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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -1, 'A4': 0, 'A5': -2, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 1, 'Lhash': '1763940431118584662', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [-0.8944271909999159, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 1727.8349390972744, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [7, [1]], [23, [1, -1]]], 'bad_primes': [2, 3, 7, 23], 'central_character': '216384.1', 'coefficient_field': '1.1.1.1', 'conductor': 216384, 'conductor_radical': 966, 'degree': 2, 'euler_factors': [[1], [1, 1], [1, 2, 5], [1], [1, 1, 11], [1, 0, 13], [1, 6, 17], [1, -1, 19], [1, -1], [1, -4, 29], [1, -10, 31], [1, -4, 37], [1, -3, 41], [1, 12, 43], [1, -3, 47], [1, -3, 53], [1, -15, 59], [1, -3, 61], [1, 4, 67], [1, 6, 71], [1, -10, 73], [1, -10, 79], [1, 0, 83], [1, 12, 89], [1, -2, 97]], 'gamma_factors': [[], [0]], 'index': 127, 'label': '2-216384-1.1-c1-0-127', 'leading_term': '4.52855861965', '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': 1, 'origin': 'EllipticCurve/Q/216384/u', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 0.928119027321403, 0.81169741889274, -0.4589835272969899, -1.499539643925283, -0.4731505000964349, 2.535168876888575, 4.750927546528275, 3.605219743434524, 0.3621084207789929, -0.8631245430409632, 1.483512527885723, 3.868826300266784, 2.488092292105391, -1.063692924948325, -2.133573675065138, -0.1534614395074101, 0.8736409415599398, -0.5849828886293708, -1.200814041680229, 0.586452110329746, 1.065946972052925, -1.945979224656429, -4.224189853084326, -2.118345913119265, 0.8041487728366636, 0.2204313088031194, -1.167401750327246, 0.4829012755486098, 2.083296972125663, -0.2380206696376104, 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2.998702301983224, -0.4446113750762297, -3.792359643777227, -0.2943661316437528, 1.289673100657729, -2.807354195546141, -2.523076465227525, 1.933844739218898, 1.225552371208738, -1.15979689975849, 0.6679128045198058, 0.9477817644347517, -1.549441314265563, -0.7798721459578409, 0.5788609672300598, -0.5659841972912296, 1.089710953596102, 3.467349599612986, 0.4427779491219318, -1.323666791472941, 1.368431472264121, -1.547328377125884, -7.126927365714722, -2.3682804818493, 5.29274997882802, 3.192682110145338, -0.7568976442876938, 0.2340925834198678, -0.1552599006974202, -0.4811885661571423, 2.99514563096015, 2.821871783838327, -1.409555723689471, -1.310430696057732, 0.2790114080208136, -0.2274390928933223, 2.792025944144426, 5.535134126955984, 1.338376215084442, -0.876074307230909, 2.439452563560984], 'positive_zeros': ['0.6728720382980502', '1.297427752918586', '2.283026556035684', '2.625978691569099', '3.420250774743131', '4.017646067891043', '4.419426653586319', '4.929750313897650', '5.363264365181217', '6.155446628563321', '6.527818707242059', '6.953466269306931', '7.483281823256242', '8.123791869603033', '8.359538237188636', '8.907061636372781', '9.539919534237457', '10.13795475535970', '10.34387771566899', '11.12149967782741', '11.34891355634758', '11.81365655511354', '12.10185645291850', '12.75142374307582', '13.19002196504679', '13.59214421004826', '13.99744562584515', '14.74222655875117', '15.21621632213012', '15.46518275167526', '15.89288126367839', '16.27283736244317', '16.76442451662537', '17.29478017383852', '17.66045816355087', '18.21880461542377', '18.29491381073108', '19.17335322173493', '19.40782722992597', '19.69899084144041'], 'prelabel': '2-216384-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 41.567233960143106, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1763940431118584662, 'z1': {'__RealLiteral__': 0, 'data': '0.6728720382980502', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.297427752918586', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.283026556035684', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1727.8349390972744, 'bad_primes': [2, 3, 7, 23], 'central_character': '1.1', 'conductor': 216384, 'conductor_radical': 966, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, -2, 0, 0, 0, 1, 0, -1, 0, 0, 0, 2, 0, -6, 0, 1, 0, 0, 0, 1, 0, -1, 0, -1, 0, 4, 0, 10, 0, 1, 0, 0, 0, 4, 0, 0, 0, 3, 0, -12, 0, -2, 0, 3, 0, 0, 0, 6, 0, 3, 0, 2, 0, -1, 0, 15, 0, 3, 0, 0, 0, 0, 0, -4, 0, -1, 0, -6, 0, 10, 0, 1, 0, 0, 0, 10, 0, 1, 0, 0, 0, 12, 0, -4, 0, -12, 0, 0, 0, -10, 0, -2, 0, 2, 0, -1, 0], 'euler11': [1, 1, 11], 'euler13': [1, 0, 13], 'euler17': [1, 6, 17], 'euler19': [1, -1, 19], 'euler2': [1, 0, 0], 'euler23': [1, -1, 0], 'euler29': [1, -4, 29], 'euler3': [1, 1, 0], 'euler31': [1, -10, 31], 'euler37': [1, -4, 37], 'euler41': [1, -3, 41], 'euler43': [1, 12, 43], 'euler47': [1, -3, 47], 'euler5': [1, 2, 5], 'euler53': [1, -3, 53], 'euler59': [1, -15, 59], 'euler61': [1, -3, 61], 'euler67': [1, 4, 67], 'euler7': [1, 0, 0], 'euler71': [1, 6, 71], 'euler73': [1, -10, 73], 'euler79': [1, -10, 79], 'euler83': [1, 0, 83], 'euler89': [1, 12, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 2, 5], [1, 0, 0], [1, 1, 11], [1, 0, 13], [1, 6, 17], [1, -1, 19], [1, -1, 0], [1, -4, 29], [1, -10, 31], [1, -4, 37], [1, -3, 41], [1, 12, 43], [1, -3, 47], [1, -3, 53], [1, -15, 59], [1, -3, 61], [1, 4, 67], [1, 6, 71], [1, -10, 73], [1, -10, 79], [1, 0, 83], [1, 12, 89], [1, -2, 97]], 'index': 127, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/216384/u'], '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': '2-216384-1.1-c1-0-127', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-216384-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 41.567233960143106, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1763940431118584662, 'z1': {'__RealLiteral__': 0, 'data': '0.6728720382980502', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1763940431118584662', 'Lhash_array': ['1763940431118584662'], 'label': '2-216384-1.1-c1-0-127', 'type': 'ECQ', 'url': 'EllipticCurve/Q/216384/u'}