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lfunc_lfunctions • Show schema
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{'Lhash': '1679356531477833686367024152559', 'a10': 0, 'a2': 1, 'a3': 1, 'a4': 1, 'a5': 0, 'a6': 1, 'a7': 2, 'a8': 1, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 15.570828394149682, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1, -1]], [5, [1]], [13, [1, 1]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '1950.1', 'coefficient_field': '1.1.1.1', 'conductor': 1950, 'conductor_radical': 390, 'degree': 2, 'euler_factors': [[1, -1], [1, -1], [1], [1, -2, 7], [1, -2, 11], [1, 1], [1, -2, 17], [1, 4, 19], [1, 0, 23], [1, -4, 29], [1, -8, 31], [1, -6, 37], [1, 6, 41], [1, -4, 43], [1, 8, 47], [1, -2, 53], [1, -10, 59], [1, 14, 61], [1, 16, 67], [1, 4, 71], [1, -8, 73], [1, 8, 79], [1, -12, 83], [1, -6, 89], [1, -12, 97], [1, -4, 101], [1, -6, 103], [1, 4, 107], [1, 18, 109], [1, -6, 113]], 'euler_factors_factorization': [[[[1, -1], 1]], [[[1, -1], 1]], [1], [[[1, -2, 7], 1]], [[[1, -2, 11], 1]], [[[1, 1], 1]], [[[1, -2, 17], 1]], [[[1, 4, 19], 1]], [[[1, 0, 23], 1]], [[[1, -4, 29], 1]], [[[1, -8, 31], 1]], [[[1, -6, 37], 1]], [[[1, 6, 41], 1]], [[[1, -4, 43], 1]], [[[1, 8, 47], 1]], [[[1, -2, 53], 1]], [[[1, -10, 59], 1]], [[[1, 14, 61], 1]], [[[1, 16, 67], 1]], [[[1, 4, 71], 1]], [[[1, -8, 73], 1]], [[[1, 8, 79], 1]], [[[1, -12, 83], 1]], [[[1, -6, 89], 1]], [[[1, -12, 97], 1]], [[[1, -4, 101], 1]], [[[1, -6, 103], 1]], [[[1, 4, 107], 1]], [[[1, 18, 109], 1]], [[[1, -6, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 20, 'label': '2-1950-1.1-c1-0-20', 'leading_term': '3.87167139459734288405407718460000000000000000000000000000000000000000000000000000000000000', '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/1950/2/a/z', 'plot_delta': {'__RealLiteral__': 0, 'data': 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['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.32477871361042248821887123096', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.38909622796055435807922194933', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.33391362755583657763695615911', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 15.570828394149682, 'bad_primes': [2, 3, 5, 13], 'central_character': '1.1', 'conductor': 1950, 'conductor_radical': 390, 'degree': 2, 'dirichlet_coefficients': [1, 1, 1, 1, 0, 1, 2, 1, 1, 0, 2, 1, -1, 2, 0, 1, 2, 1, -4, 0, 2, 2, 0, 1, 0, -1, 1, 2, 4, 0, 8, 1, 2, 2, 0, 1, 6, -4, -1, 0, -6, 2, 4, 2, 0, 0, -8, 1, -3, 0, 2, -1, 2, 1, 0, 2, -4, 4, 10, 0, -14, 8, 2, 1, 0, 2, -16, 2, 0, 0, -4, 1, 8, 6, 0, -4, 4, -1, -8, 0, 1, -6, 12, 2, 0, 4, 4, 2, 6, 0, -2, 0, 8, -8, 0, 1, 12, -3, 2, 0], 'euler11': [1, -2, 11], 'euler13': [1, 1, 0], 'euler17': [1, -2, 17], 'euler19': [1, 4, 19], 'euler2': [1, -1, 0], 'euler23': [1, 0, 23], 'euler29': [1, -4, 29], 'euler3': [1, -1, 0], 'euler31': [1, -8, 31], 'euler37': [1, -6, 37], 'euler41': [1, 6, 41], 'euler43': [1, -4, 43], 'euler47': [1, 8, 47], 'euler5': [1, 0, 0], 'euler53': [1, -2, 53], 'euler59': [1, -10, 59], 'euler61': [1, 14, 61], 'euler67': [1, 16, 67], 'euler7': [1, -2, 7], 'euler71': [1, 4, 71], 'euler73': [1, -8, 73], 'euler79': [1, 8, 79], 'euler83': [1, -12, 83], 'euler89': [1, -6, 89], 'euler97': [1, -12, 97], 'euler_factors': [[1, -1, 0], [1, -1, 0], [1, 0, 0], [1, -2, 7], [1, -2, 11], [1, 1, 0], [1, -2, 17], [1, 4, 19], [1, 0, 23], [1, -4, 29], [1, -8, 31], [1, -6, 37], [1, 6, 41], [1, -4, 43], [1, 8, 47], [1, -2, 53], [1, -10, 59], [1, 14, 61], [1, 16, 67], [1, 4, 71], [1, -8, 73], [1, 8, 79], [1, -12, 83], [1, -6, 89], [1, -12, 97]], 'index': 20, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/1950/z', 'ModularForm/GL2/Q/holomorphic/1950/2/a/z/1/1', 'ModularForm/GL2/Q/holomorphic/1950/2/a/z'], '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': '2-1950-1.1-c1-0-20', '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': '2-1950-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.9459888993951417, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 551090746829692979, 'z1': {'__RealLiteral__': 0, 'data': '1.32477871361042248821887123096', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20722524
{'Lhash': '1679356531477833686367024152559', 'Lhash_array': ['1679356531477833686367024152559'], 'label': '2-1950-1.1-c1-0-20', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1950/2/a/z'}
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id: 24555226
{'Lhash': '1679356531477833686367024152559', 'Lhash_array': ['1679356531477833686367024152559'], 'label': '2-1950-1.1-c1-0-20', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1950/2/a/z/1/1'}
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id: 42895
{'Lhash': '551090746829692979', 'Lhash_array': ['551090746829692979'], 'label': '2-1950-1.1-c1-0-20', 'type': 'ECQ', 'url': 'EllipticCurve/Q/1950/z'}