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lfunc_lfunctions • Show schema
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{'Lhash': '2181539478700804725836193760111', 'a10': [-1.8124077092840754, -0.4295485179093498], 'a2': [2.500784832916083, 0.6961410371453437], 'a3': [0.0, 0.0], 'a4': [4.056978637884795, 2.448399152223369], 'a5': [-0.7169906423592513, 0.02782250218824018], 'a6': [0.0, 0.0], 'a7': [2.728586550861358, 0.4267431493694743], 'a8': [4.878412398584141, 5.1708150535336825], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.821094307351343, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]]], 'bad_primes': [3], 'central_character': '729.685', 'coefficient_field': 'CDF', 'conductor': 729, 'conductor_radical': 3, 'conjugate': '2546186757062945728003878507618', 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.500784832916083, -0.6961410371453437], [1.712333799060533, 1.0333987423037259]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.7169906423592513, -0.02782250218824018], [4.98496470583896, -0.38746210335965475]], 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47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.72093120794329101901604271844', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.69854611214415801265738587109', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.01640884291222921562938627192', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.821094307351343, 'bad_primes': [3], 'central_character': '243.103', 'conductor': 729, 'conductor_radical': 3, 'degree': 2, 'index': 20, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/729/2/i/a/685/25'], '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': '2-3e6-243.103-c1-0-20', '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': '2-3e6-243.103-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': -0.13155939674998757, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.72093120794329101901604271844', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2181539478700804725836193760111', 'Lhash_array': ['2181539478700804725836193760111'], 'label': '2-3e6-243.103-c1-0-20', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/729/2/i/a/685/25'}