-
lfunc_lfunctions • Show schema
Hide schema
{'A10': 0, 'A2': 0, 'A3': 1, 'A4': 1, 'A5': 0, 'A6': 0, 'A7': -2, 'A8': 0, 'A9': -2, 'Lhash': '1768946312837567941,1966316932625957623', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.5773502691896257, 0], 'a4': [0.5, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [-0.7559289460184544, 0], 'a8': [0.0, 0], 'a9': [-0.6666666666666666, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 20.715905697917382, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 0, -1]], [3, [1, -1, 3]], [5, [1, 0, -1]], [19, [1, -2, 1]]], 'bad_primes': [2, 3, 5, 19], 'central_character': '324900.1', 'coefficient_field': '1.1.1.1', 'conductor': 324900, 'conductor_radical': 570, 'degree': 4, 'euler_factors': [[1, 0, -1], [1, -1, 3], [1, 0, -1], [1, 2, 15, 14, 49], [1, 0, 22, 0, 121], [1, 2, 27, 26, 169], [1, 0, 25, 0, 289], [1, -2, 1], [1, 0, 37, 0, 529], [1, 0, 49, 0, 841], [1, -4, 66, -124, 961], [1, 20, 174, 740, 1369], [1, 0, 46, 0, 1681], [1, -4, 90, -172, 1849], [1, 0, 94, 0, 2209], [1, 0, 97, 0, 2809], [1, 0, 109, 0, 3481], [1, -16, 186, -976, 3721], [1, 14, 183, 938, 4489], [1, 0, -2, 0, 5041], [1, 26, 315, 1898, 5329], [1, -28, 354, -2212, 6241], [1, 0, 130, 0, 6889], [1, 0, 142, 0, 7921], [1, 20, 294, 1940, 9409], [1, 0, 58, 0, 10201], [1, -16, 270, -1648, 10609], [1, 0, -11, 0, 11449], [1, -22, 339, -2398, 11881], [1, 0, 82, 0, 12769]], 'gamma_factors': [[], [0, 0]], 'index': 15, 'label': '4-570e2-1.1-c1e2-0-15', 'load_key': 'Costa', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 1, 'origin': 'EllipticCurve/2.0.3.1/36100.2/i', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.052734375', 'prec': 37}, 'plot_values': [-2.503137999733363e-74, 0.21161468718588317, 0.423807805129264, 0.6370287726565197, 0.8514733077219717, 1.0669674278550239, 1.2828645768698663, 1.497960380731715, 1.710429552599382, 1.9177893812944482, 2.1168939895354195, 2.303963078882009, 2.4746481338186426, 2.624137995986639, 2.7473043175354865, 2.8388856601001375, 2.893706952155026, 2.9069287142208586, 2.8743180048941173, 2.7925305612750453, 2.6593912662851134, 2.474158058393881, 2.237752907416438, 1.9529427170169633, 1.6244531716503448, 1.2589997845906444, 0.865222838360804, 0.45351658752384255, 0.03574798279480625, -0.37513385342583355, -0.7655893470806414, -1.1220659936674175, -1.4316388554186246, -1.6826841971533242, -1.8655503919548906, -1.973185757417506, -2.0016806310691644, -1.9506812455787779, -1.823636184903651, -1.6278425858880827, -1.3742687772497808, -1.0771424553839, -0.7533082575511332, -0.421374920960655, -0.1006890879429179, 0.18981097856570314, 0.432794297050999, 0.6137103560979615, 0.721852018988636, 0.751223020818997, 0.7011308186874209, 0.5764381991062031, 0.3874262605114512, 0.14924641670888458, -0.11903142488857468, -0.39573524358531575, -0.6582001863969668, -0.8845690571140653, -1.0556573972773986, -1.1567393796810799, -1.1791036305513125, -1.121232752698866, -0.9894776203936225, -0.7981273412641381, -0.5688169079465865, -0.3292646407523441, -0.11138715161755375, 0.05110352454606288, 0.1254626204578756, 0.08283236201738998, -0.09891544968632032, -0.4326620953048866, -0.9200914424047756, -1.5505196475853962, -2.3006688470470715, -3.1354802493938654, -4.009979294498173, -4.872114622764656, -5.666401057439672, -6.338112948029345, -6.837706409925465, -7.125104829405688, -7.173467539571925, -6.972080588265278, -6.528061936416868, -5.866658964970695, -5.030028284226701, -4.074517974003314, -3.0666095486779015, -2.077808597166297, -1.1788862134147593, -0.4339558431463959, 0.10508803880260917, 0.4032487282153451, 0.4457586779321657, 0.2397022258021823, -0.18628727355006278, -0.7842996417156509, -1.4912464817979711, -2.2344610619280414, -2.9383150930123803, -3.531249109571627, -3.95254888972276, -4.1582002142180405, -4.125221656614162, -3.854006539279316, -3.368390265645209, -2.7133812690468777, -1.9507312696520773, -1.1527490499414814, -0.3949568513282304, 0.2516725968782401, 0.7280949063051069, 0.9934034069389654, 1.0291872711704249, 0.8415376591887472, 0.46044308008893065, -0.06340639147984849, -0.6641009903499274, -1.2677135050180608, -1.8004505886558027, -2.196856768448382, -2.4071475453872657, -2.4028253503717973, -2.1799090561075394, -1.7593673589263739, -1.1846613532514583, -0.5166370626673951, 0.17367427268234767, 0.8135299743875831, 1.3372349130804586, 1.6941394715424887, 1.8548970444169628, 1.81518883201261, 1.5964126828330523, 1.243191724705292, 0.8179458174839959, 0.3931376479574124, 0.042109229906351714, -0.17037637984872456, -0.1967076409916249, -0.01301128484068309, 0.377125451905124, 0.9423367943123503, 1.6266866860152096, 2.3560799132860453, 3.0471353523470053, 3.6174460311974364, 3.9959447773005503, 4.132047829800197, 4.002373163427916, 3.6141147196083887, 3.004566196644688, 2.2367784329535807, 1.3918405532127454, 0.5587304654758, -0.17697707169227225, -0.7440759327184849, -1.0949092778379763, -1.2115131334283546, -1.107850661774014, -0.8277726647438185, -0.43891038759989004, -0.02326412904263561, 0.3342810873610437, 0.5579703502948755, 0.5920747335574549, 0.40913674478065964, 0.014367348899172842, -0.5544944651249059, -1.2319299210462036, -1.933421820115487, -2.5671128701871635, -3.0467507759681727, -3.3041091537273126, -3.299103691507513, -3.0261077305644726, -2.5154776921011917, -1.8299607982848187, -1.056385054667928, -0.29372173604884455, 0.3608371528607141, 0.8258139872710009, 1.047367783546368, 1.0074185567697227, 0.7266964905061383, 0.26214792936487, -0.3010565999362337, -0.8618661965955303, -1.318328654178747, -1.5830512730407174, -1.596858341721371, -1.33856313628367, -0.829290133260054, -0.13054888432018497, 0.663831489174103, 1.4408797467228829, 2.0849517638015067, 2.49512677228281, 2.600958442907011, 2.3741798616565983, 1.834497025888675, 1.0484358686860007, 0.1212168406144412, -0.817327981272225, -1.6308634185773567, -2.196102568183788, -2.420938899803507, -2.2584414419906347, -1.714552978004334, -0.8482277041971769, 0.23614757040138676, 1.4030494902147803, 2.504804853169168, 3.402501571751441, 3.985725195593545, 4.188157145753587, 3.996661753820834, 3.4524541640711455, 2.6441380473552454, 1.6936494584467208, 0.7372477290808783, -0.09551908558217934, -0.7016068777042098, -1.0199271263544087, -1.0400167157310733, -0.8025378424724354, -0.39150655314875865, 0.08053186660446018, 0.4920198386457471, 0.7334563725380496, 0.7265921527203943, 0.4385882982370663, -0.11124524546975802, -0.8533391449223167, -1.6781987701527512, -2.453617406879503, -3.046054235012878, -3.342738861729951, -3.2708908734356523, -2.810857821004174, -2.000920170667651, -0.932840692169697, 0.2612637119599638, 1.4287219512963951, 2.419656275444308, 3.110133643956996, 3.42136643298459, 3.331816554102046, 2.880192569665602, 2.158810018411897, 1.2983685981253494, 0.44662291510727475, -0.25555387034452554, -0.6967680592399579, -0.8126312407240581, -0.5953204082935669], 'positive_zeros': ['1.48109148596417694739908979766001', '2.33781996488856416573534190523477', '2.82472085926719920887026261705426', '3.51384028187047429851121601779269', '3.66799687366253934383020441612726', '4.83927108424393723147034620441040', '5.04232457297975737403552478087047', '5.83155197036465984734881773824110', '6.16405291198814194603724361929949', '6.73658328391236577993070354478503', '7.28525571954875851977561289073918', '7.43787684836816796966712604055887', '8.212897546680009661007353346285192', '8.598780862883343002846950199438028'], 'prelabel': '4-570e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.133418129484463, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1429420236249831613, 'z1': {'__RealLiteral__': 0, 'data': '1.48109148596417694739908979766001', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.33781996488856416573534190523477', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.82472085926719920887026261705426', 'prec': 113}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 20.715905697917382, 'bad_primes': [2, 3, 5, 19], 'central_character': '1.1', 'conductor': 324900, 'conductor_radical': 570, 'degree': 4, 'dirichlet_coefficients': [1, 0, 1, 1, 0, 0, -2, 0, -2, 0, 0, 1, -2, 0, 0, 1, 0, 0, 2, 0, -2, 0, 0, 0, 1, 0, -5, -2, 0, 0, 4, 0, 0, 0, 0, -2, -20, 0, -2, 0, 0, 0, 4, 0, 0, 0, 0, 1, -11, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 16, 0, 4, 1, 0, 0, -14, 0, 0, 0, 0, 0, -26, 0, 1, 2, 0, 0, 28, 0, 1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 4, 0, 4, 0, 0, 0, -20, 0, 0, 1], 'euler11': [1, 0, 22, 0, 121], 'euler13': [1, 2, 27, 26, 169], 'euler17': [1, 0, 25, 0, 289], 'euler19': [1, -2, 1, 0, 0], 'euler2': [1, 0, -1, 0, 0], 'euler23': [1, 0, 37, 0, 529], 'euler29': [1, 0, 49, 0, 841], 'euler3': [1, -1, 3, 0, 0], 'euler31': [1, -4, 66, -124, 961], 'euler37': [1, 20, 174, 740, 1369], 'euler41': [1, 0, 46, 0, 1681], 'euler43': [1, -4, 90, -172, 1849], 'euler47': [1, 0, 94, 0, 2209], 'euler5': [1, 0, -1, 0, 0], 'euler53': [1, 0, 97, 0, 2809], 'euler59': [1, 0, 109, 0, 3481], 'euler61': [1, -16, 186, -976, 3721], 'euler67': [1, 14, 183, 938, 4489], 'euler7': [1, 2, 15, 14, 49], 'euler71': [1, 0, -2, 0, 5041], 'euler73': [1, 26, 315, 1898, 5329], 'euler79': [1, -28, 354, -2212, 6241], 'euler83': [1, 0, 130, 0, 6889], 'euler89': [1, 0, 142, 0, 7921], 'euler97': [1, 20, 294, 1940, 9409], 'euler_factors': [[1, 0, -1, 0, 0], [1, -1, 3, 0, 0], [1, 0, -1, 0, 0], [1, 2, 15, 14, 49], [1, 0, 22, 0, 121], [1, 2, 27, 26, 169], [1, 0, 25, 0, 289], [1, -2, 1, 0, 0], [1, 0, 37, 0, 529], [1, 0, 49, 0, 841], [1, -4, 66, -124, 961], [1, 20, 174, 740, 1369], [1, 0, 46, 0, 1681], [1, -4, 90, -172, 1849], [1, 0, 94, 0, 2209], [1, 0, 97, 0, 2809], [1, 0, 109, 0, 3481], [1, -16, 186, -976, 3721], [1, 14, 183, 938, 4489], [1, 0, -2, 0, 5041], [1, 26, 315, 1898, 5329], [1, -28, 354, -2212, 6241], [1, 0, 130, 0, 6889], [1, 0, 142, 0, 7921], [1, 20, 294, 1940, 9409]], 'index': 15, 'instance_types': ['ECNF', 'BMF'], 'instance_urls': ['EllipticCurve/2.0.3.1/36100.2/i', 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/36100.2/i'], 'is_instance_Artin': False, 'is_instance_BMF': True, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, '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': '4-570e2-1.1-c1e2-0-15', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 1, 'prelabel': '4-570e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.133418129484463, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1429420236249831613, 'z1': {'__RealLiteral__': 0, 'data': '1.48109148596417694739908979766001', 'prec': 113}}
-
lfunc_instances • Show schema
Hide schema
-
id: 9758586
{'Lhash': '1768946312837567941,1966316932625957623', 'Lhash_array': ['1768946312837567941', '1966316932625957623'], 'label': '4-570e2-1.1-c1e2-0-15', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/36100.2/i'}
-
id: 9758476
{'Lhash': '1768946312837567941,1966316932625957623', 'Lhash_array': ['1768946312837567941', '1966316932625957623'], 'label': '4-570e2-1.1-c1e2-0-15', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.3.1/36100.2/i'}