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lfunc_lfunctions • Show schema
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{'Lhash': '3287470006976601040582733719015', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': -1, 'a6': 0, 'a7': -2, 'a8': 0, 'a9': -3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.034315276808656, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1, 1]], [19, [1, -1]]], 'bad_primes': [2, 5, 19], 'central_character': '380.1', 'coefficient_field': '1.1.1.1', 'conductor': 380, 'conductor_radical': 190, 'degree': 2, 'euler_factors': [[1], [1, 0, 3], [1, 1], [1, 2, 7], [1, 4, 11], [1, 4, 13], [1, -6, 17], [1, -1], [1, 2, 23], [1, 6, 29], [1, 8, 31], [1, -4, 37], [1, -6, 41], [1, 6, 43], [1, -6, 47], [1, -8, 53], [1, 12, 59], [1, -6, 61], [1, 0, 67], [1, 0, 71], [1, 10, 73], [1, 8, 79], [1, -14, 83], [1, -14, 89], [1, -16, 97], [1, 14, 101], [1, 20, 103], [1, 4, 107], [1, 2, 109], [1, 0, 113]], 'euler_factors_factorization': [[1], [[[1, 0, 3], 1]], [[[1, 1], 1]], [[[1, 2, 7], 1]], [[[1, 4, 11], 1]], [[[1, 4, 13], 1]], [[[1, -6, 17], 1]], [[[1, -1], 1]], [[[1, 2, 23], 1]], [[[1, 6, 29], 1]], [[[1, 8, 31], 1]], [[[1, -4, 37], 1]], [[[1, -6, 41], 1]], [[[1, 6, 43], 1]], [[[1, -6, 47], 1]], [[[1, -8, 53], 1]], [[[1, 12, 59], 1]], [[[1, -6, 61], 1]], [[[1, 0, 67], 1]], [[[1, 0, 71], 1]], [[[1, 10, 73], 1]], [[[1, 8, 79], 1]], [[[1, -14, 83], 1]], [[[1, -14, 89], 1]], [[[1, -16, 97], 1]], [[[1, 14, 101], 1]], [[[1, 20, 103], 1]], [[[1, 4, 107], 1]], [[[1, 2, 109], 1]], [[[1, 0, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 5, 'label': '2-380-1.1-c1-0-5', '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': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/380/2/a/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [-3.239416239728025e-120, 0.2056283186981369, 0.41737040465671255, 0.640056599464176, 0.8761931012429545, 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-1.5179476862028884, -1.4179977324454542, -0.8777672031645841, -0.18373041697816342, 0.35748597328513215, 0.5264158702439796, 0.2678115767614811, -0.28829259471103486], 'positive_zeros': ['2.59335656559048749217684354708292', '3.57032525010301463495530674647642', '5.16746475704162288042683266443388', '5.88641650006632163841711617715213', '7.38646682250914023626660516960676', '7.890968979292844991614448934934157', '9.152851132600398164852591532223646', '9.980294986705641550878798015673645', '10.87957085208589286331284849800850'], 'prelabel': '2-380-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.7419286084132886, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 326594808215740583, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.59335656559048749217684354708', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.57032525010301463495530674648', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.16746475704162288042683266443', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.034315276808656, 'bad_primes': [2, 5, 19], 'central_character': '1.1', 'conductor': 380, 'conductor_radical': 190, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, -1, 0, -2, 0, -3, 0, -4, 0, -4, 0, 0, 0, 6, 0, 1, 0, 0, 0, -2, 0, 1, 0, 0, 0, -6, 0, -8, 0, 0, 0, 2, 0, 4, 0, 0, 0, 6, 0, -6, 0, 3, 0, 6, 0, -3, 0, 0, 0, 8, 0, 4, 0, 0, 0, -12, 0, 6, 0, 6, 0, 4, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 8, 0, -8, 0, 9, 0, 14, 0, -6, 0, 0, 0, 14, 0, 8, 0, 0, 0, -1, 0, 16, 0, 12, 0], 'euler11': [1, 4, 11], 'euler13': [1, 4, 13], 'euler17': [1, -6, 17], 'euler19': [1, -1, 0], 'euler2': [1, 0, 0], 'euler23': [1, 2, 23], 'euler29': [1, 6, 29], 'euler3': [1, 0, 3], 'euler31': [1, 8, 31], 'euler37': [1, -4, 37], 'euler41': [1, -6, 41], 'euler43': [1, 6, 43], 'euler47': [1, -6, 47], 'euler5': [1, 1, 0], 'euler53': [1, -8, 53], 'euler59': [1, 12, 59], 'euler61': [1, -6, 61], 'euler67': [1, 0, 67], 'euler7': [1, 2, 7], 'euler71': [1, 0, 71], 'euler73': [1, 10, 73], 'euler79': [1, 8, 79], 'euler83': [1, -14, 83], 'euler89': [1, -14, 89], 'euler97': [1, -16, 97], 'euler_factors': [[1, 0, 0], [1, 0, 3], [1, 1, 0], [1, 2, 7], [1, 4, 11], [1, 4, 13], [1, -6, 17], [1, -1, 0], [1, 2, 23], [1, 6, 29], [1, 8, 31], [1, -4, 37], [1, -6, 41], [1, 6, 43], [1, -6, 47], [1, -8, 53], [1, 12, 59], [1, -6, 61], [1, 0, 67], [1, 0, 71], [1, 10, 73], [1, 8, 79], [1, -14, 83], [1, -14, 89], [1, -16, 97]], 'index': 5, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/380/a', 'ModularForm/GL2/Q/holomorphic/380/2/a/a/1/1', 'ModularForm/GL2/Q/holomorphic/380/2/a/a'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-380-1.1-c1-0-5', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-380-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.7419286084132886, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 326594808215740583, 'z1': {'__RealLiteral__': 0, 'data': '2.59335656559048749217684354708', 'prec': 103}}
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lfunc_instances • Show schema
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id: 10485210
{'Lhash': '3287470006976601040582733719015', 'Lhash_array': ['3287470006976601040582733719015'], 'label': '2-380-1.1-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/380/2/a/a'}
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id: 24549169
{'Lhash': '3287470006976601040582733719015', 'Lhash_array': ['3287470006976601040582733719015'], 'label': '2-380-1.1-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/380/2/a/a/1/1'}
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id: 94179
{'Lhash': '326594808215740583', 'Lhash_array': ['326594808215740583'], 'label': '2-380-1.1-c1-0-5', 'type': 'ECQ', 'url': 'EllipticCurve/Q/380/a'}