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lfunc_lfunctions • Show schema
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{'Lhash': '1722182041528160953110020799235', 'a10': 0, 'a2': 0, 'a3': -20, 'a4': 0, 'a5': 74, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 157, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 62.87045736668842, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [7, [1]]], 'bad_primes': [2, 7], 'central_character': '392.1', 'coefficient_field': '1.1.1.1', 'conductor': 392, 'conductor_radical': 14, 'degree': 2, 'euler_factors': [[1], [1, 20, 243], [1, -74, 3125], [1], [1, -124, 161051], [1, 478, 371293], [1, -1198, 1419857], [1, 3044, 2476099], [1, -184, 6436343], [1, 3282, 20511149], [1, -5728, 28629151], [1, -10326, 69343957], [1, -8886, 115856201], [1, 9188, 147008443], [1, 23664, 229345007], [1, -11686, 418195493], [1, 16876, 714924299], [1, -18482, 844596301], [1, 15532, 1350125107], [1, 31960, 1804229351], [1, -4886, 2073071593], [1, -44560, 3077056399], [1, 67364, 3939040643], [1, 71994, 5584059449], [1, 48866, 8587340257], [1, 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 35, 'label': '2-392-1.1-c5-0-35', 'load_key': 'CMFs-workshop', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/392/6/a/b', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [-1.1127286107191163e-60, 0.20959834156422782, 0.4152530431767312, 0.6130805894076007, 0.7993172711706079, 0.9703779683087321, 1.1229135495783356, 1.253866368505885, 1.3605232865160244, 1.4405656018350346, 1.4921152076229374, 1.5137762496865659, 1.5046715073788395, 1.4644726854413108, 1.3934237841178525, 1.2923567141816004, 1.162698346532678, 1.006468236164482, 0.826266340291665, 0.625250162172966, 0.4071008965643589, 0.17597832963734455, -0.06353554574140304, -0.30650400181310294, -0.547713675818066, -0.7817625578301052, -1.0031568317960982, -1.206415234390706, 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'9.455995787613354179364649354084834', '10.11222346291505666033096583388459'], 'prelabel': '2-392-1.1-c5-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.929089315090883, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c5-0', 'trace_hash': 1038264716052794064, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.35856208423527519470182892394', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.57053165742938981066271684668', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.39548302817365484310860293740', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 62.87045736668842, 'bad_primes': [2, 7], 'central_character': '1.1', 'conductor': 392, 'conductor_radical': 14, 'degree': 2, 'dirichlet_coefficients': [1, 0, -20, 0, 74, 0, 0, 0, 157, 0, 124, 0, -478, 0, -1480, 0, 1198, 0, -3044, 0, 0, 0, 184, 0, 2351, 0, 1720, 0, -3282, 0, 5728, 0, -2480, 0, 0, 0, 10326, 0, 9560, 0, 8886, 0, -9188, 0, 11618, 0, -23664, 0, 0, 0, -23960, 0, 11686, 0, 9176, 0, 60880, 0, -16876, 0, 18482, 0, 0, 0, -35372, 0, -15532, 0, -3680, 0, -31960, 0, 4886, 0, -47020, 0, 0, 0, 44560, 0, -72551, 0, -67364, 0, 88652, 0, 65640, 0, -71994, 0, 0, 0, -114560, 0, -225256, 0, -48866, 0, 19468, 0], 'euler11': [1, -124, 161051], 'euler13': [1, 478, 371293], 'euler17': [1, -1198, 1419857], 'euler19': [1, 3044, 2476099], 'euler2': [1, 0, 0], 'euler23': [1, -184, 6436343], 'euler29': [1, 3282, 20511149], 'euler3': [1, 20, 243], 'euler31': [1, -5728, 28629151], 'euler37': [1, -10326, 69343957], 'euler41': [1, -8886, 115856201], 'euler43': [1, 9188, 147008443], 'euler47': [1, 23664, 229345007], 'euler5': [1, -74, 3125], 'euler53': [1, -11686, 418195493], 'euler59': [1, 16876, 714924299], 'euler61': [1, -18482, 844596301], 'euler67': [1, 15532, 1350125107], 'euler7': [1, 0, 0], 'euler71': [1, 31960, 1804229351], 'euler73': [1, -4886, 2073071593], 'euler79': [1, -44560, 3077056399], 'euler83': [1, 67364, 3939040643], 'euler89': [1, 71994, 5584059449], 'euler97': [1, 48866, 8587340257], 'euler_factors': [[1, 0, 0], [1, 20, 243], [1, -74, 3125], [1, 0, 0], [1, -124, 161051], [1, 478, 371293], [1, -1198, 1419857], [1, 3044, 2476099], [1, -184, 6436343], [1, 3282, 20511149], [1, -5728, 28629151], [1, -10326, 69343957], [1, -8886, 115856201], [1, 9188, 147008443], [1, 23664, 229345007], [1, -11686, 418195493], [1, 16876, 714924299], [1, -18482, 844596301], [1, 15532, 1350125107], [1, 31960, 1804229351], [1, -4886, 2073071593], [1, -44560, 3077056399], [1, 67364, 3939040643], [1, 71994, 5584059449], [1, 48866, 8587340257]], 'index': 35, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/392/6/a/b/1/1', 'ModularForm/GL2/Q/holomorphic/392/6/a/b'], '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': '2-392-1.1-c5-0-35', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 1, 'prelabel': '2-392-1.1-c5-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.929089315090883, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c5-0', 'trace_hash': 1038264716052794064, 'z1': {'__RealLiteral__': 0, 'data': '1.35856208423527519470182892394', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20400622
{'Lhash': '1722182041528160953110020799235', 'Lhash_array': ['1722182041528160953110020799235'], 'label': '2-392-1.1-c5-0-35', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/392/6/a/b'}
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id: 24581570
{'Lhash': '1722182041528160953110020799235', 'Lhash_array': ['1722182041528160953110020799235'], 'label': '2-392-1.1-c5-0-35', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/392/6/a/b/1/1'}