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lfunc_lfunctions • Show schema
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{'Lhash': '2620429379803558321127443989484', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.36534102436639504, -0.9308737486442042], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.9555728057861407, 0.2947551744109042], 'a8': [0.0, 0.0], 'a9': [-0.7330518718298263, -0.6801727377709194], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.2934502274282054, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-0.36534102436639504, 0.9308737486442042]]], [7, [[1.0, 0], [-0.9555728057861407, -0.2947551744109042]]]], 'bad_primes': [2, 3, 7], 'central_character': '588.149', 'coefficient_field': 'CDF', 'conductor': 588, 'conductor_radical': 42, 'conjugate': '1973311697239370927808987529373', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.36534102436639504, 0.9308737486442042]], [[1.0, 0], [0, 0], [-0.9555728057861407, 0.2947551744109042]], [[1.0, 0], [-0.9555728057861407, 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[[1.0, 0], [1.4888308262251286, -1.0150676699606132], [0.36534102436639504, -0.9308737486442042]], [[1.0, 0], [-0.9888308262251285, -1.7127052311122342], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [-0.6234898018587335, 0.7818314824680298]], [[1.0, 0], [-0.14282009041008062, 0.04405416353761935], [0.8262387743159949, -0.5633200580636221]], [[1.0, 0], [0.8262387743159949, -1.4310875362987383], [-0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [0.9009688679024191, 0.4338837391175581]], [[1.0, 0], [0, 0], [-0.07473009358642425, -0.9972037971811801]], [[1.0, 0], [0.4450418679126288, 0], [1.0, 0]], [[1.0, 0], [0, 0], [0.7330518718298263, 0.6801727377709194]], [[1.0, 0], [-1.4497285761747285, 0.2185114244044078], [0.9555728057861407, -0.2947551744109042]], [[1.0, 0], [0, 0], [-0.07473009358642425, -0.9972037971811801]], [[1.0, 0], [-1.4497285761747285, 1.3451515405316519], [0.07473009358642425, -0.9972037971811801]], [[1.0, 0], [0, 0], [0.9009688679024191, 0.4338837391175581]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-588-147.2-c0-0-0', 'leading_term': '1.0587458021175105327337862508351', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/588/1/z/a/149/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [1.0587458021175105, 1.0861198774239336, 1.1284379542511347, 1.1851673507240132, 1.254998683155495, 1.3360830425972279, 1.4262573251549533, 1.5232103008000866, 1.6245816089695482, 1.7280084523835813, 1.8311404336196662, 1.931639722671701, 2.0271781297491263, 2.1154377778782707, 2.194118689740885, 2.2609545205623274, 2.3137364668686184, 2.3503447058610796, 2.368786335243266, 2.3672385483865312, 2.3440956188847886, 2.298018144720363, 2.2279829003537737, 2.133331561975303, 2.0138165100798604, 1.8696418805996178, 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'8.760332554025244268183448785120875', '9.014108037172229645821252531473391', '10.29958024115877648227223473392924', '10.93457115634280473634913611373011'], 'prelabel': '2-588-147.2-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5417104645732861, 'root_angle': 0.272108843537415, 'root_number': '0.65632780710351820757022637180935 + 0.75447585092081442621596822944542*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.1360544217687075', 'prec': 60}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.06715429261956956760919668483', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.41845638561531586576518534399', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.65024968572362047871172068240', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.2934502274282054, 'bad_primes': [2, 3, 7], 'central_character': '147.2', 'conductor': 588, 'conductor_radical': 42, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/588/1/z/a/149/1'], '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': '2-588-147.2-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-588-147.2-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5417104645732861, 'root_angle': 0.1360544217687075, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.06715429261956956760919668483', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2620429379803558321127443989484', 'Lhash_array': ['2620429379803558321127443989484'], 'label': '2-588-147.2-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/588/1/z/a/149/1'}