{"count": 6, "status":"OK", "data":[{"pols": "[X^4, -9*(3*X+1)*(3*X+2)*(3*X^2+3*X+1), 243*(3*X+1)*(3*X+2)*(3*X+4)*(3*X+5)]", "text": "Hadamard product $B\\ast f$", "degz": 2, "h3": null, "sol": "1 18 810 35280 311850 -224756532 -41527742256 -5161210591680 -496059075330390 -33108414482929500", "n_discr_factors": "1", "c3": null, "operator": "4 2 0 0 0 0 1 -18 -135 -378 -486 -243 9720 56862 107163 78732 19683", "new_number": "2.21", "id": 13, "operator_tex": "\\theta^4-3^{2} x(3\\theta+1)(3\\theta+2)(3\\theta^2+3\\theta+1)+3^{5} x^{2}(3\\theta+1)(3\\theta+2)(3\\theta+4)(3\\theta+5)", "superseek": "18 -5177", "discriminant": "2 1 -243 19683", "aesz": "134", "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "cc6d92c4b8a8dadb92b447c54e3a2a2f", "dim_h": null, "inst": " 18 -207/2 -5177 -155979 -923301 864871525/4 14999353992 412867187721 -15028199534105 -9414668043657531/4", "cleanlist": "True", "n_sing_real": "1", "sol_explicit": "A_{n}=\\dbinom{2n}{n}\\dbinom{3n}{n}\\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": "1-243z+19683z^2", "discr_factors": "19683, 1/19683-1/81*z+z^2", "dm_basis": ["13/16-198*lambda", "2610000001/240000000+43/2000000000*I", "850500001462499997223/729000001350000003541+3402000002925/729000001350000003541*I", "1", "-33/8-1/125000000*I", "-1440000001/80000000-9/250000000*I", "-729000001349999997709/729000001350000003541-2916000002700/729000001350000003541*I", "0", "9/2+9/1000000000*I", "1080000001/40000000+27/500000000*I", "0", "0", "-1080000001/40000000-27/500000000*I", "0", "0", "0"], "q": "0 1 -63 3564 -150735 6501681 -261382950 9012994434 -373193040123 13202314506639", "yuk": "1 18 -810 -139761 -9983466 -115412607 46702921761 5144778419274 211387990129686 -10955557460502306", "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","27","1","0","0","0","1","1"]},{"re":"1/162","im":"-1/486*3^(1/2)","approx_re":"0.00617283950617","approx_im":"-0.003564","exponents":["0","1","1","2"],"monodromy":["3/16+198*lambda","-13/96+33*lambda","-143/1152+121/4*lambda",".9648440e-2+.57748434e-1*I","33/8+1/125000000*I","27/16-1/500000000*I","121/192-3/1000000000*I","143/1152-121/4*lambda","-9/2-9/1000000000*I","-3/4+1/500000000*I","5/16+3/1000000000*I","-13/96+33*lambda","27.000000025+.54000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-7*I","4.500000045-.14000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-7*I","33/8-9/500000000*I","29/16-198*lambda"],"monodromy_dm":["1","-12","-1","-1","0","1","0","0","0","0","1","0","0","0","0","1"]},{"re":"1/162","im":"1/486*3^(1/2)","approx_re":"0.00617283950617","approx_im":"0.003564","exponents":["0","1","1","2"],"monodromy":["29/16+198*lambda","-13/96-33*lambda","143/1152+121/4*lambda",".9648440e-2-.57748434e-1*I","33/8","5/16","121/192","-143/1152-121/4*lambda","9/2","-3/4","27/16","-13/96-33*lambda","27","-9/2","33/8","3/16-198*lambda"],"monodromy_dm":["-2","-18","-1333333/1000000","-1","1","7","111111/250000","333333/1000000","-18","-108","-7","-6","15","90","6666667/1000000","6"]},{"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, 6*X*(48*X^3-12*X^2-7*X-1), 6912+40608*X+83700*X^2+52704*X^3+42336*X^4, 1080864+6356880*X+13654656*X^2+12783744*X^3+4603392*X^4, 419904*(169*X^2+361*X+238)*(2*X+1)^2, 362797056*(2*X+1)^2*(2*X+3)^2]", "text": "This is operator \"5.38\" from ...", "degz": 5, "h3": null, "sol": "1 0 -432 7200 1587600 -76204800 -8324316000 779155977600 44704074214800 -7922861987040000", "n_discr_factors": "3", "c3": null, "operator": "4 5 0 0 0 0 1 0 -6 -42 -72 288 6912 40608 83700 52704 42336 1080864 6356880 13654656 12783744 4603392 99937152 551333952 1077053760 890196480 283855104 3265173504 17414258688 31926140928 23219011584 5804752896", "new_number": "5.38", "id": 247, "operator_tex": "\\theta^4+2 3 x\\theta(48\\theta^3-12\\theta^2-7\\theta-1)+2^{2} 3^{3} x^{2}\\left(392\\theta^4+488\\theta^3+775\\theta^2+376\\theta+64\\right)+2^{4} 3^{5} x^{3}\\left(1184\\theta^4+3288\\theta^3+3512\\theta^2+1635\\theta+278\\right)+2^{6} 3^{8} x^{4}(169\\theta^2+361\\theta+238)(2\\theta+1)^2+2^{11} 3^{11} x^{5}(2\\theta+1)^2(2\\theta+3)^2", "superseek": "18 64744/3", "discriminant": "5 1 288 42336 4603392 283855104 5804752896", "aesz": "223", "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "e3ab25cffe4a0968b175bd9e98c96427", "dim_h": null, "inst": " 18 -873 64744/3 -229968 -1628892 -2539244900/3 103073101740 -4227953354280 -129441534425950/3 6772362915828510", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "(36z+1)(13824z^2+36z+1)(1+108z)^2", "discr_factors": "5804752896, (1/108+z)^2, z^2+1/384*z+1/13824, z+1/36", "dm_basis": null, "q": "0 1 -6 1791 -66236 2739399 -98335674 6995913197 -609427373016 35265125115648", "yuk": "1 18 -6966 582714 -14724918 -203611482 -182825057070 35354073896838 -2164712132116278 -31454292864923136", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/36","im":"0","approx_re":"-0.0277777777778","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/108","im":"0","approx_re":"-0.00925925925926","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/768","im":"-5/2304*15^(1/2)","approx_re":"-0.00130208333333","approx_im":"-0.008405","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/768","im":"5/2304*15^(1/2)","approx_re":"-0.00130208333333","approx_im":"0.008405","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":"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, -126*X^4-252*X^3-231*X^2-105*X-18, 7857*X^4+31428*X^3+47169*X^2+31482*X+7128, -349920*X^4-2099520*X^3-4425516*X^2-3828708*X-1006020, 10707552*X^4+85660416*X^3+233519112*X^2+248793120*X+73483200, -2834352*(16*X^2+80*X+35)*(2*X+5)^2, 76527504*(2*X+11)*(2*X+7)*(2*X+5)*(2*X+1)]", "text": "This is operator \"6.7\" from ...", "degz": 6, "h3": null, "sol": "1 18 378 8820 266490 8688708 247642164 6595916184 212629478490 7830581178420", "n_discr_factors": "3", "c3": null, "operator": "4 6 0 0 0 0 1 -18 -105 -231 -252 -126 7128 31482 47169 31428 7857 -1006020 -3828708 -4425516 -2099520 -349920 73483200 248793120 233519112 85660416 10707552 -2480058000 -7652750400 -6065513280 -1813985280 -181398528 29463089040 84486364416 58160903040 14693280768 1224440064", "new_number": "6.7", "id": 429, "operator_tex": "\\theta^4-3 x\\left(42\\theta^4+84\\theta^3+77\\theta^2+35\\theta+6\\right)+3^{3} x^{2}\\left(291\\theta^4+1164\\theta^3+1747\\theta^2+1166\\theta+264\\right)-2^{2} 3^{5} x^{3}\\left(360\\theta^4+2160\\theta^3+4553\\theta^2+3939\\theta+1035\\right)+2^{3} 3^{8} x^{4}\\left(204\\theta^4+1632\\theta^3+4449\\theta^2+4740\\theta+1400\\right)-2^{4} 3^{11} x^{5}(16\\theta^2+80\\theta+35)(2\\theta+5)^2+2^{4} 3^{14} x^{6}(2\\theta+11)(2\\theta+7)(2\\theta+5)(2\\theta+1)", "superseek": "-9 217/3", "discriminant": "6 1 -126 7857 -349920 10707552 -181398528 1224440064", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "9492f991c909a6774f5546668ff53b6a", "dim_h": null, "inst": " -9 18 217/3 -9 -146079 24412075/3 -308382426 9737440047 -856982681864/3 8889098301450", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "6", "laurent": null, "discriminant_tex": "(27z-1)(34992z^3-1944z^2+27z-1)(-1+36z)^2", "discr_factors": "1224440064, z-1/27, (-1/36+z)^2, z^3-1/18*z^2+1/1296*z-1/34992", "dm_basis": null, "q": "0 1 -33 1386 -66479 3301242 -165260790 8325015305 -422661117873 21630151957212", "yuk": "1 -9 135 1944 -441 -18259884 1757671488 -105775172127 4985569303623 -208246791691008", "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":"-1/216*(17+12*2^(1/2))^(1/3)-1/216/(17+12*2^(1/2))^(1/3)+1/54","im":"-1/18*3^(1/2)*(1/12*(17+12*2^(1/2))^(1/3)-1/12/(17+12*2^(1/2))^(1/3))","approx_re":"0.002095","approx_im":"-0.023494","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/216*(17+12*2^(1/2))^(1/3)-1/216/(17+12*2^(1/2))^(1/3)+1/54","im":"1/18*3^(1/2)*(1/12*(17+12*2^(1/2))^(1/3)-1/12/(17+12*2^(1/2))^(1/3))","approx_re":"0.002095","approx_im":"0.023494","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/36","im":"0","approx_re":"0.0277777777778","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"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":"1/108*(17+12*2^(1/2))^(1/3)+1/108/(17+12*2^(1/2))^(1/3)+1/54","im":"0","approx_re":"0.051365","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": "[X^4, 27+132*X+258*X^2+252*X^3+261*X^4, 12582+47520*X+73764*X^2+58104*X^3+29106*X^4, 1986768+6507054*X+8543394*X^2+5552064*X^3+1797714*X^4, 151397262+448488090*X+515524014*X^2+281458152*X^3+66412629*X^4, 6111709281+16709489190*X+17145782568*X^2+7984605780*X^3+1467308601*X^4, 1771470*(2*X+3)*(5066*X^3+26325*X^2+44815*X+23766), 23436548100*(X+1)*(2*X+5)*(2*X+3)*(X+3)]", "text": "This is operator \"7.17\" from ...", "degz": 7, "h3": null, "sol": "1 -27 783 -23481 717903 -22219677 693312669 -21750039891 684693321327 -21597894376101", "n_discr_factors": "4", "c3": null, "operator": "4 7 0 0 0 0 1 27 132 258 252 261 12582 47520 73764 58104 29106 1986768 6507054 8543394 5552064 1797714 151397262 448488090 515524014 281458152 66412629 6111709281 16709489190 17145782568 7984605780 1467308601 126302268060 322366796190 298678699350 120190696560 17948534040 1054644664500 2531147194800 2132725877100 749969539200 93746192400", "new_number": "7.17", "id": 439, "operator_tex": "\\theta^4+3 x\\left(87\\theta^4+84\\theta^3+86\\theta^2+44\\theta+9\\right)+2 3^{3} x^{2}\\left(539\\theta^4+1076\\theta^3+1366\\theta^2+880\\theta+233\\right)+2 3^{5} x^{3}\\left(3699\\theta^4+11424\\theta^3+17579\\theta^2+13389\\theta+4088\\right)+3^{7} x^{4}\\left(30367\\theta^4+128696\\theta^3+235722\\theta^2+205070\\theta+69226\\right)+3^{9} x^{5}\\left(74547\\theta^4+405660\\theta^3+871096\\theta^2+848930\\theta+310507\\right)+2 3^{11} 5 x^{6}(2\\theta+3)(5066\\theta^3+26325\\theta^2+44815\\theta+23766)+2^{2} 3^{14} 5^{2} 7^{2} x^{7}(\\theta+1)(2\\theta+5)(2\\theta+3)(\\theta+3)", "superseek": "0 18", "discriminant": "7 1 261 29106 1797714 66412629 1467308601 17948534040 93746192400", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "c248fd7c807d0aae71ef687a9ee40c80", "dim_h": null, "inst": " 0 -27/2 18 -999/2 1566 -63197/2 145800 -5170527/2 46391668/3 -249533325", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "6", "laurent": null, "discriminant_tex": "(27z+1)(1323z^2+72z+1)(36z+1)^2(45z+1)^2", "discr_factors": "93746192400, (z+1/36)^2, z^2+8/147*z+1/1323, z+1/27, (z+1/45)^2", "dm_basis": null, "q": "0 1 24 522 10670 210759 4055238 76621037 1426709406 26268081381", "yuk": "1 0 -108 486 -32076 195750 -6824898 50009400 -1323686988 11273175810", "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":"-1/36","im":"0","approx_re":"-0.0277777777778","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"-4/147","im":"-1/441*3^(1/2)","approx_re":"-0.0272108843537","approx_im":"-0.003928","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-4/147","im":"1/441*3^(1/2)","approx_re":"-0.0272108843537","approx_im":"0.003928","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/45","im":"0","approx_re":"-0.0222222222222","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":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","3/2","5/2","3"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -3*(3*X^2+3*X+1)*(17*X^2+17*X+6), 5859*X^4+46764*X^3+65907*X^2+38286*X+9072, 297432*X^4-1784592*X^3-5447088*X^2-4181544*X-1189728, -30338064*X^4-60676128*X^3+137518560*X^2+167856624*X+59836320, 578207808*X^4+5782078080*X^3+3287848320*X^2-328784832*X-725594112, 22141957824*X^4-88159684608*X^3-148259284416*X^2-88159684608*X-15917720832, -22039921152*(3*X^2+3*X+1)*(17*X^2+17*X+6), 14281868906496*(X+1)^4]", "text": "Hadamard product $d \\ast g$. This operator has a second MUM-point at infinity. It can be reduced to an operator of degree 4 with a single MUM-point defined over $Q(\\sqrt{?})$.", "degz": 8, "h3": "162", "sol": "1 18 378 6552 21546 -5570532 -361058256 -15509667456 -509913925974 -11554728615612", "n_discr_factors": "3", "c3": "702", "operator": "4 8 0 0 0 0 1 -18 -105 -258 -306 -153 9072 38286 65907 46764 5859 -1189728 -4181544 -5447088 -1784592 297432 59836320 167856624 137518560 -60676128 -30338064 -725594112 -328784832 3287848320 5782078080 578207808 -15917720832 -88159684608 -148259284416 -88159684608 22141957824 -132239526912 -771397240320 -1895433219072 -2248071957504 -1124035978752 14281868906496 57127475625984 85691213438976 57127475625984 14281868906496", "new_number": "8.15", "id": 458, "operator_tex": "\\theta^4-3 x(3\\theta^2+3\\theta+1)(17\\theta^2+17\\theta+6)+3^{3} x^{2}\\left(217\\theta^4+1732\\theta^3+2441\\theta^2+1418\\theta+336\\right)+2^{3} 3^{6} x^{3}\\left(51\\theta^4-306\\theta^3-934\\theta^2-717\\theta-204\\right)-2^{4} 3^{8} x^{4}\\left(289\\theta^4+578\\theta^3-1310\\theta^2-1599\\theta-570\\right)+2^{6} 3^{11} x^{5}\\left(51\\theta^4+510\\theta^3+290\\theta^2-29\\theta-64\\right)+2^{6} 3^{13} x^{6}\\left(217\\theta^4-864\\theta^3-1453\\theta^2-864\\theta-156\\right)-2^{9} 3^{16} x^{7}(3\\theta^2+3\\theta+1)(17\\theta^2+17\\theta+6)+2^{12} 3^{20} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "18 9799/3", "discriminant": "8 1 -153 5859 297432 -30338064 578207808 22141957824 -1124035978752 14281868906496", "aesz": "178", "n_sing_complex": "4", "inst_int": "", "c2h": "0", "hash": "e748913f322a008ae5c350f96f1cd860", "dim_h": "27", "inst": " 18 -423/2 9799/3 -150003/2 1914237 -324455821/6 1628820972 -103046534199/2 1691501544869 -57212542607211", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "7", "laurent": null, "discriminant_tex": "(1728z^2-72z+1)(2187z^2-81z+1)(-1+1944z^2)^2", "discr_factors": "14281868906496, z^2-1/27*z+1/2187, (-1/1944+z^2)^2, z^2-1/24*z+1/1728", "dm_basis": null, "q": "0 1 -33 1224 -44609 1661721 -62614674 2389779914 -92178406965 3589034423679", "yuk": "1 18 -1674 88209 -4801770 239279643 -11680323039 558685593414 -26379917556714 1233104626297710", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/108*6^(1/2)","im":"0","approx_re":"-0.02268","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":"1/54","im":"-1/162*3^(1/2)","approx_re":"0.0185185185185","approx_im":"-0.010692","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/54","im":"1/162*3^(1/2)","approx_re":"0.0185185185185","approx_im":"0.010692","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/48","im":"-1/144*3^(1/2)","approx_re":"0.0208333333333","approx_im":"-0.012028","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/48","im":"1/144*3^(1/2)","approx_re":"0.0208333333333","approx_im":"0.012028","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/108*6^(1/2)","im":"0","approx_re":"0.02268","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": "[9*X^4, -18-117*X-300*X^2-366*X^3+15*X^4, -5052-23736*X-41729*X^2-32600*X^3-8603*X^4, -46848-245880*X-489388*X^2-433188*X^3-133216*X^4, -276144-1356992*X-2552500*X^2-2190424*X^3-721604*X^4, -611584-3034560*X-5690672*X^2-4779920*X^3-1518944*X^4, -111424-1102656*X-3047248*X^2-3267456*X^3-1172656*X^4, -66816-330624*X-692736*X^2-724224*X^3-311424*X^4, -9216*(X+1)^4]", "text": "This operator has a second MUM-point at infininty corresponding to operator 8.34", "degz": 8, "h3": null, "sol": "1 2 46 632 16846 371252 10387504 276173312 8072876494 234674601932", "n_discr_factors": "2", "c3": null, "operator": "4 8 0 0 0 0 9 -18 -117 -300 -366 15 -5052 -23736 -41729 -32600 -8603 -46848 -245880 -489388 -433188 -133216 -276144 -1356992 -2552500 -2190424 -721604 -611584 -3034560 -5690672 -4779920 -1518944 -111424 -1102656 -3047248 -3267456 -1172656 -66816 -330624 -692736 -724224 -311424 -9216 -36864 -55296 -36864 -9216", "new_number": "8.33", "id": 478, "operator_tex": "3^{2} \\theta^4+3 x\\left(5\\theta^4-122\\theta^3-100\\theta^2-39\\theta-6\\right)-x^{2}\\left(5052+23736\\theta+41729\\theta^2+32600\\theta^3+8603\\theta^4\\right)-2^{2} x^{3}\\left(33304\\theta^4+108297\\theta^3+122347\\theta^2+61470\\theta+11712\\right)-2^{2} x^{4}\\left(180401\\theta^4+547606\\theta^3+638125\\theta^2+339248\\theta+69036\\right)-2^{4} x^{5}\\left(94934\\theta^4+298745\\theta^3+355667\\theta^2+189660\\theta+38224\\right)-2^{4} x^{6}\\left(73291\\theta^4+204216\\theta^3+190453\\theta^2+68916\\theta+6964\\right)-2^{7} 3 x^{7}\\left(811\\theta^4+1886\\theta^3+1804\\theta^2+861\\theta+174\\right)-2^{10} 3^{2} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "4/3 95/3", "discriminant": "8 9 15 -8603 -133216 -721604 -1518944 -1172656 -311424 -9216", "aesz": "322", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "a19da26bf1a7748e3b7e6151e803da30", "dim_h": null, "inst": " 4/3 18 95/3 14575/12 18158/3 187103 4924031/3 527352805/12 1590965963/3 39385718023/3", "cleanlist": "True", "n_sing_real": "7", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "7", "laurent": null, "discriminant_tex": "-(-1+13z+827z^2+1928z^3+64z^4)(3+22z+12z^2)^2", "discr_factors": "-9216, (1/4+11/6*z+z^2)^2, -1/64+13/64*z+827/64*z^2+241/8*z^3+z^4", "dm_basis": null, "q": "0 1 -5 -77 461 -3514 -11817 -693433 -4229517 -222501606", "yuk": "1 4/3 436/3 2569/3 233636/3 2269754/3 121245745/3 562980879 67501392676/3 1159814189596/3", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-11/12-1/12*85^(1/2)","im":"0","approx_re":"-1.684962","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-11/12+1/12*85^(1/2)","im":"0","approx_re":"-0.148371","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","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}]}