{"count": 12, "status":"OK", "data":[{"pols": "[X^4, -4*(4*X+1)*(4*X+3)*(10*X^2+10*X+3), 144*(4*X+1)*(4*X+3)*(4*X+5)*(4*X+7)]", "text": "Hadamard product $C\\ast c$", "degz": 2, "h3": "12", "sol": "1 36 6300 1718640 575675100 216636756336 87874675224336 37563969509352000 16692217815436148700 7642084994921759382000", "n_discr_factors": "2", "c3": "-224", "operator": "4 2 0 0 0 0 1 -36 -312 -952 -1280 -640 15120 101376 198144 147456 36864", "new_number": "2.11", "id": 2, "operator_tex": "\\theta^4-2^{2} x(4\\theta+1)(4\\theta+3)(10\\theta^2+10\\theta+3)+2^{4} 3^{2} x^{2}(4\\theta+1)(4\\theta+3)(4\\theta+5)(4\\theta+7)", "superseek": "64 246848", "discriminant": "2 1 -640 36864", "aesz": "69", "n_sing_complex": "0", "inst_int": "", "c2h": "72", "hash": "729adc350de26d9415643078ed8d3867", "dim_h": "8", "inst": " 64 2616 246848 32024824 5160268864 951777326520 192563937712192 41708381444805880 9517654613752418368 2263204057578067144632", "cleanlist": "True", "n_sing_real": "3", 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{"pols": "[X^4, -12*(4*X+1)*(4*X+3)*(3*X^2+3*X+1), 432*(4*X+1)*(4*X+3)*(4*X+5)*(4*X+7)]", "text": "", "degz": 2, "h3": null, "sol": "1 36 3780 388080 8108100 -13827878064 -6049207788624 -1780617654129600 -405415553383655100 -64108077643407798000", "n_discr_factors": "1", "c3": null, "operator": "4 2 0 0 0 0 1 -36 -300 -876 -1152 -576 45360 304128 594432 442368 110592", "new_number": "2.22", "id": 14, "operator_tex": "\\theta^4-2^{2} 3 x(4\\theta+1)(4\\theta+3)(3\\theta^2+3\\theta+1)+2^{4} 3^{3} x^{2}(4\\theta+1)(4\\theta+3)(4\\theta+5)(4\\theta+7)", "superseek": "36 -206716/3", "discriminant": "2 1 -576 110592", "aesz": "135", "n_sing_complex": "2", "inst_int": "Hadamard product $C \\ast f$.", "c2h": null, "hash": "85e55291bd94bb32087b43f104c60645", "dim_h": null, "inst": " 36 -477 -206716/3 -4431924 -27005472 113639010155/3 5461011241452 275264717743692 -42134583877440448 -11379150026239273560", "cleanlist": "True", "n_sing_real": "1", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "3", "laurent": null, "discriminant_tex": "1-576z+110592z^2", "discr_factors": "110592, 1/110592-1/192*z+z^2", "dm_basis": ["19/24-1162393719353719131361189363784404603456366390101814206736549803033200099854000208071729302850101578/768799759549186043811713254203741173211443985818991590275710787225120378790852066470688698366857287*I", "8750000003/1000000000+113/6000000000*I", "378000000701999998397/324000000648000002005+1707000001584/324000000648000002005*I", "1", "-17/4-9/1000000000*I", "-12000000009/1000000000-53/2000000000*I", "-324000000647999998643/324000000648000002005-1476000001476/324000000648000002005*I", "0", "3+3/500000000*I", "9000000009/500000000+41/1000000000*I", "0", "0", "-9000000009/500000000-41/1000000000*I", "0", "0", "0"], "q": "0 1 -156 22446 -2570800 297228021 -32847734088 3343576302482 -362209122322368 37293313471891074", "yuk": "1 36 -3780 -1860408 -283646916 -3375683964 8182006866936 1873126855818072 140935535201123388 -30716111646655947000", "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","18","1","0","0","0","1","1"]},{"re":"1/384","im":"-1/1152*3^(1/2)","approx_re":"0.00260416666667","approx_im":"-0.001504","exponents":["0","1","1","2"],"monodromy":["5/24+I*tan(801/812)","-19/144+52*lambda","-323/1728+221/3*lambda",".92182440e-1+247/9*lambda","17/4+9/1000000000*I","41/24-3/1000000000*I","289/288-1/250000000*I","323/1728-221/3*lambda","-3-3/500000000*I","-1/2+1/500000000*I","7/24+3/1000000000*I","-19/144+52*lambda","18.000000018+.41e-7*I","3.000000039-.12000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-7*I","17/4-9/500000000*I","43/24-I*tan(801/812)"],"monodromy_dm":["1","-11","-1","-1","0","1","0","0","0","0","1","0","0","0","0","1"]},{"re":"1/384","im":"1/1152*3^(1/2)","approx_re":"0.00260416666667","approx_im":"0.001504","exponents":["0","1","1","2"],"monodromy":["43/24+I*tan(801/812)","-19/144-52*lambda","323/1728+221/3*lambda",".92182440e-1-247/9*lambda","17/4","7/24","289/288","-323/1728-221/3*lambda","3","-1/2","41/24","-19/144-52*lambda","18","-3","17/4","5/24-I*tan(801/812)"],"monodromy_dm":["-2","-15","-1333333/1000000","-1","1","6","111111/250000","333333/1000000","-12","-60","-4333333/1000000","-4","10","50","1111111/250000","4333333/1000000"]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/4","3/4","5/4","7/4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -3*(3*X+1)*(3*X+2)*(17*X^2+17*X+6), 648*(3*X+1)*(3*X+2)*(3*X+4)*(3*X+5)]", "text": "Hadamard product $B\\ast g$.", "degz": 2, "h3": "36", "sol": "1 36 3780 524160 82952100 14193715536 2558150090496 478581063966720 92098312591711140 18122109528268746000", "n_discr_factors": "2", "c3": "-156", "operator": "4 2 0 0 0 0 1 -36 -264 -723 -918 -459 25920 151632 285768 209952 52488", "new_number": "2.25", "id": 17, "operator_tex": "\\theta^4-3 x(3\\theta+1)(3\\theta+2)(17\\theta^2+17\\theta+6)+2^{3} 3^{4} x^{2}(3\\theta+1)(3\\theta+2)(3\\theta+4)(3\\theta+5)", "superseek": "27 2618", "discriminant": "2 1 -459 52488", "aesz": "138", "n_sing_complex": "0", "inst_int": "", "c2h": "108", "hash": "c524254b716132352b27914640b03c8b", "dim_h": "15", "inst": " 27 189/4 2618 43713 2319057 196286095/2 5214508191 272574896067 14990046252383 3356489455171983/4", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": 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{"pols": "[X^4, -4*(4*X+1)*(4*X+3)*(11*X^2+11*X+3), -16*(4*X+1)*(4*X+3)*(4*X+5)*(4*X+7)]", "text": "Hadamard product C*b\nRelated to (:case 8.139)\nA-Incarnation: double cover of $B_5$.\n\nA:Incarnation: double cover of B", "degz": 2, "h3": "10", "sol": "1 36 7980 2716560 1127025900 523922935536 262254770874096 138273159697358400 75764606627820696300 42763759729830497358000", "n_discr_factors": "1", "c3": "-200", "operator": "4 2 0 0 0 0 1 -36 -324 -1028 -1408 -704 -1680 -11264 -22016 -16384 -4096", "new_number": "2.7", "id": 68, "operator_tex": "\\theta^4-2^{2} x(4\\theta+1)(4\\theta+3)(11\\theta^2+11\\theta+3)-2^{4} x^{2}(4\\theta+1)(4\\theta+3)(4\\theta+5)(4\\theta+7)", "superseek": "92 585396", "discriminant": "2 1 -704 -4096", "aesz": "51", "n_sing_complex": "0", "inst_int": "", "c2h": "64", "hash": "e09b9b149b6845daa8d5ef03df33f22d", "dim_h": "7", "inst": " 92 5052 585396 99982012 21054159152 5072639293460 1341406276920276 379798413120428604 113300338464448477848 35222259453038284682544", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "A_{n}=\\dbinom{2n}{n}\\dbinom{4n}{2n}\\sum_{k=0}^{n}\\dbinom{n}{k}^2\\dbinom{n+k}{n}", "n_sing_rational": "1", "n_sing": "3", "laurent": null, "discriminant_tex": "1-704z-4096z^2", "discr_factors": "-4096, -1/4096+11/64*z+z^2", "dm_basis": ["-96920449/100000000*I", "13/3", "1", "1", "-8/3", "-5", "-1", "0", "0", "10", "0", "0", "-10", "0", "0", "0"], "q": "0 1 -180 9766 -918864 -84667391 -28201300344 -8416763367758 -2661445469478720 -878785166425741292", "yuk": "1 92 40508 15805784 6398889276 2631769894092 1095690103233560 460102352983654760 194456787524058334524 82595946740582956156976", "gv2": null, "gv0": "920 50520 5853960 999820120 210541591520 50726392934600 13414062769202760 3797984131204286040 1133003384644484778480 352222594530382846825440", "gv1": "0 3 -1840 340009 1947267584 1647668876313 1015529214081408 546679951529049217 273876590223518607136 131454144000215093321340 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"spectrum":[{"re":"-11/128-5/128*5^(1/2)","im":"0","approx_re":"-0.173284","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["5.6666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666667+3.876817960*I","-2.3333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333-1.938408980*I","133/90+760/3*lambda","-.168701507-.904590857*I","38/3","-16/3","361/90","-133/90-760/3*lambda","20","-10","22/3","-2.3333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333-1.938408980*I","40","-20","38/3","-3.6666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666667-3.876817960*I"],"monodromy_dm":["-9","-40","-6","-4","5","21","3","2","-30","-120","-17","-12","20","80","12","9"]},{"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","10","1","0","0","0","1","1"]},{"re":"-11/128+5/128*5^(1/2)","im":"0","approx_re":"0.001409","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["1.+.969204490*I","0","160/3*lambda",".93935734e-1","8/3","1","32/45","-160/3*lambda","0","0","1","0","10","0","8/3","1.-.969204490*I"],"monodromy_dm":["1","-7","-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":["1/4","3/4","5/4","7/4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -36-276*X-852*X^2-1152*X^3-144*X^4, 28080+146880*X+235008*X^2-27648*X^3-69120*X^4, 2177280+14929920*X+36578304*X^2+35831808*X^3+1990656*X^4, 8957952*(28*X^2+52*X+31)*(2*X+1)^2, 1289945088*(2*X+1)^2*(2*X+3)^2]", "text": "This is operator \"5.130\" from ...", "degz": 5, "h3": null, "sol": "1 36 3780 558000 98828100 19642358736 4224083227056 961146142482240 228062168165016900 55880542340983760400", "n_discr_factors": "3", "c3": null, "operator": "4 5 0 0 0 0 1 -36 -276 -852 -1152 -144 28080 146880 235008 -27648 -69120 2177280 14929920 36578304 35831808 1990656 277696512 1576599552 3224862720 2866544640 1003290624 11609505792 61917364224 113515167744 82556485632 20639121408", "new_number": "5.130", "id": 215, "operator_tex": "\\theta^4-2^{2} 3 x\\left(12\\theta^4+96\\theta^3+71\\theta^2+23\\theta+3\\right)-2^{4} 3^{3} x^{2}\\left(160\\theta^4+64\\theta^3-544\\theta^2-340\\theta-65\\right)+2^{8} 3^{5} x^{3}\\left(32\\theta^4+576\\theta^3+588\\theta^2+240\\theta+35\\right)+2^{12} 3^{7} x^{4}(28\\theta^2+52\\theta+31)(2\\theta+1)^2+2^{16} 3^{9} x^{5}(2\\theta+1)^2(2\\theta+3)^2", "superseek": "108 122756", "discriminant": "5 1 -144 -69120 1990656 1003290624 20639121408", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "829aca3d7a00547e299bf794c8643162", "dim_h": null, "inst": " 108 -1782 122756 -5930658 607239072 -41331999138 4771667104452 -382997107073250 141465586799209792/3 -4165834540165763472", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "(144z-1)(6912z^2+288z-1)(1+144z)^2", "discr_factors": "20639121408, z-1/144, z^2+1/24*z-1/6912, (1/144+z)^2", "dm_basis": null, "q": "0 1 -132 13806 -1431248 144826485 -15086199672 1583568090194 -171961794163776 18870884255228418", "yuk": "1 108 -14148 3314520 -379576260 75904884108 -8927708513544 1636681816827144 -196094519201080260 34376137592211293976", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/48-1/72*3^(1/2)","im":"0","approx_re":"-0.04489","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/144","im":"0","approx_re":"-0.00694444444444","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":"-1/48+1/72*3^(1/2)","im":"0","approx_re":"0.003223","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/144","im":"0","approx_re":"0.00694444444444","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": "[X^4, 16*X^4-1408*X^3-1000*X^2-296*X-36, -152064*X^4+178176*X^2+24912+127104*X-285696*X^3, -20127744*X^4+8017920*X+20791296*X^3+21786624*X^2+1002240, 552960*(2*X+1)*(824*X^3+1668*X^2+1342*X+405), 132710400*(2*X+1)*(6*X+5)*(6*X+7)*(2*X+3)]", "text": "B-incarnation as fibre product 61131- x 182--1\n", "degz": 5, "h3": null, "sol": "1 36 4572 918000 228519900 64165466736 19456165015056 6223308826692672 2070528619453479900 710013798698305186800", "n_discr_factors": "4", "c3": null, "operator": "4 5 0 0 0 0 1 -36 -296 -1000 -1408 16 24912 127104 178176 -285696 -152064 1002240 8017920 21786624 20791296 -20127744 223948800 1189969920 2406481920 2300313600 911278080 13934592000 65824358400 109353369600 76441190400 19110297600", "new_number": "5.134", "id": 219, "operator_tex": "\\theta^4+2^{2} x\\left(4\\theta^4-352\\theta^3-250\\theta^2-74\\theta-9\\right)-2^{4} 3 x^{2}\\left(3168\\theta^4+5952\\theta^3-3712\\theta^2-2648\\theta-519\\right)-2^{8} 3^{3} x^{3}\\left(2912\\theta^4-3008\\theta^3-3152\\theta^2-1160\\theta-145\\right)+2^{12} 3^{3} 5 x^{4}(2\\theta+1)(824\\theta^3+1668\\theta^2+1342\\theta+405)+2^{16} 3^{4} 5^{2} x^{5}(2\\theta+1)(6\\theta+5)(6\\theta+7)(2\\theta+3)", "superseek": "176 1215248/3", "discriminant": "5 1 16 -152064 -20127744 911278080 19110297600", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "5bd656df18dc5d02b2f2a068ba88ab74", "dim_h": null, "inst": " 176 -3238 1215248/3 -18807038 3651829680 -560878854674/3 52269749105328 -2096680151943998 962753159449556144 -16565341526826099078", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "5", "n_sing": "5", "laurent": null, "discriminant_tex": "(48z-1)(432z-1)(16z+1)(1+240z)^2", "discr_factors": "19110297600, z+1/16, z-1/432, (1/240+z)^2, z-1/48", "dm_basis": null, "q": "0 1 -152 16812 -2161728 269541070 -37931046432 5043309372344 -760500779492864 104106569458703589", "yuk": "1 176 -25728 10937408 -1203676160 456478710176 -40383266625024 17928523943127680 -1073500238999003136 701847053238737366384", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/16","im":"0","approx_re":"-0.0625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/240","im":"0","approx_re":"-0.00416666666667","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":"1/432","im":"0","approx_re":"0.00231481481481","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/48","im":"0","approx_re":"0.0208333333333","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": "[25*X^4, -4995*X^4-13230*X^3-11715*X^2-5100*X-900, 186624*X^4+1463832*X^3+2585844*X^2+1717200*X+415440, 8188128*X^4+9447840*X^3-45585828*X^2-61279740*X-20664720, -136048896*X^4-1292464512*X^3-2424315744*X^2-1707224688*X-415285056, -11337408*(3*X+2)*(3*X+4)*(6*X+5)*(6*X+7)]", "text": "This is operator \"5.65\" from ...", "degz": 5, "h3": null, "sol": "1 36 2196 161280 13032900 1115973936 99328836096 9088750224576 849053816612100 80605604422371600", "n_discr_factors": "3", "c3": null, "operator": "4 5 0 0 0 0 25 -900 -5100 -11715 -13230 -4995 415440 1717200 2585844 1463832 186624 -20664720 -61279740 -45585828 9447840 8188128 -415285056 -1707224688 -2424315744 -1292464512 -136048896 -3174474240 -13672914048 -21529737792 -14693280768 -3673320192", "new_number": "5.65", "id": 277, "operator_tex": "5^{2} \\theta^4-3 5 x\\left(333\\theta^4+882\\theta^3+781\\theta^2+340\\theta+60\\right)+2^{2} 3^{2} x^{2}\\left(5184\\theta^4+40662\\theta^3+71829\\theta^2+47700\\theta+11540\\right)+2^{2} 3^{5} x^{3}\\left(8424\\theta^4+9720\\theta^3-46899\\theta^2-63045\\theta-21260\\right)-2^{4} 3^{8} x^{4}\\left(1296\\theta^4+12312\\theta^3+23094\\theta^2+16263\\theta+3956\\right)-2^{6} 3^{11} x^{5}(3\\theta+2)(3\\theta+4)(6\\theta+5)(6\\theta+7)", "superseek": "63/5 14016/5", "discriminant": "5 25 -4995 186624 8188128 -136048896 -3673320192", "aesz": "273", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "cf49bc645cb0404ce7bc9ca1d41d3152", "dim_h": null, "inst": " 63/5 -747/4 14016/5 -55584 6071598/5 -29280858 3789513648/5 -103572330372/5 2946639866493/5 -172753730633619/10", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "-(-1+27z)(108z+5)^2(108z-1)^2", "discr_factors": "-3673320192, (z+5/108)^2, (z-1/108)^2, -1/27+z", "dm_basis": null, "q": "0 1 -60 2916 -132140 5799354 -248943456 10506838262 -437619310824 18036699887331", "yuk": "1 63/5 -7407/5 75699 -17794287/5 758949813/5 -6324591123 1299803181327/5 -53029050944751/5 2148100463051892/5", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-5/108","im":"0","approx_re":"-0.0462962962963","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","1/6","5/6","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":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["2/3","5/6","7/6","4/3"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, 8*X*(4*X^3-8*X^2-5*X-1), -768*X^4-1920*X^3-720*X^2-1184*X-576, -12928*X^4+43776*X^3+49536*X^2+52480*X+21888, 798976*X^4+3610624*X^3+7907584*X^2+7096320*X+2393856, 12072960*X^4+74870784*X^3+185812992*X^2+189333504*X+71073792, 691863552*X+324882432-103809024*X^3-83755008*X^4+366796800*X^2, -1367801856*X^4-10769006592*X^3-27168473088*X^2-29974855680*X-12247400448, -127210881024*X+7134511104*X^3-69343838208-59103903744*X^2+5833949184*X^4, 58350108672*X^4+615096778752*X^3+1952435404800*X^2+2512494526464*X+1124959518720, -764411904*(X+1)*(368*X^3+1752*X^2+1297*X-1035), -18345885696*(X+1)*(X+2)*(39*X^2+513*X+1172), 330225942528*(X+3)*(X+2)*(X+1)*(17*X+82), -7925422620672*(X+1)*(X+2)*(X+3)*(X+4)]", "text": "This is operator \"13.9\" from ...", "degz": 13, "h3": null, "sol": "1 0 36 -192 -4284 -155520 -2431440 -24917760 300589380 21072871680", "n_discr_factors": "5", "c3": null, "operator": "4 13 0 0 0 0 1 0 -8 -40 -64 32 -576 -1184 -720 -1920 -768 21888 52480 49536 43776 -12928 2393856 7096320 7907584 3610624 798976 71073792 189333504 185812992 74870784 12072960 324882432 691863552 366796800 -103809024 -83755008 -12247400448 -29974855680 -27168473088 -10769006592 -1367801856 -69343838208 -127210881024 -59103903744 7134511104 5833949184 1124959518720 2512494526464 1952435404800 615096778752 58350108672 791166320640 -200275918848 -2330691895296 -1620553236480 -281303580672 -43002756071424 -83327012831232 -51166675206144 -11557907988480 -715489542144 162471163723776 331546846298112 224223414976512 60761573425152 5613841022976 -190210142896128 -396271131033600 -277389791723520 -79254226206720 -7925422620672", "new_number": "13.9", "id": 377, "operator_tex": "\\theta^4+2^{3} x\\theta(4\\theta^3-8\\theta^2-5\\theta-1)-2^{4} x^{2}\\left(48\\theta^4+120\\theta^3+45\\theta^2+74\\theta+36\\right)-2^{7} x^{3}\\left(101\\theta^4-342\\theta^3-387\\theta^2-410\\theta-171\\right)+2^{8} x^{4}\\left(3121\\theta^4+14104\\theta^3+30889\\theta^2+27720\\theta+9351\\right)+2^{11} 3^{2} x^{5}\\left(655\\theta^4+4062\\theta^3+10081\\theta^2+10272\\theta+3856\\right)-2^{12} 3^{2} x^{6}\\left(2272\\theta^4+2816\\theta^3-9950\\theta^2-18768\\theta-8813\\right)-2^{15} 3^{3} x^{7}\\left(1546\\theta^4+12172\\theta^3+30708\\theta^2+33880\\theta+13843\\right)+2^{16} 3^{4} x^{8}\\left(1099\\theta^4+1344\\theta^3-11134\\theta^2-23964\\theta-13063\\right)+2^{19} 3^{5} x^{9}\\left(458\\theta^4+4828\\theta^3+15325\\theta^2+19721\\theta+8830\\right)-2^{20} 3^{6} x^{10}(\\theta+1)(368\\theta^3+1752\\theta^2+1297\\theta-1035)-2^{23} 3^{7} x^{11}(\\theta+1)(\\theta+2)(39\\theta^2+513\\theta+1172)+2^{24} 3^{9} x^{12}(\\theta+3)(\\theta+2)(\\theta+1)(17\\theta+82)-2^{27} 3^{10} x^{13}(\\theta+1)(\\theta+2)(\\theta+3)(\\theta+4)", "superseek": "8 2200/9", "discriminant": "13 1 32 -768 -12928 798976 12072960 -83755008 -1367801856 5833949184 58350108672 -281303580672 -715489542144 5613841022976 -7925422620672", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "31ff3b7bd4c8fed070ee43b6903d3752", "dim_h": null, "inst": " 8 -75/2 2200/9 -8117/2 47936 -4052675/6 11499480 -175321542 2998366528 -53613060132", "cleanlist": "True", "n_sing_real": "7", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "9", "laurent": null, "discriminant_tex": "-(8z+1)(5184z^3+432z^2-36z+1)(12z+1)^2(144z^2-24z-1)^2(4z-1)^3", "discr_factors": "-7925422620672, (z-1/4)^3, (z^2-1/6*z-1/144)^2, (z+1/12)^2, z^3+1/12*z^2-1/144*z+1/5184, z+1/8", "dm_basis": null, "q": "0 1 -8 54 96 2149 -74736 1483178 -32369792 559973682", "yuk": "1 8 -292 6608 -260036 5992008 -145889992 3944321648 -89764889540 2185809205520", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/18*2^(1/3)-1/36*2^(2/3)-1/36","im":"0","approx_re":"-0.141868","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/8","im":"0","approx_re":"-0.125","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","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"1/12-1/12*2^(1/2)","im":"0","approx_re":"-0.034518","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":"1/36*2^(1/3)+1/72*2^(2/3)-1/36","im":"1/24*3^(1/2)*(-2/3*2^(1/3)+1/3*2^(2/3))","approx_re":"0.029267","approx_im":"-0.022431","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/36*2^(1/3)+1/72*2^(2/3)-1/36","im":"-1/24*3^(1/2)*(-2/3*2^(1/3)+1/3*2^(2/3))","approx_re":"0.029267","approx_im":"0.022431","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/12+1/12*2^(1/2)","im":"0","approx_re":"0.201184","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","1/2","3/2","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": "[25*X^4, -900-4500*X-9460*X^2-9920*X^3-4880*X^4, 589360+1882560*X+2483904*X^2+1533952*X^3+386304*X^4, -86156800-213212160*X-208503808*X^2-92610560*X^3-17022976*X^4, 4830281728+9927114752*X+7766360064*X^2+2965504000*X^3+531300352*X^4, -109175111680-198251642880*X-142011269120*X^2-68281171968*X^3-15289286656*X^4, 344805343232+1170026266624*X+1859989274624*X^2+1703860502528*X^3+419749167104*X^4, 21403969519616-2532420091904*X-48988396978176*X^2-41337986482176*X^3-9439801245696*X^4, -168637595910144+605779367297024*X+1247258502758400*X^2+704202837852160*X^3+173190261243904*X^4, -3353510464716800-15158417056333824*X-18365142718742528*X^2-9091861650079744*X^3-2972529685692416*X^4, 76086204642099200+208379443696107520*X+235383449274286080*X^2+138309766681198592*X^3+47481310133878784*X^4, -1311110441518235648-3497608060606611456*X-3939523774042341376*X^2-2232659515268923392*X^3-581527301884215296*X^4, 20878687872489619456+51593237331156402176*X+50710531804191784960*X^2+23742977235497254912*X^3+4593671619917905920*X^4, -180432215470971551744-398910840593969053696*X-339535383106716434432*X^2-132585973029787402240*X^3-20176126330619822080*X^4, 36893488147419103232*(X+2)^4]", "text": "This is operator \"14.8\" from ...", "degz": 14, "h3": null, "sol": "1 36 1196 41488 1543916 61692912 2626061552 117909711936 5533685570284 269383919495856", "n_discr_factors": "5", "c3": null, "operator": "4 14 0 0 0 0 25 -900 -4500 -9460 -9920 -4880 589360 1882560 2483904 1533952 386304 -86156800 -213212160 -208503808 -92610560 -17022976 4830281728 9927114752 7766360064 2965504000 531300352 -109175111680 -198251642880 -142011269120 -68281171968 -15289286656 344805343232 1170026266624 1859989274624 1703860502528 419749167104 21403969519616 -2532420091904 -48988396978176 -41337986482176 -9439801245696 -168637595910144 605779367297024 1247258502758400 704202837852160 173190261243904 -3353510464716800 -15158417056333824 -18365142718742528 -9091861650079744 -2972529685692416 76086204642099200 208379443696107520 235383449274286080 138309766681198592 47481310133878784 -1311110441518235648 -3497608060606611456 -3939523774042341376 -2232659515268923392 -581527301884215296 20878687872489619456 51593237331156402176 50710531804191784960 23742977235497254912 4593671619917905920 -180432215470971551744 -398910840593969053696 -339535383106716434432 -132585973029787402240 -20176126330619822080 590295810358705651712 1180591620717411303424 885443715538058477568 295147905179352825856 36893488147419103232", "new_number": "14.8", "id": 387, "operator_tex": "5^{2} \\theta^4-2^{2} 5 x\\left(244\\theta^4+496\\theta^3+473\\theta^2+225\\theta+45\\right)+2^{4} x^{2}\\left(24144\\theta^4+95872\\theta^3+155244\\theta^2+117660\\theta+36835\\right)-2^{9} x^{3}\\left(33248\\theta^4+180880\\theta^3+407234\\theta^2+416430\\theta+168275\\right)+2^{14} x^{4}\\left(32428\\theta^4+181000\\theta^3+474021\\theta^2+605903\\theta+294817\\right)-2^{19} x^{5}\\left(29162\\theta^4+130236\\theta^3+270865\\theta^2+378135\\theta+208235\\right)+2^{24} x^{6}\\left(25019\\theta^4+101558\\theta^3+110864\\theta^2+69739\\theta+20552\\right)-2^{29} x^{7}\\left(17583\\theta^4+76998\\theta^3+91248\\theta^2+4717\\theta-39868\\right)+2^{34} x^{8}\\left(10081\\theta^4+40990\\theta^3+72600\\theta^2+35261\\theta-9816\\right)-2^{39} x^{9}\\left(5407\\theta^4+16538\\theta^3+33406\\theta^2+27573\\theta+6100\\right)+2^{44} x^{10}\\left(2699\\theta^4+7862\\theta^3+13380\\theta^2+11845\\theta+4325\\right)-2^{49} x^{11}\\left(1033\\theta^4+3966\\theta^3+6998\\theta^2+6213\\theta+2329\\right)+2^{54} x^{12}\\left(255\\theta^4+1318\\theta^3+2815\\theta^2+2864\\theta+1159\\right)-2^{59} x^{13}\\left(35\\theta^4+230\\theta^3+589\\theta^2+692\\theta+313\\right)+2^{65} x^{14}\\left((\\theta+2)^4\\right)", "superseek": "92/5 -76/5", "discriminant": "14 25 -4880 386304 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null, "gv1": null, 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{"pols": "[X^4, -864*X^4-216*X^3-282*X^2-174*X-36, 301536*X^4+239328*X^3+293652*X^2+140400*X+26064, -55302912*X^4-88926336*X^3-105048576*X^2-58113936*X-12913344, 5816883456*X^4+14961646080*X^3+19628039232*X^2+12355488576*X+3037849920, -354869268480*X^4-1255976534016*X^3-1906906116096*X^2-1335411173376*X-352231711488, 11796547829760*X^4+50640664264704*X^3+85369210896384*X^2+63970311831552*X+17547096158208, -178322008965120*X^4-777929764110336*X^3-1224353960165376*X^2-823686696271872*X-201757731323904, 743008370688*(6*X+5)^2*(6*X+7)^2]", "text": "This is operator \"8.25\" from ...", "degz": 8, "h3": null, "sol": "1 36 1908 116496 7816500 571265136 45282874896 3849203343168 344621130915636 31900564060477200", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 1 -36 -174 -282 -216 -864 26064 140400 293652 239328 301536 -12913344 -58113936 -105048576 -88926336 -55302912 3037849920 12355488576 19628039232 14961646080 5816883456 -352231711488 -1335411173376 -1906906116096 -1255976534016 -354869268480 17547096158208 63970311831552 85369210896384 50640664264704 11796547829760 -201757731323904 -823686696271872 -1224353960165376 -777929764110336 -178322008965120 910185254092800 3744762188267520 5724136487780352 3851755393646592 962938848411648", "new_number": "8.25", "id": 469, "operator_tex": "\\theta^4-2 3 x\\left(144\\theta^4+36\\theta^3+47\\theta^2+29\\theta+6\\right)+2^{2} 3^{2} x^{2}\\left(8376\\theta^4+6648\\theta^3+8157\\theta^2+3900\\theta+724\\right)-2^{4} 3^{4} x^{3}\\left(42672\\theta^4+68616\\theta^3+81056\\theta^2+44841\\theta+9964\\right)+2^{6} 3^{5} x^{4}\\left(374028\\theta^4+962040\\theta^3+1262091\\theta^2+794463\\theta+195335\\right)-2^{8} 3^{7} x^{5}\\left(633840\\theta^4+2243328\\theta^3+3405968\\theta^2+2385208\\theta+629129\\right)+2^{12} 3^{8} x^{6}\\left(438960\\theta^4+1884384\\theta^3+3176664\\theta^2+2380392\\theta+652943\\right)-2^{19} 3^{10} x^{7}\\left(5760\\theta^4+25128\\theta^3+39548\\theta^2+26606\\theta+6517\\right)+2^{22} 3^{11} x^{8}(6\\theta+5)^2(6\\theta+7)^2", "superseek": "-54 -197216/3", "discriminant": "8 1 -864 301536 -55302912 5816883456 -354869268480 11796547829760 -178322008965120 962938848411648", "aesz": "299", "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "c9e3907e21d64cf5564bf2d00992459e", "dim_h": null, "inst": " -54 -1530 -197216/3 -3553920 -222887448 -46187215136/3 -1137791347128 -88358802830496 -7126833307040540 -592327036101212712", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "6", "laurent": null, "discriminant_tex": "(1-144z+6912z^2)(108z-1)^2(3456z^2-252z+1)^2", "discr_factors": "962938848411648, 1/6912-1/48*z+z^2, (z-1/108)^2, (z^2-7/96*z+1/3456)^2", "dm_basis": null, "q": "0 1 -30 1179 -7420 1565673 81731862 7825382963 675317911944 61224964477299", "yuk": "1 -54 -12294 -1774998 -227463174 -27860931054 -3325481277030 -390262432064958 -45239707276677126 -5195461480834328658", "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":"7/192-1/576*345^(1/2)","im":"0","approx_re":"0.004212","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/108","im":"0","approx_re":"0.00925925925926","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"1/96","im":"-1/288*3^(1/2)","approx_re":"0.0104166666667","approx_im":"-0.006014","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/96","im":"1/288*3^(1/2)","approx_re":"0.0104166666667","approx_im":"0.006014","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"7/192+1/576*345^(1/2)","im":"0","approx_re":"0.068705","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":["5/6","5/6","7/6","7/6"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -736*X^4-896*X^3-700*X^2-252*X-36, 166656*X^4+463872*X^3+473472*X^2+204672*X+33840, -4460544*X^4-64364544*X^3-99846144*X^2-49600512*X-9061632, -2448949248*X^4-927203328*X^3+8059944960*X^2+6023282688*X+1332412416, 146087608320*X^4+582312001536*X^3-2463105024*X^2-160271695872*X-49304567808, 11529369944064*X^4-10078006542336*X^3-11015685144576*X^2-1638899122176*X+467820085248, -146767085568*(2*X+1)*(1336*X^3+2772*X^2+2234*X+663), -84537841287168*(2*X+1)*(4*X+3)*(4*X+5)*(2*X+3)]", "text": "This is operator \"8.78\" from ...", "degz": 8, "h3": null, "sol": "1 36 3780 555120 95199300 17826144336 3532282505136 728151261963840 154550955916302660 33549072371964349200", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 1 -36 -252 -700 -896 -736 33840 204672 473472 463872 166656 -9061632 -49600512 -99846144 -64364544 -4460544 1332412416 6023282688 8059944960 -927203328 -2448949248 -49304567808 -160271695872 -2463105024 582312001536 146087608320 467820085248 -1638899122176 -11015685144576 -10078006542336 11529369944064 -97306577731584 -522490824622080 -1062593699512320 -1009757548707840 -392161652637696 -3804202857922560 -18260173718028288 -30771774228529152 -21641687369515008 -5410421842378752", "new_number": "8.78", "id": 527, "operator_tex": "\\theta^4-2^{2} x\\left(184\\theta^4+224\\theta^3+175\\theta^2+63\\theta+9\\right)+2^{4} 3 x^{2}\\left(3472\\theta^4+9664\\theta^3+9864\\theta^2+4264\\theta+705\\right)-2^{8} 3^{2} x^{3}\\left(1936\\theta^4+27936\\theta^3+43336\\theta^2+21528\\theta+3933\\right)-2^{16} 3^{3} x^{4}\\left(1384\\theta^4+524\\theta^3-4555\\theta^2-3404\\theta-753\\right)+2^{19} 3^{4} x^{5}\\left(3440\\theta^4+13712\\theta^3-58\\theta^2-3774\\theta-1161\\right)+2^{22} 3^{5} x^{6}\\left(11312\\theta^4-9888\\theta^3-10808\\theta^2-1608\\theta+459\\right)-2^{26} 3^{7} x^{7}(2\\theta+1)(1336\\theta^3+2772\\theta^2+2234\\theta+663)-2^{32} 3^{9} x^{8}(2\\theta+1)(4\\theta+3)(4\\theta+5)(2\\theta+3)", "superseek": "52 48732", "discriminant": "8 1 -736 166656 -4460544 -2448949248 146087608320 11529369944064 -392161652637696 -5410421842378752", "aesz": null, "n_sing_complex": "3", "inst_int": "", "c2h": null, "hash": "2fb524ad6efb19e0117ae7acbd9f67b9", "dim_h": null, "inst": " 52 -399 48732 -992750 98106208 -13164377111/3 346622274844 -20762287104686 1625571068932672 -109698228104560776", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "7", "laurent": null, "discriminant_tex": "-(256z-1)(110592z^3+6912z^2-288z+1)(-1+96z+13824z^2)^2", "discr_factors": "-5410421842378752, z^3+1/16*z^2-1/384*z+1/110592, z-1/256, (-1/13824+1/144*z+z^2)^2", "dm_basis": null, "q": "0 1 -108 7662 -522608 37550709 -2726199720 203058824274 -15495782553792 1207671346097154", "yuk": "1 52 -3140 1315816 -63539140 12263276052 -947833839368 118891440271544 -10630291061138372 1185041309253233704", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/192*(-36+12*I*3^(1/2))^(1/3)-1/16/(-36+12*I*3^(1/2))^(1/3)-1/48+1/96*I*3^(1/2)*(1/2*(-36+12*I*3^(1/2))^(1/3)-6/(-36+12*I*3^(1/2))^(1/3))","im":"0","approx_re":"-0.091906","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/288-1/288*7^(1/2)","im":"0","approx_re":"-0.012659","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":"-1/192*(-36+12*I*3^(1/2))^(1/3)-1/16/(-36+12*I*3^(1/2))^(1/3)-1/48-1/96*I*3^(1/2)*(1/2*(-36+12*I*3^(1/2))^(1/3)-6/(-36+12*I*3^(1/2))^(1/3))","im":"0","approx_re":"0.00385","approx_im":"0.0","exponents":["0","1","1","2"],"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":"-1/288+1/288*7^(1/2)","im":"0","approx_re":"0.005714","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/96*(-36+12*I*3^(1/2))^(1/3)+1/8/(-36+12*I*3^(1/2))^(1/3)-1/48","im":"0","approx_re":"0.025556","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","5/4","3/2"],"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":[]}]}]}