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lfunc_lfunctions • Show schema
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{'Lhash': '1388424106822171472130855529802', 'a10': 0, 'a2': 0, 'a3': -1, 'a4': 0, 'a5': 2, 'a6': 0, 'a7': -2, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.1325108752343365, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]]], 'bad_primes': [2, 3], 'central_character': '768.1', 'coefficient_field': '1.1.1.1', 'conductor': 768, 'conductor_radical': 6, 'degree': 2, 'euler_factors': [[1], [1, 1], [1, -2, 5], [1, 2, 7], [1, 0, 11], [1, -4, 13], [1, 2, 17], [1, -4, 19], [1, -4, 23], [1, -6, 29], [1, 2, 31], [1, -8, 37], [1, 2, 41], [1, -4, 43], [1, -12, 47], [1, -6, 53], [1, 4, 59], [1, 0, 61], [1, 12, 67], [1, -12, 71], [1, -6, 73], [1, 10, 79], [1, -16, 83], [1, -10, 89], [1, 2, 97], [1, 10, 101], [1, 6, 103], [1, -12, 107], [1, 4, 109], [1, 6, 113]], 'euler_factors_factorization': [[1], [[[1, 1], 1]], [[[1, -2, 5], 1]], [[[1, 2, 7], 1]], [[[1, 0, 11], 1]], [[[1, -4, 13], 1]], [[[1, 2, 17], 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-2.373059081140203, -0.8673334246634657, 1.1977785579350058, 3.256091122295255, 4.731604339262725, 5.22390924887189, 4.63379966194346, 3.186278693682256], 'positive_zeros': ['1.09527349773841298009626376824493', '2.63713724931622987423343237649442', '3.87120361857012739887619384713410', '5.12505772656764585053702097554611', '6.02952025279743756519610804547594', '6.53729896264740462444493449031156', '7.60982656432259660497620212593611', '8.889403972374772412587674256599645', '9.494482055881130926006645834293658', '10.34935950175211712364487117086984'], 'prelabel': '2-768-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.4763906951921655, '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': 1636210429938901289, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.09527349773841298009626376824', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.63713724931622987423343237649', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.87120361857012739887619384713', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.1325108752343365, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 768, 'conductor_radical': 6, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, 2, 0, -2, 0, 1, 0, 0, 0, 4, 0, -2, 0, -2, 0, 4, 0, 2, 0, 4, 0, -1, 0, -1, 0, 6, 0, -2, 0, 0, 0, -4, 0, 8, 0, -4, 0, -2, 0, 4, 0, 2, 0, 12, 0, -3, 0, 2, 0, 6, 0, 0, 0, -4, 0, -4, 0, 0, 0, -2, 0, 8, 0, -12, 0, -4, 0, 12, 0, 6, 0, 1, 0, 0, 0, -10, 0, 1, 0, 16, 0, -4, 0, -6, 0, 10, 0, -8, 0, 2, 0, 8, 0, -2, 0, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, -4, 13], 'euler17': [1, 2, 17], 'euler19': [1, -4, 19], 'euler2': [1, 0, 0], 'euler23': [1, -4, 23], 'euler29': [1, -6, 29], 'euler3': [1, 1, 0], 'euler31': [1, 2, 31], 'euler37': [1, -8, 37], 'euler41': [1, 2, 41], 'euler43': [1, -4, 43], 'euler47': [1, -12, 47], 'euler5': [1, -2, 5], 'euler53': [1, -6, 53], 'euler59': [1, 4, 59], 'euler61': [1, 0, 61], 'euler67': [1, 12, 67], 'euler7': [1, 2, 7], 'euler71': [1, -12, 71], 'euler73': [1, -6, 73], 'euler79': [1, 10, 79], 'euler83': [1, -16, 83], 'euler89': [1, -10, 89], 'euler97': [1, 2, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, -2, 5], [1, 2, 7], [1, 0, 11], [1, -4, 13], [1, 2, 17], [1, -4, 19], [1, -4, 23], [1, -6, 29], [1, 2, 31], [1, -8, 37], [1, 2, 41], [1, -4, 43], [1, -12, 47], [1, -6, 53], [1, 4, 59], [1, 0, 61], [1, 12, 67], [1, -12, 71], [1, -6, 73], [1, 10, 79], [1, -16, 83], [1, -10, 89], [1, 2, 97]], 'index': 2, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/768/d', 'ModularForm/GL2/Q/holomorphic/768/2/a/d/1/1', 'ModularForm/GL2/Q/holomorphic/768/2/a/d'], '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': '2-768-1.1-c1-0-2', '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': '2-768-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.4763906951921655, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1636210429938901289, 'z1': {'__RealLiteral__': 0, 'data': '1.09527349773841298009626376824', 'prec': 103}}
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lfunc_instances • Show schema
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id: 14394751
{'Lhash': '1388424106822171472130855529802', 'Lhash_array': ['1388424106822171472130855529802'], 'label': '2-768-1.1-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/768/2/a/d'}
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id: 24550469
{'Lhash': '1388424106822171472130855529802', 'Lhash_array': ['1388424106822171472130855529802'], 'label': '2-768-1.1-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/768/2/a/d/1/1'}
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id: 93359
{'Lhash': '1636210429938901289', 'Lhash_array': ['1636210429938901289'], 'label': '2-768-1.1-c1-0-2', 'type': 'ECQ', 'url': 'EllipticCurve/Q/768/d'}