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lfunc_lfunctions • Show schema
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{'Lhash': '945147954829945992478676771222', 'a10': [3.2471868405208952, 1.8747641964837491], 'a2': [0.25881904510252074, -0.9659258262890683], 'a3': [-1.5307114669181505, -0.8105074984509912], 'a4': [-0.8660254037844386, -0.5], 'a5': [-0.9704493582526371, 3.621766311171453], 'a6': [-1.179067405349994, 1.268778961695548], 'a7': [2.296795397123901, 2.296795397123901], 'a8': [-0.7071067811865476, 0.7071067811865476], 'a9': [1.6861551899094327, 2.481306243804155], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.868499407297962, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.25881904510252074, 0.9659258262890683]]], [3, [[1.0, 0], [1.5307114669181505, 0.8105074984509912]]], [13, [[1.0, 0], [3.264120652215265, 1.5315078738882777]]]], 'bad_primes': [2, 3, 13], 'central_character': '234.227', 'coefficient_field': 'CDF', 'conductor': 234, 'conductor_radical': 78, 'conjugate': '2608691695878447456537099867669', 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[53.5, 92.66471820493493]], [[1.0, 0], [0.9230718306371517, -0.9230718306371517], [0, -109.0]], [[1.0, 0], [-10.019349904291655, -5.784674364347838], [56.5, 97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-234-117.110-c1-0-1', '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/234/2/z/a/227/9', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.8322585430163166, 0.7393709095732363, 0.6374034154140633, 0.5195209082965203, 0.37790166765727257, 0.20449941306653963, -0.008251097163079129, -0.2668052173958031, -0.5759351114308167, -0.938188898127563, -1.3533796167971996, -1.8181263468229127, -2.3254897065043587, -2.8647556736252304, -3.4214249033746027, -3.9774598138047996, -4.511829030251206, -5.001368797988547, -5.4219545477212705, 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'5.30811500796894446661582709340837', '7.26248647746236258255433848749521', '7.80798372938560600837692037252982', '9.222755105277459584260203440068898', '9.912782656054874433429330366167250', '11.44733082099355310536843325734165', '11.95779340420232499485124719876635'], 'prelabel': '2-234-117.110-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3669306519710362, 'root_angle': -0.11624912565789162, 'root_number': '0.7448977218513166 - 0.667178674704699*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.116249125658', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.74559027121493917260602139422', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.06883363584553074411071308856', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.02209291776911377597755338632', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.868499407297962, 'bad_primes': [2, 3, 13], 'central_character': '117.110', 'conductor': 234, 'conductor_radical': 78, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/234/2/z/a/227/9'], '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': '2-234-117.110-c1-0-1', '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': '2-234-117.110-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3669306519710362, 'root_angle': -0.11624912565789162, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.74559027121493917260602139422', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '945147954829945992478676771222', 'Lhash_array': ['945147954829945992478676771222'], 'factors': ['2-234-117.110-c1-0-1'], 'label': '2-234-117.110-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/234/2/z/a/227/9'}