{"count": 3, "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, -472*(X+1/2)^4-446*(X+1/2)^2-15, 83344*(X+1)^4+102060*(X+1)^2+9252, -6524928*(X+3/2)^4-5576448*(X+3/2)^2-69888, 9216*(12*X+19)*(12*X+23)*(12*X+25)*(12*X+29)]", "text": "Sporadic YY-Operator.", "degz": 4, "h3": null, "sol": "1 156 21062 2714208 342489420 42745344432 5302680749912 655600683760704 80913588850087846 9978933506757141000", "n_discr_factors": "2", "c3": null, "operator": "4 4 0 0 0 0 1 -156 -682 -1154 -944 -472 194656 537496 602124 333376 83344 -45649344 -104815872 -93662976 -39149568 -6524928 2919859200 5977276416 4551966720 1528823808 191102976", "new_number": "4.32", "id": 129, "operator_tex": "\\theta^4-2 x\\left(236\\theta^4+472\\theta^3+577\\theta^2+341\\theta+78\\right)+2^{2} x^{2}\\left(20836\\theta^4+83344\\theta^3+150531\\theta^2+134374\\theta+48664\\right)-2^{6} 3 x^{3}\\left(33984\\theta^4+203904\\theta^3+487828\\theta^2+545916\\theta+237757\\right)+2^{10} 3^{2} x^{4}(12\\theta+19)(12\\theta+23)(12\\theta+25)(12\\theta+29)", "superseek": "-14 -196", "discriminant": "4 1 -472 83344 -6524928 191102976", "aesz": "356\n", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "e73c971c3ed3a4fd581234510642c285", "dim_h": null, "inst": " -14 -42 -196 -1218 -208446/5 -1249164 -31158358 -665413042 -13244743400 -255577395122", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "(128z-1)^2(108z-1)^2", "discr_factors": "191102976, (z-1/128)^2, (z-1/108)^2", "dm_basis": null, "q": "0 1 -58 2285 -73180 2053050 -53567538 1306009292 -30756537128 694691706071", "yuk": "1 -14 -350 -5306 -78302 -5211164 -269825066 -10687316808 -340691555806 -9655417943906", "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","-1/2","1","3/2"],"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":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["19/12","23/12","25/12","29/12"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, 295*X^4+572*X^3+424*X^2+138*X+17, 1686*X^4+1488*X^3-946*X^2-962*X-202, 2258*X^4-1032*X^3-1450*X^2-318*X+8, -519*X^4-1056*X^3-870*X^2-342*X-54, -9*(X+1)^4]", "text": "A-incarnation: $7 \\times 7$ linear Pfaffian in $P^7$.\nThere is a second MUM point at infinity, associated to\nthe 7 fold linear section of $G(2,7)$ AESZ 27/5.7\n", "degz": 5, "h3": null, "sol": "1 -17 1549 -215585 36505501 -6921832517 1412721479989 -303643747364513 67815981014552605 -15600719128907479517", "n_discr_factors": "2", "c3": null, "operator": "4 5 0 0 0 0 1 17 138 424 572 295 -202 -962 -946 1488 1686 8 -318 -1450 -1032 2258 -54 -342 -870 -1056 -519 -9 -36 -54 -36 -9", "new_number": "5.46", "id": 256, "operator_tex": "\\theta^4+x\\left(295\\theta^4+572\\theta^3+424\\theta^2+138\\theta+17\\right)+2 x^{2}\\left(843\\theta^4+744\\theta^3-473\\theta^2-481\\theta-101\\right)+2 x^{3}\\left(1129\\theta^4-516\\theta^3-725\\theta^2-159\\theta+4\\right)-3 x^{4}\\left(173\\theta^4+352\\theta^3+290\\theta^2+114\\theta+18\\right)-3^{2} x^{5}\\left((\\theta+1)^4\\right)", "superseek": "-42 -41706", "discriminant": "5 1 295 1686 2258 -519 -9", "aesz": "243\n", "n_sing_complex": "3", "inst_int": "", "c2h": null, "hash": "93c30005b5a976a2b7c5206d5e679a45", "dim_h": null, "inst": " -42 875 -41706 2954224 -257813864 25738516377 -2820518451954 330947014189001 -40915701638541114 5271607385884271558", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "5", "laurent": null, "discriminant_tex": "-(z^3+57z^2-289z-1)(3z+1)^2", "discr_factors": "-9, (z+1/3)^2, z^3+57*z^2-289*z-1", "dm_basis": null, "q": "0 1 70 1127 47530 -3054373 361505368 -45010753732 5899877798258 -806209019396627", "yuk": "1 -42 6958 -1126104 189077294 -32226733042 5559518418328 -967437829020264 169444871453845806 -29827546494497598210", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-7/6*(-756+84*I*3^(1/2))^(1/3)-98/(-756+84*I*3^(1/2))^(1/3)-19+1/2*I*3^(1/2)*(7/3*(-756+84*I*3^(1/2))^(1/3)-196/(-756+84*I*3^(1/2))^(1/3))","im":"0","approx_re":"-61.684843","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/3","im":"0","approx_re":"-0.333333333333","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-7/6*(-756+84*I*3^(1/2))^(1/3)-98/(-756+84*I*3^(1/2))^(1/3)-19-1/2*I*3^(1/2)*(7/3*(-756+84*I*3^(1/2))^(1/3)-196/(-756+84*I*3^(1/2))^(1/3))","im":"0","approx_re":"-0.003458","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":"7/3*(-756+84*I*3^(1/2))^(1/3)+196/(-756+84*I*3^(1/2))^(1/3)-19","im":"0","approx_re":"4.688301","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","1","1"],"monodromy":[],"monodromy_dm":[]}]}]}