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lfunc_lfunctions • Show schema
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{'Lhash': '2006674996131108168823492935465', 'a10': [0.0, 0.0], 'a2': [2.414213562373095, 0.0], 'a3': [2.8284271247461903, 0.0], 'a4': [3.8284271247461903, 0.0], 'a5': [0.0, 0.0], 'a6': [6.82842712474619, 0.0], 'a7': [-2.0, 0.0], 'a8': [4.414213562373095, 0.0], 'a9': [5.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 24.15474661143733, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [5, 11], 'central_character': '3025.1', 'coefficient_field': 'CDF', 'conductor': 3025, 'conductor_radical': 55, 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.414213562373095, 0], [2.0, 0]], [[1.0, 0], [-2.8284271247461903, 0], [3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.0, 0], [7.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.17157287525381, 0], [13.0, 0]], [[1.0, 0], [-6.82842712474619, 0], [17.0, 0]], [[1.0, 0], [0, 0], [19.0, 0]], [[1.0, 0], [-2.8284271247461903, 0], [23.0, 0]], 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'2-55e2-1.1-c1-0-121', 'leading_term': '8.67434051995894157715498772901', '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/3025/2/a/o/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [8.67434051995894, 8.669394252835838, 8.654318821297794, 8.628416269499128, 8.59056234272611, 8.539262375696364, 8.472724638028978, 8.3889469568176, 8.285812096511249, 8.161187434380999, 8.01302483297061, 7.839457161945986, 7.638888547448698, 7.410076037788629, 7.152200912816817, 6.864928305153901, 6.548454144525938, 6.203538698281659, 5.831526186402058, 5.434350124172315, 5.014524213515186, 4.575118782887064, 4.119722977601176, 3.652393133453447, 3.177588027224406, 2.700091984191762, 2.224927127858034, 1.7572563706694375, 1.302279054715044, 0.8651214452444533, 0.45072454382033056, 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'8.543595794065615730625616272980768'], 'prelabel': '2-55e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.914747868552092, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.58298745393235635248050307252', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.78585550565994987651273464998', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.10348990680387451660398411655', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 24.15474661143733, 'bad_primes': [5, 11], 'central_character': '1.1', 'conductor': 3025, 'conductor_radical': 55, 'degree': 2, 'index': 121, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3025/2/a/o/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': '2-55e2-1.1-c1-0-121', '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': '2-55e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.914747868552092, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.58298745393235635248050307252', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2006674996131108168823492935465', 'Lhash_array': ['2006674996131108168823492935465'], 'label': '2-55e2-1.1-c1-0-121', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3025/2/a/o/1/2'}