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lfunc_lfunctions • Show schema
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{'Lhash': '1334312225621116365243485765495', 'a10': 0, 'a2': -1, 'a3': -1, 'a4': 1, 'a5': 0, 'a6': 1, 'a7': -3, 'a8': -1, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 37.1304369398954, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1, 1]], [5, [1]], [31, [1, -1]]], 'bad_primes': [2, 3, 5, 31], 'central_character': '4650.1', 'coefficient_field': '1.1.1.1', 'conductor': 4650, 'conductor_radical': 930, 'degree': 2, 'euler_factors': [[1, 1], [1, 1], [1], [1, 3, 7], [1, 3, 11], [1, -1, 13], [1, -2, 17], [1, 0, 19], [1, 4, 23], [1, -10, 29], [1, -1], [1, 3, 37], [1, -7, 41], [1, -1, 43], [1, -7, 47], [1, 9, 53], [1, 0, 59], [1, -7, 61], [1, -2, 67], [1, -7, 71], [1, 4, 73], [1, 10, 79], [1, 9, 83], [1, -10, 89], [1, -2, 97], [1, -2, 101], [1, -1, 103], [1, 18, 107], [1, 10, 109], [1, -6, 113]], 'euler_factors_factorization': [[[[1, 1], 1]], [[[1, 1], 1]], [1], [[[1, 3, 7], 1]], [[[1, 3, 11], 1]], [[[1, -1, 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3.1793337422169174, 3.1858649647624935, 3.088643168492612, 2.892705194414342, 2.6080101067475017, 2.2490048374472233, 1.8339458048940085, 1.3840068059265362, 0.9222154428891999, 0.47227036230080766], 'positive_zeros': ['1.05258675015093679696375135861477', '2.41087241799822553469236564908260', '3.15773327322568209826294856380092', '4.15051595575684229069799281245153', '5.17785411129813587456287280061542', '5.98312328222860303879633802028967', '6.46513946037455035213859743970394', '7.24061871170606088819831761137819', '7.972229178322202396417527504979803'], 'prelabel': '2-4650-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.093474947835217, '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': 1723512051822465546, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.05258675015093679696375135861', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.41087241799822553469236564908', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.15773327322568209826294856380', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 37.1304369398954, 'bad_primes': [2, 3, 5, 31], 'central_character': '1.1', 'conductor': 4650, 'conductor_radical': 930, 'degree': 2, 'dirichlet_coefficients': [1, -1, -1, 1, 0, 1, -3, -1, 1, 0, -3, -1, 1, 3, 0, 1, 2, -1, 0, 0, 3, 3, -4, 1, 0, -1, -1, -3, 10, 0, 1, -1, 3, -2, 0, 1, -3, 0, -1, 0, 7, -3, 1, -3, 0, 4, 7, -1, 2, 0, -2, 1, -9, 1, 0, 3, 0, -10, 0, 0, 7, -1, -3, 1, 0, -3, 2, 2, 4, 0, 7, -1, -4, 3, 0, 0, 9, 1, -10, 0, 1, -7, -9, 3, 0, -1, -10, 3, 10, 0, -3, -4, -1, -7, 0, 1, 2, -2, -3, 0], 'euler11': [1, 3, 11], 'euler13': [1, -1, 13], 'euler17': [1, -2, 17], 'euler19': [1, 0, 19], 'euler2': [1, 1, 0], 'euler23': [1, 4, 23], 'euler29': [1, -10, 29], 'euler3': [1, 1, 0], 'euler31': [1, -1, 0], 'euler37': [1, 3, 37], 'euler41': [1, -7, 41], 'euler43': [1, -1, 43], 'euler47': [1, -7, 47], 'euler5': [1, 0, 0], 'euler53': [1, 9, 53], 'euler59': [1, 0, 59], 'euler61': [1, -7, 61], 'euler67': [1, -2, 67], 'euler7': [1, 3, 7], 'euler71': [1, -7, 71], 'euler73': [1, 4, 73], 'euler79': [1, 10, 79], 'euler83': [1, 9, 83], 'euler89': [1, -10, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, 1, 0], [1, 1, 0], [1, 0, 0], [1, 3, 7], [1, 3, 11], [1, -1, 13], [1, -2, 17], [1, 0, 19], [1, 4, 23], [1, -10, 29], [1, -1, 0], [1, 3, 37], [1, -7, 41], [1, -1, 43], [1, -7, 47], [1, 9, 53], [1, 0, 59], [1, -7, 61], [1, -2, 67], [1, -7, 71], [1, 4, 73], [1, 10, 79], [1, 9, 83], [1, -10, 89], [1, -2, 97]], 'index': 44, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/4650/b', 'ModularForm/GL2/Q/holomorphic/4650/2/a/b/1/1', 'ModularForm/GL2/Q/holomorphic/4650/2/a/b'], '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': '2-4650-1.1-c1-0-44', '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': '2-4650-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.093474947835217, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1723512051822465546, 'z1': {'__RealLiteral__': 0, 'data': '1.05258675015093679696375135861', 'prec': 103}}
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lfunc_instances • Show schema
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id: 19977870
{'Lhash': '1334312225621116365243485765495', 'Lhash_array': ['1334312225621116365243485765495'], 'label': '2-4650-1.1-c1-0-44', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4650/2/a/b'}
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id: 24566826
{'Lhash': '1334312225621116365243485765495', 'Lhash_array': ['1334312225621116365243485765495'], 'label': '2-4650-1.1-c1-0-44', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4650/2/a/b/1/1'}
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id: 97131
{'Lhash': '1723512051822465546', 'Lhash_array': ['1723512051822465546'], 'label': '2-4650-1.1-c1-0-44', 'type': 'ECQ', 'url': 'EllipticCurve/Q/4650/b'}