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lfunc_lfunctions • Show schema
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{'Lhash': '1032543601100871719563455525492', 'a10': [-304.06399181009647, 0.0], 'a2': [-8.446221994724903, 0.0], 'a3': [-9.0, 0.0], 'a4': [39.3386659841747, 0.0], 'a5': [36.0, 0.0], 'a6': [76.01599795252412, 0.0], 'a7': [0.0, 0.0], 'a8': [-61.98400204747588, 0.0], 'a9': [81.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 23.57642151250816, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [9.0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 7], 'central_character': '147.1', 'coefficient_field': 'CDF', 'conductor': 147, 'conductor_radical': 21, 'degree': 2, 'euler_factors': [[[1.0, 0], [8.446221994724903, 0], [32.0, 0]], [[1.0, 0], [9.0, 0]], [[1.0, 0], [-36.0, 0], [3125.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-295.5697759577992, 0], [161051.0, 0]], [[1.0, 0], [-1148.127983620193, 0], [371293.0, 0]], [[1.0, 0], [1032.3839508605788, 0], [1419857.0, 0]], [[1.0, 0], [2108.5119344807717, 0], [2476099.0, 0]], 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['0.814533279844596986429365072054226', '1.95607142238872516671517008718025', '4.21902896428097380529159442164194', '6.10798913122270606452282899625244', '6.72840305859930952293190095178648', '8.350334454298132775655542657808180', '8.953705187776048323470145902574630', '10.11836501561123996283428693267260', '10.83297079356045490295806825366572', '11.67161402015328850697049868118103'], 'prelabel': '2-147-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.855555736731704, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.814533279844596986429365072054', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.95607142238872516671517008718', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.21902896428097380529159442164', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 23.57642151250816, 'bad_primes': [3, 7], 'central_character': '1.1', 'conductor': 147, 'conductor_radical': 21, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/147/6/a/h/1/1'], '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': '2-147-1.1-c5-0-6', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-147-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.855555736731704, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '0.814533279844596986429365072054', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1032543601100871719563455525492', 'Lhash_array': ['1032543601100871719563455525492'], 'label': '2-147-1.1-c5-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/147/6/a/h/1/1'}