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lfunc_lfunctions • Show schema
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{'Lhash': '592658847336622662244995551691', 'a10': [0, 0], 'a2': [0, -2.0], 'a3': [0, 0], 'a4': [-4.0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [0, -14.0], 'a8': [0, 8.0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 26.55085950258329, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 2.0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '450.199', 'coefficient_field': 'CDF', 'conductor': 450, 'conductor_radical': 30, 'conjugate': '1520573813272430767998421200167', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 2.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 14.0], [-343.0, 0]], [[1.0, 0], [6.0, 0], [1331.0, 0]], [[1.0, 0], [0, -68.0], [-2197.0, 0]], [[1.0, 0], [0, -78.0], [-4913.0, 0]], [[1.0, 0], [44.0, 0], [6859.0, 0]], [[1.0, 0], [0, 120.0], [-12167.0, 0]], [[1.0, 0], [-126.0, 0], [24389.0, 0]], [[1.0, 0], [244.0, 0], [29791.0, 0]], 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'2-450-5.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.1527526141455, 'root_angle': -0.14758361765043326, 'root_number': '0.8944271909999158785636694674925104941762473438446102897 - 0.4472135954999579392818347337462552470881236719223051449*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.07379180882521663', 'prec': 67}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.46752539479720959482519751673', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.44919589353584210765304264684', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.74001390302376578162910707036', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 26.55085950258329, 'bad_primes': [2, 3, 5], 'central_character': '5.4', 'conductor': 450, 'conductor_radical': 30, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/450/4/c/f/199/1'], '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': '2-450-5.4-c3-0-5', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-450-5.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.1527526141455, 'root_angle': -0.07379180882521663, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.46752539479720959482519751673', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '592658847336622662244995551691', 'Lhash_array': ['592658847336622662244995551691'], 'label': '2-450-5.4-c3-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/450/4/c/f/199/1'}