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lfunc_lfunctions • Show schema
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{'Lhash': '861871203064389085457799927826', 'a10': [2.179994567551564, 0.4976180115768205], 'a2': [-0.14231483827328514, 0.9898214418809327], 'a3': [0.0512012187933495, 1.731293861594292], 'a4': [-0.9594929736144974, -0.28173255684142967], 'a5': [0.1823074034071501, -2.2286237929859185], 'a6': [-1.7209584795748407, -0.19570874170422867], 'a7': [1.9675893702254341, 1.2644929073350988], 'a8': [0.41541501300188644, -0.9096319953545183], 'a9': [-2.994756870388151, 0.1772887116061446], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.50967773946835, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.14231483827328514, -0.9898214418809327]]], [3, [[1.0, 0], [-0.0512012187933495, -1.731293861594292]]], [5, [[1.0, 0], [-0.1823074034071501, 2.2286237929859185]]], [23, [[1.0, 0], [-0.5858114019311697, -4.75991859188447]]]], 'bad_primes': [2, 3, 5, 23], 'central_character': '690.659', 'coefficient_field': 'CDF', 'conductor': 690, 'conductor_radical': 690, 'conjugate': '2234485638148456161303426068512', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.14231483827328514, -0.9898214418809327]], [[1.0, 0], [-0.0512012187933495, -1.731293861594292]], [[1.0, 0], [-0.1823074034071501, 2.2286237929859185]], [[1.0, 0], [-1.9675893702254341, -1.2644929073350988], [2.907905091013205, 6.367423967481629]], [[1.0, 0], [-0.5904765122992969, -4.1068543511855875], [-10.554422709759471, 3.0990581252557265]], [[1.0, 0], [2.6037025651134607, 4.051440273510613], [-5.400395169024524, 11.82521593960874]], [[1.0, 0], [-2.0739681886209502, -7.063286993848624], [-14.30131005813008, 9.190893896745159]], [[1.0, 0], [1.436779148264578, -4.8932204103468395], [-15.983817123792441, -10.272175531656353]], [[1.0, 0], [-0.5858114019311697, -4.75991859188447]], [[1.0, 0], [-0.8922863664625432, -3.0388482916963406], [-24.396352452104253, 15.67858370621233]], [[1.0, 0], [-0.5206822194580083, 1.1401350249926008], [-20.300682752303835, 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[-32.817786027149026, 71.86092763300695]], [[1.0, 0], [12.036669925044055, 10.429833861443413], [11.812131576682667, 82.15517967611741]], [[1.0, 0], [-6.454481876535333, -14.133343871964852], [-58.28260532113037, 67.26171211752899]], [[1.0, 0], [-5.686113560342592, -6.562124861372336], [-13.804539312508659, 96.01267986245047]], [[1.0, 0], [2.8842637926294583, 2.4992288030687875], [14.373798665601798, 99.9719656299742]], [[1.0, 0], [-1.5951010007646895, -11.094171146727172], [-98.82777628229323, 29.01845335466726]], [[1.0, 0], [-10.092528835210246, -4.609103482190911], [70.07009853214551, 80.86520445590564]], [[1.0, 0], [-0.7345772931032657, -2.5017405130996], [-91.69663507859875, 58.929849102660135]], [[1.0, 0], [-8.668215947617567, -1.2463013009284747], [108.4227060184382, 31.835778923081556]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 8, 'label': '2-690-345.314-c1-0-8', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': 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'rational': False, 'root_analytic_conductor': 2.3472702740563025, 'root_angle': -0.836228310063635, 'root_number': '-0.8705369430453261 - 0.49210306927847813*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.418114155032', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.67989649743329645784800154727', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.26478345132948109036012924614', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.99294790671465679869667435390', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.50967773946835, 'bad_primes': [2, 3, 5, 23], 'central_character': '345.314', 'conductor': 690, 'conductor_radical': 690, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/690/2/n/a/659/12'], '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': '2-690-345.314-c1-0-8', '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': '2-690-345.314-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.3472702740563025, 'root_angle': -0.4181141550318175, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.67989649743329645784800154727', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '861871203064389085457799927826', 'Lhash_array': ['861871203064389085457799927826'], 'label': '2-690-345.314-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/690/2/n/a/659/12'}