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lfunc_lfunctions • Show schema
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{'Lhash': '2383773437734507173620378300705', 'a10': [2.469617434058037, 0.7891682390326951], 'a2': [-1.3471066840724542, -0.430469025282095], 'a3': [-1.469617434058037, 0.9166376587903592], 'a4': [1.629392836545366, 1.159775402487329], 'a5': [-1.8332753175807184, 0.0], 'a6': [2.3743155879653384, -0.6021839326524817], 'a7': [0.0, -1.0], 'a8': [-1.6957185940351687, -2.2637443428628137], 'a9': [1.319550804974658, -2.6942133681449083], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.341486753957511, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.3471066840724542, 0.430469025282095]]], [3, [[1.0, 0], [1.469617434058037, -0.9166376587903592]]], [7, [[1.0, 0], [0, 1.0]]]], 'bad_primes': [2, 3, 7], 'central_character': '168.155', 'coefficient_field': 'CDF', 'conductor': 168, 'conductor_radical': 42, 'conjugate': '543723252453861046134651575694', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.3471066840724542, 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7.734925200527083, 6.320081315309081, 4.049224713196651], 'positive_zeros': ['1.88046567193304654987738991144144', '4.43152898310474941800042136229722', '6.10808917657276020033904666108535', '6.77537249003668918442478652312945', '7.992875918426305277489913942361052', '8.786579797698587278844111419016640', '10.24942362526500631062315558356035', '11.13099111090405994244682963337489', '11.88144525432949124963360231946205', '12.69887492103049170493243577807249'], 'prelabel': '2-168-24.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1582256921505028, 'root_angle': 0.3089198078504553, 'root_number': '-0.36180568539630403 + 0.9322535309747615*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.30891980785', 'prec': 44}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.88046567193304654987738991144', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.43152898310474941800042136230', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.10808917657276020033904666109', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.341486753957511, 'bad_primes': [2, 3, 7], 'central_character': '24.11', 'conductor': 168, 'conductor_radical': 42, 'degree': 2, 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/168/2/j/d/155/1'], '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': '2-168-24.11-c1-0-10', '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': '2-168-24.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1582256921505028, 'root_angle': 0.3089198078504553, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.88046567193304654987738991144', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2383773437734507173620378300705', 'Lhash_array': ['2383773437734507173620378300705'], 'factors': ['2-168-24.11-c1-0-10'], 'label': '2-168-24.11-c1-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/168/2/j/d/155/1'}