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lfunc_lfunctions • Show schema
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{'Lhash': '2343290445367599838993959484614', 'a10': 0, 'a2': -1, 'a3': 0, 'a4': -1, 'a5': 0, 'a6': 0, 'a7': 1, 'a8': 3, 'a9': -3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.591398116223624, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [1]], [23, [1, -1]]], 'bad_primes': [5, 23], 'central_character': '575.1', 'coefficient_field': '1.1.1.1', 'conductor': 575, 'conductor_radical': 115, 'degree': 2, 'euler_factors': [[1, 1, 2], [1, 0, 3], [1], [1, -1, 7], [1, 1, 11], [1, -1, 13], [1, 0, 17], [1, 5, 19], [1, -1], [1, 5, 29], [1, 2, 31], [1, 4, 37], [1, 5, 41], [1, 9, 43], [1, 6, 47], [1, -2, 53], [1, -8, 59], [1, 8, 61], [1, -8, 67], [1, 10, 71], [1, 3, 73], [1, 3, 79], [1, -3, 83], [1, -10, 89], [1, 2, 97], [1, -10, 101], [1, 17, 103], [1, -12, 107], [1, 4, 109], [1, 6, 113]], 'euler_factors_factorization': [[[[1, 1, 2], 1]], [[[1, 0, 3], 1]], [1], [[[1, -1, 7], 1]], [[[1, 1, 11], 1]], [[[1, -1, 13], 1]], [[[1, 0, 17], 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-1.9764786332048445, -1.320422065306155, -0.29694568655897685, 0.6489781663892908, 1.1199205918979336, 0.9109401574843877, 0.08776273075260294, -1.029831002152419], 'positive_zeros': ['1.84853022192843271860137591061176', '3.45669534591572732448701916279561', '4.71005068669161340794561492507939', '5.59281137519846907484522339715267', '6.82010351386441826584168969706236', '8.012758465331867631000910585381615', '8.505482513228530618054181619568678', '9.259076113837488174563171822228007', '10.27352977146449202845403451736108'], 'prelabel': '2-575-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.142754796103284, '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': 745976355888604066, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.84853022192843271860137591061', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.45669534591572732448701916280', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.71005068669161340794561492508', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.591398116223624, 'bad_primes': [5, 23], 'central_character': '1.1', 'conductor': 575, 'conductor_radical': 115, 'degree': 2, 'dirichlet_coefficients': [1, -1, 0, -1, 0, 0, 1, 3, -3, 0, -1, 0, 1, -1, 0, -1, 0, 3, -5, 0, 0, 1, 1, 0, 0, -1, 0, -1, -5, 0, -2, -5, 0, 0, 0, 3, -4, 5, 0, 0, -5, 0, -9, 1, 0, -1, -6, 0, -6, 0, 0, -1, 2, 0, 0, 3, 0, 5, 8, 0, -8, 2, -3, 7, 0, 0, 8, 0, 0, 0, -10, -9, -3, 4, 0, 5, -1, 0, -3, 0, 9, 5, 3, 0, 0, 9, 0, -3, 10, 0, 1, -1, 0, 6, 0, 0, -2, 6, 3, 0], 'euler11': [1, 1, 11], 'euler13': [1, -1, 13], 'euler17': [1, 0, 17], 'euler19': [1, 5, 19], 'euler2': [1, 1, 2], 'euler23': [1, -1, 0], 'euler29': [1, 5, 29], 'euler3': [1, 0, 3], 'euler31': [1, 2, 31], 'euler37': [1, 4, 37], 'euler41': [1, 5, 41], 'euler43': [1, 9, 43], 'euler47': [1, 6, 47], 'euler5': [1, 0, 0], 'euler53': [1, -2, 53], 'euler59': [1, -8, 59], 'euler61': [1, 8, 61], 'euler67': [1, -8, 67], 'euler7': [1, -1, 7], 'euler71': [1, 10, 71], 'euler73': [1, 3, 73], 'euler79': [1, 3, 79], 'euler83': [1, -3, 83], 'euler89': [1, -10, 89], 'euler97': [1, 2, 97], 'euler_factors': [[1, 1, 2], [1, 0, 3], [1, 0, 0], [1, -1, 7], [1, 1, 11], [1, -1, 13], [1, 0, 17], [1, 5, 19], [1, -1, 0], [1, 5, 29], [1, 2, 31], [1, 4, 37], [1, 5, 41], [1, 9, 43], [1, 6, 47], [1, -2, 53], [1, -8, 59], [1, 8, 61], [1, -8, 67], [1, 10, 71], [1, 3, 73], [1, 3, 79], [1, -3, 83], [1, -10, 89], [1, 2, 97]], 'index': 21, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/575/c', 'ModularForm/GL2/Q/holomorphic/575/2/a/c/1/1', 'ModularForm/GL2/Q/holomorphic/575/2/a/c'], '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': '2-575-1.1-c1-0-21', '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': '2-575-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.142754796103284, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 745976355888604066, 'z1': {'__RealLiteral__': 0, 'data': '1.84853022192843271860137591061', 'prec': 103}}
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lfunc_instances • Show schema
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id: 11808928
{'Lhash': '2343290445367599838993959484614', 'Lhash_array': ['2343290445367599838993959484614'], 'label': '2-575-1.1-c1-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/575/2/a/c'}
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id: 24549789
{'Lhash': '2343290445367599838993959484614', 'Lhash_array': ['2343290445367599838993959484614'], 'label': '2-575-1.1-c1-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/575/2/a/c/1/1'}
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id: 32545
{'Lhash': '745976355888604066', 'Lhash_array': ['745976355888604066'], 'label': '2-575-1.1-c1-0-21', 'type': 'ECQ', 'url': 'EllipticCurve/Q/575/c'}