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lfunc_lfunctions • Show schema
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{'Lhash': '830371153801099079275655780185', 'a10': [4.282672231310729, 0.0], 'a2': [-1.3633282379326837, 0.0], 'a3': [-0.3633282379326836, 0.0], 'a4': [-0.14133611565536414, 0.0], 'a5': [-3.1413361156553643, 0.0], 'a6': [0.49533564641195227, 0.0], 'a7': [0.0, 0.0], 'a8': [2.9193439933780447, 0.0], 'a9': [-2.867992591520731, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 47.34330335841716, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [7, 11], 'central_character': '5929.1', 'coefficient_field': 'CDF', 'conductor': 5929, 'conductor_radical': 77, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.3633282379326837, 0], [2.0, 0]], [[1.0, 0], [0.3633282379326836, 0], [3.0, 0]], [[1.0, 0], [3.1413361156553643, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-4.778007877722681, 0], [13.0, 0]], [[1.0, 0], [-4.778007877722681, 0], [17.0, 0]], [[1.0, 0], 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'3.47321808347612200726010995262230', '4.44931249462997610935806203638897', '5.19797355413528827064907491362191', '5.97418502396502564632088931388178', '7.03694123958476851385411642418983', '7.59399629285060307517949035337472', '8.177640581824599414631886228812954'], 'prelabel': '2-77e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.8806470159729285, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.65504734005695103753546160553', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.23799549330227407322031050418', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.03603504392090148691326895857', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 47.34330335841716, 'bad_primes': [7, 11], 'central_character': '1.1', 'conductor': 5929, 'conductor_radical': 77, 'degree': 2, 'index': 91, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5929/2/a/t/1/2'], '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': '2-77e2-1.1-c1-0-91', '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': '2-77e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.8806470159729285, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.65504734005695103753546160553', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '830371153801099079275655780185', 'Lhash_array': ['830371153801099079275655780185'], 'factors': ['2-77e2-1.1-c1-0-91'], 'label': '2-77e2-1.1-c1-0-91', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5929/2/a/t/1/2'}