Lfunction data - 8-1575e4-1.1-c3e4-0-1

Formats: - HTML - YAML - JSON - 2026-04-13T18:47:13.118077

• lfunc_lfunctions •

  Column	Type
  A10	numeric
  A2	numeric
  A3	numeric
  A4	numeric
  A5	numeric
  A6	numeric
  A7	numeric
  A8	numeric
  A9	numeric
  Lhash	text
  a10	jsonb
  a2	jsonb
  a3	jsonb
  a4	jsonb
  a5	jsonb
  a6	jsonb
  a7	jsonb
  a8	jsonb
  a9	jsonb
  accuracy	smallint
  algebraic	boolean
  analytic_conductor	double precision
  analytic_normalization	numeric
  bad_lfactors	jsonb
  bad_primes	bigint[]
  central_character	text
  coeff_info	jsonb
  coefficient_field	text
  conductor	numeric
  conductor_radical	integer
  conjugate	text
  credit	text
  degree	smallint
  dirichlet_coefficients	jsonb
  euler_factors	jsonb
  euler_factors_factorization	jsonb
  gamma_factors	jsonb
  group	text
  index	smallint
  label	text
  leading_term	text
  load_key	text
  motivic_weight	smallint
  mu_imag	numeric[]
  mu_real	smallint[]
  nu_imag	numeric[]
  nu_real_doubled	smallint[]
  order_of_vanishing	smallint
  origin	text
  plot_delta	numeric
  plot_values	jsonb
  positive_zeros	jsonb
  precision	smallint
  prelabel	text
  primitive	boolean
  rational	boolean
  root_analytic_conductor	double precision
  root_angle	double precision
  root_number	text
  self_dual	boolean
  sign_arg	numeric
  spectral_label	text
  st_group	text
  symmetry_type	text
  trace_hash	bigint
  types	jsonb
  values	jsonb
  z1	numeric
  z2	numeric
  z3	numeric

  
  {'Lhash': '391199111186848709184675170263,897743647836525011063888457519,946565892105860681760557764988,1605589793201251253985810554352', 'a10': 0, 'a2': 6, 'a3': 0, 'a4': 10, 'a5': 0, 'a6': 0, 'a7': 28, 'a8': 3, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 74573841.5748797, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1]], [7, [1, -28, 294, -1372, 2401]]], 'bad_primes': [3, 5, 7], 'central_character': '1575.1', 'coefficient_field': '1.1.1.1', 'conductor': 6153500390625, 'conductor_radical': 105, 'degree': 8, 'euler_factors': [[1, -6, 26, -99, 298, -792, 1664, -3072, 4096], [1], [1], [1, -28, 294, -1372, 2401], [1, 57, 4001, 182772, 7206874, 243269532, 7088015561, 134403018387, 3138428376721], [1, 43, 4464, 221093, 13201958, 485741321, 21546875376, 455993473039, 23298085122481], [1, -99, 13790, -926229, 90687946, -4550563077, 332857076510, -11740199773203, 582622237229761], [1, 12, -10212, 154020, 95206646, 1056423180, -480432536772, 3872252373348, 2213314919066161], [1, -156, 28082, -3613896, 479553835, -43970272632, 4157143834898, -280979815188228, 21914624432020321], [1, 378, 143760, 29729988, 5852097929, 725084677332, 85511800626960, 5483701178878482, 353814783205469041], [1, 93, 16330, -936891, 385099458, -27910919781, 14492935110730, 2458884860942403, 787662783788549761], [1, 81, 107185, 469746, 5937897606, 23794044138, 275007385148665, 10526900923401237, 6582952005840035281], [1, -465, 105716, -566235, -2050285754, -39025482435, 502162019941556, -152232599493191865, 22563490300366186081], [1, -64, 64662, 2492176, 5477627255, 198145437232, 408751977474438, -32165927163957952, 39959630797262576401], [1, -744, 588276, -247094976, 101020317878, -25654141693248, 6341153676882804, -832633071988458648, 116191483108948578241], [1, -729, 333446, -137056347, 63585804370, -20404537772319, 7390617561020534, -2405527658423754957, 491258904256726154641], [1, 231, 701280, 148812447, 204019205798, 30562951552413, 29580364631760480, 2001152034109290909, 1779197418239532716881], [1, 1353, 1374808, 931878711, 511309944510, 211518761701491, 70830622834497688, 15822179663604592773, 2654348974297586158321], [1, 1487, 1603371, 1080212116, 674138302124, 324887836644508, 145038346676691699, 40456116647290586189, 8182718904632857144561], [1, -1725, 1434819, -706812600, 347044577276, -252976004478600, 183800721275245299, -79088663739324578475, 16409682740640811134241], [1, 512, 1030980, 484092568, 566560915526, 188320238525656, 156022560619433220, 30142252394633171456, 22902048046490258711521], [1, -1629, 1989837, -1837769472, 1504809477470, -906092022705408, 483704413231540077, -195238249855685241651, 59091511031674153381441], [1, -321, 661434, -144132717, 79870144034, -82413213855279, 216249478918951146, -60007821940880469363, 106890007738661124410161], [1, -978, 526228, 159100050, -360762420714, 112160603148450, 261525470779825108, -342648562825920534402, 246990403565262140303521], [1, 2616, 5183100, 6945540936, 7789652954246, 6339007682681928, 4317377198747499900, 1988764449440342607672, 693842360995438000295041], [1, -1350, 3340352, -3795739530, 4859911445998, -3910754233498530, 3545850958100351552, -1476475118123887216350, 1126825030131969720661201], [1, -247, 3317424, -886031387, 4883494266038, -968190419422349, 3961177745760421296, -322278976405823412001, 1425760886846178945447841], [1, -1122, 4258116, -3210094866, 7220940035654, -3932504244929238, 6390283922893856484, -2062751236335413356854, 2252191588960823337718801], [1, -1735, 4582243, -4611892390, 7710081211408, -5972534389929310, 7684880243200396363, -3768234839832406789915, 2812664781782894485727281], [1, -2145, 6739485, -9134900790, 15233945891978, -13180720945188630, 14031282607432066365, -6443669956976255445585, 4334523100191686738306881]], 'euler_factors_factorization': [[[[1, -6, 26, -99, 298, -792, 1664, -3072, 4096], 1]], [1], [1], [[[1, -7], 4]], [[[1, 57, 4001, 182772, 7206874, 243269532, 7088015561, 134403018387, 3138428376721], 1]], [[[1, 43, 4464, 221093, 13201958, 485741321, 21546875376, 455993473039, 23298085122481], 1]], [[[1, -99, 13790, -926229, 90687946, -4550563077, 332857076510, -11740199773203, 582622237229761], 1]], [[[1, 12, -10212, 154020, 95206646, 1056423180, -480432536772, 3872252373348, 2213314919066161], 1]], [[[1, -156, 28082, -3613896, 479553835, -43970272632, 4157143834898, -280979815188228, 21914624432020321], 1]], [[[1, 378, 143760, 29729988, 5852097929, 725084677332, 85511800626960, 5483701178878482, 353814783205469041], 1]], [[[1, 93, 16330, -936891, 385099458, -27910919781, 14492935110730, 2458884860942403, 787662783788549761], 1]], [[[1, 81, 107185, 469746, 5937897606, 23794044138, 275007385148665, 10526900923401237, 6582952005840035281], 1]], [[[1, -465, 105716, -566235, -2050285754, -39025482435, 502162019941556, -152232599493191865, 22563490300366186081], 1]], [[[1, -64, 64662, 2492176, 5477627255, 198145437232, 408751977474438, -32165927163957952, 39959630797262576401], 1]], [[[1, -744, 588276, -247094976, 101020317878, -25654141693248, 6341153676882804, -832633071988458648, 116191483108948578241], 1]], [[[1, -729, 333446, -137056347, 63585804370, -20404537772319, 7390617561020534, -2405527658423754957, 491258904256726154641], 1]], [[[1, 231, 701280, 148812447, 204019205798, 30562951552413, 29580364631760480, 2001152034109290909, 1779197418239532716881], 1]], [[[1, 1353, 1374808, 931878711, 511309944510, 211518761701491, 70830622834497688, 15822179663604592773, 2654348974297586158321], 1]], [[[1, 1487, 1603371, 1080212116, 674138302124, 324887836644508, 145038346676691699, 40456116647290586189, 8182718904632857144561], 1]], [[[1, -1725, 1434819, -706812600, 347044577276, -252976004478600, 183800721275245299, -79088663739324578475, 16409682740640811134241], 1]], [[[1, 512, 1030980, 484092568, 566560915526, 188320238525656, 156022560619433220, 30142252394633171456, 22902048046490258711521], 1]], [[[1, -1629, 1989837, -1837769472, 1504809477470, -906092022705408, 483704413231540077, -195238249855685241651, 59091511031674153381441], 1]], [[[1, -321, 661434, -144132717, 79870144034, -82413213855279, 216249478918951146, -60007821940880469363, 106890007738661124410161], 1]], [[[1, -978, 526228, 159100050, -360762420714, 112160603148450, 261525470779825108, -342648562825920534402, 246990403565262140303521], 1]], [[[1, 2616, 5183100, 6945540936, 7789652954246, 6339007682681928, 4317377198747499900, 1988764449440342607672, 693842360995438000295041], 1]], [[[1, -1350, 3340352, -3795739530, 4859911445998, -3910754233498530, 3545850958100351552, -1476475118123887216350, 1126825030131969720661201], 1]], [[[1, -247, 3317424, -886031387, 4883494266038, -968190419422349, 3961177745760421296, -322278976405823412001, 1425760886846178945447841], 1]], [[[1, -1122, 4258116, -3210094866, 7220940035654, -3932504244929238, 6390283922893856484, -2062751236335413356854, 2252191588960823337718801], 1]], [[[1, -1735, 4582243, -4611892390, 7710081211408, -5972534389929310, 7684880243200396363, -3768234839832406789915, 2812664781782894485727281], 1]], [[[1, -2145, 6739485, -9134900790, 15233945891978, -13180720945188630, 14031282607432066365, -6443669956976255445585, 4334523100191686738306881], 1]]], 'gamma_factors': [[], [0, 0, 0, 0]], 'group': 'GL2', 'index': 1, 'label': '8-1575e4-1.1-c3e4-0-1', 'leading_term': '20.2898274817442321080850000445654855508008541718528245241366276607170998181157156410044752', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3, 3, 3, 3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1575/4/a/bm', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0146484375', 'prec': 40}, 'plot_values': [20.28982748174423, 20.13406380478187, 19.927712132286217, 19.620763778160942, 19.166850551737518, 18.55268952144011, 17.798184063267534, 16.926178819223455, 15.956889813653335, 14.90142627678008, 13.768911104430375, 12.569437764114161, 11.31609313120368, 10.02405959867073, 8.708884617544612, 7.385899654124436, 6.069831693178418, 4.774910882573159, 3.5147747519253345, 2.3025400421719358, 1.15050052507712, 0.06981363887365072, -0.9295872087029493, -1.839080613955267, -2.651550955267, -3.361457215455828, -3.964824916732691, -4.459338003370052, -4.844381083992807, -5.120993374853933, -5.291834690953417, -5.361155393045317, -5.334695344226633, -5.219562660062764, -5.024135151219063, -4.757901700377907, -4.431286305660082, -4.05547674662671, -3.642242624879272, -3.203719368610093, -2.7522051290139613, -2.299950960125756, -1.8589541301628103, -1.4407495007970959, -1.0562122647437524, -0.7153663619746506, -0.42721610579974695, -0.19958954996385456, -0.038996726838923045, 0.04948365237170655, 0.062292905838209796, -0.0025407773860882583, -0.14536559348030142, -0.36489879630808386, -0.6582434829672097, -1.0209382276199905, -1.447035007532581, -1.9292040790335585, -2.458861087664421, -3.0263187207606905, -3.620962213199483, -4.231449452165507, -4.845909593800964, -5.452156764755362, -6.037931471792567, -6.591128793560355, -7.1000147155961875, -7.5534559526040335, -7.941156426207511, -8.253831895986961, -8.483398905180985, -8.623166686059266, -8.667959424734201, -8.614209083035668, -8.460073151361073, -8.205497189168318, -7.852190747624526, -7.403623993833715, -6.865024908806017, -6.243260302803083, -5.5467099499251225, -4.785148691199089, -3.969581267519706, -3.112020622597206, -2.2252838964375306, -1.3227512989305463, -0.4181169771780553, 0.47485189002589506, 1.3425878708535122, 2.1720073696990765, 2.9507174895561294, 3.6672454778361296, 4.311334032132675, 4.874088519624868, 5.348113594755079, 5.727718141131824, 6.009050889610473, 6.190073378099838, 6.270627307686585, 6.252539479384575, 6.139468847781815, 5.936787926078137, 5.651586575537482, 5.292509775521824, 4.86945959318562, 4.393428834807957, 3.876380950547706, 3.330869205712197, 2.7697501411607335, 2.206003025159365, 1.6524380249205288, 1.1213494106930588, 0.6242934262535916, 0.1718905820308471, -0.22646108708163637, -0.5627780722019929, -0.8306192530483172, -1.025233679186496, -1.1436638274310826, -1.1847769751026305, -1.149274977276395, -1.0396637344273028, -0.8601684326530672, -0.6166220345005461, -0.31631110483381714, 0.032224231834570696, 0.41940369528719346, 0.8348389954186067, 1.2676080634667268, 1.7065273558136784, 2.1404250730208148, 2.558420470736572, 2.9501906690249977, 3.3062232143161263, 3.6180594553146372, 3.8784866439211103, 4.081703773312192, 4.223475508265255, 4.301222602124297, 4.314054675410984, 4.262791692214752, 4.14993627988543, 3.9795695166445104, 3.757228648092089, 3.489772016853033, 3.1851571053721544, 2.8522066199303606, 2.500381263584332, 2.139514197072948, 1.7795143761818775, 1.43009229329872, 1.1005052758929958, 0.7992860224452757, 0.5340003626821942, 0.3110319810918694, 0.1354099578137537, 0.010666106782064607, -0.06126991595896795, -0.08013068060573635, -0.04731011879349146, 0.03416972097433453, 0.15974174953620937, 0.3234310060451913, 0.5180161396740272, 0.7352281873381898, 0.9660096673601515, 1.2007693019112333, 1.4296343206043651, 1.6427654831728749, 1.8306464387808679, 1.9843442065206187, 2.095771714789273, 2.157975940361091, 2.1652904140035596, 2.1135207018788456, 2.0001296056663813, 1.8242899231882765, 1.5868783302289067, 1.2905259130605695, 0.9395858542126254, 0.5399409839132212, 0.09886483358283112, -0.3751008004234048, -0.8724306090330904, -1.3828964935903227, -1.8958024866875511, -2.400285984336962, -2.885648077897555, -3.341615625497516, -3.758610759436066, -4.128065904032461, -4.442617151884014, -4.6962800361709265, -4.884629113415942, -5.004931458397536, -5.056156643436258, -5.03900549130979, -4.955853898206318, -4.810685027732697, -4.608937245960808, -4.357319692781466, -4.063563990378744, -3.7362249583720875, -3.384413700437529, -3.0174673504619673, -2.644663996126257, -2.274993761484963, -1.9168621487044297, -1.577815347833639, -1.26434071331463, -0.9817108932499877, -0.7338172980172452, -0.5230767779241114, -0.3503976963904967, -0.21518770011106625, -0.11540490963391764, -0.04766303484106476, -0.007379766377580072, 0.011036744240069176, 0.013968406171513318, 0.008343272678383149, 0.0013751641180041328, 0.0002951286875755368, 0.012082786045295757, 0.04321012116782578, 0.09940210326996737, 0.18542140550378744, 0.30489618163636856, 0.4601809049785765, 0.6522471450143658, 0.8806479220424814, 1.143540066839742, 1.4376956549417237, 1.7585815658678874, 2.100579302169539, 2.4571251685654056, 2.8208501842301636, 3.1838608855221664, 3.5380975961100147, 3.875450980699442, 4.18798595658101, 4.468343658407181, 4.709949454865058, 4.907076282982543, 5.055097661929486, 5.150712890932037, 5.191940851737197, 5.178116357288022, 5.1100501057647865, 4.98987264387483, 4.820943577296552, 4.607788760273643, 4.355952548014781, 4.071681889202336, 3.7618141501527798, 3.4336266469004064, 3.0944684282837343, 2.7515266536439764, 2.411746095796936, 2.0815793961424376, 1.7667290875687227, 1.4720565072836598, 1.2015485667892254, 0.9581572037524356, 0.743766174731504, 0.5592433690974244, 0.40448281754243415, 0.27845400665808256, 0.17932606676528418, 0.10461458772403358, 0.051325376514785075, 0.01612060239442351, -0.00450482722372593, -0.01405496554127079, -0.015873193207743004, -0.012996495261427475, -0.008031576827936709, -0.0030570192042483867, 0.0004451596837786763, 0.0016265675989148914, 0.00027718060095031645, -0.00320160811881825, -0.007853898609642985, -0.012252715448372762, -0.014605067144629719, -0.01287470573809791, -0.0049158291684350385, 0.011389967892660322, 0.0379959670152323, 0.07656157136575786, 0.12834359177737528, 0.19409718239261153, 0.27399877932211586, 0.36761530361807926, 0.4738897080524144, 0.591137460759131, 0.7170997408196746, 0.8490344069267605, 0.983788747037548, 1.117899834688913, 1.2477731186583947, 1.3697874541722739, 1.480422519597766, 1.5764300640016295, 1.6549778541686753, 1.7136924872639847, 1.750789837202089, 1.7652112592509968, 1.756577284072053, 1.725175574730342, 1.6720507048373985, 1.5989371806006456, 1.508097503637057, 1.402266803144691, 1.2846383015868919, 1.1586303491417922, 1.027734950536263, 0.8954535467617847, 0.7651643584044056, 0.6399378004480516, 0.522454565617338, 0.41495515404228267, 0.31914027754956575, 0.23612774687797988, 0.16646529750725786, 0.11013871708761458, 0.06660553067303622, 0.0348658433770719, 0.013549190342580215, 0.001006483897880096, -0.004580304485284087, -0.005086293177736084, -0.0023363613197459753, 0.0019959337114471005, 0.006476071944403329, 0.009978384442008638, 0.011735708933044244, 0.011365322258683658, 0.008870506007497609, 0.004618359546208738, -0.0007049506552772118, -0.006158989658682614, -0.010629462874387721, -0.012918973656292411, -0.011844721234626508, -0.006336673236478387, 0.004474964769459856, 0.0211789824936828, 0.04401668265788456, 0.07284063963968909, 0.10710447302314725, 0.14586067350825366, 0.1877913672064986, 0.23126357975627948, 0.27442296148409034, 0.31527978559564546, 0.35181147550811886, 0.38206905653236095, 0.404328341759708, 0.4171893179831363, 0.4196383343068828, 0.41112681733479617, 0.3916864812385759, 0.3619105544741997, 0.3229088368889048, 0.27629230893460266, 0.2241608558999699, 0.16893653859375113, 0.11322957927411698, 0.059726496601853196, 0.011062417963905136, -0.03037397593334274, -0.06258499156274436, -0.08408539859252673, -0.09399104637068514, -0.09210923253829002, -0.07898132085276238, -0.055866262489917405, -0.024674784926958224, 0.01211501293680455, 0.05159190734842901, 0.09060140009839973, 0.12594439496274026, 0.15459303607336003, 0.17392595004504602, 0.18194816750571832, 0.17748448134972308, 0.160351645041386, 0.1314750521680992, 0.09294451332025769, 0.04801190921355791, 0.0010113792805183743, -0.04279992874689029, -0.07746746090075268, -0.09663074998467402, -0.09388263558157207, -0.0631692325031308, 0.0007983913753453163, 0.10210921083920489, 0.24322071829172845, 0.42459839019645645, 0.6444312038450081, 0.898354874080096, 1.1793089779836585, 1.4776483647025564, 1.781201485682869, 2.0754615077270078, 2.344121981558132, 2.569703743406558, 2.733976024330717, 2.8187714739709158, 2.807182201193963, 2.684122346807441, 2.437047225770837, 2.057252720683267, 1.540689618582462, 0.8881517064180835, 0.10596445165890513, -0.7931101262409641, -1.7903467551898777, -2.8612938535614463, -3.9755782180055323, -5.097691244057952, -6.188285211628238, -7.204966652409541, -8.103217966249673, -8.838566719650093, -9.368031902436382, -9.651320756795991, -9.65263710009171, -9.34278747757979, -8.700231436262497, -7.712111974334156, -6.375450811431564, -4.69829318621577, -2.699672220431048, -0.40940948810261, 2.132186120660969, 4.874620131828823, 7.758847986781507, 10.718974520939193, 13.683921185100193, 16.579254314185672, 19.329822493958893, 21.86210634552234, 24.1066322514294, 26.000325338149647, 27.48859421884784, 28.527267403112674, 29.084631572267845, 29.14240179982246, 28.696296900970243, 27.75666357868999, 26.348529004226013, 24.510569397492, 22.293917854167734, 19.760895170043792, 16.982835834689542, 14.037783293583074, 11.007926460391422, 7.976896796650786, 5.0270530194436365, 2.2368460575204088, -0.32195795655093945, -2.586390521036734, -4.504111960315326, -6.035260213036009, -7.153525636816379, -7.8464242898462615, -8.115524205826885, -7.976328880173121, -7.456955629654208, -6.596780837139774, -5.4448736352704215, -4.057851164115609, -2.497532740544789, -0.8286207790763733, 0.8839768658497874, 2.577343177141158, 4.192590468296857, 5.677240222790663, 6.986829465516803, 8.085765144832285, 8.948363917438906, 9.559813637828181, 9.915405693911772, 10.020107776810475, 9.888392119248016, 9.542695833048791, 9.01152623191697, 8.328347553878407, 7.530092661089888, 6.654698517419992, 5.739497238823808, 4.820156842750794, 3.9289069075102154, 3.093226889261556, 2.3352481596010373, 1.6713085887836903, 1.1115176076417184, 0.6599462023402513, 0.3151196317757924, 0.0706247696805277, -0.08401828704268557, -0.1623225849644208, -0.1797451568377006, -0.15256187711944066, -0.09680583798771585, -0.02732783380908439, 0.04301534507948116, 0.10395661054012229, 0.1481879985793302, 0.17150875482438802, 0.17273341885517465, 0.15338407451105157, 0.11722305110279432, 0.06963146432932664, 0.016902030373194068, -0.03450961389445202, -0.07868413489449277, -0.11086010672105999, -0.1279399850620489, -0.12884457548734582, -0.11461155477399179, -0.08830574477733158, -0.05473346679200755, -0.01993852685278906, 0.00948762165334035, 0.027200119056768716, 0.02798650021139316, 0.008656791095207256, -0.031131381550758282, -0.08814276877151403, -0.15502656689705574, -0.22005460225705864, -0.26711046407808786, -0.27596363091412157, -0.22288663769584574, -0.08169588597974398, 0.17505659084665418, 0.5746967910059156, 1.142783343390691, 1.9011191140916166, 2.8661948150057084, 4.047643702968549, 5.446674222567374, 7.054684536227285, 8.852740610785728, 10.811179815263916, 12.889779919229074, 15.038400156758158, 17.198107142569913, 19.30287700664837, 21.282464404436446, 23.06432650525698, 24.57622285659149, 25.749902705698858, 26.524707257093105, 26.849247402882217, 26.684277876083996, 26.006316333753734, 24.808625289873603, 23.101708068163514, 20.91460348965326, 18.294943101088695, 15.306957838009124, 12.029764796719704, 8.555435473040195, 4.985403166453271, 1.426700720307772, -2.0119390081384623, -5.224237850983194, -8.110490452108968, -10.5816356919724, -12.563200315202907, -13.997911782639706, -14.84806396341787, -15.097548336406584, -14.752381698092428, -13.840188253047698, -12.409327502264581, -10.526692543137228, -8.27485768647761, -5.748878429067236, -3.051686820261907, -0.2895909291600707, 2.431310502389229, 5.009915004304608, 7.35566972597705, 9.390594303932472, 11.051940180358491, 12.296503751695523, 13.101178738812905, 13.461788347764696, 13.393872642158726, 12.932536162476275, 12.12768816483299, 11.041138418562848, 9.74508038487115, 8.316725257904652, 6.833238482789347, 5.368739587227008, 3.990851910422192, 2.755992092080724, 1.7069397048038792, 0.8714373592781957, 0.26047858667886814, -0.13195167454791035, -0.3278881639886518, -0.363838732539742, -0.28841066258713544, -0.15910515448871365, -0.03872770586852747, 0.008578873117008726, -0.07861129818404189, -0.35511539448718, -0.865517647051951, -1.6411457361731037, -2.697783703106532, -4.034133330519179, -5.631269167475175, -7.453071418369263, -9.447675735266133, -11.549778245610357, -13.68357366282216, -15.766509617391822, -17.71376164380299, -19.4422042354033, -20.8746415161932, -21.944644451938924, -22.59971695918815, -22.803737849791045, -22.539764639975626, -21.812051600212275, -20.644091657353734, -19.078287292763445, -17.175585634405174, -15.011835600952189, -12.67204173299678, -10.24794698633936, -7.834380554169314, -5.523103683156577, -3.396661466817409, -1.5261359425144394, 0.03236439987744943, 1.2412644666718216, 2.084969389348118, 2.5691068375048185, 2.719723719715412, 2.5824600975234495, 2.2215093838293893, 1.714500147196197, 1.1479454086062053, 0.6131745076844027, 0.2016474948410439, -0.0013243575291574218, 0.07867334639108728, 0.5009594332965317, 1.3055944827549024, 2.5104895798502027, 4.109924260632557, 6.073928703938719, 8.348419237844299, 10.857543661422122, 13.506976659475349, 16.18799219307137, 18.78167165359115, 21.164949041188017, 23.216717789599198, 24.82349952204478, 25.884556880675618, 26.31739629764028, 26.062134955864003, 25.084720121027146, 23.378753653439162, 20.966345127431364, 17.897988856198545, 14.250763787429811, 10.124481022885483, 5.638371014847976, 0.9267161360133748, -3.8680366685355834, -8.601237402050025, -13.130395234674856, -17.321536241748092, -21.05668860438523, -24.236154088048117, -26.781468161226297, -28.640575532850537, -29.788493734412132, -30.225747956724614, -29.97840543545085, -29.09770067504653, -27.654242855541334, -25.73460166113173, -23.438519008707328, -20.872801569865366, -18.14555017125604, -15.362707199750098, -12.623720725405912, -10.01650749901011, -7.614858361883346, -5.476750987388551, -3.642422100090798, -2.1341039631268126, -0.9567873883341392, -0.09945446926425071, 0.4626826077183034, 0.7653913110979932, 0.8526107053832883, 0.7730429622754204, 0.5767599810796192, 0.31229089378120367, 0.023953599585607985, -0.2505150317100608, -0.48154162312681165, -0.6486529719472383, -0.740820899688233, -0.75612045277073, -0.7008192677682408, -0.5879685136229263, -0.43559390939698633, -0.2647242772247012, -0.097316606751928, 0.04578603860014271, 0.14664090211972697, 0.19169680303937522, 0.1728724900166341, 0.0881269192261984, -0.05843617970032166, -0.25697117141894865, -0.4927647150206882, -0.7474288216124202, -1.0004481572177872, -1.2309135160013664, -1.4191351901440066, -1.5482685279094746, -1.6058999221372066, -1.5850377023234192, -1.484729846136326, -1.3105060503748542, -1.074144048039927, -0.792855490112482, -0.48824449283822574, -0.18499624682555527, 0.09100731755073131, 0.31455054676276883, 0.4627946334336035, 0.5170752221552696, 0.46453326437362746, 0.2992140734327394, 0.02260621517710902, -0.3559147845096276, -0.8192904298171475, -1.343990780791547, -1.9012173681241773, -2.4582725967718737, -2.9808621586653414, -3.43581112430607, -3.7926709215020207, -4.0258245332053635, -4.117325068947109, -4.058083286838449, -3.848476352520335, -3.4994842421005763, -3.0329874187994754, -2.480320571322244, -1.8810942616756763, -1.2819875645306187, -0.7339024216565719, -0.2891926838657259, 0.0008644663359200083, 0.08904119938028003, -0.0648563492257362, -0.4916406096846636, -1.2106229568599882, -2.228013437904718, -3.536118438853717, -5.113146972764461, -6.923695497423587, -8.920016791965836, -11.043922335845219, -13.229409230645947, -15.405347716818184, -17.498501270487434, -19.437314057899687, -21.1550041955959, -22.59200567878348, -23.698999059157888, -24.439963063100148, -24.792137262852382, -24.74692939356903, -24.31155970293015, -23.50789112723635, -22.369430171256734, -20.940834304740388, -19.276809196446234, -17.437720571898197, -15.485851713386396, -13.484539069577457, -11.495071216125307, -9.573254871758206, -7.766862547496357, -6.115272668532219, -4.647939643420645, -3.3836393535854543, -2.3300673029182737, -1.4851014771540687, -0.8380026909657082, -0.3707149590055562, -0.059189541408743426, 0.12407316905123798, 0.20793593046030595, 0.22091076528023448, 0.18955850664572382, 0.13672403578027942, 0.08048219989604814, 0.0335322542245681, 0.0029201122656163933, -0.009849305512107725, -0.008229637036884405, 0.000247683946014128, 0.005097239143001437, -0.005809398179754709, -0.04488955669380946, -0.12354016800831649, -0.2509112149732542, -0.43292759242305257, -0.6715904738490498, -0.9645716331946542, -1.3051558196569868, -1.6825299473613513, -2.082317386957742, -2.487434926879207, -2.879290137545024, -3.238804027092202, -3.5475421650004315, -3.789015115028037, -3.949905764938131, -4.020658006054399, -3.9960634815719405, -3.8757185862175936, -3.6642328431623463, -3.3707182366941413, -3.008156100159895, -2.5927044279932114, -2.1429930242687676, -1.6787562022487141, -1.2195224761234442, -0.7838050833536963, -0.38820254912598956, -0.04614969146462063, 0.23258353761184333, 0.442044410868165, 0.5804450985665603, 0.6501913312499638, 0.6571754346919406, 0.6102313098743631, 0.5206819755204705, 0.40125812491336454, 0.26509800581085013, 0.12498597405403306, -0.007394210144023502, -0.12229171137494549, -0.21237489592536893, -0.2730471163286396, -0.3025256391694722, -0.3017501276657224, -0.2741150202815871, -0.2250289062508524, -0.16126145504903158, -0.09029800871390616, -0.019690012192971004, 0.04362211084711814, 0.09389153978066804, 0.12700130792069428, 0.1407964108797032, 0.13526162114931461, 0.11246263687787303, 0.076238898351346, 0.03184319177777482, -0.014435727522272165, -0.05558631905364469, -0.08456402207713219, -0.09539632130647925, -0.08405838379441555, -0.047992060695318244, 0.01583113096812486], 'positive_zeros': ['0.30860168497251271866437364121239', '0.70819486668873435668825550315583', '0.74670882649796384997303032885001', '1.26658701767835621029768382095402', '1.66133540625240165111280020966732', '1.82977136159468825754415174507918', '2.28679113450539817336637444312324', '2.33856158935470784456520370407840', '2.65449876408670224317334151951784', '3.18299664900038292049732060008942', '3.24223155243258649142400444229833', '3.25079084071184732101874032841772', '3.98027756180955965345425804189608', '4.06978432001380651431915621168262', '4.10309909681837281106141139984213', '4.19483807229602355175289279528194', '4.82110425338040218458222715834615', '4.87150717242869349285469048366377', '4.97860836032626804527140371433931', '5.06317534180188349411491486236243', '5.42356670990799494835259755944390', '5.54710812613582622688643754773334', '5.72785911448922691678448777803936', '5.81528602504639125278818984590842', '6.11022503844699043753583525489765', '6.38917216681353528033645764141636', '6.78029385752833221639773190840837', '6.97975588244094281074248841757625', '7.35925679015425522530707714431274', '7.44698961672183811950567098283212', '7.57792997530600237949769826506003', '7.71449059061699983941632782431883', '7.76757102815539065926650328869333', '7.88638230344989184804959677577302', '8.340950501556601530437176789537212', '8.570874143881588419377696387368591', '8.885736881393338133033782639098209', '8.972779907518526349072818821034418', '8.983661903625232716641630476685269', '9.433253232692087319736196481939297'], 'prelabel': '8-1575e4-1.1-c3e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 9.639917440468125, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3e4-0', 'trace_hash': 899865343588272544, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.30860168497251271866437364121', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.70819486668873435668825550316', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '0.74670882649796384997303032885', 'prec': 103}}
• lfunc_search •

  Column	Type
  algebraic	boolean
  analytic_conductor	double precision
  bad_primes	bigint[]
  central_character	text
  conductor	numeric
  conductor_radical	bigint
  degree	smallint
  dirichlet_coefficients	numeric[]
  euler11	numeric[]
  euler13	numeric[]
  euler17	numeric[]
  euler19	numeric[]
  euler2	numeric[]
  euler23	numeric[]
  euler29	numeric[]
  euler3	numeric[]
  euler31	numeric[]
  euler37	numeric[]
  euler41	numeric[]
  euler43	numeric[]
  euler47	numeric[]
  euler5	numeric[]
  euler53	numeric[]
  euler59	numeric[]
  euler61	numeric[]
  euler67	numeric[]
  euler7	numeric[]
  euler71	numeric[]
  euler73	numeric[]
  euler79	numeric[]
  euler83	numeric[]
  euler89	numeric[]
  euler97	numeric[]
  euler_factors	numeric[]
  index	smallint
  instance_types	text[]
  instance_urls	text[]
  is_instance_Artin	boolean
  is_instance_BMF	boolean
  is_instance_CMF	boolean
  is_instance_DIR	boolean
  is_instance_ECNF	boolean
  is_instance_ECQ	boolean
  is_instance_G2Q	boolean
  is_instance_HMF	boolean
  is_instance_MaassGL3	boolean
  is_instance_MaassGL4	boolean
  is_instance_MaassGSp4	boolean
  is_instance_NF	boolean
  label	text
  motivic_weight	smallint
  mu_imag	numeric[]
  mu_real	smallint[]
  nu_imag	numeric[]
  nu_real_doubled	smallint[]
  order_of_vanishing	smallint
  prelabel	text
  primitive	boolean
  rational	boolean
  root_analytic_conductor	double precision
  root_angle	double precision
  self_dual	boolean
  spectral_label	text
  trace_hash	bigint
  z1	numeric

  
  {'algebraic': True, 'analytic_conductor': 74573841.5748797, 'bad_primes': [3, 5, 7], 'central_character': '1.1', 'conductor': 6153500390625, 'conductor_radical': 105, 'degree': 8, 'dirichlet_coefficients': [1, 6, 0, 10, 0, 0, 28, 3, 0, 0, -57, 0, -43, 168, 0, 54, 99, 0, -12, 0, 0, -342, 156, 0, 0, -258, 0, 280, -378, 0, -93, 240, 0, 594, 0, 0, -81, -72, 0, 0, 465, 0, 64, -570, 0, 936, 744, 0, 490, 0, 0, -430, 729, 0, 0, 84, 0, -2268, -231, 0, -1353, -558, 0, 441, 0, 0, -1487, 990, 0, 0, 1725, 0, -512, -486, 0, -120, -1596, 0, 1629, 0, 0, 2790, 321, 0, 0, 384, 0, -171, 978, 0, -1204, 1560, 0, 4464, 0, 0, -2616, 2940, 0, 0], 'euler11': [1, 57, 4001, 182772, 7206874, 243269532, 7088015561, 134403018387, 3138428376721], 'euler13': [1, 43, 4464, 221093, 13201958, 485741321, 21546875376, 455993473039, 23298085122481], 'euler17': [1, -99, 13790, -926229, 90687946, -4550563077, 332857076510, -11740199773203, 582622237229761], 'euler19': [1, 12, -10212, 154020, 95206646, 1056423180, -480432536772, 3872252373348, 2213314919066161], 'euler2': [1, -6, 26, -99, 298, -792, 1664, -3072, 4096], 'euler23': [1, -156, 28082, -3613896, 479553835, -43970272632, 4157143834898, -280979815188228, 21914624432020321], 'euler29': [1, 378, 143760, 29729988, 5852097929, 725084677332, 85511800626960, 5483701178878482, 353814783205469041], 'euler3': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler31': [1, 93, 16330, -936891, 385099458, -27910919781, 14492935110730, 2458884860942403, 787662783788549761], 'euler37': [1, 81, 107185, 469746, 5937897606, 23794044138, 275007385148665, 10526900923401237, 6582952005840035281], 'euler41': [1, -465, 105716, -566235, -2050285754, -39025482435, 502162019941556, -152232599493191865, 22563490300366186081], 'euler43': [1, -64, 64662, 2492176, 5477627255, 198145437232, 408751977474438, -32165927163957952, 39959630797262576401], 'euler47': [1, -744, 588276, -247094976, 101020317878, -25654141693248, 6341153676882804, -832633071988458648, 116191483108948578241], 'euler5': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler53': [1, -729, 333446, -137056347, 63585804370, -20404537772319, 7390617561020534, -2405527658423754957, 491258904256726154641], 'euler59': [1, 231, 701280, 148812447, 204019205798, 30562951552413, 29580364631760480, 2001152034109290909, 1779197418239532716881], 'euler61': [1, 1353, 1374808, 931878711, 511309944510, 211518761701491, 70830622834497688, 15822179663604592773, 2654348974297586158321], 'euler67': [1, 1487, 1603371, 1080212116, 674138302124, 324887836644508, 145038346676691699, 40456116647290586189, 8182718904632857144561], 'euler7': [1, -28, 294, -1372, 2401, 0, 0, 0, 0], 'euler71': [1, -1725, 1434819, -706812600, 347044577276, -252976004478600, 183800721275245299, -79088663739324578475, 16409682740640811134241], 'euler73': [1, 512, 1030980, 484092568, 566560915526, 188320238525656, 156022560619433220, 30142252394633171456, 22902048046490258711521], 'euler79': [1, -1629, 1989837, -1837769472, 1504809477470, -906092022705408, 483704413231540077, -195238249855685241651, 59091511031674153381441], 'euler83': [1, -321, 661434, -144132717, 79870144034, -82413213855279, 216249478918951146, -60007821940880469363, 106890007738661124410161], 'euler89': [1, -978, 526228, 159100050, -360762420714, 112160603148450, 261525470779825108, -342648562825920534402, 246990403565262140303521], 'euler97': [1, 2616, 5183100, 6945540936, 7789652954246, 6339007682681928, 4317377198747499900, 1988764449440342607672, 693842360995438000295041], 'euler_factors': [[1, -6, 26, -99, 298, -792, 1664, -3072, 4096], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, -28, 294, -1372, 2401, 0, 0, 0, 0], [1, 57, 4001, 182772, 7206874, 243269532, 7088015561, 134403018387, 3138428376721], [1, 43, 4464, 221093, 13201958, 485741321, 21546875376, 455993473039, 23298085122481], [1, -99, 13790, -926229, 90687946, -4550563077, 332857076510, -11740199773203, 582622237229761], [1, 12, -10212, 154020, 95206646, 1056423180, -480432536772, 3872252373348, 2213314919066161], [1, -156, 28082, -3613896, 479553835, -43970272632, 4157143834898, -280979815188228, 21914624432020321], [1, 378, 143760, 29729988, 5852097929, 725084677332, 85511800626960, 5483701178878482, 353814783205469041], [1, 93, 16330, -936891, 385099458, -27910919781, 14492935110730, 2458884860942403, 787662783788549761], [1, 81, 107185, 469746, 5937897606, 23794044138, 275007385148665, 10526900923401237, 6582952005840035281], [1, -465, 105716, -566235, -2050285754, -39025482435, 502162019941556, -152232599493191865, 22563490300366186081], [1, -64, 64662, 2492176, 5477627255, 198145437232, 408751977474438, -32165927163957952, 39959630797262576401], [1, -744, 588276, -247094976, 101020317878, -25654141693248, 6341153676882804, -832633071988458648, 116191483108948578241], [1, -729, 333446, -137056347, 63585804370, -20404537772319, 7390617561020534, -2405527658423754957, 491258904256726154641], [1, 231, 701280, 148812447, 204019205798, 30562951552413, 29580364631760480, 2001152034109290909, 1779197418239532716881], [1, 1353, 1374808, 931878711, 511309944510, 211518761701491, 70830622834497688, 15822179663604592773, 2654348974297586158321], [1, 1487, 1603371, 1080212116, 674138302124, 324887836644508, 145038346676691699, 40456116647290586189, 8182718904632857144561], [1, -1725, 1434819, -706812600, 347044577276, -252976004478600, 183800721275245299, -79088663739324578475, 16409682740640811134241], [1, 512, 1030980, 484092568, 566560915526, 188320238525656, 156022560619433220, 30142252394633171456, 22902048046490258711521], [1, -1629, 1989837, -1837769472, 1504809477470, -906092022705408, 483704413231540077, -195238249855685241651, 59091511031674153381441], [1, -321, 661434, -144132717, 79870144034, -82413213855279, 216249478918951146, -60007821940880469363, 106890007738661124410161], [1, -978, 526228, 159100050, -360762420714, 112160603148450, 261525470779825108, -342648562825920534402, 246990403565262140303521], [1, 2616, 5183100, 6945540936, 7789652954246, 6339007682681928, 4317377198747499900, 1988764449440342607672, 693842360995438000295041]], 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1575/4/a/bm'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '8-1575e4-1.1-c3e4-0-1', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3, 3, 3, 3], 'order_of_vanishing': 0, 'prelabel': '8-1575e4-1.1-c3e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 9.639917440468125, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e4-0', 'trace_hash': 899865343588272544, 'z1': {'__RealLiteral__': 0, 'data': '0.30860168497251271866437364121', 'prec': 103}}
• lfunc_instances •

  Column	Type
  Lhash	text
  Lhash_array	text[]
  factors	text[]
  label	text
  type	text
  url	text

  
  {'Lhash': '391199111186848709184675170263,897743647836525011063888457519,946565892105860681760557764988,1605589793201251253985810554352', 'Lhash_array': ['391199111186848709184675170263', '897743647836525011063888457519', '946565892105860681760557764988', '1605589793201251253985810554352'], 'factors': ['2-1575-1.1-c3-0-6', '2-1575-1.1-c3-0-45', '2-1575-1.1-c3-0-47', '2-1575-1.1-c3-0-115'], 'label': '8-1575e4-1.1-c3e4-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1575/4/a/bm'}