{"count": 13, "status":"OK", "data":[{"pols": "[X^4, -12*(6*X+1)*(6*X+5)*(11*X^2+11*X+3), -144*(6*X+1)*(6*X+5)*(6*X+7)*(6*X+11)]", "text": "Hadamard product D*b", "degz": 2, "h3": "5", "sol": "1 180 263340 600359760 1674535082220 5241848970037680 17682527926185922800 62858194850514176942400 232283449582150476496229100 884380168260018662188830073200", "n_discr_factors": "1", "c3": "-310", "operator": "4 2 0 0 0 0 1 -180 -1956 -6708 -9504 -4752 -55440 -476928 -984960 -746496 -186624", "new_number": "2.8", "id": 69, "operator_tex": "\\theta^4-2^{2} 3 x(6\\theta+1)(6\\theta+5)(11\\theta^2+11\\theta+3)-2^{4} 3^{2} x^{2}(6\\theta+1)(6\\theta+5)(6\\theta+7)(6\\theta+11)", "superseek": "684 195638820", "discriminant": "2 1 -4752 -186624", "aesz": "63", "n_sing_complex": "0", "inst_int": "", "c2h": "62", "hash": "06c1a4c0aa33f5051126908a9898430d", "dim_h": "6", "inst": " 684 253314 195638820 225040578570 319342448936304 518678194659431382 924742518999240521412 1765350300279949945903098 3550840060459824682540995768 7442817913346821405606737574632", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "A_{n}=\\dbinom{3n}{n}\\dbinom{6n}{3n}\\sum_{k=0}^{n}\\dbinom{n}{k}^2\\dbinom{n+k}{n}", "n_sing_rational": "1", "n_sing": "3", "laurent": null, "discriminant_tex": "1-4752z-186624z^2", "discr_factors": "-186624, -1/186624+11/432*z+z^2", "dm_basis": ["-18778337/12500000*I", "41/12", "1", "1", "-31/12", "-5/2", "-1", "0", "0", "5", "0", "0", "-5", "0", "0", "0"], "q": "0 1 -1236 518886 -341674576 -139917999999 -394931030325048 -772657012856807950 -1652733244361094441792 -3681781681705227994077036", "yuk": "1 684 2027196 5282248824 14402599055676 39917806117038684 112034490051721453848 317186684016739498845000 903859353743348774901441852 2588562404075212193577668163696", "gv2": null, "gv0": "3420 1266570 978194100 1125202892850 1596712244681520 2593390973297156910 4623712594996202607060 8826751501399749729515490 17754200302299123412704978840 37214089566734107028033687873160", "gv1": "1 -611 -3437965 524537945 45789504955348 237013737984797903 922140400732269341707 3194302059028418771226413 10422130250486093277576627602 32835948356762502255457871199012 101197837229894144239785401837134687 307353612113700782742506313245639065747 924111578878985088236416673619227863043666 2758694347598875436399107807565293524221631211 8192783760701900165883854702691298475934825311210 24238246646997852102562442441857224687577031126730717 71504687170135476618498894144695286670786901837784141886 210493121686083905667207826208012300271051389728190355845174 618640193094906782902605489784535343596488530257809790743381583"}, {"pols": "[9*X^4, -2496*X^4-2688*X^3-1956*X^2-612*X-72, 16384*X^4-475136*X^3-822272*X^2-428544*X-72192, 9437184*X^4+37748736*X^3+30605312*X^2+9437184*X+983040, -16777216*(2*X+1)^4]", "text": "Sporadic operator. There is a second MUM-point\nhiding at infinity, corresponding to Operator 4.56", "degz": 4, "h3": "12", "sol": "1 8 936 108800 16748200 2810179008 509793064704 97163659726848 19240100389996200 3922510470614964800", "n_discr_factors": "3", "c3": "-88", "operator": "4 4 0 0 0 0 9 -72 -612 -1956 -2688 -2496 -72192 -428544 -822272 -475136 16384 983040 9437184 30605312 37748736 9437184 -16777216 -134217728 -402653184 -536870912 -268435456", "new_number": "4.33", "id": 130, "operator_tex": "3^{2} \\theta^4-2^{2} 3 x\\left(208\\theta^4+224\\theta^3+163\\theta^2+51\\theta+6\\right)+2^{9} x^{2}\\left(32\\theta^4-928\\theta^3-1606\\theta^2-837\\theta-141\\right)+2^{16} x^{3}\\left(144\\theta^4+576\\theta^3+467\\theta^2+144\\theta+15\\right)-2^{24} x^{4}\\left((2\\theta+1)^4\\right)", "superseek": "76/3 144196/3", "discriminant": "4 9 -2496 16384 9437184 -268435456", "aesz": "55", "n_sing_complex": "0", "inst_int": "", "c2h": "48", "hash": "7e88cd5b7dc1c51022b66ac6f009218f", "dim_h": "6", "inst": " 76/3 3476/3 144196/3 3563196 309069600 95147523676/3 10621019178308/3 1274833553965780/3 161052568610071312/3 7072463333697906400", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "-(64z+1)(256z-1)(-3+128z)^2", "discr_factors": "-268435456, z-1/256, z+1/64, (-3/128+z)^2", "dm_basis": null, "q": "0 1 -36 -2082 -18768 -4144851 -572787192 -73468972270 -9672435358272 -1347029244663546", "yuk": "1 76/3 27884/3 3893368/3 684161516/3 115901100076/3 20551869035192/3 1214336526053240 652714780314640876/3 117407322516745879816/3", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/64","im":"0","approx_re":"-0.015625","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":"1/256","im":"0","approx_re":"0.00390625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"3/128","im":"0","approx_re":"0.0234375","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": "[25*X^4, -600-5250*X-16895*X^2-23290*X^3-13085*X^4, -165120-1038720*X-1974144*X^2-935232*X^3+129216*X^4, 921600+9400320*X+32044032*X^2+39813120*X^3+8801280*X^4, -3538944*(3*X+1)*(2*X+1)^2*(3*X+2)]", "text": "Sporadic Operator.", "degz": 4, "h3": "10", "sol": "1 24 3960 974400 292030200 98002929024 35404004091456 13469740411944960 5325269471817867000 2168604409044940152000", "n_discr_factors": "3", "c3": "-120", "operator": "4 4 0 0 0 0 25 -600 -5250 -16895 -23290 -13085 -165120 -1038720 -1974144 -935232 129216 921600 9400320 32044032 39813120 8801280 -7077888 -60162048 -187564032 -254803968 -127401984", "new_number": "4.44", "id": 142, "operator_tex": "5^{2} \\theta^4-5 x\\left(2617\\theta^4+4658\\theta^3+3379\\theta^2+1050\\theta+120\\right)+2^{6} 3 x^{2}\\left(673\\theta^4-4871\\theta^3-10282\\theta^2-5410\\theta-860\\right)+2^{10} 3^{2} x^{3}\\left(955\\theta^4+4320\\theta^3+3477\\theta^2+1020\\theta+100\\right)-2^{17} 3^{3} x^{4}(3\\theta+1)(2\\theta+1)^2(3\\theta+2)", "superseek": "379/5 1364199/5", "discriminant": "4 25 -13085 129216 8801280 -127401984", "aesz": "232", "n_sing_complex": "0", "inst_int": "", "c2h": "52", "hash": "8d5ff690c87757ed51a092dee764eede", "dim_h": "6", "inst": " 379/5 3346 1364199/5 177727432/5 5658116533 5162925665472/5 1034132839801394/5 44368440569992104 50146684202347697994/5 2362720295938250247382", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "-(27z+1)(512z-1)(-5+96z)^2", "discr_factors": "-127401984, (-5/96+z)^2, z-1/512, z+1/27", "dm_basis": null, "q": "0 1 -114 1029 -116984 -43625010 -7822436202 -1800503860710 -431538538385184 -107734627015030629", "yuk": "1 379/5 134219/5 36833752/5 11374689867/5 3536322833504/5 1115191980709544/5 354707564051878521/5 113583207870554476107/5 36556932783511508671378/5", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/27","im":"0","approx_re":"-0.037037037037","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":"1/512","im":"0","approx_re":"0.001953125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"5/96","im":"0","approx_re":"0.0520833333333","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": "[X^4, 280*X^4+776*X^3+580*X^2+192*X+24, -6768*X^4+41184*X^3+101328*X^2+57216*X+9888, -41472*X^4+746496*X^3+5446656*X^2+4499712*X+928512, -82944*(3*X+1)*(3*X+2)*(42*X^2+258*X+223), 11943936*(3*X+1)*(3*X+2)*(3*X+4)*(3*X+5)]", "text": "This is operator \"5.101\" from ...", "degz": 5, "h3": "16", "sol": "1 -24 2160 -309120 54608400 -10824637824 2311144932096 -519918637455360 121579349447247120 -29291011307905776000", "n_discr_factors": "2", "c3": "-114", "operator": "4 5 0 0 0 0 1 24 192 580 776 280 9888 57216 101328 41184 -6768 928512 4499712 5446656 746496 -41472 -36993024 -209267712 -366031872 -223948800 -31352832 477757440 2794881024 5267275776 3869835264 967458816", "new_number": "5.101", "id": 183, "operator_tex": "\\theta^4+2^{2} x\\left(70\\theta^4+194\\theta^3+145\\theta^2+48\\theta+6\\right)-2^{4} 3 x^{2}\\left(141\\theta^4-858\\theta^3-2111\\theta^2-1192\\theta-206\\right)-2^{8} 3^{2} x^{3}\\left(18\\theta^4-324\\theta^3-2364\\theta^2-1953\\theta-403\\right)-2^{10} 3^{4} x^{4}(3\\theta+1)(3\\theta+2)(42\\theta^2+258\\theta+223)+2^{14} 3^{6} x^{5}(3\\theta+1)(3\\theta+2)(3\\theta+4)(3\\theta+5)", "superseek": "-52 -44772", "discriminant": "5 1 280 -6768 -41472 -31352832 967458816", "aesz": "348\n", "n_sing_complex": "2", "inst_int": "", "c2h": "40", "hash": "8759f016475d17d0fc88f4b98a374d3f", "dim_h": "6", "inst": " -52 461/2 -44772 3546761/2 -178670332 32517931641/2 -1653102364436 366947580015355/2 -21196688793453600 5118794506088892927/2", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "5", "laurent": null, "discriminant_tex": "(746496z^3+17280z^2+352z+1)(-1+36z)^2", "discr_factors": "967458816, z^3+5/216*z^2+11/23328*z+1/746496, (-1/36+z)^2", "dm_basis": null, "q": "0 1 96 5712 419072 25422576 2011912704 92161450240 10068708114432 59645210003352", "yuk": "1 -52 1792 -1208896 113498144 -22333791552 3511935410176 -567014111001600 93938580597429024 -15452386130428883296", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/2592*(1502+342*57^(1/2))^(1/3)+41/648/(1502+342*57^(1/2))^(1/3)-5/648","im":"-1/16*3^(1/2)*(1/162*(1502+342*57^(1/2))^(1/3)+82/81/(1502+342*57^(1/2))^(1/3))","approx_re":"-0.009925","approx_im":"-0.017537","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/2592*(1502+342*57^(1/2))^(1/3)+41/648/(1502+342*57^(1/2))^(1/3)-5/648","im":"1/16*3^(1/2)*(1/162*(1502+342*57^(1/2))^(1/3)+82/81/(1502+342*57^(1/2))^(1/3))","approx_re":"-0.009925","approx_im":"0.017537","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/1296*(1502+342*57^(1/2))^(1/3)-41/324/(1502+342*57^(1/2))^(1/3)-5/648","im":"0","approx_re":"-0.003299","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":"1/36","im":"0","approx_re":"0.0277777777778","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","2/3","4/3","5/3"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -320*X^4-832*X^3-640*X^2-224*X-32, 13312*X^4+120832*X^3+212992*X^2+125952*X+26368, 917504*X^4+786432*X^3-6291456*X^2-6881280*X-1900544, -262144*(2*X+1)*(56*X^3+468*X^2+646*X+249), -16777216*(2*X+1)*(4*X+3)*(4*X+5)*(2*X+3)]", "text": "This is operator \"5.14\" from ...", "degz": 5, "h3": "16", "sol": "1 32 2448 273920 38525200 6236600832 1103685859584 207343941083136 40648001362459920 8227704225727500800", "n_discr_factors": "3", "c3": "40", "operator": "4 5 0 0 0 0 1 -32 -224 -640 -832 -320 26368 125952 212992 120832 13312 -1900544 -6881280 -6291456 786432 917504 -65273856 -299892736 -461373440 -260046848 -29360128 -754974720 -3623878656 -6106906624 -4294967296 -1073741824", "new_number": "5.14", "id": 221, "operator_tex": "\\theta^4-2^{5} x\\left(10\\theta^4+26\\theta^3+20\\theta^2+7\\theta+1\\right)+2^{8} x^{2}\\left(52\\theta^4+472\\theta^3+832\\theta^2+492\\theta+103\\right)+2^{16} x^{3}\\left(14\\theta^4+12\\theta^3-96\\theta^2-105\\theta-29\\right)-2^{18} x^{4}(2\\theta+1)(56\\theta^3+468\\theta^2+646\\theta+249)-2^{24} x^{5}(2\\theta+1)(4\\theta+3)(4\\theta+5)(2\\theta+3)", "superseek": "64 23360", "discriminant": "5 1 -320 13312 917504 -29360128 -1073741824", "aesz": "116", "n_sing_complex": "0", "inst_int": "", "c2h": "40", "hash": "0b366ad8c78b6697205c5a7fff270f5b", "dim_h": "6", "inst": " 64 12 23360 654490 53956288 3558145052 286700496448 24007522298674 2129883087617536 196912935173735108", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "-(-1+256z)(32z+1)^2(64z-1)^2", "discr_factors": "-1073741824, -1/256+z, (z+1/32)^2, (z-1/64)^2", "dm_basis": null, "q": "0 1 -96 6816 -493568 32166192 -2164343808 130369476096 -8668096954368 469785092535960", "yuk": "1 64 160 630784 41887520 6744536064 768559962112 98338270281728 12291851458808608 1552684770873814528", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/32","im":"0","approx_re":"-0.03125","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":"1/256","im":"0","approx_re":"0.00390625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/64","im":"0","approx_re":"0.015625","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"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": "[9*X^4, -216-1764*X-5556*X^2-7584*X^3-3216*X^4, 56448+309504*X+547840*X^2+206848*X^3-57344*X^4, -552960-1179648*X+3096576*X^2+8257536*X^3+1703936*X^4, 524288*(8*X^2-28*X-33)*(2*X+1)^2, -16777216*(2*X+1)^2*(2*X+3)^2]", "text": "This is operator \"5.32\" from ...", "degz": 5, "h3": "12", "sol": "1 24 2664 470400 102047400 24865372224 6530512133376 1807527662493696 520080121087698600 154177852438395614400", "n_discr_factors": "3", "c3": "-60", "operator": "4 5 0 0 0 0 9 -216 -1764 -5556 -7584 -3216 56448 309504 547840 206848 -57344 -552960 -1179648 3096576 8257536 1703936 -17301504 -83886080 -123731968 -41943040 16777216 -150994944 -805306368 -1476395008 -1073741824 -268435456", "new_number": "5.32", "id": 241, "operator_tex": "3^{2} \\theta^4-2^{2} 3 x\\left(268\\theta^4+632\\theta^3+463\\theta^2+147\\theta+18\\right)-2^{7} x^{2}\\left(448\\theta^4-1616\\theta^3-4280\\theta^2-2418\\theta-441\\right)+2^{12} x^{3}\\left(416\\theta^4+2016\\theta^3+756\\theta^2-288\\theta-135\\right)+2^{19} x^{4}(8\\theta^2-28\\theta-33)(2\\theta+1)^2-2^{24} x^{5}(2\\theta+1)^2(2\\theta+3)^2", "superseek": "220/3 89212", "discriminant": "5 9 -3216 -57344 1703936 16777216 -268435456", "aesz": "215", "n_sing_complex": "0", "inst_int": "", "c2h": "48", "hash": "ced61f5675491a3c4446c0e55e7bc36b", "dim_h": "6", "inst": " 220/3 3538/3 89212 7484350 2459418080/3 101765882498 41645703700340/3 2027421395102806 311986325809618928 50032192549267851440", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "-(16z-1)(4096z^2-384z+1)(3+64z)^2", "discr_factors": "-268435456, z-1/16, z^2-3/32*z+1/4096, (3/64+z)^2", "dm_basis": null, "q": "0 1 -100 4062 -254928 1863469 -1363683960 -138587625198 -25730687151168 -4253310930124026", "yuk": "1 220/3 9508 7226392/3 479007908 307427260220/3 21981433037800 4761492123072280 1038039754771644580 682314094545643821928/3", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-3/64","im":"0","approx_re":"-0.046875","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":"3/64-1/32*2^(1/2)","im":"0","approx_re":"0.002681","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":"3/64+1/32*2^(1/2)","im":"0","approx_re":"0.091069","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","3/2","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[121*X^4, -2904-24684*X-79068*X^2-108768*X^3-48048*X^4, 50688+204864*X-399968*X^2-2703872*X^3-1989248*X^4, -1297296-7767936*X-17613696*X^2-22758912*X^3-23232768*X^4, -18432*(964*X^2+1360*X+669)*(2*X+1)^2, -5308416*(2*X+1)^2*(2*X+3)^2]", "text": "This is operator \"5.83\" from ...", "degz": 5, "h3": "11", "sol": "1 24 3240 675600 171901800 49034994624 15064673467536 4875632664439680 1640033450646762600 568302437330193508800", "n_discr_factors": "2", "c3": "-88", "operator": "4 5 0 0 0 0 121 -2904 -24684 -79068 -108768 -48048 50688 204864 -399968 -2703872 -1989248 -1297296 -7767936 -17613696 -22758912 -23232768 -12331008 -74391552 -167362560 -171343872 -71073792 -47775744 -254803968 -467140608 -339738624 -84934656", "new_number": "5.83", "id": 297, "operator_tex": "11^{2} \\theta^4-2^{2} 3 11 x\\left(364\\theta^4+824\\theta^3+599\\theta^2+187\\theta+22\\right)-2^{5} x^{2}\\left(62164\\theta^4+84496\\theta^3+12499\\theta^2-6402\\theta-1584\\right)-2^{4} 3 x^{3}\\left(484016\\theta^4+474144\\theta^3+366952\\theta^2+161832\\theta+27027\\right)-2^{11} 3^{2} x^{4}(964\\theta^2+1360\\theta+669)(2\\theta+1)^2-2^{16} 3^{4} x^{5}(2\\theta+1)^2(2\\theta+3)^2", "superseek": "852/11 1678156/11", "discriminant": "5 121 -48048 -1989248 -23232768 -71073792 -84934656", "aesz": "316", "n_sing_complex": "2", "inst_int": "", "c2h": "50", "hash": "b8201d587a016cc013e2477aadb5c1ff", "dim_h": "6", "inst": " 852/11 21572/11 1678156/11 15912512 22956446184/11 3433194654748/11 563991930666972/11 9018115493682352 18385133020280565556/11 322819093214895368408", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "5", "laurent": null, "discriminant_tex": "-(2304z^3+1664z^2+432z-1)(11+192z)^2", "discr_factors": "-84934656, z^3+13/18*z^2+3/16*z-1/2304, (11/192+z)^2", "dm_basis": null, "q": "0 1 -108 3282 -216528 -12519609 -2779275096 -499664503174 -98806684879296 -20228146546192713", "yuk": "1 852/11 173428/11 45311064/11 11202581876/11 2869555773852/11 67415462809928 193449232218772248/11 50790026471621588340/11 13402761971784577601388/11", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/432*(89027+11799*57^(1/2))^(1/3)+53/108/(89027+11799*57^(1/2))^(1/3)-13/54","im":"-1/8*3^(1/2)*(1/54*(89027+11799*57^(1/2))^(1/3)+106/27/(89027+11799*57^(1/2))^(1/3))","approx_re":"-0.362258","approx_im":"-0.240689","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/432*(89027+11799*57^(1/2))^(1/3)+53/108/(89027+11799*57^(1/2))^(1/3)-13/54","im":"1/8*3^(1/2)*(1/54*(89027+11799*57^(1/2))^(1/3)+106/27/(89027+11799*57^(1/2))^(1/3))","approx_re":"-0.362258","approx_im":"0.240689","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-11/192","im":"0","approx_re":"-0.0572916666667","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":"1/216*(89027+11799*57^(1/2))^(1/3)-53/54/(89027+11799*57^(1/2))^(1/3)-13/54","im":"0","approx_re":"0.002294","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","3/2","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[121*X^4, -53273*X^4-98098*X^3-71555*X^2-22506*X-2662, 1248736*X^4+1373824*X^3-93484*X^2-295768*X-59532, -8191552*X^4-4101504*X^3-2319504*X^2-1258224*X-250272, 2048*(2*X+1)*(1964*X^3+3078*X^2+1853*X+419), -262144*(2*X+1)*(X+1)^2*(2*X+3)]", "text": "This is operator \"5.86\" from ...", "degz": 5, "h3": "33", "sol": "1 22 2850 568300 138119170 37615727772 11031077174964 3407461875743640 1093860581057179650 361723380553923894220", "n_discr_factors": "3", "c3": "-276", "operator": "4 5 0 0 0 0 121 -2662 -22506 -71555 -98098 -53273 -59532 -295768 -93484 1373824 1248736 -250272 -1258224 -2319504 -4101504 -8191552 858112 5511168 13893632 16629760 8044544 -786432 -3670016 -6029312 -4194304 -1048576", "new_number": "5.86", "id": 300, "operator_tex": "11^{2} \\theta^4-11 x\\left(4843\\theta^4+8918\\theta^3+6505\\theta^2+2046\\theta+242\\right)+2^{2} x^{2}\\left(312184\\theta^4+343456\\theta^3-23371\\theta^2-73942\\theta-14883\\right)-2^{4} x^{3}\\left(511972\\theta^4+256344\\theta^3+144969\\theta^2+78639\\theta+15642\\right)+2^{11} x^{4}(2\\theta+1)(1964\\theta^3+3078\\theta^2+1853\\theta+419)-2^{18} x^{5}(2\\theta+1)(\\theta+1)^2(2\\theta+3)", "superseek": "741/11 138745", "discriminant": "5 121 -53273 1248736 -8191552 8044544 -1048576", "aesz": "320\n", "n_sing_complex": "0", "inst_int": "", "c2h": "6", "hash": "d19e7569ce62abdd5393977835e411a9", "dim_h": "6", "inst": " 741/11 22232/11 138745 157326644/11 19999995398/11 2909079079700/11 42234678016062 7222906721199284 14317861835506930871/11 2688992762246137303028/11", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "-(z-1)(64z^2-416z+1)(-11+128z)^2", "discr_factors": "-1048576, z^2-13/2*z+1/64, z-1, (-11/128+z)^2", "dm_basis": null, "q": "0 1 -98 1903 -131400 -14622585 -2450519310 -444459362517 -84911071039168 -16907623125532026", "yuk": "1 741/11 178597/11 41208006/11 10069083813/11 2499999425491/11 628361122601062/11 159351440154602667/11 40679410663863451301/11 10437721278084593812965/11", "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":"13/4-15/8*3^(1/2)","im":"0","approx_re":"0.002405","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"11/128","im":"0","approx_re":"0.0859375","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1","im":"0","approx_re":"1.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"13/4+15/8*3^(1/2)","im":"0","approx_re":"6.497595","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","1","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, 288*X^4-768*X^3-528*X^2-144*X-16, -44032*X^4-262144*X^3-64000*X^2-23040*X-5120, -18644992*X^4-33423360*X^3-30851072*X^2-14401536*X-2572288, -3670016*(2*X+1)*(186*X^3+375*X^2+317*X+100), -6576668672*(2*X+1)*(X+1)^2*(2*X+3)]", "text": "This is operator \"5.91\" from ...", "degz": 5, "h3": "16", "sol": "1 16 1488 183040 27611920 4644009216 840155264256 159984411045888 31647762945461520 6447385477360072960", "n_discr_factors": "4", "c3": "68", "operator": "4 5 0 0 0 0 1 -16 -144 -528 -768 288 -5120 -23040 -64000 -262144 -44032 -2572288 -14401536 -30851072 -33423360 -18644992 -367001600 -1897398272 -3703046144 -3435134976 -1365245952 -19730006016 -92073361408 -151263379456 -105226698752 -26306674688", "new_number": "5.91", "id": 306, "operator_tex": "\\theta^4+2^{4} x\\left(18\\theta^4-48\\theta^3-33\\theta^2-9\\theta-1\\right)-2^{9} x^{2}\\left(86\\theta^4+512\\theta^3+125\\theta^2+45\\theta+10\\right)-2^{14} x^{3}\\left(1138\\theta^4+2040\\theta^3+1883\\theta^2+879\\theta+157\\right)-2^{19} 7 x^{4}(2\\theta+1)(186\\theta^3+375\\theta^2+317\\theta+100)-2^{27} 7^{2} x^{5}(2\\theta+1)(\\theta+1)^2(2\\theta+3)", "superseek": "112 186800", "discriminant": "5 1 288 -44032 -18644992 -1365245952 -26306674688", "aesz": "331", "n_sing_complex": "0", "inst_int": "", "c2h": "40", "hash": "a30093d8c1ab2f66122cef8935b79efb", "dim_h": "6", "inst": " 112 -2242 186800 -11675813 1250599376 -109453519578 12996262564592 -1335165142501083 167689997418831488 -18917764674198834614", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "5", "n_sing": "5", "laurent": null, "discriminant_tex": "-(32z+1)(256z-1)(64z+1)(1+224z)^2", "discr_factors": "-26306674688, z-1/256, (1/224+z)^2, z+1/64, z+1/32", "dm_basis": null, "q": "0 1 -80 4224 -353280 32901040 -3889583616 442866134016 -57164706250752 7080975365853336", "yuk": "1 112 -17824 5043712 -747269856 156324922112 -23641955203072 4457718059655168 -683604553707824352 122246008118333198464", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/32","im":"0","approx_re":"-0.03125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/64","im":"0","approx_re":"-0.015625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/224","im":"0","approx_re":"-0.00446428571429","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":"1/256","im":"0","approx_re":"0.00390625","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","1","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[16*X^4, -288-2400*X-7636*X^2-10472*X^3-5128*X^4, -26424-143496*X-285795*X^2-241290*X^3-85527*X^4, -784728-4313736*X-7404372*X^2-1481328*X^3+1265787*X^4, -8612406-34179894*X-29773818*X^2+29597400*X^3+22024548*X^4, -39234780-121404744*X+67263372*X^2+479110464*X^3-54377568*X^4, -102509064-240211332*X+66371076*X^2-85030560*X^3-1465359984*X^4, -17006112*(2*X+1)*(100*X^3+162*X^2+95*X+21), 1224440064*(2*X+1)*(X+1)^2*(2*X+3)]", "text": "This is operator \"8.30\" from ...", "degz": 8, "h3": "36", "sol": "1 18 1926 310860 61060230 13432459068 3181130504244 793444983882408 205654006502505990 54906028842418516620", "n_discr_factors": "3", "c3": "-204", "operator": "4 8 0 0 0 0 16 -288 -2400 -7636 -10472 -5128 -26424 -143496 -285795 -241290 -85527 -784728 -4313736 -7404372 -1481328 1265787 -8612406 -34179894 -29773818 29597400 22024548 -39234780 -121404744 67263372 479110464 -54377568 -102509064 -240211332 66371076 -85030560 -1465359984 -357128352 -2329837344 -5986151424 -7210591488 -3401222400 3673320192 17142160896 28162121472 19591041024 4897760256", "new_number": "8.30", "id": 475, "operator_tex": "2^{4} \\theta^4-2^{2} x\\left(1282\\theta^4+2618\\theta^3+1909\\theta^2+600\\theta+72\\right)-3^{2} x^{2}\\left(9503\\theta^4+26810\\theta^3+31755\\theta^2+15944\\theta+2936\\right)+3^{4} x^{3}\\left(15627\\theta^4-18288\\theta^3-91412\\theta^2-53256\\theta-9688\\right)+2 3^{6} x^{4}\\left(15106\\theta^4+20300\\theta^3-20421\\theta^2-23443\\theta-5907\\right)-2^{2} 3^{8} x^{5}\\left(2072\\theta^4-18256\\theta^3-2563\\theta^2+4626\\theta+1495\\right)-2^{2} 3^{10} x^{6}\\left(6204\\theta^4+360\\theta^3-281\\theta^2+1017\\theta+434\\right)-2^{5} 3^{12} x^{7}(2\\theta+1)(100\\theta^3+162\\theta^2+95\\theta+21)+2^{8} 3^{14} x^{8}(2\\theta+1)(\\theta+1)^2(2\\theta+3)", "superseek": "229/4 297111/4", "discriminant": "8 16 -5128 -85527 1265787 22024548 -54377568 -1465359984 -3401222400 4897760256", "aesz": "314", "n_sing_complex": "2", "inst_int": "", "c2h": "0", "hash": "893692ba7eb3effcbc0c3b48d405456a", "dim_h": "6", "inst": " 229/4 1293 297111/4 6150238 2540085295/4 74831355661 9685903435429 1342462084703074 392130689138916953/2 29842706359594087140", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "7", "laurent": null, "discriminant_tex": "(z-1)(11664z^3+3888z^2+324z-1)(-4-9z+648z^2)^2", "discr_factors": "4897760256, z-1, (-1/162-1/72*z+z^2)^2, z^3+1/3*z^2+1/36*z-1/11664", "dm_basis": null, "q": "0 1 -78 1029 -60368 -6625650 -865943982 -127452930702 -19739639668632 -3184583094643149", "yuk": "1 229/4 41605/4 4011113/2 1574502533/4 79377665526 32327149677353/2 13289059513408817/4 2749362351046398085/4 142931636191137234925", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/36*2^(1/3)-1/72*2^(2/3)-1/9","im":"-1/36*3^(1/2)*(2^(1/3)-1/2*2^(2/3))","approx_re":"-0.168156","approx_im":"-0.022431","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/36*2^(1/3)-1/72*2^(2/3)-1/9","im":"1/36*3^(1/2)*(2^(1/3)-1/2*2^(2/3))","approx_re":"-0.168156","approx_im":"0.022431","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/144-1/144*129^(1/2)","im":"0","approx_re":"-0.071929","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":"1/18*2^(1/3)+1/36*2^(2/3)-1/9","im":"0","approx_re":"0.002979","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/144+1/144*129^(1/2)","im":"0","approx_re":"0.085818","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1","im":"0","approx_re":"1.0","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","1","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[16*X^4, -240-1536*X-4020*X^2-4968*X^3-1944*X^4, 73116+319248*X+512001*X^2+294462*X^3+32913*X^4, -2386260-7989840*X-7779645*X^2+196830*X^3+1120230*X^4, -10731609-64892664*X-136142937*X^2-126964098*X^3-22652946*X^4, -177343830-419641560*X-134926965*X^2+124199730*X^3-149492385*X^4, 30114990+1562436540*X+5464984950*X^2+6557981940*X^3+3059328690*X^4, -239148450-3348078300*X-12515435550*X^2-18334714500*X^3-9526079925*X^4, -1076168025*(X+1)^4]", "text": "This operator has a second MUM-point at infininty corresponding to operator 8.31", "degz": 8, "h3": "11", "sol": "1 15 459 19545 1019259 60504165 3910479525 267933366135 19147233606075 1412455648664085", "n_discr_factors": "3", "c3": "-88", "operator": "4 8 0 0 0 0 16 -240 -1536 -4020 -4968 -1944 73116 319248 512001 294462 32913 -2386260 -7989840 -7779645 196830 1120230 -10731609 -64892664 -136142937 -126964098 -22652946 -177343830 -419641560 -134926965 124199730 -149492385 30114990 1562436540 5464984950 6557981940 3059328690 -239148450 -3348078300 -12515435550 -18334714500 -9526079925 -1076168025 -4304672100 -6457008150 -4304672100 -1076168025", "new_number": "8.32", "id": 477, "operator_tex": "2^{4} \\theta^4-2^{2} 3 x\\left(162\\theta^4+414\\theta^3+335\\theta^2+128\\theta+20\\right)+3^{3} x^{2}\\left(1219\\theta^4+10906\\theta^3+18963\\theta^2+11824\\theta+2708\\right)+3^{5} 5 x^{3}\\left(922\\theta^4+162\\theta^3-6403\\theta^2-6576\\theta-1964\\right)-3^{7} x^{4}\\left(10358\\theta^4+58054\\theta^3+62251\\theta^2+29672\\theta+4907\\right)-3^{9} 5 x^{5}\\left(1519\\theta^4-1262\\theta^3+1371\\theta^2+4264\\theta+1802\\right)+2 3^{11} 5 x^{6}\\left(1727\\theta^4+3702\\theta^3+3085\\theta^2+882\\theta+17\\right)-3^{13} 5^{2} x^{7}\\left(239\\theta^4+460\\theta^3+314\\theta^2+84\\theta+6\\right)-3^{16} 5^{2} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "69/4 14365/12", "discriminant": "8 16 -1944 32913 1120230 -22652946 -149492385 3059328690 -9526079925 -1076168025", "aesz": "317", "n_sing_complex": "3", "inst_int": "", "c2h": "50", "hash": "cda8cce31025f51636125bea67a820d1", "dim_h": "6", "inst": " 69/4 -30 14365/12 3015/2 1376205/4 9897421/3 388901931/2 7471470879/2 636889759589/4 4303811481090", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "7", "laurent": null, "discriminant_tex": "-(27z-1)(243z^3+2214z^2-117z+1)(-4-45z+405z^2)^2", "discr_factors": "-1076168025, z-1/27, (-4/405-1/9*z+z^2)^2, z^3+82/9*z^2-13/27*z+1/243", "dm_basis": null, "q": "0 1 -36 972 -26604 669816 -17273412 416721960 -10686110652 249004225278", "yuk": "1 69/4 -891/4 64677/2 385029/4 86012847/2 1425292821/2 266786724735/4 7650786565125/4 464292634869735/4", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/108*(-4526396+3852*I*107^(1/2))^(1/3)-6841/27/(-4526396+3852*I*107^(1/2))^(1/3)-82/27+1/6*I*3^(1/2)*(1/18*(-4526396+3852*I*107^(1/2))^(1/3)-13682/9/(-4526396+3852*I*107^(1/2))^(1/3))","im":"0","approx_re":"-9.163702","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/18-1/90*105^(1/2)","im":"0","approx_re":"-0.058299","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*(-4526396+3852*I*107^(1/2))^(1/3)-6841/27/(-4526396+3852*I*107^(1/2))^(1/3)-82/27-1/6*I*3^(1/2)*(1/18*(-4526396+3852*I*107^(1/2))^(1/3)-13682/9/(-4526396+3852*I*107^(1/2))^(1/3))","im":"0","approx_re":"0.010727","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/27","im":"0","approx_re":"0.037037037037","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/54*(-4526396+3852*I*107^(1/2))^(1/3)+13682/27/(-4526396+3852*I*107^(1/2))^(1/3)-82/27","im":"0","approx_re":"0.041864","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/18+1/90*105^(1/2)","im":"0","approx_re":"0.169411","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":[]}]}, {"pols": "[X^4, -9*(3*X+1)^2*(3*X+2)^2]", "text": "A-incarnation: X(3,3) in P^5.", "degz": 1, "h3": "9", "sol": "1 36 8100 2822400 1200622500 572679643536 294230074634496 159259227403161600 89595913068008532900 51926300783585192250000", "n_discr_factors": "1", "c3": "-144", "operator": "4 1 0 0 0 0 1 -36 -324 -1053 -1458 -729", "new_number": "1.4", "id": 560, "operator_tex": "\\theta^4-3^{2} x(3\\theta+1)^2(3\\theta+2)^2", "superseek": "117 713814", "discriminant": "1 1 -729", "aesz": "4", "n_sing_complex": "0", "inst_int": null, "c2h": "54", "hash": "1f2a9672b7cdc68eae658b2304b40dbd", "dim_h": "6", "inst": " 117 5868 713814 126605376 27754210287 6962329389948 1917383766758001 565426952047351440 175694524219617543105 56893915767467678536512", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "A_{n}=\\dbinom{2n}{n}^2\\dbinom{3n}{n}^2", "n_sing_rational": "2", "n_sing": "2", "laurent": null, "discriminant_tex": "1-729z", "discr_factors": "-729, -1/729+z", "dm_basis": null, "q": "0 1 -180 8910 -948840 -106787835 -36085459176 -11118592651770 -3670279528638960 -1261012927291005150", "yuk": "1 117 47061 19273095 8102791125 3469276285992 1503863167548807 657662631997994460 289498599456346728405 128081308156101208196640", "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":"1/729","im":"0","approx_re":"0.00137174211248","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":["1/3","1/3","2/3","2/3"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -16*(4*X+1)*(2*X+1)^2*(4*X+3)]", "text": "A-incarnation of $X(2,4)$ in $P^5$.", "degz": 1, "h3": "8", "sol": "1 48 15120 7392000 4414410000 2956651746048 2133278987583744 1621682968820428800 1281351259836532170000 1043032815185819858400000", "n_discr_factors": "1", "c3": "-176", "operator": "4 1 0 0 0 0 1 -48 -448 -1472 -2048 -1024", "new_number": "1.6", "id": 579, "operator_tex": "\\theta^4-2^{4} x(4\\theta+1)(2\\theta+1)^2(4\\theta+3)", "superseek": "160 1956896", "discriminant": "1 1 -1024", "aesz": "6", "n_sing_complex": "0", "inst_int": null, "c2h": "56", "hash": "483b4ca5270ed3bfca9243827b62064e", "dim_h": "6", "inst": " 160 11536 1956896 485487816 148865410272 52234325667792 20120573535223712 8299111953203204936 3606882539577061044992 1633630970021158628102832", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": null, "n_sing_rational": "2", "n_sing": "2", "laurent": null, "discriminant_tex": "1-1024z", "discr_factors": "-1024, -1/1024+z", "dm_basis": null, "q": "0 1 -256 19296 -2836480 -378262992 -191836950528 -81951834648064 -37892767852527616 -18211822225201935720", "yuk": "1 160 92448 52836352 31071312672 18608176284160 11282614397171712 6901356722581733376 4249145320071112239904 2629417371351677554635520", "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":"1/1024","im":"0","approx_re":"0.0009765625","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","1/2","1/2","3/4"],"monodromy":[],"monodromy_dm":[]}]}]}