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lfunc_lfunctions • Show schema
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{'Lhash': '1317699146134124894839606491124', 'a10': 0, 'a2': 0, 'a3': 1, 'a4': 0, 'a5': -1, 'a6': 0, 'a7': 5, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 44.0774219157468, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [5, [1, 1]], [23, [1, -1]]], 'bad_primes': [2, 3, 5, 23], 'central_character': '5520.1', 'coefficient_field': '1.1.1.1', 'conductor': 5520, 'conductor_radical': 690, 'degree': 2, 'euler_factors': [[1], [1, -1], [1, 1], [1, -5, 7], [1, 0, 11], [1, -4, 13], [1, 3, 17], [1, -4, 19], [1, -1], [1, -1, 29], [1, 1, 31], [1, 1, 37], [1, -11, 41], [1, 4, 43], [1, 6, 47], [1, -1, 53], [1, -1, 59], [1, -6, 61], [1, -9, 67], [1, 13, 71], [1, 0, 73], [1, 16, 79], [1, 9, 83], [1, -8, 89], [1, -2, 97], [1, 7, 101], [1, -16, 103], [1, -3, 107], [1, 12, 109], [1, -1, 113]], 'euler_factors_factorization': [[1], [[[1, -1], 1]], [[[1, 1], 1]], [[[1, -5, 7], 1]], [[[1, 0, 11], 1]], [[[1, 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5.0322810735951, 5.267217975873624, 5.340109935428829, 5.24377436610074, 4.980098478454012, 4.560056046732465, 4.003175268318429, 3.3364853773843723, 2.5930026605129615, 1.809845998921028, 1.0260961021395696, 0.28052959914359177, -0.3906320537691968, -0.9558189564352727, -1.3899235627951387], 'positive_zeros': ['1.03948134122832008320279790044805', '1.79060270377778587290331546596409', '2.79078782779929178015018546739683', '3.80233378073640689226968908072682', '4.42605182400092039828195277893126', '5.11549302962715067142613094614342', '5.92405361571973205732057203306728', '6.98971243095208194554643329575646', '7.58180751753748820471225455751311', '8.244172834418588563827014645606490'], 'prelabel': '2-5520-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.639082912251269, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'trace_hash': 447508621799732774, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.03948134122832008320279790045', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.79060270377778587290331546596', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.79078782779929178015018546740', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 44.0774219157468, 'bad_primes': [2, 3, 5, 23], 'central_character': '1.1', 'conductor': 5520, 'conductor_radical': 690, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, -1, 0, 5, 0, 1, 0, 0, 0, 4, 0, -1, 0, -3, 0, 4, 0, 5, 0, 1, 0, 1, 0, 1, 0, 1, 0, -1, 0, 0, 0, -5, 0, -1, 0, 4, 0, 11, 0, -4, 0, -1, 0, -6, 0, 18, 0, -3, 0, 1, 0, 0, 0, 4, 0, 1, 0, 6, 0, 5, 0, -4, 0, 9, 0, 1, 0, -13, 0, 0, 0, 1, 0, 0, 0, -16, 0, 1, 0, -9, 0, 3, 0, 1, 0, 8, 0, 20, 0, -1, 0, -4, 0, 2, 0, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, -4, 13], 'euler17': [1, 3, 17], 'euler19': [1, -4, 19], 'euler2': [1, 0, 0], 'euler23': [1, -1, 0], 'euler29': [1, -1, 29], 'euler3': [1, -1, 0], 'euler31': [1, 1, 31], 'euler37': [1, 1, 37], 'euler41': [1, -11, 41], 'euler43': [1, 4, 43], 'euler47': [1, 6, 47], 'euler5': [1, 1, 0], 'euler53': [1, -1, 53], 'euler59': [1, -1, 59], 'euler61': [1, -6, 61], 'euler67': [1, -9, 67], 'euler7': [1, -5, 7], 'euler71': [1, 13, 71], 'euler73': [1, 0, 73], 'euler79': [1, 16, 79], 'euler83': [1, 9, 83], 'euler89': [1, -8, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, 1, 0], [1, -5, 7], [1, 0, 11], [1, -4, 13], [1, 3, 17], [1, -4, 19], [1, -1, 0], [1, -1, 29], [1, 1, 31], [1, 1, 37], [1, -11, 41], [1, 4, 43], [1, 6, 47], [1, -1, 53], [1, -1, 59], [1, -6, 61], [1, -9, 67], [1, 13, 71], [1, 0, 73], [1, 16, 79], [1, 9, 83], [1, -8, 89], [1, -2, 97]], 'index': 39, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/5520/ba', 'ModularForm/GL2/Q/holomorphic/5520/2/a/ba/1/1', 'ModularForm/GL2/Q/holomorphic/5520/2/a/ba'], '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': '2-5520-1.1-c1-0-39', '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': '2-5520-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.639082912251269, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 447508621799732774, 'z1': {'__RealLiteral__': 0, 'data': '1.03948134122832008320279790045', 'prec': 103}}
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lfunc_instances • Show schema
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id: 21349233
{'Lhash': '1317699146134124894839606491124', 'Lhash_array': ['1317699146134124894839606491124'], 'label': '2-5520-1.1-c1-0-39', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5520/2/a/ba'}
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id: 24570683
{'Lhash': '1317699146134124894839606491124', 'Lhash_array': ['1317699146134124894839606491124'], 'label': '2-5520-1.1-c1-0-39', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5520/2/a/ba/1/1'}
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id: 43044
{'Lhash': '447508621799732774', 'Lhash_array': ['447508621799732774'], 'label': '2-5520-1.1-c1-0-39', 'type': 'ECQ', 'url': 'EllipticCurve/Q/5520/ba'}