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lfunc_lfunctions • Show schema
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{'A10': -2, 'A2': -1, 'A3': 0, 'A4': 1, 'A5': 2, 'A6': 0, 'A7': -1, 'A8': -1, 'A9': 0, 'Lhash': '1349813699144091932', 'a10': [-0.6324555320336759, 0], 'a2': [-0.7071067811865475, 0], 'a3': [0.0, 0], 'a4': [0.5, 0], 'a5': [0.8944271909999159, 0], 'a6': [0.0, 0], 'a7': [-0.3779644730092272, 0], 'a8': [-0.35355339059327373, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 290.76725392029056, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1]], [7, [1, 1]], [17, [1]]], 'bad_primes': [2, 3, 7, 17], 'central_character': '36414.1', 'coefficient_field': '1.1.1.1', 'conductor': 36414, 'conductor_radical': 714, 'degree': 2, 'euler_factors': [[1, 1], [1], [1, -2, 5], [1, 1], [1, 0, 11], [1, 2, 13], [1], [1, -4, 19], [1, 0, 23], [1, 6, 29], [1, 0, 31], [1, -6, 37], [1, 6, 41], [1, 12, 43], [1, 8, 47], [1, -2, 53], [1, 4, 59], [1, 2, 61], [1, -12, 67], [1, 0, 71], [1, 2, 73], [1, -8, 79], [1, 12, 83], [1, 10, 89], [1, -14, 97]], 'gamma_factors': [[], [0]], 'index': 8, 'label': '2-36414-1.1-c1-0-8', 'leading_term': '1.28757809532', 'load_key': 'Cremona', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'EllipticCurve/Q/36414/bh', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [1.287578095318299, 0.8759224515035021, -0.203318669830038, -1.426234106090913, -2.009620838164552, -1.465997952451826, -0.2143244894805078, 0.5416759821312349, -0.09509117454664956, -1.588175120457293, -2.225770374185503, -0.9635637661283925, 0.9882693068873354, 1.042070972626862, -1.747404481856946, -4.860016730605037, -4.477061129224993, 0.1183741047858789, 5.093290999601721, 5.983817804560859, 2.766019864310181, -0.2405301670001759, 0.2038021920798973, 2.41764163847847, 2.604350583575915, 0.332043203356321, -1.093305125248277, 0.2092648068216912, 1.798601668037178, 0.7541110727485786, -1.643371117189355, -1.821719721934519, 0.4036294351916661, 1.398288447284267, -0.6123678807058546, -2.77754828859703, -2.19527472725349, -0.2825288627570064, 0.1053457437108421, -0.5127320831719949, 0.0622719247054922, 0.8950231434249264, -0.6843308516285602, -3.473539135815929, -3.3182112670216, -0.2523484802360713, 0.7811812868770848, -1.751565176297691, -2.737302357104243, 0.9996510553328076, 4.591596064424514, 2.902734498176322, -0.6618319229218784, -0.04974373106972906, 2.806850187168966, 1.677351158450423, -2.296536828362122, -2.218772331109546, 2.116650966190038, 3.555409513646727, 0.2539850019101786, -1.239227055313361, 1.984446032314137, 4.131940174537675, 1.451001046846941, -1.442351822238531, -0.5863847406650884, 0.8044282977035676, -0.2332434923874838, -0.8314213441536779, 0.9270476709005814, 1.693576549133759, -0.1233265694340801, -1.043577041197538, -0.05022355793783974, -0.882794205456103, -3.621269216050821, -3.341087198911338, 0.1544122871480903, 1.377120858278214, -0.1533319504825727, 0.6583373797975028, 3.286918791589309, 2.082767023194361, -1.668870649461917, -1.393721856697573, 1.675839084103248, 1.108365642227279, -1.088456362106824, 1.31454910453637, 4.4367139138885, 0.7881506769626131, -4.556369808675688, -1.945628237350567, 4.273874753088842, 3.30973151031091, -2.422567151294115, -3.153237380068992, 0.08392086088803691, 0.1503112405641104, -1.591938409227475, -0.5308201709915866, 0.6222251286555064, -1.081885917656921, -1.763358034501788, 0.2722235332155404, 0.5941523621315477, -0.9991345954327634, 0.1872489254529115, 2.504622610662089, 0.640983620062559, -2.531039176194538, -1.365976495753232, 0.9657585892671479, -0.2558134087878299, -1.626964713951455, -0.3534713018386952, -0.2974813378267462, -1.772013907482757, -0.4263507123811639, 1.020582374671183], 'positive_zeros': ['0.4594645069333180', '1.545745240165770', '1.981061820445788', '2.864641847387471', '3.368238357968954', '4.244783463156350', '5.214824857605784', '5.472725108529631', '6.284590030031548', '6.724887860070433', '7.325533325167628', '7.957553377478190', '8.444204757369049', '9.309548082574135', '9.542863611500645', '9.986825045332634', '10.43381752536904', '11.27259474059675', '11.60056490325862', '12.19894527318492', '12.93663762004685', '13.25435090213305', '13.85216630146790', '14.38430367973300', '15.01776894565797', '15.37350148420689', '16.09590061999108', '16.57293144737704', '16.96316201080667', '17.38929993229538', '17.98523504520324', '18.52038971119895', '18.60712816785389', '19.48819655476674', '19.96937240612584'], 'prelabel': '2-36414-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 17.05189883620855, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1349813699144091932, 'z1': {'__RealLiteral__': 0, 'data': '0.4594645069333180', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.545745240165770', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.981061820445788', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 290.76725392029056, 'bad_primes': [2, 3, 7, 17], 'central_character': '1.1', 'conductor': 36414, 'conductor_radical': 714, 'degree': 2, 'dirichlet_coefficients': [1, -1, 0, 1, 2, 0, -1, -1, 0, -2, 0, 0, -2, 1, 0, 1, 0, 0, 4, 2, 0, 0, 0, 0, -1, 2, 0, -1, -6, 0, 0, -1, 0, 0, -2, 0, 6, -4, 0, -2, -6, 0, -12, 0, 0, 0, -8, 0, 1, 1, 0, -2, 2, 0, 0, 1, 0, 6, -4, 0, -2, 0, 0, 1, -4, 0, 12, 0, 0, 2, 0, 0, -2, -6, 0, 4, 0, 0, 8, 2, 0, 6, -12, 0, 0, 12, 0, 0, -10, 0, 2, 0, 0, 8, 8, 0, 14, -1, 0, -1], 'euler11': [1, 0, 11], 'euler13': [1, 2, 13], 'euler17': [1, 0, 0], 'euler19': [1, -4, 19], 'euler2': [1, 1, 0], 'euler23': [1, 0, 23], 'euler29': [1, 6, 29], 'euler3': [1, 0, 0], 'euler31': [1, 0, 31], 'euler37': [1, -6, 37], 'euler41': [1, 6, 41], 'euler43': [1, 12, 43], 'euler47': [1, 8, 47], 'euler5': [1, -2, 5], 'euler53': [1, -2, 53], 'euler59': [1, 4, 59], 'euler61': [1, 2, 61], 'euler67': [1, -12, 67], 'euler7': [1, 1, 0], 'euler71': [1, 0, 71], 'euler73': [1, 2, 73], 'euler79': [1, -8, 79], 'euler83': [1, 12, 83], 'euler89': [1, 10, 89], 'euler97': [1, -14, 97], 'euler_factors': [[1, 1, 0], [1, 0, 0], [1, -2, 5], [1, 1, 0], [1, 0, 11], [1, 2, 13], [1, 0, 0], [1, -4, 19], [1, 0, 23], [1, 6, 29], [1, 0, 31], [1, -6, 37], [1, 6, 41], [1, 12, 43], [1, 8, 47], [1, -2, 53], [1, 4, 59], [1, 2, 61], [1, -12, 67], [1, 0, 71], [1, 2, 73], [1, -8, 79], [1, 12, 83], [1, 10, 89], [1, -14, 97]], 'index': 8, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/36414/bh'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-36414-1.1-c1-0-8', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-36414-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 17.05189883620855, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1349813699144091932, 'z1': {'__RealLiteral__': 0, 'data': '0.4594645069333180', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1349813699144091932', 'Lhash_array': ['1349813699144091932'], 'label': '2-36414-1.1-c1-0-8', 'type': 'ECQ', 'url': 'EllipticCurve/Q/36414/bh'}