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lfunc_lfunctions • Show schema
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{'Lhash': '499978996465706018335479911013', 'a10': [43166922325.924095, 0], 'a2': [-1937.9551395599815, 0], 'a3': [0, 0], 'a4': [1658518.1229469478, 0], 'a5': [-22274469.33354983, 0], 'a6': [0, 0], 'a7': [47820541.31785039, 0], 'a8': [850052776.4200836, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 25.15296098583559, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '10.5', 'prec': 14}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]]], 'bad_primes': [3], 'central_character': '9.1', 'coefficient_field': 'CDF', 'conductor': 9, 'conductor_radical': 3, 'degree': 2, 'euler_factors': [[[1.0, 0], [1937.9551395599815, 0], [2097152.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [22274469.33354983, 0], [476837158203125.0, 0]], [[1.0, 0], [-47820541.31785039, 0], [558545864083284030, 0]], [[1.0, 0], [160110646361.6561, 0], [7400249944258161000000, 0]], [[1.0, 0], [786968302363.168, 0], [247064529073450400000000, 0]], [[1.0, 0], [-2974766331727.84, 0], 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'group': 'GL2', 'index': 0, 'label': '2-3e2-1.1-c21-0-0', 'leading_term': '0.271735689594187163203408730296364380693838921807175364', 'load_key': 'CMFs-workshop', 'motivic_weight': 21, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [21], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/9/22/a/e/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.09765625', 'prec': 34}, 'plot_values': [0.27173568959418715, 0.2543845069061342, 0.20287940108168134, 0.1188515754208978, 0.0049729522558891225, -0.1351128098892305, -0.29688463312720964, -0.4750614690073123, -0.66374012858092, -0.8565502526874498, -1.0468227601949556, -1.2277677693346696, -1.3926577313407258, -1.5350113527545712, -1.6487738176062, -1.7284888559662963, -1.769458341803309, -1.7678853393482756, -1.7209968498535806, -1.6271429342390469, -1.4858693941297516, -1.2979617747415073, -1.0654590966822357, -0.7916364170809039, -0.48095604915742873, 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'9.881748268042164303783479361148596', '11.09432143062809884988752872425474', '12.81626208261011362283744084378735', '15.05653681714102024596849310279350', '16.28840568283866407544562494978522'], 'prelabel': '2-3e2-1.1-c21-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.015272772824584, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c21-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.39441388374342991176490321881', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.47909800498750747947282194614', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.75658686997557929485351830652', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 25.15296098583559, 'bad_primes': [3], 'central_character': '1.1', 'conductor': 9, 'conductor_radical': 3, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9/22/a/e/1/1'], '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': '2-3e2-1.1-c21-0-0', 'motivic_weight': 21, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [21], 'order_of_vanishing': 0, 'prelabel': '2-3e2-1.1-c21-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.015272772824584, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c21-0', 'z1': {'__RealLiteral__': 0, 'data': '0.39441388374342991176490321881', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '499978996465706018335479911013', 'Lhash_array': ['499978996465706018335479911013'], 'label': '2-3e2-1.1-c21-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9/22/a/e/1/1'}