416 -5307120 -23925780 -36343404 -22044960 -4901472 37371456 181293552 303800544 204073344 45349632 -90699264 -445938048 -767164608 -544195584 -136048896", "new_number": "5.66", "id": 278, "operator_tex": "5^{2} \\theta^4-5 x\\left(757\\theta^4+1298\\theta^3+1049\\theta^2+400\\theta+60\\right)+2^{2} 3^{2} x^{2}\\left(5456\\theta^4+17498\\theta^3+22121\\theta^2+11940\\theta+2340\\right)-2^{2} 3^{4} x^{3}\\left(15128\\theta^4+68040\\theta^3+112171\\theta^2+73845\\theta+16380\\right)+2^{4} 3^{8} x^{4}(2\\theta+1)(216\\theta^3+864\\theta^2+1015\\theta+356)-2^{6} 3^{10} x^{5}(2\\theta+1)(3\\theta+2)(3\\theta+4)(2\\theta+3)", "superseek": "49/5 6032/15", "discriminant": "5 25 -3785 196416 -4901472 45349632 -136048896", "aesz": "274", "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "729d44a3b7b561b49603f26a25d26069", "dim_h": null, "inst": " 49/5 -68/5 6032/15 36276/5 350082/5 26161264/15 274004448/5 6603998596/5 97583032357/3 4784860673996/5", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "-(81z-1)(1296z^2-56z+1)(-5+36z)^2", "discr_factors": "-136048896, z-1/81, z^2-7/162*z+1/1296, (-5/36+z)^2", "dm_basis": null, "q": "0 1 -32 804 -20180 436314 -9036624 170450550 -3377965032 57874309731", "yuk": "1 49/5 -99 54337/5 2321169/5 43760299/5 1883664801/5 93983525713/5 3381249602321/5 118563384368092/5", "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":"1/81","im":"0","approx_re":"0.0123456790123","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"7/324","im":"-1/81*2^(1/2)","approx_re":"0.0216049382716","approx_im":"-0.017459","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"7/324","im":"1/81*2^(1/2)","approx_re":"0.0216049382716","approx_im":"0.017459","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"5/36","im":"0","approx_re":"0.138888888889","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","2/3","4/3","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -12-64*X-125*X^2-122*X^3-61*X^4, -576-4176*X-8264*X^2-6176*X^3-1544*X^4, 622080+2414592*X+2823168*X^2+1345536*X^3+224256*X^4, -51609600-174735360*X-164007936*X^2-60162048*X^3-7520256*X^4, 1769472*(16*X^2+80*X+35)*(2*X+5)^2, -42467328*(2*X+11)*(2*X+7)*(2*X+5)*(2*X+1)]", "text": "This is operator \"6.5\" from ...", "degz": 6, "h3": null, "sol": "1 12 324 5760 215460 2549232 200116224 -782825472 277853698980 -7114516952400", "n_discr_factors": "3", "c3": null, "operator": "4 6 0 0 0 0 1 -12 -64 -125 -122 -61 -576 -4176 -8264 -6176 -1544 622080 2414592 2823168 1345536 224256 -51609600 -174735360 -164007936 -60162048 -7520256 1548288000 4777574400 3786670080 1132462080 113246208 -16349921280 -46883930112 -32275169280 -8153726976 -679477248", "new_number": "6.5", "id": 427, "operator_tex": "\\theta^4-x\\left(12+64\\theta+125\\theta^2+122\\theta^3+61\\theta^4\\right)-2^{3} x^{2}\\left(193\\theta^4+772\\theta^3+1033\\theta^2+522\\theta+72\\right)+2^{9} 3 x^{3}\\left(146\\theta^4+876\\theta^3+1838\\theta^2+1572\\theta+405\\right)-2^{12} 3^{2} x^{4}\\left(204\\theta^4+1632\\theta^3+4449\\theta^2+4740\\theta+1400\\right)+2^{16} 3^{3} x^{5}(16\\theta^2+80\\theta+35)(2\\theta+5)^2-2^{19} 3^{4} x^{6}(2\\theta+11)(2\\theta+7)(2\\theta+5)(2\\theta+1)", "superseek": "-11 -3422/3", "discriminant": "6 1 -61 -1544 224256 -7520256 113246208 -679477248", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "6a4aeb5833b7673c962d5598842d3f2c", "dim_h": null, "inst": " -11 68 -3422/3 30735 -1014993 37434552 -1486568559 62556815721 -8291619038429/3 127231570499928", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "6", "laurent": null, "discriminant_tex": "-(24z-1)(27648z^3-1728z^2+27z+1)(-1+32z)^2", "discr_factors": "-679477248, z-1/24, (-1/32+z)^2, z^3-1/16*z^2+1/1024*z+1/27648", "dm_basis": null, "q": "0 1 -16 -114 20776 -936859 27143952 -486221306 1441150448 149478220674", "yuk": "1 -11 533 -30809 1967573 -126874136 8085832967 -509893015748 32029091616725 -2014863426369056", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/96*(17+12*2^(1/2))^(1/3)-1/96/(17+12*2^(1/2))^(1/3)+1/48","im":"0","approx_re":"-0.016119","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/32","im":"0","approx_re":"0.03125","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"1/192*(17+12*2^(1/2))^(1/3)+1/192/(17+12*2^(1/2))^(1/3)+1/48","im":"1/6*3^(1/2)*(-1/32*(17+12*2^(1/2))^(1/3)+1/32/(17+12*2^(1/2))^(1/3))","approx_re":"0.03931","approx_im":"-0.026431","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/192*(17+12*2^(1/2))^(1/3)+1/192/(17+12*2^(1/2))^(1/3)+1/48","im":"-1/6*3^(1/2)*(-1/32*(17+12*2^(1/2))^(1/3)+1/32/(17+12*2^(1/2))^(1/3))","approx_re":"0.03931","approx_im":"0.026431","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":["1/2","5/2","7/2","11/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[25*X^4, 5*X^2*(-1-2*X+107*X^2), 4800+20800*X+34276*X^2+23768*X^3+8696*X^4, -190080-604260*X-613836*X^2-152928*X^3+11088*X^4, -2115072-7610544*X-10054080*X^2-5688000*X^3-1016640*X^4, -13379904-41383872*X-44831232*X^2-20601216*X^3-4567104*X^4, -19968768-43390080*X-11736576*X^2+24634368*X^3+12358656*X^4, 39191040+151352064*X+204353280*X^2+106002432*X^3+12690432*X^4, -26873856*(X+1)^4]", "text": "This is operator \"8.84\" from ...", "degz": 8, "h3": null, "sol": "1 0 -12 144 324 -21600 182400 2116800 -59931900 239904000", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 25 0 0 -5 -10 535 4800 20800 34276 23768 8696 -190080 -604260 -613836 -152928 11088 -2115072 -7610544 -10054080 -5688000 -1016640 -13379904 -41383872 -44831232 -20601216 -4567104 -19968768 -43390080 -11736576 24634368 12358656 39191040 151352064 204353280 106002432 12690432 -26873856 -107495424 -161243136 -107495424 -26873856", "new_number": "8.84", "id": 534, "operator_tex": "5^{2} \\theta^4+5 x\\theta^2(-1-2\\theta+107\\theta^2)+2^{2} x^{2}\\left(2174\\theta^4+5942\\theta^3+8569\\theta^2+5200\\theta+1200\\right)+2^{2} 3^{2} x^{3}\\left(308\\theta^4-4248\\theta^3-17051\\theta^2-16785\\theta-5280\\right)-2^{4} 3^{2} x^{4}\\left(7060\\theta^4+39500\\theta^3+69820\\theta^2+52851\\theta+14688\\right)-2^{6} 3^{4} x^{5}\\left(881\\theta^4+3974\\theta^3+8648\\theta^2+7983\\theta+2581\\right)+2^{7} 3^{4} x^{6}\\left(1192\\theta^4+2376\\theta^3-1132\\theta^2-4185\\theta-1926\\right)+2^{8} 3^{6} x^{7}\\left(68\\theta^4+568\\theta^3+1095\\theta^2+811\\theta+210\\right)-2^{12} 3^{8} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "1/5 224/5", "discriminant": "8 25 535 8696 11088 -1016640 -4567104 12358656 12690432 -26873856", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "258fab6f0a4f132fe597fc6f30e54eea", "dim_h": null, "inst": " 1/5 -6 224/5 -448/5 -4334/5 162734/15 4944/5 -5368254/5 52756707/5 93552762/5", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "7", "laurent": null, "discriminant_tex": "-(9z-1)(576z^3+368z^2+16z+1)(-5-36z+72z^2)^2", "discr_factors": "-26873856, z-1/9, (-5/72-1/2*z+z^2)^2, z^3+23/36*z^2+1/36*z+1/576", "dm_basis": null, "q": "0 1 0 28 -324 1306 -6192 2566 -308712 9605779", "yuk": "1 1/5 -239/5 6049/5 -28911/5 -541749/5 11722657/5 1695793/5 -2748574959/5 38459645452/5", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/216*(76276+3348*93^(1/2))^(1/3)-421/54/(76276+3348*93^(1/2))^(1/3)-23/108","im":"0","approx_re":"-0.597246","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/4-1/12*19^(1/2)","im":"0","approx_re":"-0.113242","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/432*(76276+3348*93^(1/2))^(1/3)+421/108/(76276+3348*93^(1/2))^(1/3)-23/108","im":"1/8*3^(1/2)*(-1/54*(76276+3348*93^(1/2))^(1/3)+842/27/(76276+3348*93^(1/2))^(1/3))","approx_re":"-0.020821","approx_im":"-0.049733","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/432*(76276+3348*93^(1/2))^(1/3)+421/108/(76276+3348*93^(1/2))^(1/3)-23/108","im":"-1/8*3^(1/2)*(-1/54*(76276+3348*93^(1/2))^(1/3)+842/27/(76276+3348*93^(1/2))^(1/3))","approx_re":"-0.020821","approx_im":"0.049733","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":"1/9","im":"0","approx_re":"0.111111111111","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/4+1/12*19^(1/2)","im":"0","approx_re":"0.613242","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}]}