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lfunc_lfunctions • Show schema
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{'Lhash': '512175615490409201904673301093', 'a10': [0.0, 0.0], 'a2': [-0.7922869913932613, 0.0], 'a3': [0.0, 0.0], 'a4': [-1.3722813232690143, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-3.4641016151377544, 0.0], 'a8': [2.6718146237444933, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 16.169706409309285, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '2025.1', 'coefficient_field': 'CDF', 'conductor': 2025, 'conductor_radical': 15, 'degree': 2, 'euler_factors': [[[1.0, 0], [0.7922869913932613, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [3.4641016151377544, 0], [7.0, 0]], [[1.0, 0], [4.372281323269014, 0], [11.0, 0]], [[1.0, 0], [5.840962589317538, 0], [13.0, 0]], [[1.0, 0], [0.7922869913932613, 0], [17.0, 0]], [[1.0, 0], [0.3722813232690143, 0], [19.0, 0]], [[1.0, 0], 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'5.08624936394520101909453912558653', '5.95199138279401374934314039356234', '7.02653141153192896595670319299505', '7.69134044935546024078864542740922', '8.344087891451294784128114595166909', '9.474182876071039092353083807119861'], 'prelabel': '2-45e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.021157346997166, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.40403531966789307930224693327', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.26565737197796142338681266266', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.15572607210087292342372784192', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 16.169706409309285, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 2025, 'conductor_radical': 15, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2025/2/a/w/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': '2-45e2-1.1-c1-0-0', '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': '2-45e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.021157346997166, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.40403531966789307930224693327', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '512175615490409201904673301093', 'Lhash_array': ['512175615490409201904673301093'], 'label': '2-45e2-1.1-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2025/2/a/w/1/2'}