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lfunc_lfunctions • Show schema
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{'Lhash': '2943832815745767255245067917095', 'a10': [0, 0], 'a2': [0, 0], 'a3': [1.455937842830475, -0.938213727150772], 'a4': [0, 0], 'a5': [-1.8117347388106282, 0], 'a6': [0, 0], 'a7': [-1.6926579420852959, -2.033447587496558], 'a8': [0, 0], 'a9': [1.2395100043717133, -2.7319617400436695], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.048920523745066, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-1.455937842830475, 0.938213727150772]]], [7, [[1.0, 0], [1.6926579420852959, 2.033447587496558]]]], 'bad_primes': [2, 3, 7], 'central_character': '1008.929', 'coefficient_field': 'CDF', 'conductor': 1008, 'conductor_radical': 42, 'conjugate': '249926519424315990813482094017', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.455937842830475, 0.938213727150772]], [[1.0, 0], [1.8117347388106282, 0], [5.0, 0]], [[1.0, 0], [1.6926579420852959, 2.033447587496558]], [[1.0, 0], 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'GL2', 'index': 45, 'label': '2-1008-63.47-c1-0-45', 'leading_term': '0.5222697204064400814171928993564504511173313994365925818', '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/1008/2/df/e/929/20', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [0.52226972040644, 0.6912452725109032, 0.8629035103034709, 1.0377280944062595, 1.2160063840352164, 1.397760624353068, 1.582693728570777, 1.7701515621188717, 1.9591022849961073, 2.1481322829422402, 2.3354575875094605, 2.5189494079327153, 2.696172368049016, 2.8644341372634265, 3.020845261250483, 3.1623880646197557, 3.2859934777850075, 3.3886245255790546, 3.467365016841767, 3.5195117145351236, 3.542667972322498, 3.5348365246856592, 3.4945088412842695, 3.4207482279938977, 3.313263699738814, 3.172471583574323, 2.99954185070287, 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'8.543613726903365723528907353772223', '9.710326781788720361202500775208384', '10.06265727287559176337015087276657'], 'prelabel': '2-1008-63.47-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.837061952750603, 'root_angle': -0.9894882082450013, 'root_number': '-0.999454764935763542349270749981737176942155344893848514692 - 0.0330177656300005007979364413989496854326681457473590985*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.4947441041225007', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.32227461984852601233025477772', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.06919792606697196370684784531', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.14028446059657526276065997259', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.048920523745066, 'bad_primes': [2, 3, 7], 'central_character': '63.47', 'conductor': 1008, 'conductor_radical': 42, 'degree': 2, 'index': 45, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1008/2/df/e/929/20'], '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': '2-1008-63.47-c1-0-45', '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': '2-1008-63.47-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.837061952750603, 'root_angle': -0.49474410412250064, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.32227461984852601233025477772', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2943832815745767255245067917095', 'Lhash_array': ['2943832815745767255245067917095'], 'label': '2-1008-63.47-c1-0-45', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1008/2/df/e/929/20'}