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lfunc_lfunctions • Show schema
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{'Lhash': '1136972285269708613456154115817', 'a10': [0.0, 0.0], 'a2': [-1.3633282379326837, 0.0], 'a3': [0.0, 0.0], 'a4': [-0.14133611565536414, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-4.141336115655364, 0.0], 'a8': [2.9193439933780447, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 77.2552639555888, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [43, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [3, 5, 43], 'central_character': '9675.1', 'coefficient_field': 'CDF', 'conductor': 9675, 'conductor_radical': 645, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.3633282379326837, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [4.141336115655364, 0], [7.0, 0]], [[1.0, 0], [-1.7780078777226807, 0], [11.0, 0]], [[1.0, 0], [3.0, 0], [13.0, 0]], [[1.0, 0], [-3.1413361156553643, 0], [17.0, 0]], [[1.0, 0], [-2.867992591520731, 0], [19.0, 0]], [[1.0, 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'6.06470790640337593356752631267192', '6.82932042503882766674415601578872', '7.59766238335122171898835970633303'], 'prelabel': '2-9675-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.78949736649308, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.896912986169064803367874093887', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.01918716772857776788422049166', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.98834700022929616800229546205', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 77.2552639555888, 'bad_primes': [3, 5, 43], 'central_character': '1.1', 'conductor': 9675, 'conductor_radical': 645, 'degree': 2, 'index': 151, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9675/2/a/bq/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': '2-9675-1.1-c1-0-151', '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': '2-9675-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.78949736649308, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.896912986169064803367874093887', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1136972285269708613456154115817', 'Lhash_array': ['1136972285269708613456154115817'], 'label': '2-9675-1.1-c1-0-151', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9675/2/a/bq/1/2'}