Lfunction data - 8-740e4-1.1-c0e4-0-0

Formats: - HTML - YAML - JSON - 2024-09-12T06:47:50.171847

• 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
  instance_types	text[]
  instance_urls	text[]
  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': '1463423940587382210973919817998,1830683495484681727962572243754,2016705899928097325163780737189,3240172356747914853638541882749', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 1, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.018601817375920923, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [1, 0, -1, 0, 1]], [5, [1, 0, 2, 0, 1]], [37, [1, 0, -1, 0, 1]]], 'bad_primes': [2, 5, 37], 'central_character': '740.1', 'coefficient_field': '1.1.1.1', 'conductor': 299865760000, 'conductor_radical': 370, 'degree': 8, 'euler_factors': [[1, 0, -1, 0, 1], [1, 0, 0, 0, -1, 0, 0, 0, 1], [1, 0, 2, 0, 1], [1, 0, 0, 0, -1, 0, 0, 0, 1], [1, 0, 4, 0, 6, 0, 4, 0, 1], [1, 0, 2, 0, 3, 0, 2, 0, 1], [1, -2, 1, -2, 4, -2, 1, -2, 1], [1, 0, 0, 0, -1, 0, 0, 0, 1], [1, 0, 4, 0, 6, 0, 4, 0, 1], [1, -2, 2, 0, -1, 0, 2, -2, 1], [1, 0, 0, 0, 2, 0, 0, 0, 1], [1, 0, -1, 0, 1], [1, -6, 17, -30, 36, -30, 17, -6, 1], [1, 0, 4, 0, 6, 0, 4, 0, 1], [1, 0, 0, 0, 2, 0, 0, 0, 1], [1, 2, 2, 0, -1, 0, 2, 2, 1], [1, 0, 0, 0, -1, 0, 0, 0, 1], [1, 4, 5, 0, -4, 0, 5, 4, 1], [1, 0, 0, 0, -1, 0, 0, 0, 1], [1, 0, 2, 0, 3, 0, 2, 0, 1], [1, 4, 8, 12, 14, 12, 8, 4, 1], [1, 0, 0, 0, -1, 0, 0, 0, 1], [1, 0, 0, 0, -1, 0, 0, 0, 1], [1, 2, 5, 6, 8, 6, 5, 2, 1], [1, 0, -2, 0, 3, 0, -2, 0, 1], [1, 0, -2, 0, 3, 0, -2, 0, 1], [1, 0, -4, 0, 6, 0, -4, 0, 1], [1, 0, 0, 0, -1, 0, 0, 0, 1], [1, -2, 5, -6, 8, -6, 5, -2, 1], [1, 4, 10, 16, 19, 16, 10, 4, 1]], 'euler_factors_factorization': [[[[1, 0, -1, 0, 1], 1]], [[[1, 0, 0, 0, -1, 0, 0, 0, 1], 1]], [[[1, 0, 1], 2]], [[[1, 0, 0, 0, -1, 0, 0, 0, 1], 1]], [[[1, 0, 1], 4]], [[[1, -1, 1], 2], [[1, 1, 1], 2]], [[[1, -1], 4], [[1, 1, 1], 2]], [[[1, 0, 0, 0, -1, 0, 0, 0, 1], 1]], [[[1, 0, 1], 4]], [[[1, -1, 1], 2], [[1, 0, -1, 0, 1], 1]], [[[1, 0, 0, 0, 1], 2]], [[[1, 0, -1, 0, 1], 1]], [[[1, -1], 4], [[1, -1, 1], 2]], [[[1, 0, 1], 4]], [[[1, 0, 0, 0, 1], 2]], [[[1, 1, 1], 2], [[1, 0, -1, 0, 1], 1]], [[[1, 0, 0, 0, -1, 0, 0, 0, 1], 1]], [[[1, 1], 4], [[1, 0, -1, 0, 1], 1]], [[[1, 0, 0, 0, -1, 0, 0, 0, 1], 1]], [[[1, -1, 1], 2], [[1, 1, 1], 2]], [[[1, 1], 4], [[1, 0, 1], 2]], [[[1, 0, 0, 0, -1, 0, 0, 0, 1], 1]], [[[1, 0, 0, 0, -1, 0, 0, 0, 1], 1]], [[[1, 0, 1], 2], [[1, 1, 1], 2]], [[[1, 0, -1, 0, 1], 2]], [[[1, 0, -1, 0, 1], 2]], [[[1, -1], 4], [[1, 1], 4]], [[[1, 0, 0, 0, -1, 0, 0, 0, 1], 1]], [[[1, -1, 1], 2], [[1, 0, 1], 2]], [[[1, 1, 1], 4]]], 'gamma_factors': [[], [0, 0, 0, 0]], 'group': 'GL2', 'index': 0, 'label': '8-740e4-1.1-c0e4-0-0', 'leading_term': '1.02228329759509915459872437301386089727020368217195994023413099551854709620015206854950373', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, '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': [0, 0, 0, 0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/740/1/bm/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.015625', 'prec': 27}, 'plot_values': [1.022283297595099, 1.0262358852925506, 1.0310288197058448, 1.0377126961233964, 1.0473626174861796, 1.0608556823455852, 1.078149031062539, 1.0989736956040095, 1.1230627330919962, 1.1502010320216738, 1.180401855989967, 1.213743983686253, 1.2503146674478742, 1.2901848293953786, 1.3333314288601477, 1.3796991433694406, 1.4292198507842244, 1.48181318520409, 1.5373963039000285, 1.5958705311801467, 1.6571145851154805, 1.7209806115683604, 1.7872882801192271, 1.8558250211146734, 1.9263444517740143, 1.998567027558933, 2.0721879359947173, 2.146867996248155, 2.2222295920973627, 2.2978592566448364, 2.373318674235003, 2.4481360308634983, 2.5218033662900448, 2.5937821216398667, 2.6635192169394832, 2.7304379360368265, 2.7939365946511807, 2.8533968799034284, 2.9082036753171896, 2.9577366143518526, 3.001370423146326, 3.038485939198275, 3.0684934828694113, 3.0908243500134844, 3.1049321713876887, 3.110305919208993, 3.1064959607972242, 3.0931042015938437, 3.0697852379530524, 3.03626009397109, 2.992343525071033, 2.93793091124725, 2.8729974657534227, 2.7976108738748584, 2.7119576314873868, 2.616324745972183, 2.511095128671584, 2.396756989018779, 2.2739264387587856, 2.143322595520481, 2.0057576427928514, 1.8621409716360713, 1.7134952389897506, 1.5609246746942875, 1.405599237598452, 1.2487522551814187, 1.091687859896951, 0.9357440588233942, 0.7822718924136748, 0.6326267164450288, 0.48816653044049735, 0.35021337708573436, 0.22003018208314878, 0.09880766304821834, -0.012344678963934872, -0.11243350673069746, -0.2006028136565538, -0.2761475359428261, -0.3385256944492271, -0.3873834765265061, -0.4225691616212558, -0.4441421019527988, -0.4523819218861844, -0.4477980776965697, -0.4311316050938942, -0.40335421037584857, -0.36566794957803755, -0.3194959343002852, -0.26646886206898185, -0.20841050112629395, -0.14732276386777773, -0.08535818521139023, -0.024791611996831442, 0.03200840193103541, 0.08261058064183702, 0.12456118190011463, 0.15542245026787746, 0.17281139524402586, 0.17444306297742157, 0.15817353628664615, 0.1220397351422927, 0.06429999543733006, -0.01651967911043829, -0.12159241015272435, -0.251760530703267, -0.40750460127910954, -0.5889075468009929, -0.7956429590273297, -1.0269657692152512, -1.2817023978769264, -1.5582394494002398, -1.85454035344687, -2.1681631437941893, -2.4962796911341143, -2.8356995271425136, -3.182913221237293, -3.5341363801588406, -3.8853588381544655, -4.232406326610619, -4.570998928542018, -4.896811491798396, -5.205544675939497, -5.493016793435899, -5.755217064027425, -5.988364936860299, -6.188986731556645, -6.354020142313844, -6.480838205891393, -6.567286592025664, -6.611745343402605, -6.6132228838768485, -6.5713301408473646, -6.486277943448461, -6.358905478652672, -6.190742069641103, -5.983922230543793, -5.741135290902121, -5.465611221680449, -5.161137770812744, -4.831924073585815, -4.482509361093711, -4.117710803843001, -3.7425987235756915, -3.362333833791936, -2.9820569220265862, -2.6068179468810793, -2.2415281492688446, -1.8908078251436722, -1.5588886005462426, -1.2495526297544683, -0.966091264077955, -0.7112010520236363, -0.4869299130000623, -0.29465515156452426, -0.13507855677766323, -0.008195845718156984, 0.0866940582894014, 0.15095514116614947, 0.18656528372578168, 0.19607136259025754, 0.18251889157735202, 0.1493657562398641, 0.10038379414211354, 0.03956303623679916, -0.028994276887333886, -0.10118637172463182, -0.17303143994627315, -0.24076968969488016, -0.3009630615540679, -0.3505931242240396, -0.38715786829574494, -0.4087312263727238, -0.4140131806880351, -0.402371626541452, -0.37387414338775943, -0.3292716439562847, -0.2699721484563823, -0.19800330077796816, -0.11595788195974055, -0.026899712133464794, 0.06573516777780092, 0.15824731226826225, 0.24680082987854912, 0.32756104878325504, 0.3968289639653618, 0.45118017833776625, 0.48761487305191714, 0.503679573607627, 0.4975786281643974, 0.46828166293390056, 0.41562715547192136, 0.3403674139419478, 0.24420014034715493, 0.12978685762092548, 0.0007489719765650823, -0.1383981077534602, -0.282322190805125, -0.4249712153658116, -0.5597072952662351, -0.6794705408917401, -0.7769479636454016, -0.8447629919773345, -0.8757051710263536, -0.8629308653663574, -0.8001613250245772, -0.6818946130689791, -0.503643533318018, -0.2620858896555973, 0.0447941937809529, 0.41756578764801483, 0.8552162572390638, 1.3551264762956763, 1.913058649224234, 2.523165941930466, 3.1780504686675815, 3.8688870731568246, 4.585562424248815, 5.316860041234001, 6.050736580548485, 6.774543714643263, 7.475271427916692, 8.139860911001213, 8.755639727112685, 9.310527993719468, 9.793280671782131, 10.193819668325283, 10.503699054459947, 10.71616131111935, 10.82625603459569, 10.831063480068075, 10.73004090308274, 10.5248345735619, 10.219190467187943, 9.818979119515102, 9.332318604935939, 8.769139426435615, 8.14088646051223, 7.46033873963119, 6.741499901842995, 5.999020469575481, 5.247785790667087, 4.502619611842598, 3.778038987907876, 3.0877130751641033, 2.4440945253675666, 1.8581575287799248, 1.3391809409020017, 0.894424528920578, 0.5289565619928207, 0.24557121392875295, 0.044754457124469904, -0.0753222266687753, -0.11870335969574596, -0.09148582235632187, -0.0016034207302606997, 0.14145008139701304, 0.3269436227223411, 0.5432667602937823, 0.7783322335765851, 1.0199739051026078, 1.2563375540320612, 1.4762774341907396, 1.669775795985803, 1.8282407921223294, 1.9447681100651508, 2.0143870103954313, 2.034299165615489, 2.003901296726531, 1.9247747282653391, 1.8006532585230315, 1.6373598979363275, 1.4425147948571586, 1.2252410681904493, 0.995861400349997, 0.7655621173721019, 0.5459103681482146, 0.34841188701609144, 0.18408758271097886, 0.06304733019402811, -0.005951636351646187, -0.01587186752893708, 0.03829069300665562, 0.159245147112295, 0.3472279129266622, 0.5999094935670407, 0.9123841125859642, 1.2772710892082015, 1.684891830951575, 2.1235155190476407, 2.5797014521873614, 3.0387912813499196, 3.485337692825943, 3.903572429311394, 4.277965519743326, 4.593931427323707, 4.8382508192811455, 4.999508994042643, 5.068605530334481, 5.039365235825372, 4.908666576129822, 4.676587806841705, 4.346600989623203, 3.9257988333632294, 3.42457118386255, 2.856327824383607, 2.2372550852122903, 1.5860475719554972, 0.9232018811679817, 0.2704003127444333, -0.3500680674663693, -0.9159260880881547, -1.4057177048431786, -1.7994908624716346, -2.0794210769734636, -2.230431961773904, -2.240753130093904, -2.1023417066417007, -1.8112102092705549, -1.3676615067793274, -0.776357288330365, -0.046269175183493626, 0.8095022799536957, 1.7741071757565283, 2.8273457919258553, 3.946155814301378, 5.105268856729907, 6.278149961971366, 7.4375726544869005, 8.556273296243113, 9.607810539759688, 10.5677457160501, 11.413967894431034, 12.127139018733745, 12.69138169750356, 13.09527680623502, 13.331602087383482, 13.397286219790836, 13.293645620483877, 13.026888699765376, 12.607208695325506, 12.048216387069695, 11.366691280000333, 10.582551775693922, 9.71756719845984, 8.794514273305625, 7.836668402296846, 6.867475729952639, 5.909346184222452, 4.982925705208084, 4.106682982000681, 3.296647854183161, 2.5657063947764893, 1.923314730722095, 1.3754614428877139, 0.9247468795912439, 0.5703428830672371, 0.3082303209652577, 0.13158160957700832, 0.031205740521879605, -0.0039973758805087216, 0.01352405949630433, 0.07056447059744593, 0.15374130434007685, 0.25005384698325916, 0.3474095049177044, 0.4350878208447565, 0.5041236945151706, 0.547593828523822, 0.5608071510393889, 0.5413917814797479, 0.489263195125672, 0.4064901020248792, 0.2970804981316843, 0.16667993358332764, 0.02216527108112086, -0.1287617889668689, -0.27800021044069945, -0.4175100947523473, -0.5398173961187174, -0.6383675111921404, -0.7078445369316828, -0.7444712694815773, -0.7462802416734885, -0.7131409154367501, -0.6467447332825721, -0.5505476830066941, -0.42964001363288384, -0.2904145004162796, -0.14023307806908827, 0.012930272507543698, 0.16090867211029428, 0.295800506594065, 0.41037201883800406, 0.4984395218316977, 0.5552575911220048, 0.5777663046273371, 0.5647525420905652, 0.5169551575166191, 0.4371157677243451, 0.3298125229747757, 0.20123019294893732, 0.058876353655785404, -0.08877414255726149, -0.23277102979708947, -0.3641788576167155, -0.4745750971545294, -0.5565729271059826, -0.6043028334949078, -0.6138230717369583, -0.5834716951699598, -0.5141552635667516, -0.40945900779453026, -0.27565456287809, -0.12160289834004726, 0.041475906082246834, 0.2003924727465184, 0.3404557210346977, 0.44603814968890176, 0.5012648777081028, 0.49068732526249786, 0.399972028402517, 0.21661937833598247, -0.06930677662048197, -0.46465600561909726, -0.972714467857578, -1.592803893923561, -2.3200546877922976, -3.145389735194043, -4.055584533506962, -5.0335091854661425, -6.058729011147342, -7.108001860725827, -8.155853737426327, -9.175413144934216, -10.139714668728743, -11.022314247712295, -11.797993359936209, -12.44376380621496, -12.940345439329281, -13.272327082768365, -13.428478055984266, -13.402382606432694, -13.19346709548037, -12.806329714364333, -12.250344996660118, -11.539612338197175, -10.693192306552882, -9.733699179528733, -8.686315880341228, -7.578174164822825, -6.437946563610243, -5.294249915420196, -4.174568074672359, -3.104540085621264, -2.1074268993363083, -1.203011771782079, -0.4070005437030874, 0.26926225715644336, 0.8189183844436797, 1.2397936794292734, 1.5342423668576173, 1.708785865060459, 1.7736415902182066, 1.742138806006528, 1.6299965783244736, 1.454543091367716, 1.2339200998830202, 0.9862631209026012, 0.7289314991340441, 0.47781090470100246, 0.24671410659116802, 0.04692198176913731, -0.11314441376919007, -0.22811474773558654, -0.2956866505387532, -0.3164725637416312, -0.29375278335319666, -0.23310887805276517, -0.1418865276608623, -0.028662683012812537, 0.09728625343219306, 0.226569145711732, 0.35036317069428713, 0.4608229351350448, 0.5514271161321787, 0.6173229505015035, 0.6556850644011624, 0.6656305059067076, 0.6481007828172083, 0.6057457625258441, 0.5427904203396022, 0.4645094557183143, 0.37677310193811814, 0.28565614404315687, 0.1970702303647321, 0.11622910617847086, 0.047285769888395925, -0.006901325068494822, -0.04491240984241724, -0.06685722810256296, -0.07427965593695758, -0.06993016193260525, -0.05743581319525503, -0.04086251574971178, -0.024188630389956944, -0.010735049670991568, -0.002579659986176322, 1.4549560203268493e-05, -0.0008948351698342149, -0.0005202371933960807, 0.00893501940276816, 0.0383920244255942, 0.10183326136443599, 0.21604731642009797, 0.4001594198768668, 0.6749821280535336, 1.0621963039841533, 1.5833813936315038, 2.2589398601672293, 3.106955707646075, 4.142018406129705, 5.374107412144846, 6.807716299957292, 8.440917686319946, 10.26459269746647, 12.262048706986754, 14.409368569659087, 16.67526471150843, 19.021285383036517, 21.402744507140653, 23.770830587040564, 26.073176237198183, 28.254928975127974, 30.26078840023019, 32.03844083305866, 33.5390159183295, 34.71819338588764, 35.53838794819508, 35.97225071322462, 36.00192470362147, 35.619157159528, 34.826499553871265, 33.63952559694975, 32.08433092922147, 30.196157178544972, 28.019064667001544, 25.606279458792834, 23.016443359121393, 20.311225167197755, 17.55391605022515, 14.808456284466217, 12.135833999705929, 9.591901859668825, 7.226059363029046, 5.0802535811269145, 3.1869976524641372, 1.5685757569912728, 0.2368929857977323, -0.8064241740640978, -1.5697859977284703, -2.070703571463068, -2.334538022180318, -2.3931310315547094, -2.283003440536794, -2.0434373435201807, -1.7146103341256045, -1.3358336527401298, -0.9436746866678617, -0.5703910716221069, -0.2426911289538296, 0.019182285596672687, 0.2021041519979326, 0.30028387354028774, 0.3150853474425892, 0.25445675841167587, 0.13208885315952004, -0.033702452322730427, -0.22134041699474016, -0.4075716386216597, -0.5689497637879743, -0.683323379310017, -0.73130034926471, -0.6975865513725035, -0.5718659436829627, -0.3495041074028798, -0.031991230489507014, 0.3730768853704816, 0.8523710161871713, 1.3873751562367742, 1.9552858946567506, 2.530516293415088, 3.0858723047179066, 3.593789866829292, 4.027871681003714, 4.364919803335093, 4.585743828934461, 4.675966310269201, 4.627026658422165, 4.437428637312969, 4.112235593814941, 3.6626618226918835, 3.105823285553122, 2.464524755206303, 1.7655088600295665, 1.038025269068706, 0.31261549087583734, -0.38010130013499194, -1.011357272466529, -1.5556599210320547, -1.9919172591630274, -2.3044519016742395, -2.483848773203991, -2.5273142947257377, -2.438736518848943, -2.2285261079220104, -1.912911837249392, -1.512991006205025, -1.05361709586833, -0.5621020476708091, -0.06664892540883909, 0.4051328638588984, 0.827659635522805, 1.1788049658996562, 1.4410211351247688, 1.602175557983579, 1.6561728040876338, 1.6033716936363667, 1.450364189072324, 1.2095101083395003, 0.8982571844837057, 0.5382038929772684, 0.15375036719980104, -0.22927371478557068, -0.5850384503532211, -0.8892356333153758, -1.120428055692997, -1.2612122645255586, -1.2992389710768815, -1.22804610446542, -1.0473058989849928, -0.7628535689704136, -0.38647062521038233, 0.0647205158865295, 0.5692725142880797, 1.1024947699978354, 1.6377330446439253, 2.14802573933546, 2.6074617157486433, 2.992421725451485, 3.2828899413045174, 3.4639465159116103, 3.5262226873429765, 3.466213331825427, 3.286582079631305, 2.9964344700586603, 2.6103412581866277, 2.1474041962894814, 1.6303647872631974, 1.084613551177002, 0.5364262059330688, 0.01150925184235416, -0.46627824317078764, -0.876200298023522, -1.2018877922709317, -1.432138198293353, -1.5614557737718737, -1.5904489527738508, -1.5256498111732852, -1.3790113630718699, -1.1672191257192137, -0.9108514149361393, -0.6330084138927677, -0.3579260924964263, -0.1096207659187845, 0.08943743638935463, 0.2197251514628647, 0.26580231296514345, 0.21719163899783211, 0.06897234197067871, -0.1778945572070084, -0.5165736653210032, -0.9347103617592247, -1.4152151243502482, -1.9371372368525914, -2.4767247215993238, -3.008747156561726, -3.5081706264478814, -3.951290079814346, -4.316858150617104, -4.587314739843604, -4.750140189382217, -4.798071385140149, -4.7292792115847115, -4.54755822555877, -4.262446223529066, -3.888143935974274, -3.4425659767662724, -2.9464610595144216, -2.422445433338455, -1.8933798647581908, -1.381108481009636, -0.9053984396034477, -0.4829276123755726, -0.12635779817276185, 0.15615574196163745, 0.3612000852875014, 0.4901735834331737, 0.5488672470486843, 0.5467917827134805, 0.4963691131910295, 0.41200666871934544, 0.30883539544506916, 0.2015220156057038, 0.10318109886463762, 0.024375519946335127, -0.02778495019352156, -0.05023067771070717, -0.04424235360199157, -0.015494381582301257, 0.026242268633014914, 0.06769540674003437, 0.09293060921143877, 0.08440756806118371, 0.024208835340192133, -0.10467108945851164, -0.3170372511777427, -0.6243002073899333, -1.0334305112877558, -1.5461139643818245, -2.1582064642233743, -2.859675043736174, -3.634663592869976, -4.4618584111981185, -5.315318193764708, -6.165996936847107, -6.982777729267129, -7.733728467660363, -8.387779650532268, -8.916980933070601, -9.29737059126283, -9.509964526254997, -9.542006291768113, -9.38846130873583, -9.051607943451495, -8.540781840039218, -7.872257123304661, -7.069063603735515, -6.159249199627882, -5.174466320400798, -4.148684251068794, -3.1167402284092436, -2.1124161943925146, -1.1669719503068174, -0.3078403081350041, 0.44274659895537677, 1.068469325527451, 1.55927531960515, 1.9116195727941843, 2.1286715859301304, 2.219360552448954, 2.1974091144726478, 2.080436815562097, 1.8890671704676976, 1.6451768798527282, 1.3705217585918827, 1.0856473756023701, 0.8089504225310903, 0.5555510906366554, 0.3366994665592184, 0.1595357462074151, 0.02708184622844419, -0.06153854327253168, -0.11052820882622381, -0.12665319968144434, -0.11836748706322921, -0.09479418537175631, -0.06472184385841967, -0.035695554815891636, -0.013244047810643441, -0.0002773659714230125, 0.0032424553935379427, 0.000357128735537214, -0.00310304885786126, 0.000994995998028082, 0.02236428594840855, 0.07139378145541389, 0.1581467924508371, 0.29130879674966337, 0.4771560771155889, 0.7186547014360892, 1.0148843035771342, 1.36057863010827, 1.7459192898813756, 2.1567569715122152, 2.5755249111250533, 2.981921767890753, 3.353868451682163, 3.6689562829565423, 3.9065963798824495, 4.049078910414905, 4.082760789722514, 3.999560113273939, 3.7987759708147757, 3.4870561472682686, 3.078401905289515, 2.594246546511456, 2.0634031423570516, 1.5202227150813103, 1.002917386920167, 0.5519113719220748, 0.20792017199259222, 0.009244328452366913, -0.010494798957049776, 0.17560958109853547, 0.5857653686915751, 1.2278938750319508, 2.0986606088595026, 3.183018904423997, 4.454354565767709, 5.875275391158326, 7.398917861330388, 8.970906087110826, 10.5322619706894, 12.021769365863602, 13.378580440545628, 14.545396868412709, 15.472501018501054, 16.119259004889567, 16.455746815497637, 16.46480751412905, 16.14454025619182, 15.506880577094485, 14.576593896370374, 13.390706901238191, 11.998019191934857, 10.454973441155547, 8.822534392149576, 7.16370940499328, 5.5411340432986345, 4.012766454659338, 2.629049128642538, 1.4309040848967003, 0.44801644583175326, -0.30278858286207344, -0.8178185595554547, -1.106066138210888, -1.18837677472371, -1.0955997422656039, -0.8661286755778099, -0.5432293769992159, -0.17227622172916007, 0.2026002062404608, 0.5415437570217155, 0.8115650304233809, 0.9886818883231657, 1.0597267662303607, 1.0232963826200132, 0.8899029398296229, 0.6813531951127374, 0.42949254034085893, 0.17423661327967718, -0.038988062148512394, -0.16226617783932007, -0.14826422830244476, 0.04658475673945742, 0.45897091488253944, 1.1160333206991075, 2.0332446999039586, 3.2127223380500474, 4.642327480582582, 6.296189459432575, 8.135231337438576, 10.10826959188109, 12.15428825117939, 14.206641263463254, 16.195221114584147, 18.04907302833592, 19.700181465897558, 21.08900147718644, 22.165462639621428, 22.890421586982974, 23.238141920076252, 23.199941536409376, 22.781976249635527, 22.00386745526126, 20.898338198969906, 19.511531825645626, 17.898189166277916, 16.118272028486984, 14.23471663713972, 12.311723787932653, 10.410143981749801, 8.584617856889038, 6.881863117120093, 5.339530414786629, 3.984401726281859, 2.8319990744249117, 1.887015284910439, 1.1441923284389748, 0.5895851711892417, 0.20237179794961827, -0.0431271024893517, -0.1753709598441422, -0.22334089814891359, -0.21456920483834027, -0.17351057782932416, -0.12026729895969285, -0.06967333641413344, -0.03096142741369314, -0.007908662613387674, 0.0005967080503299562, -0.000398976410939402, -0.003157550413779348, 0.0013445927165650522, 0.02195801846199, 0.06598710119806814, 0.13800171464376168, 0.23892718542712874, 0.36556860626364707, 0.510495952207202, 0.662296249061935, 0.8062724652330149, 0.9257238877561486, 1.0031651366810066, 1.0216954722570866, 0.9665884719999202, 0.8271120637679691, 0.5975088316450595, 0.27781479373191864, -0.1254724993427702, -0.5990360605217362, -1.123466427873947, -1.6741891827147115, -2.2226928688181715, -2.7383009612739158, -3.190250376597155, -3.5496923192788272, -3.7917984583827327, -3.8981343511432383, -3.858056818101828, -3.669758365068434, -3.3411148932368464, -2.8903206724076345, -2.344868421916989, -1.7402509965852988, -1.11842507453722, -0.5259322284987338, -0.010877580543671458, 0.3799388243175755, 0.6037651617713478, 0.624477981455673, 0.41523923269801394, -0.039438318750706795, -0.7423069887891486, -1.6830414457771234, -2.838046530563335, -4.170959415096095, -5.63422334583815, -7.1723632286179235, -8.72395486436121, -10.224086392877606, -11.607951093444573, -12.816179998229444, -13.796343716735327, -14.504835230966156, -14.909769566614166, -14.995146486724641, -14.759289525372319, -14.213999610175973, -13.384710983114607, -12.31138382186972, -11.043792149061181, -9.63821126307462, -8.155266914074273, -6.658305423107214, -5.208183419322398, -3.859969140840249, -2.6609152319110274, -1.6489914189760388, -0.8502987306996926, -0.2782384165867218, 0.06627690832810221, 0.19410081645967178, 0.12689501371461945, -0.10476611021326913, -0.46373897751197024, -0.9088103807442164, -1.3973036148163458, -1.8876868020944981, -2.3419892903304094, -2.727871109987951, -3.0200860146908246, -3.201505683489876, -3.263661570031775, -3.2066652715924153, -3.038373855842503, -2.773323396799932, -2.4313472248154344, -2.0357226649326314, -1.6112715575437049, -1.1826870939229261, -0.7728941904093768, -0.4013200889835319, -0.08299935534002627, 0.1719316611065748, 0.35856900695492017, 0.47744737553168887, 0.5336624356827013, 0.5359021373599981, 0.4954953929343496, 0.4254391051621021, 0.3389192764465711, 0.24814541401106713, 0.16348407959686206, 0.09280774039809662, 0.040874227155525376, 0.009231597927860219, -0.0035349658771143414, -0.0012889486660785363, 0.010413404779945356, 0.025226187431246088, 0.03691264857651535, 0.039746105415247965, 0.028981506635518066], 'positive_zeros': ['1.15443793449386252972175086115410', '1.44415463942121210603204209396597', '1.59090044178183410278437293238533', '2.42304464500207117343682442366885', '2.55604529841625931071427480000751', '2.80144763278416741010262044481551', '3.03133711333930172747107426393452', '3.24791354945668227586490716986349', '3.91098326614564103591735517081452', '3.96896136100766709259412529669834', '4.35728177321846310550292871526068', '4.38192199185416200915025067144064', '4.81917691633289795937113065315634', '5.00090472267369864288036427568046', '5.60499459741940231579639292108914', '5.61800805877455403063854783558869', '5.84606518034813986154252965710029', '6.07679696028216140005878011853107', '6.27187084497638680750546371117773', '6.46479103134850073221741867069533', '6.59045170453058589149057285216683', '7.13405408471555076256760807172193', '7.36354870971581762264830516389183', '7.48802752535027932945038149749991', '7.76335069770711380815944705751081', '7.921243420314088278954123553002398', '7.925050925981699548378780947404903', '7.955177587201249068206129938278996', '8.706323272906228129238647344075191', '8.904932170696850592005342927386409', '8.997046376974766708220561228386738', '9.141986826820556767599086703798686', '9.460046933865326854344466571189600', '9.674016081551268435560383385089204', '9.865580808505125747071357205472692', '10.02913424666341678169909155310898', '10.31285639807901548577887021552290', '10.52364472738008781864003336432173', '10.59878287025958678488902314946964', '10.99084945834413878145983543301991'], 'prelabel': '8-740e4-1.1-c0e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.6077072562907422, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c0e4-0', 'trace_hash': 1279017629530847851, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.15443793449386252972175086115', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.44415463942121210603204209397', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.59090044178183410278437293239', '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': 0.018601817375920923, 'bad_primes': [2, 5, 37], 'central_character': '1.1', 'conductor': 299865760000, 'conductor_radical': 370, 'degree': 8, 'dirichlet_coefficients': [1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2], 'euler11': [1, 0, 4, 0, 6, 0, 4, 0, 1], 'euler13': [1, 0, 2, 0, 3, 0, 2, 0, 1], 'euler17': [1, -2, 1, -2, 4, -2, 1, -2, 1], 'euler19': [1, 0, 0, 0, -1, 0, 0, 0, 1], 'euler2': [1, 0, -1, 0, 1, 0, 0, 0, 0], 'euler23': [1, 0, 4, 0, 6, 0, 4, 0, 1], 'euler29': [1, -2, 2, 0, -1, 0, 2, -2, 1], 'euler3': [1, 0, 0, 0, -1, 0, 0, 0, 1], 'euler31': [1, 0, 0, 0, 2, 0, 0, 0, 1], 'euler37': [1, 0, -1, 0, 1, 0, 0, 0, 0], 'euler41': [1, -6, 17, -30, 36, -30, 17, -6, 1], 'euler43': [1, 0, 4, 0, 6, 0, 4, 0, 1], 'euler47': [1, 0, 0, 0, 2, 0, 0, 0, 1], 'euler5': [1, 0, 2, 0, 1, 0, 0, 0, 0], 'euler53': [1, 2, 2, 0, -1, 0, 2, 2, 1], 'euler59': [1, 0, 0, 0, -1, 0, 0, 0, 1], 'euler61': [1, 4, 5, 0, -4, 0, 5, 4, 1], 'euler67': [1, 0, 0, 0, -1, 0, 0, 0, 1], 'euler7': [1, 0, 0, 0, -1, 0, 0, 0, 1], 'euler71': [1, 0, 2, 0, 3, 0, 2, 0, 1], 'euler73': [1, 4, 8, 12, 14, 12, 8, 4, 1], 'euler79': [1, 0, 0, 0, -1, 0, 0, 0, 1], 'euler83': [1, 0, 0, 0, -1, 0, 0, 0, 1], 'euler89': [1, 2, 5, 6, 8, 6, 5, 2, 1], 'euler97': [1, 0, -2, 0, 3, 0, -2, 0, 1], 'euler_factors': [[1, 0, -1, 0, 1, 0, 0, 0, 0], [1, 0, 0, 0, -1, 0, 0, 0, 1], [1, 0, 2, 0, 1, 0, 0, 0, 0], [1, 0, 0, 0, -1, 0, 0, 0, 1], [1, 0, 4, 0, 6, 0, 4, 0, 1], [1, 0, 2, 0, 3, 0, 2, 0, 1], [1, -2, 1, -2, 4, -2, 1, -2, 1], [1, 0, 0, 0, -1, 0, 0, 0, 1], [1, 0, 4, 0, 6, 0, 4, 0, 1], [1, -2, 2, 0, -1, 0, 2, -2, 1], [1, 0, 0, 0, 2, 0, 0, 0, 1], [1, 0, -1, 0, 1, 0, 0, 0, 0], [1, -6, 17, -30, 36, -30, 17, -6, 1], [1, 0, 4, 0, 6, 0, 4, 0, 1], [1, 0, 0, 0, 2, 0, 0, 0, 1], [1, 2, 2, 0, -1, 0, 2, 2, 1], [1, 0, 0, 0, -1, 0, 0, 0, 1], [1, 4, 5, 0, -4, 0, 5, 4, 1], [1, 0, 0, 0, -1, 0, 0, 0, 1], [1, 0, 2, 0, 3, 0, 2, 0, 1], [1, 4, 8, 12, 14, 12, 8, 4, 1], [1, 0, 0, 0, -1, 0, 0, 0, 1], [1, 0, 0, 0, -1, 0, 0, 0, 1], [1, 2, 5, 6, 8, 6, 5, 2, 1], [1, 0, -2, 0, 3, 0, -2, 0, 1]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/740/1/bm/a'], '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': '8-740e4-1.1-c0e4-0-0', 'motivic_weight': 0, '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': [0, 0, 0, 0], 'order_of_vanishing': 0, 'prelabel': '8-740e4-1.1-c0e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.6077072562907422, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0e4-0', 'trace_hash': 1279017629530847851, 'z1': {'__RealLiteral__': 0, 'data': '1.15443793449386252972175086115', 'prec': 103}}
• lfunc_instances •

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

  
  {'Lhash': '1463423940587382210973919817998,1830683495484681727962572243754,2016705899928097325163780737189,3240172356747914853638541882749', 'Lhash_array': ['1463423940587382210973919817998', '1830683495484681727962572243754', '2016705899928097325163780737189', '3240172356747914853638541882749'], 'label': '8-740e4-1.1-c0e4-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/740/1/bm/a'}