{"count": 4, "status":"OK", "data":[{"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", 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{"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": "A_{n}=\\dbinom{2n}{n}\\dbinom{3n}{n}\\sum_{j,k}^{n}(-1)^{j}8^{n-j}\\dbinom{n}{j}\\dbinom{j}{k}^3", "n_sing_rational": "3", "n_sing": "3", "laurent": "None", "discriminant_tex": "(243z-1)(216z-1)", "discr_factors": "52488, z-1/243, z-1/216", "dm_basis": ["-377989751/500000000*I", "21/2", "1", "1", "-9/2", "-18", "-1", "0", "0", "36", "0", "0", "-36", "0", "0", "0"], "q": "0 1 -120 10782 -841288 60234693 -4078954368 264886454966 -16689963727536 1025543560906530", "yuk": "1 27 405 70713 2798037 289882152 21198969351 1788576309540 139558349584341 10927743718057920", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":["1","-1","1/2","-1/6","0","1","-1","1/2","0","0","1","-1","0","0","0","1"],"monodromy_dm":["1","0","0","0","1","1","0","0","0","36","1","0","0","0","1","1"]},{"re":"1/243","im":"0","approx_re":"0.00411522633745","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["1.+.755979502*I","0","39/2*lambda",".15875139e-1","9/2","1","9/16","-39/2*lambda","0","0","1","0","36","0","9/2","1.-.755979502*I"],"monodromy_dm":["1","-15","-1","-1","0","1","0","0","0","0","1","0","0","0","0","1"]},{"re":"1/216","im":"0","approx_re":"0.00462962962963","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[".84386396e-1+.881341465*I","-.593907697+1.816219110*I",".987405021+.251865740*I","-.18197034e-1-.280246794*I","-.610146073+4.105015738*I","3.086102688+5.881005017*I","1/ln(2)^(8/3)/ln(3)^(8/5)*Zeta(5)^8-1.317777791*I","-.605925748-.688412508*I","-1.084750363+4.722447485*I","1.891556916+7.035664131*I","4.676916900-1.255046419*I","-.642466556-.856579334*I","-4.881168587+32.840125900*I","16.688821505+47.048040140*I","24.445126799-10.542222328*I","-3.847405984-5.507300063*I"],"monodromy_dm":["-2450927/1000000+271203/1000000*I","-7338521/500000+382623/15625*I","299583/500000+49333/125000*I","33897/250000-456113/500000*I","505191/1000000-1/10000*I","3414753/1000000-1697749/500000*I","-3307/40000-1004/15625*I","-7533/250000+131179/1000000*I","-1136679/125000+28/15625*I","-43465553/1000000+61118963/1000000*I","1244077/500000+18072/15625*I","4339/8000-295153/125000*I","378893/50000-1493/1000000*I","18110647/500000-5093247/100000*I","-19377/15625-3012/3125*I","548021/1000000+983843/500000*I"]},{"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, -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, -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, 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