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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 1, 'A3': 1, 'A4': 1, 'A5': 0, 'A6': 1, 'A7': -1, 'A8': 1, 'A9': 1, 'Lhash': '1666048173385791317', 'a10': [0.0, 0], 'a2': [0.7071067811865475, 0], 'a3': [0.5773502691896258, 0], 'a4': [0.5, 0], 'a5': [0.0, 0], 'a6': [0.4082482904638631, 0], 'a7': [-0.3779644730092272, 0], 'a8': [0.35355339059327373, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 192.83872088139222, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1, -1]], [5, [1]], [7, [1, 1]], [23, [1, -1]]], 'bad_primes': [2, 3, 5, 7, 23], 'central_character': '24150.1', 'coefficient_field': '1.1.1.1', 'conductor': 24150, 'conductor_radical': 4830, 'degree': 2, 'euler_factors': [[1, -1], [1, -1], [1], [1, 1], [1, 1, 11], [1, -2, 13], [1, -6, 17], [1, -5, 19], [1, -1], [1, -8, 29], [1, -4, 31], [1, -6, 37], [1, 11, 41], [1, -2, 43], [1, -3, 47], [1, 9, 53], [1, 4, 59], [1, -10, 61], [1, 6, 67], [1, 6, 71], [1, -2, 73], [1, 2, 79], [1, -4, 83], [1, -6, 89], [1, 17, 97]], 'gamma_factors': [[], [0]], 'index': 34, 'label': '2-24150-1.1-c1-0-34', 'leading_term': '5.60337669895', '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/24150/ch', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [5.603376698947948, 5.027440574104842, 3.38388499713352, 1.105992715078897, -0.8631442789428058, -1.457777589100334, -0.3061171401651577, 1.756258642486631, 3.14839390586438, 2.816356757642034, 1.206984427754321, -0.1416264015009308, -0.1741364834396475, 0.5532523661547428, 0.5647865803867379, -0.6488150661471832, -1.800105273457576, -1.288013373102514, 0.626066059298159, 1.817079253105822, 0.8607034296399405, -0.9620528544649989, -1.112425205042177, 0.8226825295351944, 2.339828216832153, 1.302448763214601, -0.9298125621629298, -1.116811992305231, 1.31752161062223, 3.224339563439172, 2.103398238626197, -0.1545757741437815, 0.05943870098531751, 2.479206532752892, 2.91149982987953, -0.53642538515789, -4.040097380068635, -3.140908475516694, 0.751937428004386, 2.363813193598537, 0.4013904498608772, -0.7148367425798093, 1.904775116055229, 4.681497337854663, 2.94879703277111, -1.639480225823088, -3.443372259751622, -1.260665082590929, 0.482884946304595, -0.7855403883068953, -2.116712854583888, -0.7022235930617978, 1.327428385439704, 0.9557129660834222, -0.5128283993238176, -0.2869943986154017, 0.6947114984159543, -0.06654191102106984, -1.375397569892233, -0.3413905868765576, 1.800289701538574, 1.412540361586275, -0.8148727828520541, -0.9404483251722296, 0.6830423785121484, -0.108137291012314, -2.60657342169703, -1.062098774057719, 4.497572282595861, 5.926199984043392, -0.1326401153271743, -5.461135277164775, -2.759678725636116, 2.877901388849358, 3.010030245492706, -0.5234273161637155, -0.5872680563919922, 2.127078932747885, 1.584167694795348, -1.732421218461942, -2.158156208582023, 0.3520396531070606, 0.9734921453774454, -0.3108847283165653, 0.4234536971607585, 2.311004403596279, 1.427302322851204, -0.6897343862024397, 0.2678558518623014, 2.456407682070239, 1.158080850609377, -1.784070991729882, -1.416492875028715, 0.7763435381645329, 0.4980686972356486, -0.2603528249440095, 2.279888844098311, 4.833338099526809, 2.795780011113275, -0.5427800139554452, -0.3124025364929769, 0.9067259218775247, -0.2412888363143281, -0.264341218037772, 2.865857577566253, 3.458193007251563, -0.7677040413968174, -2.693257678082686, 0.2808104279528715, -0.1940049055925073, -7.000882685107201, -9.975629429301893, -4.057031759334, 1.182431850471136, -0.7071121589697125, -2.591207807427443, 0.4354640063928409, 1.933618663908235, -1.480712789269805, -3.278065428633882, -0.5906118884843903], 'positive_zeros': ['0.8762690625688995', '1.539967017773856', '2.708973426093632', '3.065251312333451', '3.637697387034054', '4.423066374409473', '5.110660265843075', '5.659392844841057', '6.387942389455786', '6.883106640040863', '7.725570267142127', '7.991696029777103', '8.719707465347674', '9.450204434807167', '10.04282758056863', '10.35474540492147', '11.15845611209504', '11.87972704160650', '12.14726652401371', '12.82181637234835', '13.39654337004202', '13.81061913696558', '14.23946857452361', '14.78687974399123', '15.40259356323090', '15.88559658942813', '16.23873898553120', '16.80349459979629', '17.49565269204059', '18.11037965472215', '18.70594830242219', '19.05591408976148', '19.61818927708697'], 'prelabel': '2-24150-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 13.886638213815186, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1666048173385791317, 'z1': {'__RealLiteral__': 0, 'data': '0.8762690625688995', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.539967017773856', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.708973426093632', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 192.83872088139222, 'bad_primes': [2, 3, 5, 7, 23], 'central_character': '1.1', 'conductor': 24150, 'conductor_radical': 4830, 'degree': 2, 'dirichlet_coefficients': [1, 1, 1, 1, 0, 1, -1, 1, 1, 0, -1, 1, 2, -1, 0, 1, 6, 1, 5, 0, -1, -1, 1, 1, 0, 2, 1, -1, 8, 0, 4, 1, -1, 6, 0, 1, 6, 5, 2, 0, -11, -1, 2, -1, 0, 1, 3, 1, 1, 0, 6, 2, -9, 1, 0, -1, 5, 8, -4, 0, 10, 4, -1, 1, 0, -1, -6, 6, 1, 0, -6, 1, 2, 6, 0, 5, 1, 2, -2, 0, 1, -11, 4, -1, 0, 2, 8, -1, 6, 0, -2, 1, 4, 3, 0, 1, -17, 1, -1, 0], 'euler11': [1, 1, 11], 'euler13': [1, -2, 13], 'euler17': [1, -6, 17], 'euler19': [1, -5, 19], 'euler2': [1, -1, 0], 'euler23': [1, -1, 0], 'euler29': [1, -8, 29], 'euler3': [1, -1, 0], 'euler31': [1, -4, 31], 'euler37': [1, -6, 37], 'euler41': [1, 11, 41], 'euler43': [1, -2, 43], 'euler47': [1, -3, 47], 'euler5': [1, 0, 0], 'euler53': [1, 9, 53], 'euler59': [1, 4, 59], 'euler61': [1, -10, 61], 'euler67': [1, 6, 67], 'euler7': [1, 1, 0], 'euler71': [1, 6, 71], 'euler73': [1, -2, 73], 'euler79': [1, 2, 79], 'euler83': [1, -4, 83], 'euler89': [1, -6, 89], 'euler97': [1, 17, 97], 'euler_factors': [[1, -1, 0], [1, -1, 0], [1, 0, 0], [1, 1, 0], [1, 1, 11], [1, -2, 13], [1, -6, 17], [1, -5, 19], [1, -1, 0], [1, -8, 29], [1, -4, 31], [1, -6, 37], [1, 11, 41], [1, -2, 43], [1, -3, 47], [1, 9, 53], [1, 4, 59], [1, -10, 61], [1, 6, 67], [1, 6, 71], [1, -2, 73], [1, 2, 79], [1, -4, 83], [1, -6, 89], [1, 17, 97]], 'index': 34, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/24150/ch'], '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': '2-24150-1.1-c1-0-34', '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': '2-24150-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 13.886638213815186, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1666048173385791317, 'z1': {'__RealLiteral__': 0, 'data': '0.8762690625688995', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1666048173385791317', 'Lhash_array': ['1666048173385791317'], 'label': '2-24150-1.1-c1-0-34', 'type': 'ECQ', 'url': 'EllipticCurve/Q/24150/ch'}