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lfunc_lfunctions • Show schema
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{'Lhash': '2326960926712985538068007245792', 'a10': [0.5, 0.8660254037844386], 'a2': [-0.5, -0.8660254037844386], 'a3': [-0.5705872705100166, -1.635368510988251], 'a4': [-0.5, 0.8660254037844386], 'a5': [-1.0, 0.0], 'a6': [-1.130977039809948, 1.3118273268318232], 'a7': [2.257294542702408, -1.3800801960342477], 'a8': [1.0, 0.0], 'a9': [-2.3488603334638585, 1.8662409099256323], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.030575327340666, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.5, 0.8660254037844386]]], [3, [[1.0, 0], [0.5705872705100166, 1.635368510988251]]], [5, [[1.0, 0], [1.0, 0]]], [7, [[1.0, 0], [-2.257294542702408, 1.3800801960342477]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '630.331', 'coefficient_field': 'CDF', 'conductor': 630, 'conductor_radical': 210, 'conjugate': '724610192480347107131880866127', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], 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'5.73615171877442460080243329924341', '6.37257547253789021653837042028587', '7.62825398219148299453764288600995', '8.494272790293790469899721653701906', '9.364613986321343314077217045318378', '9.810696917747779629672434492121956', '11.09679467601640865522638211426144'], 'prelabel': '2-630-63.16-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2428944084242275, 'root_angle': 0.9803310698262121, 'root_number': '-0.9980914961676854 + 0.061752451593042955*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.490165534913', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.83564850306073028234762608199', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.06507221470593947215057963618', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.32208200425616308402086486216', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.030575327340666, 'bad_primes': [2, 3, 5, 7], 'central_character': '63.16', 'conductor': 630, 'conductor_radical': 210, 'degree': 2, 'index': 26, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/630/2/l/f/331/4'], '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': '2-630-63.16-c1-0-26', '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': '2-630-63.16-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2428944084242275, 'root_angle': 0.49016553491310605, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.83564850306073028234762608199', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2326960926712985538068007245792', 'Lhash_array': ['2326960926712985538068007245792'], 'label': '2-630-63.16-c1-0-26', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/630/2/l/f/331/4'}