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lfunc_lfunctions • Show schema
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{'Lhash': '955588034305180631155270484847', 'a10': [0.0, 0.0], 'a2': [1.0, 0.0], 'a3': [0.0, 0.0], 'a4': [1.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-2.353855785430828, 0.0], 'a8': [1.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 68.27209372819476, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 3, 5, 19], 'central_character': '8550.1', 'coefficient_field': 'CDF', 'conductor': 8550, 'conductor_radical': 570, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.353855785430828, 0], [7.0, 0]], [[1.0, 0], [-4.89449284403701, 0], [11.0, 0]], [[1.0, 0], [1.8944928440370095, 0], [13.0, 0]], [[1.0, 0], [2.353855785430828, 0], [17.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [6.167074512255475, 0], [23.0, 0]], [[1.0, 0], 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0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 36, 'label': '2-8550-1.1-c1-0-36', 'leading_term': '3.01302072827021527771013763372', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/8550/2/a/ct/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [3.0130207282702153, 3.000951123346431, 2.9647075233782942, 2.9041939726185015, 2.819277985140741, 2.7098298014487012, 2.575773722209963, 2.417148287410576, 2.234171636155571, 2.0273082103567956, 1.7973330267991914, 1.5453899901289039, 1.2730411010076672, 0.9823038790909073, 0.6756748292827399, 0.35613730374832425, 0.027152634913171513, -0.30736607120444964, -0.6430975879831925, -0.975373279112882, -1.2992539917180692, -1.6096217769591916, -1.9012846160302055, -2.169091880304675, -2.4080578329060884, 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'4.80511196436169623808503704487173', '5.90214766636485015645723240467295', '6.48727385116043342871261755055790', '6.67541649319250616002391150376641', '7.68902480232665659932584010860718'], 'prelabel': '2-8550-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.262692885990303, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.75382604176035207557325065270', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.96213978137447549832411065683', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.75898542819860631250818462158', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 68.27209372819476, 'bad_primes': [2, 3, 5, 19], 'central_character': '1.1', 'conductor': 8550, 'conductor_radical': 570, 'degree': 2, 'index': 36, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8550/2/a/ct/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': '2-8550-1.1-c1-0-36', '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': '2-8550-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.262692885990303, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.75382604176035207557325065270', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '955588034305180631155270484847', 'Lhash_array': ['955588034305180631155270484847'], 'label': '2-8550-1.1-c1-0-36', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8550/2/a/ct/1/1'}