{"count": 5, "status":"OK", "data":[{"pols": "[X^4, -4*(2*X+1)^2*(5*X^2+5*X+2), 256*(2*X+1)*(X+1)^2*(2*X+3)]", "text": "Hadamard product $I \\ast \\alpha$\nA-Incarnation: diagonal subfamily of 1,1,1,1-intersection in $P^1 \\times P^1 \\times P^1 \\times \\P^1$\nB-Incarnations:\nFibre products: 62211- x 632--1, S62211\n", "degz": 2, "h3": "48", "sol": "1 8 168 5120 190120 7939008 357713664 16993726464 839358285480 42714450658880", "n_discr_factors": "2", "c3": "-128", "operator": "4 2 0 0 0 0 1 -8 -52 -132 -160 -80 768 3584 5888 4096 1024", "new_number": "2.52", "id": 47, "operator_tex": "\\theta^4-2^{2} x(2\\theta+1)^2(5\\theta^2+5\\theta+2)+2^{8} x^{2}(2\\theta+1)(\\theta+1)^2(2\\theta+3)", "superseek": "4 644/3", "discriminant": "2 1 -80 1024", "aesz": "16", "n_sing_complex": "0", "inst_int": "", "c2h": "96", "hash": "05af0662662bfbec63e3186c4f363313", "dim_h": "16", "inst": " 4 20 644/3 3072 52512 1027868 22083628 507552272 36850292240/3 309706589472", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "(64z-1)(16z-1)", "discr_factors": "1024, z-1/64, z-1/16", "dm_basis": ["-310145437/500000000*I", "12", "1", "1", "-4", "-24", "-1", "0", "0", "48", "0", "0", "-48", "0", "0", "0"], "q": "0 1 -20 222 -2704 21293 -307224 80402 -67101504 -1187407098", "yuk": "1 4 164 5800 196772 6564004 222025448 7574684408 259866960036 8954621020120", "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","48","1","0","0","0","1","1"]},{"re":"1/64","im":"0","approx_re":"0.015625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["1.+.620290874*I","0","32/3*lambda",".8015849e-2","4","1","1/3","-32/3*lambda","0","0","1","0","48","0","4","1.-.620290874*I"],"monodromy_dm":["1","-16","-1","-1","0","1","0","0","0","0","1","0","0","0","0","1"]},{"re":"1/16","im":"0","approx_re":"0.0625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["5+512*lambda","-1.-.620290874*I","1/3+128/3*lambda","-1/7*7^(5/8)*exp(-9/4)*Zeta(5)^(1/4)-64/3*lambda","16","-3","4/3","-1/3-128/3*lambda","48","-12","5","-1.-.620290874*I","192","-48","16","-3-512*lambda"],"monodromy_dm":["-7","-88","-5","-4","2","23","5/4","1","-48","-528","-29","-24","32","352","20","17"]},{"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, -4*(2*X+1)^2*(5*X^2+5*X+2), 32*(2*X+1)*(2*X+3)*(7*X^2+14*X+8), -176*(2*X+1)*(2*X+3)^2*(2*X+5)]", "text": "This is operator \"3.31\" from ...", "degz": 3, "h3": null, "sol": "1 8 168 5360 210280 9269568 440263824 22027234944 1145252033640 61332823872320", "n_discr_factors": "1", "c3": null, "operator": "4 3 0 0 0 0 1 -8 -52 -132 -160 -80 768 3392 5280 3584 896 -7920 -29568 -35200 -16896 -2816", "new_number": "3.31", "id": 94, "operator_tex": "\\theta^4-2^{2} x(2\\theta+1)^2(5\\theta^2+5\\theta+2)+2^{5} x^{2}(2\\theta+1)(2\\theta+3)(7\\theta^2+14\\theta+8)-2^{4} 11 x^{3}(2\\theta+1)(2\\theta+3)^2(2\\theta+5)", "superseek": "4 284", "discriminant": "3 1 -80 896 -2816", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "660b0951ad934fc17fda7eb9b1750649", "dim_h": null, "inst": " 4 27 284 4368 80968 1722333 40082284 998658176 26202453860 716312822310", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "4", "laurent": null, "discriminant_tex": "1-80z+896z^2-2816z^3", "discr_factors": "-2816, -1/2816+5/176*z-7/22*z^2+z^3", "dm_basis": null, "q": "0 1 -20 210 -2864 25415 -479656 595578 -139496000 -2233947465", "yuk": "1 4 220 7672 279772 10121004 372031816 13748223416 511313265884 19101588871612", "gv2": null, "gv0": null, "gv1": null}, {"pols": "[9*X^4, -55632*X^4-95136*X^3-64164*X^2-16596*X-1512, 30232576*X^4+26054656*X^3-13438976*X^2-8615424*X-1128960, -4130603008*X^4+1056964608*X^3+1151926272*X^2+231211008*X+12386304, -822083584*(4*X+1)*(2*X+1)^2*(4*X+3)]", "text": "Sporadic Operator.", "degz": 4, "h3": null, "sol": "1 168 279720 737721600 2391487698600 8717511682047168 34277910683556443904 142115219255002478284800 612718123704257507465529000 2722381600280229607324028424000", "n_discr_factors": "2", "c3": null, "operator": "4 4 0 0 0 0 9 -1512 -16596 -64164 -95136 -55632 -1128960 -8615424 -13438976 26054656 30232576 12386304 231211008 1151926272 1056964608 -4130603008 -2466250752 -23018340352 -75631689728 -105226698752 -52613349376", "new_number": "4.62", "id": 162, "operator_tex": "3^{2} \\theta^4-2^{2} 3 x\\left(4636\\theta^4+7928\\theta^3+5347\\theta^2+1383\\theta+126\\right)+2^{9} x^{2}\\left(59048\\theta^4+50888\\theta^3-26248\\theta^2-16827\\theta-2205\\right)-2^{16} 7 x^{3}\\left(9004\\theta^4-2304\\theta^3-2511\\theta^2-504\\theta-27\\right)-2^{24} 7^{2} x^{4}(4\\theta+1)(2\\theta+1)^2(4\\theta+3)", "superseek": "4300/3 1701817028/3", "discriminant": "4 9 -55632 30232576 -4130603008 -52613349376", "aesz": "292", "n_sing_complex": "1", "inst_int": "", "c2h": null, "hash": "bce26f214ee56f65c7a275cd8fdcc0c7", "dim_h": null, "inst": " 4300/3 1768292/3 1701817028/3 2484553593752/3 1500880129466144 9350482662153015820/3 7110166243548551297772 52120041107300527753842568/3 134207871085060188820318570256/3 360162480402539472681189005683360/3", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "3", "laurent": null, "discriminant_tex": "-(65536z^2+5584z-1)(-3+896z)^2", "discr_factors": "-52613349376, z^2+349/4096*z-1/65536, (-3/896+z)^2", "dm_basis": null, "q": "0 1 -1172 98526 -341830288 -694093661395 -1640092990169880 -4223070324113649134 -11497369531205203223360 -32654543280727574249164026", "yuk": "1 4300/3 14150636/3 45949064056/3 159011444150764/3 562830048549808300/3 2019704255071014627512/3 7316361064611459285411688/3 8895153682312676407137181860 97837538021008877650058186780680/3", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-349/8192-85/8192*17^(1/2)","im":"0","approx_re":"-0.085384","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":"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":"-349/8192+85/8192*17^(1/2)","im":"0","approx_re":"0.000179","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"3/896","im":"0","approx_re":"0.00334821428571","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":["1/4","1/2","1/2","3/4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[9409*X^4, 97*X*(1727*X^3-2018*X^2-1300*X-291), -1652135*X^4-13428812*X^3-16174393*X^2-10216234*X-2709792, -81753435*X^4-364126194*X^3-568639497*X^2-443115594*X-138000348, -1175502862*X^4-5423394464*X^3-10006378570*X^2-8869415520*X-3049275024, -9726250397*X^4-50507429234*X^3-106108023451*X^2-103964102350*X-38537290992, -52762935894*X^4-312374434824*X^3-733053660150*X^2-781527778884*X-308040167808, -195453433908*X^4-1313199235080*X^3-3399527062044*X^2-3901093356168*X-1619360309088, -144*(X+1)*(3432647479*X^3+22487363787*X^2+50808614711*X+38959393614), -432*(X+1)*(X+2)*(1903493629*X^2+10262864555*X+14314039440), -438048*(X+3)*(X+2)*(X+1)*(1862987*X+5992902), -368028363456*(X+1)*(X+2)*(X+3)*(X+4)]", "text": "This is operator \"11.2\" from ...", "degz": 11, "h3": null, "sol": "1 0 18 168 2430 37200 605340 10342080 182788830 3320565360", "n_discr_factors": "3", "c3": null, "operator": "4 11 0 0 0 0 9409 0 -28227 -126100 -195746 167519 -2709792 -10216234 -16174393 -13428812 -1652135 -138000348 -443115594 -568639497 -364126194 -81753435 -3049275024 -8869415520 -10006378570 -5423394464 -1175502862 -38537290992 -103964102350 -106108023451 -50507429234 -9726250397 -308040167808 -781527778884 -733053660150 -312374434824 -52762935894 -1619360309088 -3901093356168 -3399527062044 -1313199235080 -195453433908 -5610152680416 -12926593198800 -10554620903712 -3732481622304 -494301236976 -12367330076160 -27418110089760 -21128955996816 -6900485230944 -822309247728 -15751072411776 -33773432464512 -24727927434912 -7521645111552 -816077729376 -8832680722944 -18401418172800 -12880992720960 -3680283634560 -368028363456", "new_number": "11.2", "id": 339, "operator_tex": "97^{2} \\theta^4+97 x\\theta(1727\\theta^3-2018\\theta^2-1300\\theta-291)-x^{2}\\left(1652135\\theta^4+13428812\\theta^3+16174393\\theta^2+10216234\\theta+2709792\\right)-3 x^{3}\\left(27251145\\theta^4+121375398\\theta^3+189546499\\theta^2+147705198\\theta+46000116\\right)-2 x^{4}\\left(587751431\\theta^4+2711697232\\theta^3+5003189285\\theta^2+4434707760\\theta+1524637512\\right)-x^{5}\\left(9726250397\\theta^4+50507429234\\theta^3+106108023451\\theta^2+103964102350\\theta+38537290992\\right)-2 3 x^{6}\\left(8793822649\\theta^4+52062405804\\theta^3+122175610025\\theta^2+130254629814\\theta+51340027968\\right)-2^{2} 3^{2} x^{7}\\left(5429262053\\theta^4+36477756530\\theta^3+94431307279\\theta^2+108363704338\\theta+44982230808\\right)-2^{4} 3^{2} x^{8}(\\theta+1)(3432647479\\theta^3+22487363787\\theta^2+50808614711\\theta+38959393614)-2^{4} 3^{3} x^{9}(\\theta+1)(\\theta+2)(1903493629\\theta^2+10262864555\\theta+14314039440)-2^{5} 3^{4} 13^{2} x^{10}(\\theta+3)(\\theta+2)(\\theta+1)(1862987\\theta+5992902)-2^{6} 3^{3} 13^{4} 7457 x^{11}(\\theta+1)(\\theta+2)(\\theta+3)(\\theta+4)", "superseek": "136/97 1768/97", "discriminant": "11 9409 167519 -1652135 -81753435 -1175502862 -9726250397 -52762935894 -195453433908 -494301236976 -822309247728 -816077729376 -368028363456", "aesz": null, "n_sing_complex": "6", "inst_int": "", "c2h": null, "hash": "940a6a9fb87fe9b9613bd73b990374c1", "dim_h": null, "inst": " 136/97 292/97 1768/97 10128/97 83387/97 721092/97 7043124/97 72658472/97 792624984/97 8992463150/97", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "10", "laurent": null, "discriminant_tex": "-(12z^2+6z+1)(7457z^5+6100z^4+1929z^3+257z^2+7z-1)(97+912z+2028z^2)^2", "discr_factors": "-368028363456, z^2+1/2*z+1/12, (97/2028+76/169*z+z^2)^2, z^5+6100/7457*z^4+1929/7457*z^3+257/7457*z^2+7/7457*z-1/7457", "dm_basis": null, "q": "0 1 -3 -22 -39 100 -1804 -31220 -345247 -3823451", "yuk": "1 136/97 2472/97 47872/97 650664/97 10423511/97 155806080/97 2415791668/97 37201788328/97 577823661208/97", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-38/169-1/1014*2805^(1/2)","im":"0","approx_re":"-0.277083","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/4","im":"-1/12*3^(1/2)","approx_re":"-0.25","approx_im":"-0.144338","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/4","im":"1/12*3^(1/2)","approx_re":"-0.25","approx_im":"0.144338","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-38/169+1/1014*2805^(1/2)","im":"0","approx_re":"-0.172621","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":"#ND","im":"#ND","approx_re":"#ND","approx_im":"#ND","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": "[16*X^4, -4*X*(2*X^3+82*X^2+53*X+12), -4895*X^4-18410*X^3-26199*X^2-18308*X-5120, -60679*X^4-272424*X^3-497452*X^2-430092*X-143808, -344527*X^4-1870838*X^3-4034628*X^2-3987101*X-1478544, -(X+1)*(1076509*X^3+5847783*X^2+11226106*X+7492832), -2*(X+1)*(X+2)*(944887*X^2+4249317*X+5045304), -3328*(X+3)*(X+2)*(X+1)*(518*X+1381), -621920*(X+1)*(X+2)*(X+3)*(X+4)]", "text": "This is operator \"8.40\" from ...", "degz": 8, "h3": null, "sol": "1 0 20 168 2652 40080 666920 11536560 207013660 3816224160", "n_discr_factors": "6", "c3": null, "operator": "4 8 0 0 0 0 16 0 -48 -212 -328 -8 -5120 -18308 -26199 -18410 -4895 -143808 -430092 -497452 -272424 -60679 -1478544 -3987101 -4034628 -1870838 -344527 -7492832 -18718938 -17073889 -6924292 -1076509 -20181216 -47269092 -39366058 -14167956 -1889774 -27575808 -60899072 -46538752 -14939392 -1723904 -14926080 -31096000 -21767200 -6219200 -621920", "new_number": "8.40", "id": 486, "operator_tex": "2^{4} \\theta^4-2^{2} x\\theta(2\\theta^3+82\\theta^2+53\\theta+12)-x^{2}\\left(4895\\theta^4+18410\\theta^3+26199\\theta^2+18308\\theta+5120\\right)-x^{3}\\left(60679\\theta^4+272424\\theta^3+497452\\theta^2+430092\\theta+143808\\right)-x^{4}\\left(344527\\theta^4+1870838\\theta^3+4034628\\theta^2+3987101\\theta+1478544\\right)-x^{5}(\\theta+1)(1076509\\theta^3+5847783\\theta^2+11226106\\theta+7492832)-2 x^{6}(\\theta+1)(\\theta+2)(944887\\theta^2+4249317\\theta+5045304)-2^{8} 13 x^{7}(\\theta+3)(\\theta+2)(\\theta+1)(518\\theta+1381)-2^{5} 5 13^{2} 23 x^{8}(\\theta+1)(\\theta+2)(\\theta+3)(\\theta+4)", "superseek": "5/4 35/2", "discriminant": "8 16 -8 -4895 -60679 -344527 -1076509 -1889774 -1723904 -621920", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "d3cb0fbbc65d6c5dace733d3d1ca181b", "dim_h": null, "inst": " 5/4 57/16 35/2 459/4 3615/4 97217/12 317945/4 833711 110476691/12 1694285265/16", "cleanlist": "True", "n_sing_real": "7", "sol_explicit": "", "n_sing_rational": "7", "n_sing": "7", "laurent": null, "discriminant_tex": "-(23z-1)(5z+1)(2z+1)(z+1)(13z+4)^2(4z+1)^2", "discr_factors": "-621920, z+1/5, z+1/2, (z+4/13)^2, (z+1/4)^2, z-1/23, z+1", "dm_basis": null, "q": "0 1 -3 -25 -15 88 -2373 -34656 -361587 -4196900", "yuk": "1 5/4 119/4 1895/4 29495/4 112970 7001633/4 27263785 1707469623/4 6711459452", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1","im":"0","approx_re":"-1.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/2","im":"0","approx_re":"-0.5","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-4/13","im":"0","approx_re":"-0.307692307692","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","1/3","2/3","1"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/5","im":"0","approx_re":"-0.2","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":"1/23","im":"0","approx_re":"0.0434782608696","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":[]}]}]}