Lfunction data - 8-1452e4-1.1-c1e4-0-7

Formats: - HTML - YAML - JSON - 2025-09-20T14:38:38.975565

• 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': '357894034082863741463069270817,1163705457653986824714891764738,1517985836547636009200909213255,2427671566586789322678846054264', 'a10': 0, 'a2': 0, 'a3': 1, 'a4': 0, 'a5': 1, 'a6': 0, 'a7': -2, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 18070.69656612994, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1, 1, -1, 1]], [11, [1]]], 'bad_primes': [2, 3, 11], 'central_character': '1452.1', 'coefficient_field': '1.1.1.1', 'conductor': 4444945756416, 'conductor_radical': 66, 'degree': 8, 'euler_factors': [[1], [1, -1, 1, -1, 1], [1, -1, -4, 9, 11, 45, -100, -125, 625], [1, 2, -3, -20, -19, -140, -147, 686, 2401], [1], [1, -3, -4, 51, -101, 663, -676, -6591, 28561], [1, -7, 32, -105, 191, -1785, 9248, -34391, 83521], [1, 4, -3, -88, -295, -1672, -1083, 27436, 130321], [1, 8, 116, 584, 4294, 13432, 61364, 97336, 279841], [1, 3, -20, -147, 139, -4263, -16820, 73167, 707281], [1, 0, -31, 0, 961, 0, -29791, 0, 923521], [1, 9, 44, 63, -1061, 2331, 60236, 455877, 1874161], [1, 9, 40, -9, -1721, -369, 67240, 620289, 2825761], [1, 8, 196, 1064, 13174, 45752, 362404, 636056, 3418801], [1, -12, 97, -600, 2641, -28200, 214273, -1245876, 4879681], [1, -13, 116, -819, 4499, -43407, 325844, -1935401, 7890481], [1, -6, -23, 492, -1595, 29028, -80063, -1232274, 12117361], [1, -2, -57, 236, 3005, 14396, -212097, -453962, 13845841], [1, 56, 1444, 22232, 222934, 1489544, 6482116, 16842728, 20151121], [1, -6, -35, 636, -1331, 45156, -176435, -2147466, 25411681], [1, 6, -37, -660, -1259, -48180, -197173, 2334102, 28398241], [1, -16, 177, -1568, 11105, -123872, 1104657, -7888624, 38950081], [1, -8, -19, 816, -4951, 67728, -130891, -4574296, 47458321], [1, -4, 362, -1072, 48595, -95408, 2867402, -2819876, 62742241], [1, 7, -48, -1015, -2449, -98455, -451632, 6388711, 88529281], [1, 2, -97, -396, 9005, -39996, -989497, 2060602, 104060401], [1, -6, -67, 1020, 781, 105060, -710803, -6556362, 112550881], [1, -14, 89, 252, -13051, 26964, 1018961, -17150602, 131079601], [1, 12, 490, 4032, 83139, 439488, 5821690, 15540348, 141158161], [1, -19, 248, -2565, 20711, -289845, 3166712, -27415043, 163047361]], 'euler_factors_factorization': [[1], [[[1, -1, 1, -1, 1], 1]], [[[1, -1, -4, 9, 11, 45, -100, -125, 625], 1]], [[[1, 2, -3, -20, -19, -140, -147, 686, 2401], 1]], [1], [[[1, -3, -4, 51, -101, 663, -676, -6591, 28561], 1]], [[[1, -7, 32, -105, 191, -1785, 9248, -34391, 83521], 1]], [[[1, 4, -3, -88, -295, -1672, -1083, 27436, 130321], 1]], [[[1, 2, 23], 4]], [[[1, 3, -20, -147, 139, -4263, -16820, 73167, 707281], 1]], [[[1, 0, -31, 0, 961, 0, -29791, 0, 923521], 1]], [[[1, 9, 44, 63, -1061, 2331, 60236, 455877, 1874161], 1]], [[[1, 9, 40, -9, -1721, -369, 67240, 620289, 2825761], 1]], [[[1, 2, 43], 4]], [[[1, -12, 97, -600, 2641, -28200, 214273, -1245876, 4879681], 1]], [[[1, -13, 116, -819, 4499, -43407, 325844, -1935401, 7890481], 1]], [[[1, -6, -23, 492, -1595, 29028, -80063, -1232274, 12117361], 1]], [[[1, -2, -57, 236, 3005, 14396, -212097, -453962, 13845841], 1]], [[[1, 14, 67], 4]], [[[1, -6, -35, 636, -1331, 45156, -176435, -2147466, 25411681], 1]], [[[1, 6, -37, -660, -1259, -48180, -197173, 2334102, 28398241], 1]], [[[1, -16, 177, -1568, 11105, -123872, 1104657, -7888624, 38950081], 1]], [[[1, -8, -19, 816, -4951, 67728, -130891, -4574296, 47458321], 1]], [[[1, -1, 89], 4]], [[[1, 7, -48, -1015, -2449, -98455, -451632, 6388711, 88529281], 1]], [[[1, 2, -97, -396, 9005, -39996, -989497, 2060602, 104060401], 1]], [[[1, -6, -67, 1020, 781, 105060, -710803, -6556362, 112550881], 1]], [[[1, -14, 89, 252, -13051, 26964, 1018961, -17150602, 131079601], 1]], [[[1, 3, 109], 4]], [[[1, -19, 248, -2565, 20711, -289845, 3166712, -27415043, 163047361], 1]]], 'gamma_factors': [[], [0, 0, 0, 0]], 'group': 'GL2', 'index': 7, 'label': '8-1452e4-1.1-c1e4-0-7', 'leading_term': '2.17122287856565936651610523334390026543345236318038847300571809900431810866826265713072904', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, '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': [1, 1, 1, 1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1452/2/i/m', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.015625', 'prec': 27}, 'plot_values': [2.1712228785656595, 2.1630216828867894, 2.140970451152957, 2.1046868981880995, 2.0538512975511547, 1.988392428901961, 1.9086267559332053, 1.8149578563998863, 1.7078306451019434, 1.5876728820307997, 1.4549100818281049, 1.3100349301671654, 1.1536153220850727, 0.9863099060812048, 0.8088532965836538, 0.6220482467902568, 0.42676772643725613, 0.22396319084577687, 0.014659818144074504, -0.20004531928192215, -0.41897842851284206, -0.6408851394144056, -0.8644453502506569, -1.088279167868479, -1.3109411832394173, -1.5309270128018404, -1.746690508049432, -1.9566531892871453, -2.159203551435488, -2.352716326307225, -2.535568750678991, -2.7061540548953733, -2.862891418398799, -3.0042508224899085, -3.128767985737371, -3.235063476086788, -3.3218640101568835, -3.3880230161877143, -3.4325349621675345, -3.454561949316195, -3.4534560280664186, -3.428770002675066, -3.380271070889064, -3.307972916821275, -3.2121433935920356, -3.0933047363126343, -2.95224553468197, -2.7900478350234117, -2.608069631170763, -2.407934996831551, -2.191542613782882, -1.9610702962807927, -1.7189343964246364, -1.467769104948668, -1.2104262400287722, -0.9499457068134552, -0.689501755011248, -0.4323714363129082, -0.18191729711195048, 0.05847088771651194, 0.2854322537355692, 0.49567483755385583, 0.6860145514146072, 0.8534405971125354, 0.9951655640837267, 1.1086695708729093, 1.191751292146312, 1.2425753463799596, 1.2597088319770202, 1.242163107396123, 1.1894307622703304, 1.1015000920224987, 0.9788700197881884, 0.8225770100829428, 0.6341908081475367, 0.41579301768700055, 0.1699645459652808, -0.1002207146598547, -0.3912506628615448, -0.6992274124220047, -1.01990903501779, -1.3487621248891581, -1.6810519217695545, -2.011915582964573, -2.3364312790689166, -2.6497054156392816, -2.9469710781911758, -3.223665968513245, -3.4755191582192997, -3.698634558710728, -3.889571567663325, -4.0454086603185155, -4.163822212408968, -4.243121497885616, -4.282291705962946, -4.281027509822534, -4.239762216444803, -4.159632153331952, -4.042469867431492, -3.890796470808507, -3.707767346713966, -3.4970749715946114, -3.2628931218506403, -3.009822047723077, -2.742754502065013, -2.466747381865409, -2.1869351967521125, -1.908434832175552, -1.6361803632987892, -1.3748018559024724, -1.1285399769944733, -0.9011410575370173, -0.6957291553892379, -0.5147293159389051, -0.3598184395807069, -0.2318644202397358, -0.1308844783644825, -0.05604238230944609, -0.005665932731250703, 0.022725567283837938, 0.032364142640389455, 0.027152542421438088, 0.011566629705897533, -0.009461548378407764, -0.03067679691587506, -0.04664573394901138, -0.05191360253615527, -0.04116384832537241, -0.009377578178626809, 0.048004131803575406, 0.13492632142030112, 0.2545861499763029, 0.4093094407757333, 0.6004377667828975, 0.8282547482197924, 1.0919350749473822, 1.389513260882758, 1.7178851084369713, 2.072860211249195, 2.4492193279888665, 2.840806337010945, 3.2406674795224926, 3.641217311952685, 4.034387512764129, 4.411833654293258, 4.765158624565171, 5.0861316784004975, 5.366872204754103, 5.6001118112137656, 5.779385841461831, 5.899225301529808, 5.955301096324399, 5.944632439471353, 5.86563614795125, 5.718217800351898, 5.503813847461026, 5.225427015320997, 4.88750020603095, 4.495864254157736, 4.057644563003281, 3.5810813424693673, 3.075276712423851, 2.5500136057657095, 2.0155404386421623, 1.4822597974040277, 0.9604453906411106, 0.4600044633338037, -0.009781901541967992, -0.4405339032663941, -0.8249818132098587, -1.1571608345666722, -1.432581948942187, -1.6483266581260172, -1.8031026102840453, -1.897309822474242, -1.933002783566242, -1.9137666125161852, -1.8445969151801311, -1.731797716090295, -1.5827257651543163, -1.4055162990631864, -1.2088410200517885, -1.0016741676357577, -0.7929450783026971, -0.5912429406342854, -0.4045663957666487, -0.24007841152880832, -0.10384876755701697, -0.0006715194521227002, 0.06606879230083954, 0.0944989569149148, 0.08430456602359473, 0.036715719531292365, -0.045558235913889224, -0.15844998615720618, -0.2966981599586286, -0.4540512609577247, -0.6235210126252126, -0.7976639906317315, -0.9688507468014106, -1.1295598689849606, -1.272692577503839, -1.3918497374914267, -1.4815483232224615, -1.5374556708961957, -1.556576836379706, -1.5373681774224177, -1.4797698651311846, -1.3852477951430562, -1.2567296303889937, -1.0984907998349165, -0.9159700975931875, -0.7155814712195504, -0.504436638263061, -0.2900637900418523, -0.08009504608804004, 0.118044123668247, 0.297448730098671, 0.4520264900122919, 0.576767705994503, 0.6679640566442654, 0.7233645133077296, 0.7423029818273885, 0.7257555879043698, 0.6762950595533656, 0.5979894248180107, 0.49627212627154804, 0.37772245614529226, 0.24976154429449574, 0.12034195975753424, -0.002384288050906409, -0.11044567349972094, -0.1964262364167761, -0.25380819222185036, -0.2773137663810736, -0.26318706599551445, -0.20940018196962323, -0.11580807239590245, 0.015737994023635047, 0.1814284415321879, 0.37560650798393347, 0.5909380712667216, 0.8186577115173371, 1.0489352810195003, 1.2712732490567806, 1.4749598616559234, 1.6495610800809353, 1.785397281534561, 1.8740157286792858, 1.908694568095528, 1.8848466539155995, 1.8003041730486862, 1.655573750388237, 1.4540617841399897, 1.2020669427071018, 0.9086620186474637, 0.5855224993051255, 0.24664793402273943, -0.09211491298499133, -0.4135909329611011, -0.6998635824606364, -0.9329618665231372, -1.0955518666635844, -1.1716152294446514, -1.1471805209283026, -1.0109852541482935, -0.7549871470848685, -0.3748217555458742, 0.12976442110243852, 0.7547459835066663, 1.4918100022368692, 2.328434020030971, 3.2481150494434345, 4.230830050856357, 5.253617445471491, 6.2912569834406025, 7.317114822135173, 8.303942232226486, 9.224828702262343, 10.054226646249, 10.7688504088323, 11.348329619627084, 11.776088875878873, 12.040192723467912, 12.133583764057178, 12.054197584979244, 11.805343373286473, 11.395817475885332, 10.839174748347453, 10.15319285881743, 9.359601725560312, 8.483278529488334, 7.550904012551309, 6.590014342344275, 5.628291672746064, 4.692305918331668, 3.8062636991822134, 2.9911691386595574, 2.2641872151571922, 1.6377712102745134, 1.1191298091967783, 0.7100242644384063, 0.40675516874366896, 0.20025405800322624, 0.07649824744681237, 0.017145078203254765, 0.0003319839882651788, 0.0016347793877775536, -0.004839231618474655, -0.04528378315153237, -0.14499559441930135, -0.32719127167671946, -0.6118856794765715, -1.0149124511560235, -1.5470903346981428, -2.213544512430397, -3.013270711881339, -3.9390876924557268, -4.977669182070871, -6.109765025363388, -7.310865432653222, -8.552257639942898, -9.801809879059615, -11.024942959277398, -12.186257859992828, -13.250999032080587, -14.186017469448082, -14.960897994336309, -15.549827494285294, -15.932341122544056, -16.093828556970983, -16.026161097834354, -15.7287925508252, -15.208134534037768, -14.477250680005776, -13.555670245764448, -12.469070886607831, -11.24761487914932, -9.9249423662404, -8.537331243777128, -7.122310135308265, -5.716873831185506, -4.356349264182439, -3.073467514050623, -1.8970121103358686, -0.8507726358307983, 0.04702745116501704, 0.7840613463893504, 1.354270344022381, 1.7578187739701623, 2.0007511207688644, 2.094393330189743, 2.054671944694121, 1.9012334603191876, 1.6563917574428675, 1.3439777871419802, 0.9882982944789398, 0.6130865011647977, 0.24038445242379977, -0.11029514167311055, -0.4225743002650213, -0.6837595438062499, -0.8853266976757792, -1.0228436231834253, -1.0957874085258592, -1.1073398249166415, -1.0639846847169934, -0.9746845466001789, -0.85015596933678, -0.702194632586128, -0.5428378690817746, -0.3835068970865211, -0.2343574777075103, -0.10374214962958639, 0.0022718500451230847, 0.0801554892411116, 0.1289759245820098, 0.15031329608560545, 0.14797727137552627, 0.12754744058202064, 0.09581985462586592, 0.06016105594133279, 0.02777920550417305, 0.0050121783122925815, -0.0033358503297657082, 0.005412411551936487, 0.03134857882454072, 0.0716836573799523, 0.1206293759721851, 0.1694895102104473, 0.2069552171039163, 0.2195847336703328, 0.19248748235735236, 0.11013128417551131, -0.04275502864953431, -0.2801994075850162, -0.6139617399421854, -1.052632764581433, -1.6008333781963768, -2.25850632761507, -3.020414804722471, -3.87590403655429, -4.808986279337463, -5.798641914754585, -6.81930083520576, -7.841573010652663, -8.833495004467425, -9.76185509755177, -10.593225681106878, -11.2952727844275, -11.838678919954045, -12.198520660859655, -12.35491074438216, -12.294022485149876, -12.009665264819814, -11.503442274842055, -10.784323751681082, -9.868649785523996, -8.780425729626637, -7.549851622107833, -6.2118898326755785, -4.805198132091766, -3.3710408664197513, -1.951105460357664, -0.5858206335196997, 0.6870802181711747, 1.8340380440171953, 2.8270988852035175, 3.6448627922634222, 4.273304692523715, 4.706263444258083, 4.945296019593305, 4.999330196775659, 4.884260894734883, 4.621951210192612, 4.238808314499436, 3.764440111563572, 3.2303126251007948, 2.6680945765157356, 2.108041078061178, 1.5776408272454019, 1.1004315069868187, 0.6950153738200331, 0.374352739151532, 0.14538624809724776, 0.009038648268845696, -0.03945185215111004, -0.009944748834525244, 0.08347291662516639, 0.22361736378390645, 0.3914272150023456, 0.5672576525439569, 0.7322634048412959, 0.8695706253506907, 0.9653096133777945, 1.0095210605386373, 0.9968169161362066, 0.9265273684669283, 0.8026853158156936, 0.6337718134213628, 0.43203351039194965, 0.21250059459063292, -0.008060057060805585, -0.21237573532413848, -0.38402943063601586, -0.508707628069082, -0.5753745581026435, -0.5773801500582414, -0.5131567555202622, -0.3866335023943578, -0.2074545470218903, 0.009172829388899932, 0.24318386720161791, 0.4705454571189864, 0.664364066151801, 0.7963342434507562, 0.8383625894465043, 0.7641747594862066, 0.5509623289694279, 0.18090809029909471, -0.35751666688191874, -1.0685063677999989, -1.9482242192753554, -2.984515209331288, -4.1569669568993355, -5.437474061975468, -6.791401216448315, -8.178704376986799, -9.55538970074802, -10.87567641043936, -12.094296073451373, -13.167979839639745, -14.057295343294998, -14.729153294180014, -15.15837817551284, -15.328222810824927, -15.231247911969124, -14.870443083025904, -14.2588012292662, -13.418228720153895, -12.378796926628041, -11.177718073070634, -9.857386755078041, -8.463209221386693, -7.041682122599538, -5.638361264207456, -4.295935566325945, -3.052315094182874, -1.9388782204696609, -0.9794826969338403, -0.18990367667309221, 0.4226826362282304, 0.8599658763467979, 1.1314662654158714, 1.2535306019526655, 1.2483759025605405, 1.1426978295661956, 0.9655387287758123, 0.7466482967619461, 0.515012658000604, 0.29712950641874236, 0.11550248977987095, -0.01230842939055337, -0.07442264597105637, -0.0650944424906226, 0.01537817521148849, 0.161065073720477, 0.36099119344966124, 0.6002491387204829, 0.8612809778569471, 1.1251489402185424, 1.372858295886538, 1.5868462721293048, 1.752185269703993, 1.857508707096978, 1.8957844212854376, 1.8648097214088297, 1.7672794291569904, 1.6104998259244947, 1.4059010733369284, 1.1682387644710317, 0.9145277530538496, 0.6628007628695145, 0.43094392515904345, 0.2354788663948104, 0.09037692775035794, 0.006076791858492016, -0.011149848264925207, 0.040321502820772175, 0.15729572151736967, 0.3320628774492189, 0.5528662721658495, 0.8045606206992924, 1.0696860553607257, 1.3298365456203642, 1.5666539351107696, 1.7629418565761337, 1.9040371184768419, 1.9789904020197762, 1.9809539038422717, 1.907630244542515, 1.76164760657147, 1.5505675990837982, 1.286047328907715, 0.9830943843905873, 0.6591473502720896, 0.3331004018331917, 0.023757707569610726, -0.25148848921472733, -0.4778123829511865, -0.6438076896532062, -0.7424977844458539, -0.7719540881415734, -0.7353833000113406, -0.6408776731855745, -0.5010464086545328, -0.33224534113863324, -0.15339554122524018, 0.015314585532668313, 0.15377123456301706, 0.24335976070252754, 0.2683834771068547, 0.21729001387311017, 0.08353845997388172, -0.133745542277393, -0.42937100708081133, -0.7921762470210257, -1.2058289604151826, -1.649485556235458, -2.0987713860712067, -2.527463993032845, -2.909502590755777, -3.2200841573714554, -3.4371380217969607, -3.5435133901491005, -3.5282604308845773, -3.386805306673661, -3.121547361956314, -2.7428826831352793, -2.268274547885107, -1.720954503626814, -1.1290405396242449, -0.5246338778323765, 0.05871937817348113, 0.5880451086708028, 1.0325317653377453, 1.3652810621570615, 1.5653569464855364, 1.6190237369490599, 1.5205028978840516, 1.2725386567787302, 0.8864404195400037, 0.3815106125547607, -0.2160507573882588, -0.8745285310509161, -1.5583894919968189, -2.2302782195203155, -2.8533692286180177, -3.3933231154654813, -3.8200807595807262, -4.109734907278107, -4.2461551323336915, -4.221543049512909, -4.036726114742068, -3.701438682627847, -3.2337024052351815, -2.65840343508698, -2.0058487119895916, -1.3103073147520254, -0.6077728362804861, 0.0662141235416089, 0.6784724301479954, 1.199974202676466, 1.607522940868547, 1.8848723031327699, 2.023486361207288, 2.02289618105235, 1.8903602333955256, 1.6400803856656592, 1.2922910764969342, 0.8718409121494686, 0.40640336221722123, -0.07542247340261297, -0.5456910766291351, -0.9787730606695718, -1.3528369955778463, -1.6512090533795565, -1.8629907764729188, -1.9832558882161797, -2.0130190713566236, -1.9590713439307244, -1.8329588729958997, -1.649668666074418, -1.4264286493368998, -1.1815530625059307, -0.9328296993043492, -0.696172899469643, -0.4846696425860993, -0.307881674159114, -0.17128291104725338, -0.07619220720207436, -0.02007953301177547, 0.002843708557162522, 0.0007751372699766158, -0.016723215338697032, -0.03985289341886925, -0.05971093737677115, -0.06927701622531557, -0.06418616995059329, -0.043240700368557324, -0.008573245206014093, 0.03460257546311484, 0.0785786701106282, 0.1140855225131951, 0.13148290070432792, 0.12212670233961768, 0.07981335318956365, 0.002193779539330154, -0.10807762060869129, -0.24244918780663793, -0.3859694857529679, -0.5173661940153559, -0.6095980731708683, -0.6308738465499248, -0.5463874380878225, -0.32051361528988365, 0.080971500114135, 0.6883751154183185, 1.5250743782418472, 2.605120470811949, 3.931411007620653, 5.4939623657948715, 7.26853077566415, 9.216689793278539, 11.28682347990289, 13.415388856424746, 15.529160339928053, 17.548355120141572, 19.390891187988892, 20.97642648758213, 22.230491281856494, 23.088396491036942, 23.50027661485238, 23.434643300282644, 22.880069789660798, 21.846575217199675, 20.367788625213148, 18.500083901963897, 16.319254464424432, 13.917756833589992, 11.402272990121297, 8.887892036649777, 6.491704838751974, 4.3275969314662435, 2.5012837154136895, 1.1039256459716984, 0.2072113853840625, -0.14021151024268785, 0.08455850975356936, 0.8769952917189603, 2.205133880801692, 4.010946894423951, 6.213375702488868, 8.71212149935055, 11.39225568599064, 14.130328517409323, 16.801340052009234, 19.283785974674235, 21.465168251349706, 23.248997853464342, 24.559591323168878, 25.343524914430812, 25.571812851133366, 25.243052617188717, 24.38168187357794, 23.034437093439127, 21.267887083616312, 19.165986569521216, 16.823624768610784, 14.340753909734703, 11.817761385682966, 9.350619033501413, 7.025470535869801, 4.914698492352953, 3.074107513690498, 1.540946825165718, 0.33332278570003593, -0.549345302647738, -1.1251454575750173, -1.4269595114549052, -1.499068060669464, -1.3935879639585607, -1.166759355771235, -0.8746836962742429, -0.5697028976764029, -0.29734493340435, -0.09384873991980554, 0.015561818499175192, 0.01743587091803286, -0.09001054123663395, -0.29786238941685084, -0.5881039694909671, -0.9357516819231492, -1.311613488689203, -1.684974742294531, -2.026044096464446, -2.3084405225145876, -2.5116223022130004, -2.621904286591727, -2.6330608796045736, -2.546808613876605, -2.3725245120974097, -2.1255588592415187, -1.8256793203512407, -1.4955892484260769, -1.1587591397170907, -0.8371095090521639, -0.5493317591779284, -0.3095987992202808, -0.12640880763663895, -0.0021332336714498528, 0.06676668198346675, 0.08902617838877835, 0.07736200673601022, 0.04683296723289813, 0.01297068682975334, -0.010200793749815104, -0.012049276785996444, 0.013055164100817342, 0.06451147180356587, 0.13481647267027846, 0.20952184812234703, 0.26779391006440134, 0.28366317201477603, 0.22786157353593373, 0.06998654552903344, -0.21898478326910517, -0.6639199205251237, -1.283097816638019, -2.0860309047791934, -3.071589638792923, -4.2268355941723055, -5.526933078446532, -6.935414458700109, -8.405441074781672, -9.881982091238752, -11.304785540212873, -12.611168904386538, -13.740045846970991, -14.635336447062704, -15.249672628570323, -15.547139461021052, -15.506559984203939, -15.122277146662563, -14.4054002212423, -13.383697608650754, -12.100726014378544, -10.612675756942338, -8.986093780317697, -7.294621662321765, -5.614632212248251, -4.0205915246434145, -2.581478660429318, -1.3571551102663995, -0.3948042006729443, 0.273484538994172, 0.6320979123317784, 0.6824146107660478, 0.44233669934497605, -0.05515446096967162, -0.7643436918890557, -1.629951481612872, -2.59051773022997, -3.582040314689109, -4.54225034245325, -5.414130620194983, -6.148512990207821, -6.706610350973964, -7.062761622046875, -7.204576181686462, -7.132394199767253, -6.858825946492079, -6.408093622632234, -5.812769315104173, -5.110985115926483, -4.3440402034014705, -3.553883777592102, -2.7797620254706663, -2.0559622180322523, -1.4101351939591522, -0.8621164363179744, -0.42323045767254874, -0.09641856749712824, 0.12317937249936392, 0.24691615943187847, 0.29099135969944145, 0.2746683631057676, 0.21843882904528122, 0.14210506957639252, 0.06317137451286897, -0.004377478574084836, -0.050906545328378135, -0.07146464797472596, -0.0656653803611944, -0.03713237234033076, 0.007442719015887159, 0.05947156007158577, 0.10973846845912434, 0.1497361410482769, 0.1728143267944184, 0.17503072005587333, 0.1557235520545918, 0.11775587991664493, 0.06720489428655635, 0.012719437800361775, -0.03538977595929737, -0.06631437440661811, -0.0700851208072779, -0.038844415997721954, 0.032053670017528374, 0.14320307628202858, 0.2906286468576128, 0.46572184153084506, 0.6558057650711318, 0.8450089645099633, 1.0154355699126052, 1.1488312543866421, 1.2287026662140783, 1.24187974787832, 1.1800930744376203, 1.0416716436311049, 0.8327271828536322, 0.5671788931052267, 0.26663300541141943, -0.04017331420989385, -0.3190062106572746, -0.5322908989737802, -0.6413923978114927, -0.6095500641566934, -0.4047982515893772, -0.0024255670503206188, 0.6126335717538811, 1.4433877436077822, 2.480030336533439, 3.6997664386193745, 5.066997587417386, 6.534527837505695, 8.0461754453394, 9.539511138332296, 10.94916668714205, 12.210845321741639, 13.264890495119706, 14.059675011712537, 14.55540960949651, 14.726492667438984, 14.56262509711993, 14.069782843353364, 13.270878791523343, 12.203402404480025, 10.917082776735837, 9.471651808632396, 7.93356208489797, 6.370855043752617, 4.84970423857597, 3.431273636796547, 2.1679552558707043, 1.099995245608032, 0.2543433329226128, -0.3561528734087379, -0.7330936504645362, -0.8917602042889055, -0.8588353173071037, -0.6699737778156473, -0.3669353282762832, 0.005623857645399993, 0.4036206603037452, 0.7866063432826411, 1.1201618693487045, 1.377947138493259, 1.5431182901618739, 1.608688007682894, 1.5769296326069004, 1.4585047245205727, 1.2709352822297515, 1.036149984743946, 0.7780414108070047, 0.5202919135001657, 0.2842018317725385, 0.08671136272747668, -0.06085708013901609, -0.15357983214043097, -0.19313619883566216, -0.18687454298372494, -0.1464009615502095, -0.08559691128306501, -0.018985046384967404, 0.03975461717789017, 0.07962023687782104, 0.09381071080803409, 0.0823570885658798], 'positive_zeros': ['0.28232861169980754270098328130040', '0.918001740735555867566255356576347', '1.19747968113164300815364370226902', '1.84612753659751339482699235774454', '1.91509518959696646201083725117095', '2.00315215449568553826876664006368', '2.60903694060433089684924866265731', '2.93762309949590465904108138317826', '3.00775365446401368363332543646878', '3.36554830415191208917728593451492', '3.59343128621729722763530880682997', '3.71708477891755821522566568906663', '4.02695638496569428725335211035378', '4.18382437864247706863481501891236', '4.78351326521346523724910428075699', '4.78627192991650887754016231897742', '4.80695464433314067391467184213804', '5.40535806028369771109521253923499', '5.60430383962789097437342101747773', '5.84336668159497617154560614229136', '5.99022851936361109107686147858245', '6.00967830593368681444344091405637', '6.15260379024122235375596035818634', '6.63202460669086562962209054407027', '6.95475502358097049688987112518043', '6.98663686581339314233050562196141', '7.21816579804857318477548835061798', '7.35875020174824206382475907582944', '7.49020806580229415613702990828930', '7.973135513176264171198820892097288', '8.154335575958721243630348067390985', '8.200938575748361849347353791857395', '8.533266184528616600916112945170590', '8.552672112942551718048065074977188', '8.860641521275349856752565156395448', '9.029738446927042620289144571036666', '9.116103911349451363735531391895403', '9.420251438813970426820160272530416', '9.572700089708321206560498653230515', '10.02879935851842141134964235743211'], 'prelabel': '8-1452e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.4050372058892275, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e4-0', 'trace_hash': 505721802316217396, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.28232861169980754270098328130', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.918001740735555867566255356576', 'prec': 107}, 'z3': {'__RealLiteral__': 0, 'data': '1.19747968113164300815364370227', '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': 18070.69656612994, 'bad_primes': [2, 3, 11], 'central_character': '1.1', 'conductor': 4444945756416, 'conductor_radical': 66, 'degree': 8, 'dirichlet_coefficients': [1, 0, 1, 0, 1, 0, -2, 0, 0, 0, 0, 0, 3, 0, 1, 0, 7, 0, -4, 0, -2, 0, -8, 0, 5, 0, 0, 0, -3, 0, 0, 0, 0, 0, -2, 0, -9, 0, 3, 0, -9, 0, -8, 0, 0, 0, 12, 0, 7, 0, 7, 0, 13, 0, 0, 0, -4, 0, 6, 0, 2, 0, 0, 0, 3, 0, -56, 0, -8, 0, 6, 0, -6, 0, 5, 0, 0, 0, 16, 0, 0, 0, 8, 0, 7, 0, -3, 0, 4, 0, -6, 0, 0, 0, -4, 0, -7, 0, 0, 0], 'euler11': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler13': [1, -3, -4, 51, -101, 663, -676, -6591, 28561], 'euler17': [1, -7, 32, -105, 191, -1785, 9248, -34391, 83521], 'euler19': [1, 4, -3, -88, -295, -1672, -1083, 27436, 130321], 'euler2': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, 8, 116, 584, 4294, 13432, 61364, 97336, 279841], 'euler29': [1, 3, -20, -147, 139, -4263, -16820, 73167, 707281], 'euler3': [1, -1, 1, -1, 1, 0, 0, 0, 0], 'euler31': [1, 0, -31, 0, 961, 0, -29791, 0, 923521], 'euler37': [1, 9, 44, 63, -1061, 2331, 60236, 455877, 1874161], 'euler41': [1, 9, 40, -9, -1721, -369, 67240, 620289, 2825761], 'euler43': [1, 8, 196, 1064, 13174, 45752, 362404, 636056, 3418801], 'euler47': [1, -12, 97, -600, 2641, -28200, 214273, -1245876, 4879681], 'euler5': [1, -1, -4, 9, 11, 45, -100, -125, 625], 'euler53': [1, -13, 116, -819, 4499, -43407, 325844, -1935401, 7890481], 'euler59': [1, -6, -23, 492, -1595, 29028, -80063, -1232274, 12117361], 'euler61': [1, -2, -57, 236, 3005, 14396, -212097, -453962, 13845841], 'euler67': [1, 56, 1444, 22232, 222934, 1489544, 6482116, 16842728, 20151121], 'euler7': [1, 2, -3, -20, -19, -140, -147, 686, 2401], 'euler71': [1, -6, -35, 636, -1331, 45156, -176435, -2147466, 25411681], 'euler73': [1, 6, -37, -660, -1259, -48180, -197173, 2334102, 28398241], 'euler79': [1, -16, 177, -1568, 11105, -123872, 1104657, -7888624, 38950081], 'euler83': [1, -8, -19, 816, -4951, 67728, -130891, -4574296, 47458321], 'euler89': [1, -4, 362, -1072, 48595, -95408, 2867402, -2819876, 62742241], 'euler97': [1, 7, -48, -1015, -2449, -98455, -451632, 6388711, 88529281], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0, 0, 0], [1, -1, 1, -1, 1, 0, 0, 0, 0], [1, -1, -4, 9, 11, 45, -100, -125, 625], [1, 2, -3, -20, -19, -140, -147, 686, 2401], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, -3, -4, 51, -101, 663, -676, -6591, 28561], [1, -7, 32, -105, 191, -1785, 9248, -34391, 83521], [1, 4, -3, -88, -295, -1672, -1083, 27436, 130321], [1, 8, 116, 584, 4294, 13432, 61364, 97336, 279841], [1, 3, -20, -147, 139, -4263, -16820, 73167, 707281], [1, 0, -31, 0, 961, 0, -29791, 0, 923521], [1, 9, 44, 63, -1061, 2331, 60236, 455877, 1874161], [1, 9, 40, -9, -1721, -369, 67240, 620289, 2825761], [1, 8, 196, 1064, 13174, 45752, 362404, 636056, 3418801], [1, -12, 97, -600, 2641, -28200, 214273, -1245876, 4879681], [1, -13, 116, -819, 4499, -43407, 325844, -1935401, 7890481], [1, -6, -23, 492, -1595, 29028, -80063, -1232274, 12117361], [1, -2, -57, 236, 3005, 14396, -212097, -453962, 13845841], [1, 56, 1444, 22232, 222934, 1489544, 6482116, 16842728, 20151121], [1, -6, -35, 636, -1331, 45156, -176435, -2147466, 25411681], [1, 6, -37, -660, -1259, -48180, -197173, 2334102, 28398241], [1, -16, 177, -1568, 11105, -123872, 1104657, -7888624, 38950081], [1, -8, -19, 816, -4951, 67728, -130891, -4574296, 47458321], [1, -4, 362, -1072, 48595, -95408, 2867402, -2819876, 62742241], [1, 7, -48, -1015, -2449, -98455, -451632, 6388711, 88529281]], 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1452/2/i/m'], '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': '8-1452e4-1.1-c1e4-0-7', 'motivic_weight': 1, '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': [1, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '8-1452e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.4050372058892275, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e4-0', 'trace_hash': 505721802316217396, 'z1': {'__RealLiteral__': 0, 'data': '0.28232861169980754270098328130', 'prec': 103}}
• lfunc_instances •

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

  
  {'Lhash': '357894034082863741463069270817,1163705457653986824714891764738,1517985836547636009200909213255,2427671566586789322678846054264', 'Lhash_array': ['357894034082863741463069270817', '1163705457653986824714891764738', '1517985836547636009200909213255', '2427671566586789322678846054264'], 'factors': ['2-1452-11.5-c1-0-3', '2-1452-11.4-c1-0-7', '2-1452-11.3-c1-0-10', '2-1452-11.9-c1-0-15'], 'label': '8-1452e4-1.1-c1e4-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1452/2/i/m'}