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lfunc_lfunctions • Show schema
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{'Lhash': '1740191739373590610360603037630', 'a10': 1, 'a2': 1, 'a3': 0, 'a4': -1, 'a5': 1, 'a6': 0, 'a7': 2, 'a8': -3, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.671248518244905, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1, -1]], [13, [1, 1]]], 'bad_primes': [3, 5, 13], 'central_character': '585.1', 'coefficient_field': '1.1.1.1', 'conductor': 585, 'conductor_radical': 195, 'degree': 2, 'euler_factors': [[1, -1, 2], [1], [1, -1], [1, -2, 7], [1, -4, 11], [1, 1], [1, -4, 17], [1, -6, 19], [1, 0, 23], [1, -4, 29], [1, 10, 31], [1, 2, 37], [1, -6, 41], [1, 8, 43], [1, -8, 47], [1, -4, 53], [1, 12, 59], [1, -2, 61], [1, 10, 67], [1, 0, 71], [1, 6, 73], [1, -12, 79], [1, -4, 83], [1, 14, 89], [1, 14, 97], [1, 12, 101], [1, 4, 103], [1, 4, 107], [1, 2, 109], [1, 16, 113]], 'euler_factors_factorization': [[[[1, -1, 2], 1]], [1], [[[1, -1], 1]], [[[1, -2, 7], 1]], [[[1, -4, 11], 1]], [[[1, 1], 1]], [[[1, -4, 17], 1]], [[[1, -6, 19], 1]], [[[1, 0, 23], 1]], [[[1, -4, 29], 1]], [[[1, 10, 31], 1]], [[[1, 2, 37], 1]], [[[1, -6, 41], 1]], [[[1, 8, 43], 1]], [[[1, -8, 47], 1]], [[[1, -4, 53], 1]], [[[1, 12, 59], 1]], [[[1, -2, 61], 1]], [[[1, 10, 67], 1]], [[[1, 0, 71], 1]], [[[1, 6, 73], 1]], [[[1, -12, 79], 1]], [[[1, -4, 83], 1]], [[[1, 14, 89], 1]], [[[1, 14, 97], 1]], [[[1, 12, 101], 1]], [[[1, 4, 103], 1]], [[[1, 4, 107], 1]], [[[1, 2, 109], 1]], [[[1, 16, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 7, 'label': '2-585-1.1-c1-0-7', '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/585/2/a/i', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [2.136169645349706, 2.1313058900449837, 2.1142303256574584, 2.0779653349438276, 2.0123152404833826, 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0.5922420464627807, 1.1839672425644046, 1.4509151679461034, 1.2385175038451277, 0.5690061484392821, -0.3642757910631774, -1.2663613163716596, -1.8482353857544895, -1.932582895556646], 'positive_zeros': ['1.37276923078037774007010116690664', '3.11999237486850599731326861172741', '4.13601102912022186614527931542419', '5.17362861953367702283649965368389', '5.80203985872581797785224323058761', '7.01279831140022405844648391421112', '8.069603374513132812350986247673475', '9.158186635818496855923068127669881', '9.606143923072779152442392232210794', '10.78754913503442851991561141735873'], 'prelabel': '2-585-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.161307131863703, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 1542770274153734002, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.37276923078037774007010116691', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.11999237486850599731326861173', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.13601102912022186614527931542', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.671248518244905, 'bad_primes': [3, 5, 13], 'central_character': '1.1', 'conductor': 585, 'conductor_radical': 195, 'degree': 2, 'dirichlet_coefficients': [1, 1, 0, -1, 1, 0, 2, -3, 0, 1, 4, 0, -1, 2, 0, -1, 4, 0, 6, -1, 0, 4, 0, 0, 1, -1, 0, -2, 4, 0, -10, 5, 0, 4, 2, 0, -2, 6, 0, -3, 6, 0, -8, -4, 0, 0, 8, 0, -3, 1, 0, 1, 4, 0, 4, -6, 0, 4, -12, 0, 2, -10, 0, 7, -1, 0, -10, -4, 0, 2, 0, 0, -6, -2, 0, -6, 8, 0, 12, -1, 0, 6, 4, 0, 4, -8, 0, -12, -14, 0, -2, 0, 0, 8, 6, 0, -14, -3, 0, -1], 'euler11': [1, -4, 11], 'euler13': [1, 1, 0], 'euler17': [1, -4, 17], 'euler19': [1, -6, 19], 'euler2': [1, -1, 2], 'euler23': [1, 0, 23], 'euler29': [1, -4, 29], 'euler3': [1, 0, 0], 'euler31': [1, 10, 31], 'euler37': [1, 2, 37], 'euler41': [1, -6, 41], 'euler43': [1, 8, 43], 'euler47': [1, -8, 47], 'euler5': [1, -1, 0], 'euler53': [1, -4, 53], 'euler59': [1, 12, 59], 'euler61': [1, -2, 61], 'euler67': [1, 10, 67], 'euler7': [1, -2, 7], 'euler71': [1, 0, 71], 'euler73': [1, 6, 73], 'euler79': [1, -12, 79], 'euler83': [1, -4, 83], 'euler89': [1, 14, 89], 'euler97': [1, 14, 97], 'euler_factors': [[1, -1, 2], [1, 0, 0], [1, -1, 0], [1, -2, 7], [1, -4, 11], [1, 1, 0], [1, -4, 17], [1, -6, 19], [1, 0, 23], [1, -4, 29], [1, 10, 31], [1, 2, 37], [1, -6, 41], [1, 8, 43], [1, -8, 47], [1, -4, 53], [1, 12, 59], [1, -2, 61], [1, 10, 67], [1, 0, 71], [1, 6, 73], [1, -12, 79], [1, -4, 83], [1, 14, 89], [1, 14, 97]], 'index': 7, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/585/i', 'ModularForm/GL2/Q/holomorphic/585/2/a/i/1/1', 'ModularForm/GL2/Q/holomorphic/585/2/a/i'], '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': '2-585-1.1-c1-0-7', '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': '2-585-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.161307131863703, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1542770274153734002, 'z1': {'__RealLiteral__': 0, 'data': '1.37276923078037774007010116691', 'prec': 103}}
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lfunc_instances • Show schema
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id: 11912576
{'Lhash': '1740191739373590610360603037630', 'Lhash_array': ['1740191739373590610360603037630'], 'label': '2-585-1.1-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/585/2/a/i'}
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id: 24549836
{'Lhash': '1740191739373590610360603037630', 'Lhash_array': ['1740191739373590610360603037630'], 'label': '2-585-1.1-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/585/2/a/i/1/1'}
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id: 32895
{'Lhash': '1542770274153734002', 'Lhash_array': ['1542770274153734002'], 'label': '2-585-1.1-c1-0-7', 'type': 'ECQ', 'url': 'EllipticCurve/Q/585/i'}