{"count": 15, "status":"OK", "data":[{"pols": "[X^4, -16*(4*X+1)*(4*X+3)*(3*X^2+3*X+1), 512*(4*X+1)*(4*X+3)*(4*X+5)*(4*X+7)]", "text": "Hadamard product $C\\ast d$", "degz": 2, "h3": "16", "sol": "1 48 8400 2069760 609008400 200387835648 71201249543424 26742996453888000 10470608789459504400 4232794808237739744000", "n_discr_factors": "2", "c3": "-268", "operator": "4 2 0 0 0 0 1 -48 -400 -1168 -1536 -768 53760 360448 704512 524288 131072", "new_number": "2.15", "id": 6, "operator_tex": "\\theta^4-2^{4} x(4\\theta+1)(4\\theta+3)(3\\theta^2+3\\theta+1)+2^{9} x^{2}(4\\theta+1)(4\\theta+3)(4\\theta+5)(4\\theta+7)", "superseek": "48 73328", "discriminant": "2 1 -768 131072", "aesz": "38", "n_sing_complex": "0", "inst_int": "", "c2h": "88", "hash": "9ce26bb7405c3b98d8aeae5b1102c611", "dim_h": "10", "inst": " 48 998 73328 7388135 857248528 112063100078 16141925788848 2496124778774145 406647185987371136 68996526934808894722", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "A_{n}=\\dbinom{2n}{n}\\dbinom{4n}{2n}\\sum_{k=0}^{n}\\dbinom{n}{k}\\dbinom{2k}{k}\\dbinom{2n-2k}{n-k}", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "(512z-1)(256z-1)", "discr_factors": "131072, z-1/256, z-1/512", "dm_basis": ["-268*lambda", "19/3", "1", "1", "-11/3", "-8", "-1", "0", "0", "16", "0", "0", "-16", "0", "0", "0"], "q": "0 1 -208 32000 -4613120 605381040 -78889707008 9643425928192 -1213793065402368 140184861197932696", "yuk": "1 48 8032 1979904 472848672 107156066048 24205631604736 5536680545574912 1278015887205210912 296445798584795538048", "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","16","1","0","0","0","1","1"]},{"re":"1/512","im":"0","approx_re":"0.001953125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["1+268*lambda","0","I*arctan(173/564)",".105419378","11/3","1","121/144","-I*arctan(173/564)","0","0","1","0","16","0","11/3","1-268*lambda"],"monodromy_dm":["1","-10","-1","-1","0","1","0","0","0","0","1","0","0","0","0","1"]},{"re":"1/256","im":"0","approx_re":"0.00390625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["19/6+4*I*ln(2)^(6/5)*Zeta(5)^(2/9)","-13/24-134*lambda",".49652777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777778+.595253091*I",".64137367e-1-.351740463*I","22/3+3/1000000000*I","-5/6+1/500000000*I","121/72-1/500000000*I","-.49652777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777778-.595253091*I","8+3/1000000000*I","-2+1/500000000*I","17/6-1/500000000*I","-13/24-134*lambda","32+7/500000000*I","-8+7/1000000000*I","22/3-7/1000000000*I","-7/6-4*I*ln(2)^(6/5)*Zeta(5)^(2/9)"],"monodromy_dm":["-3","-24","-5/2","-2","1","7","5/8","1/2","-8","-48","-4","-4","6","36","15/4","4"]},{"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, -16*(2*X+1)^2*(8*X^2+8*X+3), 4096*(2*X+1)^2*(2*X+3)^2]", "text": "B-Incarnations:\nFibre product 81111- x 18--21, 4*11-- x 53211, \nDouble Octics: D.O.8, D.O.36, D.O.73, D.O.249, D.O.258,D.O.265\n", "degz": 2, "h3": null, "sol": "1 48 5904 940800 169520400 32825979648 6664766701824 1399343499620352 301253424381795600 66124078946867884800", "n_discr_factors": "1", "c3": null, "operator": "4 2 0 0 0 0 1 -48 -320 -832 -1024 -512 36864 196608 360448 262144 65536", "new_number": "2.17", "id": 8, "operator_tex": "\\theta^4-2^{4} x(2\\theta+1)^2(8\\theta^2+8\\theta+3)+2^{12} x^{2}(2\\theta+1)^2(2\\theta+3)^2", "superseek": "32 1440", "discriminant": "2 1 -512 65536", "aesz": "111", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "d8535e0f3d0bfd4ebcc9c042df43c218", "dim_h": null, "inst": " 32 -96 1440 19704 -14496 15837984 163296032 7479253880 329193772800 7032903948768", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "A_{n}=\\dbinom{2n}{n}^2\\sum_{k=0}^{n}4^{n-k}\\dbinom{2k}{k}^2\\dbinom{2n-2k}{n-k}", "n_sing_rational": "2", "n_sing": "2", "laurent": null, "discriminant_tex": "(256z-1)^2", "discr_factors": "65536, (z-1/256)^2", "dm_basis": ["5/3-96*lambda", "2/3", "1/2", "1", "2/3", "0", "-1", "0", "8", "-16", "0", "0", "16", "0", "0", "0"], "q": "0 1 -128 11616 -870400 57668144 -3495272448 197815529984 -10595176022016 542166156831384", "yuk": "1 32 -736 38912 1260320 -1811968 3421042688 56010539008 3829379246880 239982260410112", "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","-16","1","0","0","0","1","1"]},{"re":"1/256","im":"0","approx_re":"0.00390625","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":["-2/3+96*lambda","48*lambda","-5/72+4*lambda","-.13526746e-1","-2/3","2/3","-1/36","-5/72-4*lambda","-8","0","2/3","-48*lambda","-16","-8","-2/3","-2/3-96*lambda"],"monodromy_dm":["-3","0","0","-1","-1","1","1/4","0","0","0","1","0","4","0","-1","1"]},{"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, -800*X^3-400*X^4-288*X-688*X^2-48, 2048*(26*X^2+52*X+21)*(X+1)^2, -589824*(X+1)*(X+2)*(2*X+1)*(2*X+5)]", "text": "Operator equivalent to AESZ 107 $=d \\ast d$", "degz": 3, "h3": null, "sol": "1 48 3984 387840 40818960 4501986048 512429938944 59675344515072 7072164147494160 849882891327824640", "n_discr_factors": "2", "c3": null, "operator": "4 3 0 0 0 0 1 -48 -288 -688 -800 -400 43008 192512 309248 212992 53248 -5898240 -23003136 -28901376 -14155776 -2359296", "new_number": "3.34", "id": 97, "operator_tex": "\\theta^4-2^{4} x\\left(25\\theta^4+50\\theta^3+43\\theta^2+18\\theta+3\\right)+2^{11} x^{2}(26\\theta^2+52\\theta+21)(\\theta+1)^2-2^{16} 3^{2} x^{3}(\\theta+1)(\\theta+2)(2\\theta+1)(2\\theta+5)", "superseek": "16 1744", "discriminant": "3 1 -400 53248 -2359296", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "931a876bfe4d4aa192c6e18e74047640", "dim_h": null, "inst": " 16 -110 1744 -29526 644016 -14438358 359438736 -9163638478 246345604992 -6752150432602", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "-(144z-1)(-1+128z)^2", "discr_factors": "-2359296, z-1/144, (-1/128+z)^2", "dm_basis": null, "q": "0 1 -96 8096 -637952 48181552 -3535150080 253974455808 -17956221681664 1253619038795416", "yuk": "1 16 -864 47104 -1890528 80502016 -3118639104 123287486464 -4691784791264 179585946086272", "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":"1/144","im":"0","approx_re":"0.00694444444444","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/128","im":"0","approx_re":"0.0078125","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","1","2","5/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[49*X^4, -53424*X^4-105336*X^3-74718*X^2-22050*X-2352, 524448*X^4+457056*X^3-309084*X^2-247296*X-40320, -1181952*X^4+653184*X^3+722304*X^2+154224*X+6048, -15552*(3*X+1)*(2*X+1)^2*(3*X+2)]", "text": "Sporadic Operator.", "degz": 4, "h3": "7", "sol": "1 48 15840 8148000 5126536800 3619570002048 2753811350113824 2207771557753956480 1839938553689058108000 1579830078681015395520000", "n_discr_factors": "2", "c3": "-120", "operator": "4 4 0 0 0 0 49 -2352 -22050 -74718 -105336 -53424 -40320 -247296 -309084 457056 524448 6048 154224 722304 653184 -1181952 -31104 -264384 -824256 -1119744 -559872", "new_number": "4.36", "id": 133, "operator_tex": "7^{2} \\theta^4-2 3 7 x\\left(1272\\theta^4+2508\\theta^3+1779\\theta^2+525\\theta+56\\right)+2^{2} 3 x^{2}\\left(43704\\theta^4+38088\\theta^3-25757\\theta^2-20608\\theta-3360\\right)-2^{4} 3^{3} x^{3}\\left(2736\\theta^4-1512\\theta^3-1672\\theta^2-357\\theta-14\\right)-2^{6} 3^{5} x^{4}(3\\theta+1)(2\\theta+1)^2(3\\theta+2)", "superseek": "1434/7 18676572/7", "discriminant": "4 49 -53424 524448 -1181952 -559872", "aesz": "109", "n_sing_complex": "1", "inst_int": "", "c2h": "46", "hash": "bca2938ac7fa09f5bdc395cab75caf82", "dim_h": "5", "inst": " 1434/7 14718 18676572/7 4988009280/7 1646787631350/7 622466594325132/7 258353389427348430/7 16404944169924970464 53786293452931561754730/7 26254922854681782077900670/7", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "3", "laurent": null, "discriminant_tex": "-(432z^2+1080z-1)(-7+36z)^2", "discr_factors": "-559872, z^2+5/2*z-1/432, (-7/36+z)^2", "dm_basis": null, "q": "0 1 -258 15801 -2799212 -619136580 -289200901266 -135520306538198 -67319605493315208 -34851846790327410108", "yuk": "1 1434/7 825642/7 504268878/7 319233419562/7 205848453920184/7 134452784879321598/7 88615212573580512924/7 58795319905330327562538/7 39210207927187109023467048/7", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-5/4-13/18*3^(1/2)","im":"0","approx_re":"-2.500926","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":"s_1","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"s_2","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-5/4+13/18*3^(1/2)","im":"0","approx_re":"0.000926","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"7/36","im":"0","approx_re":"0.194444444444","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, -48-384*X-1136*X^2-1504*X^3-1328*X^4, 61440+436224*X+1069056*X^2+1173504*X^3+620544*X^4, -6488064-60162048*X-196411392*X^2-254803968*X^3-119734272*X^4, 226492416*(3*X+1)*(2*X+1)^2*(3*X+2)]", "text": "Sporadic Operator.", "degz": 4, "h3": "16", "sol": "1 48 9360 2553600 813027600 283184149248 104664044669184 40361741131345920 16073129967819210000 6564949660340509152000", "n_discr_factors": "3", "c3": "-72", "operator": "4 4 0 0 0 0 1 -48 -384 -1136 -1504 -1328 61440 436224 1069056 1173504 620544 -6488064 -60162048 -196411392 -254803968 -119734272 452984832 3850371072 12004098048 16307453952 8153726976", "new_number": "4.45", "id": 143, "operator_tex": "\\theta^4-2^{4} x\\left(83\\theta^4+94\\theta^3+71\\theta^2+24\\theta+3\\right)+2^{11} 3 x^{2}\\left(101\\theta^4+191\\theta^3+174\\theta^2+71\\theta+10\\right)-2^{16} 3^{2} x^{3}\\left(203\\theta^4+432\\theta^3+333\\theta^2+102\\theta+11\\right)+2^{23} 3^{3} x^{4}(3\\theta+1)(2\\theta+1)^2(3\\theta+2)", "superseek": "80 104976", "discriminant": "4 1 -1328 620544 -119734272 8153726976", "aesz": "233", "n_sing_complex": "0", "inst_int": "", "c2h": "64", "hash": "03f67459f6d678669f766c99281b1e79", "dim_h": "8", "inst": " 80 2794 104976 5367454 508265072 71026691490 10979503341520 1741443998259494 281028365633566080 46168051267005890030", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "(512z-1)(432z-1)(-1+192z)^2", "discr_factors": "8153726976, z-1/432, z-1/512, (-1/192+z)^2", "dm_basis": null, "q": "0 1 -192 20256 -1451008 76300080 -3901906944 74979753472 -15535962980352 -1686551922782568", "yuk": "1 80 22432 2834432 343539488 63533134080 15341768218624 3765969646141440 891619327452400416 204869678546872506752", "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":"1/512","im":"0","approx_re":"0.001953125","approx_im":"0.0","exponents":["0","1","1","2"],"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":"1/192","im":"0","approx_re":"0.00520833333333","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, -48-432*X-1456*X^2-2048*X^3-736*X^4, 30720+195072*X+354816*X^2+24576*X^3-113664*X^4, 737280+7520256*X+25804800*X^2+31850496*X^3+2064384*X^4, 14155776*(3*X+1)*(2*X+1)^2*(3*X+2)]", "text": "This is operator \"4.46\" from ...", "degz": 4, "h3": "8", "sol": "1 48 12240 4972800 2489533200 1401972219648 851613132674304 545396655633223680 363197708573488074000 249238571558094285024000", "n_discr_factors": "3", "c3": "-78", "operator": "4 4 0 0 0 0 1 -48 -432 -1456 -2048 -736 30720 195072 354816 24576 -113664 737280 7520256 25804800 31850496 2064384 28311552 240648192 750256128 1019215872 509607936", "new_number": "4.46", "id": 144, "operator_tex": "\\theta^4-2^{4} x\\left(46\\theta^4+128\\theta^3+91\\theta^2+27\\theta+3\\right)-2^{9} 3 x^{2}\\left(74\\theta^4-16\\theta^3-231\\theta^2-127\\theta-20\\right)+2^{14} 3^{2} x^{3}\\left(14\\theta^4+216\\theta^3+175\\theta^2+51\\theta+5\\right)+2^{19} 3^{3} x^{4}(3\\theta+1)(2\\theta+1)^2(3\\theta+2)", "superseek": "208 1218192", "discriminant": "4 1 -736 -113664 2064384 509607936", "aesz": "237", "n_sing_complex": "0", "inst_int": "", "c2h": "44", "hash": "52c18dd4477f6548dd3b185e97b94c20", "dim_h": "5", "inst": " 208 5874 1218192 220754467 56417503216 15951074497098 4990351864917072 1668543662657027085 588098857643537702784 215992440329420333366982", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "(864z-1)(64z-1)(1+96z)^2", "discr_factors": "509607936, z-1/864, z-1/64, (1/96+z)^2", "dm_basis": null, "q": "0 1 -240 26496 -4041728 210043824 -104028553728 -16599411155968 -8521760778977280 -3068823070013161320", "yuk": "1 208 47200 32891392 14128333088 7052187902208 3445432124311552 1711690689666555904 854294355294526200608 428724067222139018220928", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/96","im":"0","approx_re":"-0.0104166666667","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":"1/864","im":"0","approx_re":"0.00115740740741","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":"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, -2432*X^4-2560*X^3-1760*X^2-480*X-48, 1314816*X^4+540672*X^3-918528*X^2-522240*X-76800, -160432128*X^4+254803968*X^3+212336640*X^2+60162048*X+5898240, -452984832*(3*X+1)*(2*X+1)^2*(3*X+2)]", "text": "Sporadic Operator.", "degz": 4, "h3": "4", "sol": "1 48 26640 21907200 22048765200 24896521698048 30291889001197824 38838210495451361280 51763875861113556426000 71081695744396302602208000", "n_discr_factors": "3", "c3": "-60", "operator": "4 4 0 0 0 0 1 -48 -480 -1760 -2560 -2432 -76800 -522240 -918528 540672 1314816 5898240 60162048 212336640 254803968 -160432128 -905969664 -7700742144 -24008196096 -32614907904 -16307453952", "new_number": "4.48", "id": 146, "operator_tex": "\\theta^4-2^{4} x\\left(152\\theta^4+160\\theta^3+110\\theta^2+30\\theta+3\\right)+2^{10} 3 x^{2}\\left(428\\theta^4+176\\theta^3-299\\theta^2-170\\theta-25\\right)-2^{17} 3^{2} x^{3}\\left(136\\theta^4-216\\theta^3-180\\theta^2-51\\theta-5\\right)-2^{24} 3^{3} x^{4}(3\\theta+1)(2\\theta+1)^2(3\\theta+2)", "superseek": "320 19748928", "discriminant": "4 1 -2432 1314816 -160432128 -16307453952", "aesz": "241", "n_sing_complex": "0", "inst_int": "", "c2h": "28", "hash": "b4d16d8dd1eb7839630ecf8e8d242023", "dim_h": "3", "inst": " 320 61084 19748928 9428973876 5618509433280 3845253330631020 2892405836819922752 2330756708127722933332 1979363847140433024517632 1751890593945326994096072180", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "-(64z+1)(1728z-1)(-1+384z)^2", "discr_factors": "-16307453952, z-1/1728, z+1/64, (-1/384+z)^2", "dm_basis": null, "q": "0 1 -288 -36384 -12797952 -9672066000 -7623005064192 -6428933441480192 -5742516718520303616 -5358500671498636447080", "yuk": "1 320 488992 533221376 603454817056 702313679160320 830574719950010368 992095202029233504256 1193347434561997596683040 1442956244565375675406575104", "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":"1/1728","im":"0","approx_re":"0.000578703703704","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/384","im":"0","approx_re":"0.00260416666667","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, -48-576*X-2880*X^2-4608*X^3+4608*X^4, 663552+5062656*X+12926976*X^2-3538944*X^3+7077888*X^4, 651165696+5775556608*X+18459131904*X^2+24461180928*X^3+8153726976*X^4, 260919263232*(3*X+1)*(2*X+1)^2*(3*X+2)]", "text": "Sporadic Operator.", "degz": 4, "h3": null, "sol": "1 48 -30960 -11961600 15342742800 7954873774848 -12530615872110336 -7309310076290027520 12708986986974242250000 7899153737186997034464000", "n_discr_factors": "2", "c3": null, "operator": "4 4 0 0 0 0 1 -48 -576 -2880 -4608 4608 663552 5062656 12926976 -3538944 7077888 651165696 5775556608 18459131904 24461180928 8153726976 521838526464 4435627474944 13828720951296 18786186952704 9393093476352", "new_number": "4.54", "id": 153, "operator_tex": "\\theta^4+2^{4} 3 x\\left(96\\theta^4-96\\theta^3-60\\theta^2-12\\theta-1\\right)+2^{13} 3 x^{2}\\left(288\\theta^4-144\\theta^3+526\\theta^2+206\\theta+27\\right)+2^{20} 3^{3} x^{3}\\left(288\\theta^4+864\\theta^3+652\\theta^2+204\\theta+23\\right)+2^{30} 3^{5} x^{4}(3\\theta+1)(2\\theta+1)^2(3\\theta+2)", "superseek": "1056 138459552", "discriminant": "4 1 4608 7077888 8153726976 9393093476352", "aesz": "265", "n_sing_complex": "1", "inst_int": "", "c2h": null, "hash": "fad89ac60b7ab4118edfed4cf6350d0c", "dim_h": null, "inst": " 1056 -360672 138459552 -50965971720 20236543243104 -13170624491809632 12113064315942213408 -9804996648203015791752 5994631594454921823729408 -2985511969943689684958167968", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "3", "laurent": null, "discriminant_tex": "(1769472z^2+1)(1+2304z)^2", "discr_factors": "9393093476352, (1/2304+z)^2, z^2+1/1769472", "dm_basis": null, "q": "0 1 -384 404832 -344262656 273686721072 -212302805336064 171402228919792128 -147807218604086919168 130795389166230698977944", "yuk": "1 1056 -2884320 3738408960 -3261825074400 2529567905389056 -2844854886495356928 4154781060368179200000 -5020158283883205910451424 4370086432357638013237147392", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/2304","im":"0","approx_re":"-0.000434027777778","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"-1/2304*3^(1/2)","approx_re":"0.0","approx_im":"-0.000752","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":"s_1","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"s_2","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"1/2304*3^(1/2)","approx_re":"0.0","approx_im":"0.000752","exponents":["0","1","1","2"],"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, -48+64*X+3392*X^2+6656*X^3-17408*X^4, 995328+11943936*X+49545216*X^2-24772608*X^3+102629376*X^4, -6879707136-55037657088*X-168170618880*X^2-220150628352*X^3-244611809280*X^4, 15850845241344*(2*X+1)^4]", "text": "Sporadic Operator. There is a second MUM-point corresponding to Operator AESZ 361/4.72", "degz": 4, "h3": null, "sol": "1 48 -40176 -103200000 -153639990000 -149648032541952 -2121925296750336 407721053691675389952 1129764626181960087805200 1886020876540975307019744000", "n_discr_factors": "2", "c3": null, "operator": "4 4 0 0 0 0 1 -48 64 3392 6656 -17408 995328 11943936 49545216 -24772608 102629376 -6879707136 -55037657088 -168170618880 -220150628352 -244611809280 15850845241344 126806761930752 380420285792256 507227047723008 253613523861504", "new_number": "4.73", "id": 174, "operator_tex": "\\theta^4-2^{4} x\\left(1088\\theta^4-416\\theta^3-212\\theta^2-4\\theta+3\\right)+2^{12} 3^{3} x^{2}\\left(928\\theta^4-224\\theta^3+448\\theta^2+108\\theta+9\\right)-2^{20} 3^{6} x^{3}\\left(320\\theta^4+288\\theta^3+220\\theta^2+72\\theta+9\\right)+2^{28} 3^{10} x^{4}\\left((2\\theta+1)^4\\right)", "superseek": "-2656 -2493879008", "discriminant": "4 1 -17408 102629376 -244611809280 253613523861504", "aesz": "362", "n_sing_complex": "1", "inst_int": "", "c2h": null, "hash": "57a424b3b32b72260817cb8c45a8ae8f", "dim_h": null, "inst": " -2656 -1985680 -2493879008 -3906525894360 -6910084057179168 -13205144335837069648 -26643849974502474584928 -56014700550896392414559320 -121694131730070927522488317184 -271695197484747225091573920363824", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "3", "laurent": null, "discriminant_tex": "(5308416z^2-3584z+1)(-1+6912z)^2", "discr_factors": "253613523861504, z^2-7/10368*z+1/5308416, (-1/6912+z)^2", "dm_basis": null, "q": "0 1 256 741216 1628698624 3774036294192 9014129277775872 21978114893585650176 54410587501632422412288 136359425294572151505521304", "yuk": "1 -2656 -15888096 -67334735872 -250017673127136 -863760507147398656 -2852311176608157665280 -9138840541254348782632960 -28679526682059202933927498976 -88715022031221706163961317963008", "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":"s_2","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"s_1","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/6912","im":"0","approx_re":"0.000144675925926","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"7/20736","im":"-1/5184*2^(1/2)","approx_re":"0.000337577160494","approx_im":"-0.000273","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"7/20736","im":"1/5184*2^(1/2)","approx_re":"0.000337577160494","approx_im":"0.000273","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","1/2","1/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -272*X^4-2080*X^3-1456*X^2-416*X-48, -307200*X^4-417792*X^3+333824*X^2+225280*X+43008, -36962304*X^4+42467328*X^3+38993920*X^2+12386304*X+1179648, 16777216*(2*X+1)*(52*X^3+66*X^2+29*X+3), -4294967296*(2*X+1)*(X+1)^2*(2*X+3)]", "text": "B-Incarnation as fibre product 62211- x 182--1\n", "degz": 5, "h3": null, "sol": "1 48 10128 3521280 1516853520 736106773248 385585359608064 213027552363884544 122409491094916431120 72494339833505100276480", "n_discr_factors": "3", "c3": null, "operator": "4 5 0 0 0 0 1 -48 -416 -1456 -2080 -272 43008 225280 333824 -417792 -307200 1179648 12386304 38993920 42467328 -36962304 50331648 587202560 2080374784 3087007744 1744830464 -12884901888 -60129542144 -98784247808 -68719476736 -17179869184", "new_number": "5.121", "id": 205, "operator_tex": "\\theta^4-2^{4} x\\left(17\\theta^4+130\\theta^3+91\\theta^2+26\\theta+3\\right)-2^{11} x^{2}\\left(150\\theta^4+204\\theta^3-163\\theta^2-110\\theta-21\\right)-2^{16} x^{3}\\left(564\\theta^4-648\\theta^3-595\\theta^2-189\\theta-18\\right)+2^{24} x^{4}(2\\theta+1)(52\\theta^3+66\\theta^2+29\\theta+3)-2^{32} x^{5}(2\\theta+1)(\\theta+1)^2(2\\theta+3)", "superseek": "272 1143760", "discriminant": "5 1 -272 -307200 -36962304 1744830464 -17179869184", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "36da1ed5dd29b416116a3ac9f4b4c4da", "dim_h": null, "inst": " 272 -142 1143760 76778666 28997783216 5311809815178 1592772509708944 417669471289440562 126965187540855723904 38429017372271226727750", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "-(16z-1)(16384z^2-768z+1)(1+256z)^2", "discr_factors": "-17179869184, z-1/16, z^2-3/64*z+1/16384, (1/256+z)^2", "dm_basis": null, "q": "0 1 -224 28576 -4692992 569979184 -123508935680 8997071726080 -4662181982044160 -287545014192589160", "yuk": "1 272 -864 30881792 4913833760 3624722902272 1147350950959104 546320970830168064 213846769305107401504 92557621717283853607808", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/256","im":"0","approx_re":"-0.00390625","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":"3/128-1/64*2^(1/2)","im":"0","approx_re":"0.00134","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"3/128+1/64*2^(1/2)","im":"0","approx_re":"0.045535","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":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/2","1","1","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -48-352*X-1120*X^2-1536*X^3+384*X^4, 46080+206848*X+277504*X^2-507904*X^3-126976*X^4, 5898240+36569088*X+77856768*X^2+66060288*X^3-37748736*X^4, 452984832*(X+1)*(2*X+1)*(6*X^2+11*X+6), 115964116992*(2*X+1)*(X+1)^2*(2*X+3)]", "text": "B-incarnation as self-fibre product S53211\n", "degz": 5, "h3": null, "sol": "1 48 5136 710400 112104720 19210722048 3487228571904 660942598238208 129587494310960400 26115030111268750080", "n_discr_factors": "4", "c3": null, "operator": "4 5 0 0 0 0 1 -48 -352 -1120 -1536 384 46080 206848 277504 -507904 -126976 5898240 36569088 77856768 66060288 -37748736 2717908992 13136560128 23102226432 18119393280 5435817984 347892350976 1623497637888 2667174690816 1855425871872 463856467968", "new_number": "5.133", "id": 218, "operator_tex": "\\theta^4+2^{4} x\\left(24\\theta^4-96\\theta^3-70\\theta^2-22\\theta-3\\right)-2^{10} x^{2}\\left(124\\theta^4+496\\theta^3-271\\theta^2-202\\theta-45\\right)-2^{17} 3^{2} x^{3}\\left(32\\theta^4-56\\theta^3-66\\theta^2-31\\theta-5\\right)+2^{24} 3^{3} x^{4}(\\theta+1)(2\\theta+1)(6\\theta^2+11\\theta+6)+2^{32} 3^{3} x^{5}(2\\theta+1)(\\theta+1)^2(2\\theta+3)", "superseek": "192 1016256", "discriminant": "5 1 384 -126976 -37748736 5435817984 463856467968", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "0f3cb34d2bc462fbc58cdf15040595d1", "dim_h": null, "inst": " 192 -9940 1016256 -134713756 20854352960 -3558106223428 650099875656384 -124906372712813436 24944397556163013120 -5136229055822115310300", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "5", "n_sing": "5", "laurent": null, "discriminant_tex": "(256z-1)(64z+1)(192z-1)(1+384z)^2", "discr_factors": "463856467968, z-1/192, z-1/256, (1/384+z)^2, z+1/64", "dm_basis": null, "q": "0 1 -160 25568 -4409344 816759856 -160414850048 32970378328576 -7020154360758272 1536842193102066328", "yuk": "1 192 -79328 27439104 -8621759712 2606794120192 -768550916900864 222984257350139904 -63952062837582238944 18184465818442864003584", "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":"-1/384","im":"0","approx_re":"-0.00260416666667","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":"1/192","im":"0","approx_re":"0.00520833333333","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, -1408*X^4-512*X^3-528*X^2-272*X-48, 770048*X^4+720896*X^3+735232*X^2+305152*X+47616, -203423744*X^4-352321536*X^3-362020864*X^2-170655744*X-30670848, 25165824*(2*X+1)*(512*X^3+1152*X^2+1054*X+339), -19327352832*(2*X+1)*(4*X+3)*(4*X+5)*(2*X+3)]", "text": "This is operator \"5.13\" from ...", "degz": 5, "h3": "32", "sol": "1 48 5328 779520 131619600 24257173248 4739368322304 965015828434944 202584554505899280 43534711014765484800", "n_discr_factors": "3", "c3": "360", "operator": "4 5 0 0 0 0 1 -48 -272 -528 -512 -1408 47616 305152 735232 720896 770048 -30670848 -170655744 -362020864 -352321536 -203423744 8531214336 43587207168 82040586240 70866960384 25769803776 -869730877440 -4174708211712 -7035156430848 -4947802324992 -1236950581248", "new_number": "5.13", "id": 220, "operator_tex": "\\theta^4-2^{4} x\\left(88\\theta^4+32\\theta^3+33\\theta^2+17\\theta+3\\right)+2^{9} x^{2}\\left(1504\\theta^4+1408\\theta^3+1436\\theta^2+596\\theta+93\\right)-2^{18} x^{3}\\left(776\\theta^4+1344\\theta^3+1381\\theta^2+651\\theta+117\\right)+2^{23} 3 x^{4}(2\\theta+1)(512\\theta^3+1152\\theta^2+1054\\theta+339)-2^{31} 3^{2} x^{5}(2\\theta+1)(4\\theta+3)(4\\theta+5)(2\\theta+3)", "superseek": "-80 -174096", "discriminant": "5 1 -1408 770048 -203423744 25769803776 -1236950581248", "aesz": "83", "n_sing_complex": "0", "inst_int": "", "c2h": "-16", "hash": "171e1251d8e4f7de878d0d07de6f58ab", "dim_h": "4", "inst": " -80 -2954 -174096 -13270953 -1179175536 -115795446786 -12188186517456 -1349830285576015 -155427513115593600 -18456445525841201614", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "-(128z-1)(384z-1)^2(256z-1)^2", "discr_factors": "-1236950581248, (z-1/384)^2, z-1/128, (z-1/256)^2", "dm_basis": null, "q": "0 1 -80 3840 -181248 5466544 -307951104 46314496 -945821483008 -60856937695080", "yuk": "1 -80 -23712 -4700672 -849364704 -147396942080 -25011821230080 -4180547975487488 -691113107064284384 -113306657061272435072", "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":"1/384","im":"0","approx_re":"0.00260416666667","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/256","im":"0","approx_re":"0.00390625","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"1/128","im":"0","approx_re":"0.0078125","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, -48-256*X-592*X^2-672*X^3-432*X^4, 52736+192512*X+296448*X^2+220160*X^3+71168*X^4, -13418496-40648704*X-49020928*X^2-26836992*X^3-6045696*X^4, 1341652992+3445096448*X+3228565504*X^2+1504706560*X^3+349700096*X^4, -35399925760-72058142720*X-45164265472*X^2-51438944256*X^3-21189623808*X^4, -2660732239872-5377835925504*X-2573759152128*X^2+2966748659712*X^3+1267552223232*X^4, 168637595910144+225348344086528*X-50543175139328*X^2-167503724544000*X^3-53034256171008*X^4, -1070924325453824+2634979615965184*X+7853811557203968*X^2+3438172860055552*X^3+1774062011416576*X^4, -65917921108426752-133577468635250688*X-92869150128472064*X^2-25332747903959040*X^3-68715078689488896*X^4, 295548725546188800+408138716230451200*X+1908963292051668992*X^2+3494793310839504896*X^3+2193253018529431552*X^4, -32515989309614981120-131505109119218483200*X-200860543380724121600*X^2-138350580552821637120*X^3-36749372959343247360*X^4, 14411518807585587200*(2*X+3)^4]", "text": "This is operator \"12.12\" from ...", "degz": 12, "h3": null, "sol": "1 48 2704 179968 14147856 1298461440 135536093440 15582207209472 1918136670436624 247673397166101248", "n_discr_factors": "5", "c3": null, "operator": "4 12 0 0 0 0 1 -48 -256 -592 -672 -432 52736 192512 296448 220160 71168 -13418496 -40648704 -49020928 -26836992 -6045696 1341652992 3445096448 3228565504 1504706560 349700096 -35399925760 -72058142720 -45164265472 -51438944256 -21189623808 -2660732239872 -5377835925504 -2573759152128 2966748659712 1267552223232 168637595910144 225348344086528 -50543175139328 -167503724544000 -53034256171008 -1070924325453824 2634979615965184 7853811557203968 3438172860055552 1774062011416576 -65917921108426752 -133577468635250688 -92869150128472064 -25332747903959040 -68715078689488896 295548725546188800 408138716230451200 1908963292051668992 3494793310839504896 2193253018529431552 -32515989309614981120 -131505109119218483200 -200860543380724121600 -138350580552821637120 -36749372959343247360 1167333023414432563200 3112888062438486835200 3112888062438486835200 1383505805528216371200 230584300921369395200", "new_number": "12.12", "id": 349, "operator_tex": "\\theta^4-2^{4} x\\left(27\\theta^4+42\\theta^3+37\\theta^2+16\\theta+3\\right)+2^{9} x^{2}\\left(139\\theta^4+430\\theta^3+579\\theta^2+376\\theta+103\\right)-2^{14} x^{3}\\left(369\\theta^4+1638\\theta^3+2992\\theta^2+2481\\theta+819\\right)+2^{19} x^{4}\\left(667\\theta^4+2870\\theta^3+6158\\theta^2+6571\\theta+2559\\right)-2^{24} x^{5}\\left(1263\\theta^4+3066\\theta^3+2692\\theta^2+4295\\theta+2110\\right)+2^{29} 3 x^{6}\\left(787\\theta^4+1842\\theta^3-1598\\theta^2-3339\\theta-1652\\right)-2^{34} x^{7}\\left(3087\\theta^4+9750\\theta^3+2942\\theta^2-13117\\theta-9816\\right)+2^{39} x^{8}\\left(3227\\theta^4+6254\\theta^3+14286\\theta^2+4793\\theta-1948\\right)-2^{44} x^{9}\\left(3906\\theta^4+1440\\theta^3+5279\\theta^2+7593\\theta+3747\\right)+2^{49} x^{10}\\left(3896\\theta^4+6208\\theta^3+3391\\theta^2+725\\theta+525\\right)-2^{54} 5 x^{11}\\left(408\\theta^4+1536\\theta^3+2230\\theta^2+1460\\theta+361\\right)+2^{59} 5^{2} x^{12}\\left((2\\theta+3)^4\\right)", "superseek": "48 3184", "discriminant": "12 1 -432 71168 -6045696 349700096 -21189623808 1267552223232 -53034256171008 1774062011416576 -68715078689488896 2193253018529431552 -36749372959343247360 230584300921369395200", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "2b1c995b5f2826ce90fc016ad86fd66f", "dim_h": null, "inst": " 48 46 3184 409910 -3351792 660929430 10619210928 859394914110 70266573485696 2358254619793562", "cleanlist": "True", "n_sing_real": "7", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "9", "laurent": null, "discriminant_tex": "(16z-1)(32z-1)(4096z^2-192z+1)(64z-1)^2(163840z^3+1024z^2+32z-1)^2", "discr_factors": "230584300921369395200, z-1/16, z-1/32, (z-1/64)^2, z^2-3/64*z+1/4096, (z^3+1/160*z^2+1/5120*z-1/163840)^2", "dm_basis": null, "q": "0 1 -64 3104 -146432 5759792 -207339520 4827303424 -50713985024 -7931377213800", "yuk": "1 48 416 86016 26234656 -418973952 142760843264 3642389348352 440010222258976 51224332071158400", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/960*(359+45*65^(1/2))^(1/3)+7/480/(359+45*65^(1/2))^(1/3)-1/480","im":"-1/64*3^(1/2)*(1/15*(359+45*65^(1/2))^(1/3)+14/15/(359+45*65^(1/2))^(1/3))","approx_re":"-0.009802","approx_im":"-0.019","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/960*(359+45*65^(1/2))^(1/3)+7/480/(359+45*65^(1/2))^(1/3)-1/480","im":"1/64*3^(1/2)*(1/15*(359+45*65^(1/2))^(1/3)+14/15/(359+45*65^(1/2))^(1/3))","approx_re":"-0.009802","approx_im":"0.019","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":"3/128-1/128*5^(1/2)","im":"0","approx_re":"0.005968","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/480*(359+45*65^(1/2))^(1/3)-7/240/(359+45*65^(1/2))^(1/3)-1/480","im":"0","approx_re":"0.013353","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/64","im":"0","approx_re":"0.015625","approx_im":"0.0","exponents":["0","0","1","1"],"monodromy":[],"monodromy_dm":[]},{"re":"1/32","im":"0","approx_re":"0.03125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"3/128+1/128*5^(1/2)","im":"0","approx_re":"0.040907","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":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["3/2","3/2","3/2","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -13*X^4-14*X^3-16*X^2-9*X-2, 33*X^4-88*X^3-265*X^2-324*X-148, 217*X^4+2362*X^3+6403*X^2+8178*X+4160, -1354*X^4-8268*X^3-16178*X^2-12420*X-720, 1812*X^4-15192*X^3-139320*X^2-347460*X-301320, 7580*X^4+149208*X^3+707964*X^2+1423392*X+1075344, -38540*X^4-356680*X^3-743540*X^2+429576*X+2089856, 47256*X^4-85088*X^3-3329000*X^2-13330608*X-16415360, 94304*X^4+2569088*X^3+16637888*X^2+42511200*X+38564800, -391808*X^4-5430528*X^3-25443520*X^2-46255680*X-22811520, 433728*X^4+2572416*X^3-8937408*X^2-87598848*X-152957952, 1152*(X+4)*(371*X^3+8580*X^2+53325*X+101564), -27648*(X+4)*(X+5)*(51*X^2+519*X+1330), 829440*(X+4)*(X+5)^2*(X+6)]", "text": "This is operator \"14.1\" from ...", "degz": 14, "h3": null, "sol": "1 2 16 48 264 1008 5008 21824 106792 500496", "n_discr_factors": "9", "c3": null, "operator": "4 14 0 0 0 0 1 -2 -9 -16 -14 -13 -148 -324 -265 -88 33 4160 8178 6403 2362 217 -720 -12420 -16178 -8268 -1354 -301320 -347460 -139320 -15192 1812 1075344 1423392 707964 149208 7580 2089856 429576 -743540 -356680 -38540 -16415360 -13330608 -3329000 -85088 47256 38564800 42511200 16637888 2569088 94304 -22811520 -46255680 -25443520 -5430528 -391808 -152957952 -87598848 -8937408 2572416 433728 468006912 362723328 100967040 11593728 427392 -735436800 -617932800 -194116608 -27039744 -1410048 497664000 406425600 123586560 16588800 829440", "new_number": "14.1", "id": 380, "operator_tex": "\\theta^4-x\\left(13\\theta^4+14\\theta^3+16\\theta^2+9\\theta+2\\right)+x^{2}\\left(33\\theta^4-88\\theta^3-265\\theta^2-324\\theta-148\\right)+x^{3}\\left(217\\theta^4+2362\\theta^3+6403\\theta^2+8178\\theta+4160\\right)-2 x^{4}\\left(677\\theta^4+4134\\theta^3+8089\\theta^2+6210\\theta+360\\right)+2^{2} 3 x^{5}\\left(151\\theta^4-1266\\theta^3-11610\\theta^2-28955\\theta-25110\\right)+2^{2} x^{6}\\left(1895\\theta^4+37302\\theta^3+176991\\theta^2+355848\\theta+268836\\right)-2^{2} x^{7}\\left(9635\\theta^4+89170\\theta^3+185885\\theta^2-107394\\theta-522464\\right)+2^{3} x^{8}\\left(5907\\theta^4-10636\\theta^3-416125\\theta^2-1666326\\theta-2051920\\right)+2^{5} x^{9}\\left(2947\\theta^4+80284\\theta^3+519934\\theta^2+1328475\\theta+1205150\\right)-2^{6} x^{10}\\left(6122\\theta^4+84852\\theta^3+397555\\theta^2+722745\\theta+356430\\right)+2^{6} 3 x^{11}\\left(2259\\theta^4+13398\\theta^3-46549\\theta^2-456244\\theta-796656\\right)+2^{7} 3^{2} x^{12}(\\theta+4)(371\\theta^3+8580\\theta^2+53325\\theta+101564)-2^{10} 3^{3} x^{13}(\\theta+4)(\\theta+5)(51\\theta^2+519\\theta+1330)+2^{11} 3^{4} 5 x^{14}(\\theta+4)(\\theta+5)^2(\\theta+6)", "superseek": "0 0", "discriminant": "14 1 -13 33 217 -1354 1812 7580 -38540 47256 94304 -391808 433728 427392 -1410048 829440", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "a8cf56492aecc07971e82c9104785180", "dim_h": null, "inst": " 0 1/4 0 -1/2 0 28/9 0 -14 0 2223/20", "cleanlist": "True", "n_sing_real": "9", "sol_explicit": "", "n_sing_rational": "9", "n_sing": "11", "laurent": null, "discriminant_tex": "(z-1)(6z-1)(4z-1)(3z+1)(4z+1)(5z-1)(2z+1)^2(2z-1)^2(6z^2-2z+1)^2", "discr_factors": "829440, z+1/4, z-1/4, z-1/6, (z-1/2)^2, (z^2-1/3*z+1/6)^2, z-1, (z+1/2)^2, z-1/5, z+1/3", "dm_basis": null, "q": "0 1 -1 -5 11 26 -99 -146 871 717", "yuk": "1 0 2 0 -30 0 674 0 -7198 0", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/2","im":"0","approx_re":"-0.5","approx_im":"0.0","exponents":["0","0","-1","1"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/3","im":"0","approx_re":"-0.333333333333","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/4","im":"0","approx_re":"-0.25","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":"1/6","im":"-1/6*5^(1/2)","approx_re":"0.166666666667","approx_im":"-0.372678","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/6","im":"0","approx_re":"0.166666666667","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/6","im":"1/6*5^(1/2)","approx_re":"0.166666666667","approx_im":"0.372678","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/5","im":"0","approx_re":"0.2","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/4","im":"0","approx_re":"0.25","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/2","im":"0","approx_re":"0.5","approx_im":"0.0","exponents":["0","0","-1","1"],"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":["4","5","5","6"],"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":[]}]}]}