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lfunc_lfunctions • Show schema
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{'Lhash': '2145711089957194541327049073492', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 1, 'a6': 0, 'a7': -1, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 20.122301309362665, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1, -1]], [7, [1, 1]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '2520.1', 'coefficient_field': '1.1.1.1', 'conductor': 2520, 'conductor_radical': 210, 'degree': 2, 'euler_factors': [[1], [1], [1, -1], [1, 1], [1, -4, 11], [1, 6, 13], [1, -2, 17], [1, 8, 19], [1, 4, 23], [1, 6, 29], [1, -4, 31], [1, 2, 37], [1, -2, 41], [1, 12, 43], [1, 0, 47], [1, 2, 53], [1, -4, 59], [1, -6, 61], [1, 4, 67], [1, 8, 71], [1, -6, 73], [1, 16, 79], [1, -4, 83], [1, -18, 89], [1, -6, 97], [1, 18, 101], [1, 16, 103], [1, 0, 107], [1, -14, 109], [1, 14, 113]], 'euler_factors_factorization': [[1], [1], [[[1, -1], 1]], [[[1, 1], 1]], [[[1, -4, 11], 1]], [[[1, 6, 13], 1]], [[[1, -2, 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0.95074114867205, 0.5710119642455714, 0.1565566888773914, -0.2687649224740138, -0.6799776822543421, -1.0523884907421817, -1.3629803155316889, -1.5917249950290855], 'positive_zeros': ['1.69266759276639637901572331998859', '2.54115494961707505080689479780028', '3.72240361617693861622462265492557', '4.50154877127520804472433685747902', '5.42979713341541103241638389122757', '6.35764416632480709325054896567423', '6.82457844835651829937406499450374', '7.75504922679689733526129774906834', '8.622140904396719623567268847878842'], 'prelabel': '2-2520-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.485788816848455, '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': 73549187461143265, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.69266759276639637901572331999', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.54115494961707505080689479780', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.72240361617693861622462265493', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 20.122301309362665, 'bad_primes': [2, 3, 5, 7], 'central_character': '1.1', 'conductor': 2520, 'conductor_radical': 210, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 1, 0, -1, 0, 0, 0, 4, 0, -6, 0, 0, 0, 2, 0, -8, 0, 0, 0, -4, 0, 1, 0, 0, 0, -6, 0, 4, 0, 0, 0, -1, 0, -2, 0, 0, 0, 2, 0, -12, 0, 0, 0, 0, 0, 1, 0, 0, 0, -2, 0, 4, 0, 0, 0, 4, 0, 6, 0, 0, 0, -6, 0, -4, 0, 0, 0, -8, 0, 6, 0, 0, 0, -4, 0, -16, 0, 0, 0, 4, 0, 2, 0, 0, 0, 18, 0, 6, 0, 0, 0, -8, 0, 6, 0, 0, 0], 'euler11': [1, -4, 11], 'euler13': [1, 6, 13], 'euler17': [1, -2, 17], 'euler19': [1, 8, 19], 'euler2': [1, 0, 0], 'euler23': [1, 4, 23], 'euler29': [1, 6, 29], 'euler3': [1, 0, 0], 'euler31': [1, -4, 31], 'euler37': [1, 2, 37], 'euler41': [1, -2, 41], 'euler43': [1, 12, 43], 'euler47': [1, 0, 47], 'euler5': [1, -1, 0], 'euler53': [1, 2, 53], 'euler59': [1, -4, 59], 'euler61': [1, -6, 61], 'euler67': [1, 4, 67], 'euler7': [1, 1, 0], 'euler71': [1, 8, 71], 'euler73': [1, -6, 73], 'euler79': [1, 16, 79], 'euler83': [1, -4, 83], 'euler89': [1, -18, 89], 'euler97': [1, -6, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, -1, 0], [1, 1, 0], [1, -4, 11], [1, 6, 13], [1, -2, 17], [1, 8, 19], [1, 4, 23], [1, 6, 29], [1, -4, 31], [1, 2, 37], [1, -2, 41], [1, 12, 43], [1, 0, 47], [1, 2, 53], [1, -4, 59], [1, -6, 61], [1, 4, 67], [1, 8, 71], [1, -6, 73], [1, 16, 79], [1, -4, 83], [1, -18, 89], [1, -6, 97]], 'index': 27, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/2520/n', 'ModularForm/GL2/Q/holomorphic/2520/2/a/n/1/1', 'ModularForm/GL2/Q/holomorphic/2520/2/a/n'], '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': '2-2520-1.1-c1-0-27', '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': '2-2520-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.485788816848455, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 73549187461143265, 'z1': {'__RealLiteral__': 0, 'data': '1.69266759276639637901572331999', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20233663
{'Lhash': '2145711089957194541327049073492', 'Lhash_array': ['2145711089957194541327049073492'], 'label': '2-2520-1.1-c1-0-27', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2520/2/a/n'}
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id: 24557585
{'Lhash': '2145711089957194541327049073492', 'Lhash_array': ['2145711089957194541327049073492'], 'label': '2-2520-1.1-c1-0-27', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2520/2/a/n/1/1'}
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id: 94975
{'Lhash': '73549187461143265', 'Lhash_array': ['73549187461143265'], 'label': '2-2520-1.1-c1-0-27', 'type': 'ECQ', 'url': 'EllipticCurve/Q/2520/n'}