{"count": 6, "status":"OK", "data":[{"pols": "[X^4, -12*(3*X+1)*(3*X+2)*(3*X^2+3*X+1), 288*(3*X+1)*(3*X+2)*(3*X+4)*(3*X+5)]", "text": "B*d", "degz": 2, "h3": "24", "sol": "1 24 1800 188160 23423400 3257077824 488795763456 77515931750400 12811645904789160 2186013527216376000", "n_discr_factors": "2", "c3": "-162", "operator": "4 2 0 0 0 0 1 -24 -180 -504 -648 -324 11520 67392 127008 93312 23328", "new_number": "2.14", "id": 5, "operator_tex": "\\theta^4-2^{2} 3 x(3\\theta+1)(3\\theta+2)(3\\theta^2+3\\theta+1)+2^{5} 3^{2} x^{2}(3\\theta+1)(3\\theta+2)(3\\theta+4)(3\\theta+5)", "superseek": "24 5832", "discriminant": "2 1 -324 23328", "aesz": "48", "n_sing_complex": "0", "inst_int": "", "c2h": "84", "hash": "8081a3989d09a7d612953dac3341d90c", "dim_h": "11", "inst": " 24 291/2 5832 247116 12634944 1428093585/2 44538150984 5965179917793/2 210544112347488 15478336155532764", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "A_{n}=\\dbinom{2n}{n}\\dbinom{3n}{n}\\sum_{k=0}^{n}\\dbinom{n}{k}\\dbinom{2k}{k}\\dbinom{2n-2k}{n-k}", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "(216z-1)(108z-1)", "discr_factors": "23328, z-1/216, z-1/108", "dm_basis": ["-162*lambda", "15/2", "1", "1", "-7/2", "-12", "-1", "0", "0", "24", "0", "0", "-24", "0", "0", "0"], "q": "0 1 -84 4950 -267760 12647805 -598963032 25047931322 -1164686536896 41143256426646", "yuk": "1 24 1188 157488 15816612 1579368024 154234265832 15276585787536 1527086074771620 153486657901476240", "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","24","1","0","0","0","1","1"]},{"re":"1/216","im":"0","approx_re":"0.00462962962963","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["1+162*lambda","0","189/8*lambda",".25679681e-1","7/2","1","49/96","-189/8*lambda","0","0","1","0","24","0","7/2","1-162*lambda"],"monodromy_dm":["1","-11","-1","-1","0","1","0","0","0","0","1","0","0","0","0","1"]},{"re":"1/108","im":"0","approx_re":"0.00925925925926","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["13/4+324*lambda","-9/16-81*lambda","21/64+189/4*lambda","-.54109387e-1-243/8*lambda","7+1/500000000*I","-3/4+1/1000000000*I","49/48-1/1000000000*I","-21/64-189/4*lambda","12+1/250000000*I","-3+1/500000000*I","11/4-1/500000000*I","-9/16-81*lambda","48.+.19e-7*I","-11.999999983+.80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-8*I","7-1/125000000*I","-5/4-324*lambda"],"monodromy_dm":["-3","-28","-5/2","-2","1","8","5/8","1/2","-12","-84","-13/2","-6","9","63","45/8","11/2"]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/3","2/3","4/3","5/3"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -2*(2*X+1)^2*(13*X^2+13*X+4), -12*(2*X+1)*(3*X+2)*(3*X+4)*(2*X+3)]", "text": "A-incarnation: $X(1,1,1,1,2) \\subset  Grass(2,6)$", "degz": 2, "h3": "28", "sol": "1 8 288 15200 968800 68923008 5269660704 423919926144 35416227132000 3046522120928000", "n_discr_factors": "2", "c3": "-116", "operator": "4 2 0 0 0 0 1 -8 -58 -162 -208 -104 -288 -1416 -2436 -1728 -432", "new_number": "2.61", "id": 57, "operator_tex": "\\theta^4-2 x(2\\theta+1)^2(13\\theta^2+13\\theta+4)-2^{2} 3 x^{2}(2\\theta+1)(3\\theta+2)(3\\theta+4)(2\\theta+3)", "superseek": "10 1724", "discriminant": "2 1 -104 -432", "aesz": "26", "n_sing_complex": "0", "inst_int": "", "c2h": "76", "hash": "f3fc09474973b19b8bdb783e3322eb65", "dim_h": "11", "inst": " 10 191/2 1724 45680 1478214 54700117 15538355858/7 96420345432 4412026389850 420731987451785/2", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "-(4z+1)(108z-1)", "discr_factors": "-432, z-1/108, z+1/4", "dm_basis": ["-116*lambda", "47/6", "1", "1", "-19/6", "-14", "-1", "0", "0", "28", "0", "0", "-28", "0", "0", "0"], "q": "0 1 -26 121 -1372 -68612 -2386858 -114302870 -5530073512 -279569669756", "yuk": "1 10 774 46558 2924294 184776760 11815272594 761379437052 49367219785478 3216367238247208", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/4","im":"0","approx_re":"-0.25","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["20/3+464*lambda","-17/6-232*lambda","1.0456349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349+.414911827*I","-.241563519-.227532292*I","62/3","-28/3","961/252","-1.0456349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349-.414911827*I","56","-28","34/3","-17/6-232*lambda","112","-56","62/3","-14/3-464*lambda"],"monodromy_dm":["-11","-80","-6","-4","6","41","3","2","-108","-720","-53","-36","78","520","39","27"]},{"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","28","1","0","0","0","1","1"]},{"re":"1/108","im":"0","approx_re":"0.00925925925926","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["1+116*lambda","0",".63575199e-1*I","79/7000","19/6","1","361/1008","-.63575199e-1*I","0","0","1","0","28","0","19/6","1-116*lambda"],"monodromy_dm":["1","-11","-1","-1","0","1","0","0","0","0","1","0","0","0","0","1"]},{"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": "[841*X^4, -6728-47937*X-132733*X^2-169592*X^3-87754*X^4, 5568+57768*X+239159*X^2+424220*X^3+258647*X^4, -76560-336864*X-581647*X^2-532614*X^3-272743*X^4, 75616+332792*X+552228*X^2+421124*X^3+130696*X^4, -3468*(X+1)^2*(3*X+2)*(3*X+4)]", "text": "This is operator \"5.24\" from ...", "degz": 5, "h3": "29", "sol": "1 8 264 13040 778840 51955008 3725735664 281152383072 22035642730200 1778348612268800", "n_discr_factors": "2", "c3": "-100", "operator": "4 5 0 0 0 0 841 -6728 -47937 -132733 -169592 -87754 5568 57768 239159 424220 258647 -76560 -336864 -581647 -532614 -272743 75616 332792 552228 421124 130696 -27744 -117912 -183804 -124848 -31212", "new_number": "5.24", "id": 232, "operator_tex": "29^{2} \\theta^4-29 x\\left(3026\\theta^4+5848\\theta^3+4577\\theta^2+1653\\theta+232\\right)+x^{2}\\left(5568+57768\\theta+239159\\theta^2+424220\\theta^3+258647\\theta^4\\right)-x^{3}\\left(76560+336864\\theta+581647\\theta^2+532614\\theta^3+272743\\theta^4\\right)+2^{2} 17 x^{4}\\left(1922\\theta^4+6193\\theta^3+8121\\theta^2+4894\\theta+1112\\right)-2^{2} 3 17^{2} x^{5}(\\theta+1)^2(3\\theta+2)(3\\theta+4)", "superseek": "285/29 40626/29", "discriminant": "5 841 -87754 258647 -272743 130696 -31212", "aesz": "195", "n_sing_complex": "2", "inst_int": "", "c2h": "74", "hash": "49a600431b3e9aaa9d9d6947f8df7d2b", "dim_h": "11", "inst": " 285/29 2362/29 40626/29 997476/29 30096841/29 1036931650/29 39188167891/29 1585184851720/29 67548466106031/29 2999289959592904/29", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "5", "laurent": null, "discriminant_tex": "-(27z^3-67z^2+102z-1)(-29+34z)^2", "discr_factors": "-31212, z^3-67/27*z^2+34/9*z-1/27, (-29/34+z)^2", "dm_basis": null, "q": "0 1 -25 146 -1925 -41626 -1710492 -73263248 -3311266553 -155893120414", "yuk": "1 285/29 19181/29 1097187/29 63857645/29 3762105410/29 223978352483/29 13441541586898/29 811614707938285/29 49242831792393786/29", "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":"-1/162*(4157812+472068*93^(1/2))^(1/3)+7546/81/(4157812+472068*93^(1/2))^(1/3)+67/81","im":"0","approx_re":"0.009868","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"29/34","im":"0","approx_re":"0.852941176471","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/324*(4157812+472068*93^(1/2))^(1/3)-3773/81/(4157812+472068*93^(1/2))^(1/3)+67/81","im":"1/2*3^(1/2)*(-1/162*(4157812+472068*93^(1/2))^(1/3)-7546/81/(4157812+472068*93^(1/2))^(1/3))","approx_re":"1.235807","approx_im":"-1.492036","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/324*(4157812+472068*93^(1/2))^(1/3)-3773/81/(4157812+472068*93^(1/2))^(1/3)+67/81","im":"-1/2*3^(1/2)*(-1/162*(4157812+472068*93^(1/2))^(1/3)-7546/81/(4157812+472068*93^(1/2))^(1/3))","approx_re":"1.235807","approx_im":"1.492036","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["2/3","1","1","4/3"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[25*X^4, -300-2050*X-5510*X^2-6920*X^3-3280*X^4, 58320+276240*X+460644*X^2+304992*X^3+64224*X^4, -1136160-4408560*X-5230656*X^2-1952640*X^3-152064*X^4, -1728*(2*X+1)*(586*X^3+3039*X^2+3947*X+1527), -20736*(2*X+1)*(6*X+5)*(6*X+7)*(2*X+3)]", "text": "This is operator \"5.40\" from ...", "degz": 5, "h3": "30", "sol": "1 12 396 19920 1241100 87281712 6628328784 530854264512 44210267063820 3794011978270800", "n_discr_factors": "4", "c3": "-76", "operator": "4 5 0 0 0 0 25 -300 -2050 -5510 -6920 -3280 58320 276240 460644 304992 64224 -1136160 -4408560 -5230656 -1952640 -152064 -2638656 -12097728 -18892224 -11515392 -2025216 -2177280 -10285056 -17086464 -11943936 -2985984", "new_number": "5.40", "id": 250, "operator_tex": "5^{2} \\theta^4-2 5 x\\left(328\\theta^4+692\\theta^3+551\\theta^2+205\\theta+30\\right)+2^{2} 3 x^{2}\\left(5352\\theta^4+25416\\theta^3+38387\\theta^2+23020\\theta+4860\\right)-2^{4} 3^{3} x^{3}\\left(352\\theta^4+4520\\theta^3+12108\\theta^2+10205\\theta+2630\\right)-2^{6} 3^{3} x^{4}(2\\theta+1)(586\\theta^3+3039\\theta^2+3947\\theta+1527)-2^{8} 3^{4} x^{5}(2\\theta+1)(6\\theta+5)(6\\theta+7)(2\\theta+3)", "superseek": "62/5 4060/3", "discriminant": "5 25 -3280 64224 -152064 -2025216 -2985984", "aesz": "226", "n_sing_complex": "0", "inst_int": "", "c2h": "72", "hash": "92f95cd33ac4bf18c2d05ce3040c5203", "dim_h": "11", "inst": " 62/5 55 4060/3 28790 861786 142235826/5 1037839042 202280686482/5 24925623464146/15 71113248663729", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "5", "n_sing": "5", "laurent": null, "discriminant_tex": "-(16z-1)(108z-1)(12z-1)(5+12z)^2", "discr_factors": "-2985984, z-1/108, z-1/16, z-1/12, (5/12+z)^2", "dm_basis": null, "q": "0 1 -34 681 -15884 276164 -7151058 68883986 -4231865736 -52348783680", "yuk": "1 62/5 2262/5 182762/5 9215062/5 538616312/5 30723123378/5 1779893957092/5 103567720693846/5 1211385300394048", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-5/12","im":"0","approx_re":"-0.416666666667","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":"1/108","im":"0","approx_re":"0.00925925925926","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":"1/12","im":"0","approx_re":"0.0833333333333","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","5/6","7/6","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[841*X^4, -76444*X^4-135488*X^3-104748*X^2-37004*X-5046, -363984*X^4-2977536*X^3-5070104*X^2-3166336*X-673380, 3417200*X^4+7725600*X^3-4670100*X^2-11040300*X-3654000, 10000*(2*X+1)*(68*X^3+1842*X^2+2899*X+1215), -5000000*(2*X+1)*(X+1)^2*(2*X+3)]", "text": "This is operator \"5.78\" from ...", "degz": 5, "h3": "29", "sol": "1 6 210 9780 551250 34587756 2330225436 165091881240 12143185630290 919460248406700", "n_discr_factors": "2", "c3": "-104", "operator": "4 5 0 0 0 0 841 -5046 -37004 -104748 -135488 -76444 -673380 -3166336 -5070104 -2977536 -363984 -3654000 -11040300 -4670100 7725600 3417200 12150000 53290000 76400000 37520000 1360000 -15000000 -70000000 -115000000 -80000000 -20000000", "new_number": "5.78", "id": 291, "operator_tex": "29^{2} \\theta^4-2 29 x\\left(1318\\theta^4+2336\\theta^3+1806\\theta^2+638\\theta+87\\right)-2^{2} x^{2}\\left(90996\\theta^4+744384\\theta^3+1267526\\theta^2+791584\\theta+168345\\right)+2^{2} 5^{2} x^{3}\\left(34172\\theta^4+77256\\theta^3-46701\\theta^2-110403\\theta-36540\\right)+2^{4} 5^{4} x^{4}(2\\theta+1)(68\\theta^3+1842\\theta^2+2899\\theta+1215)-2^{6} 5^{7} x^{5}(2\\theta+1)(\\theta+1)^2(2\\theta+3)", "superseek": "248/29 38708/29", "discriminant": "5 841 -76444 -363984 3417200 1360000 -20000000", "aesz": "308", "n_sing_complex": "3", "inst_int": "", "c2h": "74", "hash": "94e96c5d238b2d22a633f4e05ec1ae9f", "dim_h": "11", "inst": " 248/29 2476/29 38708/29 940480/29 27926248/29 947385848/29 35235085432/29 1402989415192/29 58850157860196/29 2572297729204788/29", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "5", "laurent": null, "discriminant_tex": "-(2000z^3+1024z^2+84z-1)(-29+100z)^2", "discr_factors": "-20000000, (-29/100+z)^2, z^3+64/125*z^2+21/500*z-1/2000", "dm_basis": null, "q": "0 1 -20 -56 564 -52084 -1877024 -73710174 -3304023696 -153370033730", "yuk": "1 248/29 20056/29 1045364/29 60210776/29 3490781248/29 204636408340/29 12085634303424/29 718330640789080/29 42901765081128248/29", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/3000*(-3837466+471750*I*111^(1/2))^(1/3)-8509/750/(-3837466+471750*I*111^(1/2))^(1/3)-64/375+1/4*I*3^(1/2)*(1/750*(-3837466+471750*I*111^(1/2))^(1/3)-17018/375/(-3837466+471750*I*111^(1/2))^(1/3))","im":"0","approx_re":"-0.40534","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/3000*(-3837466+471750*I*111^(1/2))^(1/3)-8509/750/(-3837466+471750*I*111^(1/2))^(1/3)-64/375-1/4*I*3^(1/2)*(1/750*(-3837466+471750*I*111^(1/2))^(1/3)-17018/375/(-3837466+471750*I*111^(1/2))^(1/3))","im":"0","approx_re":"-0.117186","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":"1/1500*(-3837466+471750*I*111^(1/2))^(1/3)+8509/375/(-3837466+471750*I*111^(1/2))^(1/3)-64/375","im":"0","approx_re":"0.010526","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"29/100","im":"0","approx_re":"0.29","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":[]}]}, {"pols": "[25*X^4, -2365*X^4-4460*X^3-3480*X^2-1250*X-175, 3946*X^4-9272*X^3-28834*X^2-21790*X-5490, 6174*X^4+34560*X^3+20646*X^2-6210*X-5760, -6723*X^4+8424*X^3+37098*X^2+32886*X+9234, -6561*(X+1)^4]", "text": "There is a second MUM-point at infinity,\ncorresponding to Operator AESZ 319/5.85\nFibre product: 53211- x 632--1(1)\n", "degz": 5, "h3": "30", "sol": "1 7 219 9961 546379 33440757 2199262269 152168119383 10933656369867 808865626688413", "n_discr_factors": "3", "c3": "-86", "operator": "4 5 0 0 0 0 25 -175 -1250 -3480 -4460 -2365 -5490 -21790 -28834 -9272 3946 -5760 -6210 20646 34560 6174 9234 32886 37098 8424 -6723 -6561 -26244 -39366 -26244 -6561", "new_number": "5.84", "id": 298, "operator_tex": "5^{2} \\theta^4-5 x\\left(473\\theta^4+892\\theta^3+696\\theta^2+250\\theta+35\\right)+2 x^{2}\\left(1973\\theta^4-4636\\theta^3-14417\\theta^2-10895\\theta-2745\\right)+2 3^{2} x^{3}\\left(343\\theta^4+1920\\theta^3+1147\\theta^2-345\\theta-320\\right)-3^{4} x^{4}\\left(83\\theta^4-104\\theta^3-458\\theta^2-406\\theta-114\\right)-3^{8} x^{5}\\left((\\theta+1)^4\\right)", "superseek": "46/5 1126", "discriminant": "5 25 -2365 3946 6174 -6723 -6561", "aesz": "318", "n_sing_complex": "0", "inst_int": "", "c2h": "72", "hash": "3fa38f629ecd5f39b585ce0c1bd88463", "dim_h": "11", "inst": " 46/5 717/10 1126 51481/2 3609772/5 693353459/30 4058216342/5 305088059917/10 6040466014836/5 249239441393223/5", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "-(z+1)(81z^2+92z-1)(-5+9z)^2", "discr_factors": "-6561, z+1, (-5/9+z)^2, z^2+92/81*z-1/81", "dm_basis": null, "q": "0 1 -22 75 -874 -37047 -1214304 -48755214 -2049708066 -89619902802", "yuk": "1 46/5 2914/5 152056/5 8239874/5 451221546/5 24960879448/5 1391968205352/5 78102551578626/5 880699944993500", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-46/81-13/81*13^(1/2)","im":"0","approx_re":"-1.14657","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":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"-46/81+13/81*13^(1/2)","im":"0","approx_re":"0.010767","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"5/9","im":"0","approx_re":"0.555555555556","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":[]}]}]}