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lfunc_lfunctions • Show schema
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{'Lhash': '2198902924753626687239859009179', 'a10': [3.449489742783178, 4.656035422675505e-61], 'a2': [0.5, 0.8660254037844386], 'a3': [0.0, 0.0], 'a4': [-0.5, 0.8660254037844386], 'a5': [1.724744871391589, -2.987345747344081], 'a6': [0.0, 0.0], 'a7': [0.5, 0.8660254037844386], 'a8': [-1.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.0183451964044, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.5, -0.8660254037844386]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-0.5, -0.8660254037844386]]]], 'bad_primes': [2, 3, 7], 'central_character': '378.253', 'coefficient_field': 'CDF', 'conductor': 378, 'conductor_radical': 42, 'conjugate': '1829654354720492160131892596977', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.724744871391589, 2.987345747344081], [-2.5, -4.330127018922194]], [[1.0, 0], [-0.5, -0.8660254037844386]], [[1.0, 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'0.9647212338120577 - 0.26327350993242976*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0424010824521', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.73462855171427635585311649090', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.02968964935376171483801971320', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.05339457385563941244863266042', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.0183451964044, 'bad_primes': [2, 3, 7], 'central_character': '9.4', 'conductor': 378, 'conductor_radical': 42, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/378/2/f/d/253/2'], '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': '2-378-9.4-c1-0-3', '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': '2-378-9.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.737338538225754, 'root_angle': -0.04240108245209626, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.73462855171427635585311649090', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2198902924753626687239859009179', 'Lhash_array': ['2198902924753626687239859009179'], 'label': '2-378-9.4-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/378/2/f/d/253/2'}