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lfunc_lfunctions • Show schema
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{'Lhash': '1208111243553720756523311783308', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 2, 'a6': 0, 'a7': -1, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 76.46474497557813, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [7, [1, 1]], [19, [1, -1]]], 'bad_primes': [2, 3, 7, 19], 'central_character': '9576.1', 'coefficient_field': '1.1.1.1', 'conductor': 9576, 'conductor_radical': 798, 'degree': 2, 'euler_factors': [[1], [1], [1, -2, 5], [1, 1], [1, -4, 11], [1, -2, 13], [1, -6, 17], [1, -1], [1, 0, 23], [1, -10, 29], [1, -8, 31], [1, 2, 37], [1, 6, 41], [1, -4, 43], [1, -8, 47], [1, 6, 53], [1, -4, 59], [1, 10, 61], [1, -8, 67], [1, 12, 71], [1, 14, 73], [1, 4, 79], [1, -4, 83], [1, 6, 89], [1, -14, 97], [1, 6, 101], [1, -16, 103], [1, 0, 107], [1, 10, 109], [1, 2, 113]], 'euler_factors_factorization': [[1], [1], [[[1, -2, 5], 1]], [[[1, 1], 1]], [[[1, -4, 11], 1]], [[[1, -2, 13], 1]], [[[1, -6, 17], 1]], [[[1, -1], 1]], [[[1, 0, 23], 1]], [[[1, -10, 29], 1]], [[[1, -8, 31], 1]], [[[1, 2, 37], 1]], [[[1, 6, 41], 1]], [[[1, -4, 43], 1]], [[[1, -8, 47], 1]], [[[1, 6, 53], 1]], [[[1, -4, 59], 1]], [[[1, 10, 61], 1]], [[[1, -8, 67], 1]], [[[1, 12, 71], 1]], [[[1, 14, 73], 1]], [[[1, 4, 79], 1]], [[[1, -4, 83], 1]], [[[1, 6, 89], 1]], [[[1, -14, 97], 1]], [[[1, 6, 101], 1]], [[[1, -16, 103], 1]], [[[1, 0, 107], 1]], [[[1, 10, 109], 1]], [[[1, 2, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 66, 'label': '2-9576-1.1-c1-0-66', 'leading_term': '3.17875754809360236065883638598000000000000000000000000000000000000000000000000000000000000', '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/9576/2/a/t', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 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-3.192487649221275, -2.5285569965998866, -1.8694539005714577, -1.2463602201087705, -0.6877325659049559, -0.2177254588745395, 0.14514326694873755, 0.3890060542839523, 0.5092774844728934, 0.5088655042578689, 0.397947450160349, 0.19332175538272237, -0.08262871088820505], 'positive_zeros': ['0.953031729197470419184280734853072', '1.53860957248944911385408617949409', '2.70134925506296298553437922558114', '3.34584100967352602302155182340983', '4.18290305064466179578328771321178', '4.96762823348528019770922126025595', '5.91960408483394904514317921925771', '6.16482505023945957063098815525585', '6.87000862610472789045071680173421', '7.65478047116696422669303448072141'], 'prelabel': '2-9576-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 8.744412214413163, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'trace_hash': 940075881223817937, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.953031729197470419184280734853', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.53860957248944911385408617949', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.70134925506296298553437922558', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 76.46474497557813, 'bad_primes': [2, 3, 7, 19], 'central_character': '1.1', 'conductor': 9576, 'conductor_radical': 798, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 2, 0, -1, 0, 0, 0, 4, 0, 2, 0, 0, 0, 6, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 10, 0, 8, 0, 0, 0, -2, 0, -2, 0, 0, 0, -6, 0, 4, 0, 0, 0, 8, 0, 1, 0, 0, 0, -6, 0, 8, 0, 0, 0, 4, 0, -10, 0, 0, 0, 4, 0, 8, 0, 0, 0, -12, 0, -14, 0, 0, 0, -4, 0, -4, 0, 0, 0, 4, 0, 12, 0, 0, 0, -6, 0, -2, 0, 0, 0, 2, 0, 14, 0, 0, 0], 'euler11': [1, -4, 11], 'euler13': [1, -2, 13], 'euler17': [1, -6, 17], 'euler19': [1, -1, 0], 'euler2': [1, 0, 0], 'euler23': [1, 0, 23], 'euler29': [1, -10, 29], 'euler3': [1, 0, 0], 'euler31': [1, -8, 31], 'euler37': [1, 2, 37], 'euler41': [1, 6, 41], 'euler43': [1, -4, 43], 'euler47': [1, -8, 47], 'euler5': [1, -2, 5], 'euler53': [1, 6, 53], 'euler59': [1, -4, 59], 'euler61': [1, 10, 61], 'euler67': [1, -8, 67], 'euler7': [1, 1, 0], 'euler71': [1, 12, 71], 'euler73': [1, 14, 73], 'euler79': [1, 4, 79], 'euler83': [1, -4, 83], 'euler89': [1, 6, 89], 'euler97': [1, -14, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, -2, 5], [1, 1, 0], [1, -4, 11], [1, -2, 13], [1, -6, 17], [1, -1, 0], [1, 0, 23], [1, -10, 29], [1, -8, 31], [1, 2, 37], [1, 6, 41], [1, -4, 43], [1, -8, 47], [1, 6, 53], [1, -4, 59], [1, 10, 61], [1, -8, 67], [1, 12, 71], [1, 14, 73], [1, 4, 79], [1, -4, 83], [1, 6, 89], [1, -14, 97]], 'index': 66, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/9576/t', 'ModularForm/GL2/Q/holomorphic/9576/2/a/t/1/1', 'ModularForm/GL2/Q/holomorphic/9576/2/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': 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': '2-9576-1.1-c1-0-66', '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': '2-9576-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 8.744412214413163, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 940075881223817937, 'z1': {'__RealLiteral__': 0, 'data': '0.953031729197470419184280734853', 'prec': 107}}
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lfunc_instances • Show schema
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id: 22709437
{'Lhash': '1208111243553720756523311783308', 'Lhash_array': ['1208111243553720756523311783308'], 'label': '2-9576-1.1-c1-0-66', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9576/2/a/t'}
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id: 24589215
{'Lhash': '1208111243553720756523311783308', 'Lhash_array': ['1208111243553720756523311783308'], 'label': '2-9576-1.1-c1-0-66', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9576/2/a/t/1/1'}
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id: 26015
{'Lhash': '940075881223817937', 'Lhash_array': ['940075881223817937'], 'label': '2-9576-1.1-c1-0-66', 'type': 'ECQ', 'url': 'EllipticCurve/Q/9576/t'}