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lfunc_lfunctions • Show schema
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{'Lhash': '1899137775910545707185473869277,2350498627347654302088159431171', 'a10': 75, 'a2': 5, 'a3': 0, 'a4': 7, 'a5': 15, 'a6': 0, 'a7': 15, 'a8': -15, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8053.60953433941, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [13, [1]]], 'bad_primes': [3, 13], 'central_character': '1521.1', 'coefficient_field': '1.1.1.1', 'conductor': 2313441, 'conductor_radical': 39, 'degree': 4, 'euler_factors': [[1, -5, 18, -40, 64], [1], [1, -15, 200, -1875, 15625], [1, -15, 738, -5145, 117649], [1, 17, 1778, 22627, 1771561], [1], [1, 70, 9963, 343910, 24137569], [1, 141, 18582, 967119, 47045881], [1, 145, 24962, 1764215, 148035889], [1, 34, 33767, 829226, 594823321], [1, 140, 21982, 4170740, 887503681], [1, 190, 102103, 9624070, 2565726409], [1, 538, 208503, 37079498, 4750104241], [1, -455, 170782, -36175685, 6321363049], [1, 60, 125246, 6229380, 10779215329], [1, 545, 256304, 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{'algebraic': True, 'analytic_conductor': 8053.60953433941, 'bad_primes': [3, 13], 'central_character': '1.1', 'conductor': 2313441, 'conductor_radical': 39, 'degree': 4, 'dirichlet_coefficients': [1, 5, 0, 7, 15, 0, 15, -15, 0, 75, -17, 0, 0, 75, 0, -65, -70, 0, -141, 105, 0, -85, -145, 0, 25, 0, 0, 105, -34, 0, -140, -95, 0, -350, 225, 0, -190, -705, 0, -225, -538, 0, 455, -119, 0, -725, -60, 0, -513, 125, 0, 0, -545, 0, -255, -225, 0, -170, 809, 0, 502, -700, 0, -353, 0, 0, -475, -490, 0, 1125, -127, 0, 585, -950, 0, -987, -255, 0, 240, -975, 0, -2690, -260, 0, -1050, 2275, 0, 255, -921, 0, 0, -1015, 0, -300, -2115, 0, -415, -2565, 0, 175], 'euler11': [1, 17, 1778, 22627, 1771561], 'euler13': [1, 0, 0, 0, 0], 'euler17': [1, 70, 9963, 343910, 24137569], 'euler19': [1, 141, 18582, 967119, 47045881], 'euler2': [1, -5, 18, -40, 64], 'euler23': [1, 145, 24962, 1764215, 148035889], 'euler29': [1, 34, 33767, 829226, 594823321], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 140, 21982, 4170740, 887503681], 'euler37': [1, 190, 102103, 9624070, 2565726409], 'euler41': [1, 538, 208503, 37079498, 4750104241], 'euler43': [1, -455, 170782, -36175685, 6321363049], 'euler47': [1, 60, 125246, 6229380, 10779215329], 'euler5': [1, -15, 200, -1875, 15625], 'euler53': [1, 545, 256304, 81137965, 22164361129], 'euler59': [1, -809, 561522, -166151611, 42180533641], 'euler61': [1, -502, 346963, -113944462, 51520374361], 'euler67': [1, 475, 622738, 142862425, 90458382169], 'euler7': [1, -15, 738, -5145, 117649], 'euler71': [1, 127, 672998, 45454697, 128100283921], 'euler73': [1, -585, 832884, -227574945, 151334226289], 'euler79': [1, -240, 993678, -118329360, 243087455521], 'euler83': [1, 260, 1117974, 148664620, 326940373369], 'euler89': [1, 921, 1555592, 649276449, 496981290961], 'euler97': [1, 415, 933568, 378759295, 832972004929], 'euler_factors': [[1, -5, 18, -40, 64], [1, 0, 0, 0, 0], [1, -15, 200, -1875, 15625], [1, -15, 738, -5145, 117649], [1, 17, 1778, 22627, 1771561], [1, 0, 0, 0, 0], [1, 70, 9963, 343910, 24137569], [1, 141, 18582, 967119, 47045881], [1, 145, 24962, 1764215, 148035889], [1, 34, 33767, 829226, 594823321], [1, 140, 21982, 4170740, 887503681], [1, 190, 102103, 9624070, 2565726409], [1, 538, 208503, 37079498, 4750104241], [1, -455, 170782, -36175685, 6321363049], [1, 60, 125246, 6229380, 10779215329], [1, 545, 256304, 81137965, 22164361129], [1, -809, 561522, -166151611, 42180533641], [1, -502, 346963, -113944462, 51520374361], [1, 475, 622738, 142862425, 90458382169], [1, 127, 672998, 45454697, 128100283921], [1, -585, 832884, -227574945, 151334226289], [1, -240, 993678, -118329360, 243087455521], [1, 260, 1117974, 148664620, 326940373369], [1, 921, 1555592, 649276449, 496981290961], [1, 415, 933568, 378759295, 832972004929]], 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1521/4/a/t'], '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': '4-39e4-1.1-c3e2-0-8', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3, 3], 'order_of_vanishing': 2, 'prelabel': '4-39e4-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 9.473220419621383, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e2-0', 'trace_hash': 380796944926345180, 'z1': {'__RealLiteral__': 0, 'data': '1.49815554504421215419380241640', 'prec': 103}}
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{'Lhash': '1899137775910545707185473869277,2350498627347654302088159431171', 'Lhash_array': ['1899137775910545707185473869277', '2350498627347654302088159431171'], 'label': '4-39e4-1.1-c3e2-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1521/4/a/t'}