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lfunc_lfunctions • Show schema
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{'Lhash': '1499213191246093126726595617659', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [1.926576811566759, 0], 'a6': [0, 0], 'a7': [2.6457513110645907, 0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 54.93202129503586, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-2.6457513110645907, 0]]]], 'bad_primes': [2, 3, 7], 'central_character': '2016.1457', 'coefficient_field': 'CDF', 'conductor': 2016, 'conductor_radical': 42, 'conjugate': '843690312629085981316829386097', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.926576811566759, 0], [25.0, 0]], [[1.0, 0], [-2.6457513110645907, 0]], [[1.0, 0], [-14.362373684411796, 0], [121.0, 0]], [[1.0, 0], [0, -0.11163619783838864], [-169.0, 0]], [[1.0, 0], [0, 7.197771813869281], [-289.0, 0]], [[1.0, 0], [0, 22.57838956488404], [-361.0, 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'3.32961780378443521050578365283401', '4.13795689377839041794258731208377', '5.03592670572174150438409948013513', '6.19984708409254176422501877964924', '6.38455953482289760996919593976208', '7.75949528846299791412036061161216', '8.141214415883483684680166660520294', '9.286106684895749128675493110261535'], 'prelabel': '2-2016-24.5-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.411613946707955, 'root_angle': 0.29558941606534456, 'root_number': '0.59893841658321553737617710337476387876602612243835617018 + 0.8007950881098051311738627006097526849761426764328989664*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.14779470803267228', 'prec': 64}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.18267067516567491575820004394', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.96179285653903548976763646667', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.32961780378443521050578365283', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 54.93202129503586, 'bad_primes': [2, 3, 7], 'central_character': '24.5', 'conductor': 2016, 'conductor_radical': 42, 'degree': 2, 'index': 37, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2016/3/n/a/1457/31'], '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': '2-2016-24.5-c2-0-37', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-2016-24.5-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.411613946707955, 'root_angle': 0.14779470803267228, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.18267067516567491575820004394', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1499213191246093126726595617659', 'Lhash_array': ['1499213191246093126726595617659'], 'label': '2-2016-24.5-c2-0-37', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2016/3/n/a/1457/31'}