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lfunc_lfunctions • Show schema
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{'Lhash': '2073117386266462930947027171458', 'a10': 0, 'a2': 0, 'a3': 3, 'a4': 0, 'a5': -12, 'a6': 0, 'a7': -2, 'a8': 0, 'a9': 9, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 36.81719184358216, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -3]], [13, [1, -13]]], 'bad_primes': [2, 3, 13], 'central_character': '624.1', 'coefficient_field': '1.1.1.1', 'conductor': 624, 'conductor_radical': 78, 'degree': 2, 'euler_factors': [[1], [1, -3], [1, 12, 125], [1, 2, 343], [1, -36, 1331], [1, -13], [1, 78, 4913], [1, 74, 6859], [1, -96, 12167], [1, -18, 24389], [1, -214, 29791], [1, 286, 50653], [1, 384, 68921], [1, 524, 79507], [1, 300, 103823], [1, -558, 148877], [1, 576, 205379], [1, -74, 226981], [1, 38, 300763], [1, -456, 357911], [1, 682, 389017], [1, 704, 493039], [1, -888, 571787], [1, 1020, 704969], [1, -110, 912673], [1, 990, 1030301], [1, 1208, 1092727], [1, 996, 1225043], [1, 1402, 1295029], [1, -1926, 1442897]], 'euler_factors_factorization': [[1], [[[1, -3], 1]], [[[1, 12, 125], 1]], [[[1, 2, 343], 1]], [[[1, -36, 1331], 1]], [[[1, -13], 1]], [[[1, 78, 4913], 1]], [[[1, 74, 6859], 1]], [[[1, -96, 12167], 1]], [[[1, -18, 24389], 1]], [[[1, -214, 29791], 1]], [[[1, 286, 50653], 1]], [[[1, 384, 68921], 1]], [[[1, 524, 79507], 1]], [[[1, 300, 103823], 1]], [[[1, -558, 148877], 1]], [[[1, 576, 205379], 1]], [[[1, -74, 226981], 1]], [[[1, 38, 300763], 1]], [[[1, -456, 357911], 1]], [[[1, 682, 389017], 1]], [[[1, 704, 493039], 1]], [[[1, -888, 571787], 1]], [[[1, 1020, 704969], 1]], [[[1, -110, 912673], 1]], [[[1, 990, 1030301], 1]], [[[1, 1208, 1092727], 1]], [[[1, 996, 1225043], 1]], [[[1, 1402, 1295029], 1]], [[[1, -1926, 1442897], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 28, 'label': '2-624-1.1-c3-0-28', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/624/4/a/g', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [-2.0394960227052726e-60, 0.2226763529683383, 0.4431107179066424, 0.6590675310851483, 0.8683247105138131, 1.068681950505683, 1.257970800152285, 1.4340669894160794, 1.594905360645746, 1.7384976384159216, 1.8629531310383685, 1.9665023075822532, 2.047523039627878, 2.1045691421079775, 2.1364006971850986, 2.1420155036828903, 2.12068086637904, 2.0719648284288414, 1.995765859959438, 1.8923399497661804, 1.7623240080139664, 1.6067544784702879, 1.4270800812037672, 1.2251676624899006, 1.0033002188921198, 0.7641662874515083, 0.5108400531447107, 0.24675171688351563, -0.024352110023056595, -0.2984579692438016, -0.5713447885128913, -0.8386522068155469, -1.0959571141401598, -1.3388572255413944, -1.5630602122112178, -1.764476630060647, -1.9393146286334964, -2.0841741998908025, -2.1961385473414805, -2.272860030582243, 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'0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'trace_hash': 5142191865318981, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.63540125795957993522501919198', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.12659185447439819581869711337', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.99528531785299648351322581938', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 36.81719184358216, 'bad_primes': [2, 3, 13], 'central_character': '1.1', 'conductor': 624, 'conductor_radical': 78, 'degree': 2, 'dirichlet_coefficients': [1, 0, 3, 0, -12, 0, -2, 0, 9, 0, 36, 0, 13, 0, -36, 0, -78, 0, -74, 0, -6, 0, 96, 0, 19, 0, 27, 0, 18, 0, 214, 0, 108, 0, 24, 0, -286, 0, 39, 0, -384, 0, -524, 0, -108, 0, -300, 0, -339, 0, -234, 0, 558, 0, -432, 0, -222, 0, -576, 0, 74, 0, -18, 0, -156, 0, -38, 0, 288, 0, 456, 0, -682, 0, 57, 0, -72, 0, -704, 0, 81, 0, 888, 0, 936, 0, 54, 0, -1020, 0, -26, 0, 642, 0, 888, 0, 110, 0, 324, 0], 'euler11': [1, -36, 1331], 'euler13': [1, -13, 0], 'euler17': [1, 78, 4913], 'euler19': [1, 74, 6859], 'euler2': [1, 0, 0], 'euler23': [1, -96, 12167], 'euler29': [1, -18, 24389], 'euler3': [1, -3, 0], 'euler31': [1, -214, 29791], 'euler37': [1, 286, 50653], 'euler41': [1, 384, 68921], 'euler43': [1, 524, 79507], 'euler47': [1, 300, 103823], 'euler5': [1, 12, 125], 'euler53': [1, -558, 148877], 'euler59': [1, 576, 205379], 'euler61': [1, -74, 226981], 'euler67': [1, 38, 300763], 'euler7': [1, 2, 343], 'euler71': [1, -456, 357911], 'euler73': [1, 682, 389017], 'euler79': [1, 704, 493039], 'euler83': [1, -888, 571787], 'euler89': [1, 1020, 704969], 'euler97': [1, -110, 912673], 'euler_factors': [[1, 0, 0], [1, -3, 0], [1, 12, 125], [1, 2, 343], [1, -36, 1331], [1, -13, 0], [1, 78, 4913], [1, 74, 6859], [1, -96, 12167], [1, -18, 24389], [1, -214, 29791], [1, 286, 50653], [1, 384, 68921], [1, 524, 79507], [1, 300, 103823], [1, -558, 148877], [1, 576, 205379], [1, -74, 226981], [1, 38, 300763], [1, -456, 357911], [1, 682, 389017], [1, 704, 493039], [1, -888, 571787], [1, 1020, 704969], [1, -110, 912673]], 'index': 28, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/624/4/a/g/1/1', 'ModularForm/GL2/Q/holomorphic/624/4/a/g'], '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': '2-624-1.1-c3-0-28', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-624-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.0677171855304985, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 5142191865318981, 'z1': {'__RealLiteral__': 0, 'data': '1.63540125795957993522501919198', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20582736
{'Lhash': '2073117386266462930947027171458', 'Lhash_array': ['2073117386266462930947027171458'], 'label': '2-624-1.1-c3-0-28', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/624/4/a/g'}
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id: 24566711
{'Lhash': '2073117386266462930947027171458', 'Lhash_array': ['2073117386266462930947027171458'], 'label': '2-624-1.1-c3-0-28', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/624/4/a/g/1/1'}