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lfunc_lfunctions • Show schema
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{'Lhash': '696935800900175563375925032482', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-2.124885419764574, 0.0], 'a4': [0.0, 0.0], 'a5': [-1.4848619528719296, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [1.5151380471280704, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.820234615149646, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [29, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 29], 'central_character': '1856.1', 'coefficient_field': 'CDF', 'conductor': 1856, 'conductor_radical': 58, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [2.124885419764574, 0], [3.0, 0]], [[1.0, 0], [1.4848619528719296, 0], [5.0, 0]], [[1.0, 0], [0, 0], [7.0, 0]], [[1.0, 0], [-3.155161514020715, 0], [11.0, 0]], [[1.0, 0], [6.764908886657219, 0], [13.0, 0]], [[1.0, 0], [-2.0, 0], [17.0, 0]], [[1.0, 0], [1.030276094256141, 0], [19.0, 0]], [[1.0, 0], [4.249770839529148, 0], [23.0, 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 5, 'label': '2-1856-1.1-c1-0-5', 'leading_term': '0.62198943504592709504603827072906', '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/1856/2/a/y/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [0.6219894350459271, 0.6152815538171023, 0.5950847756610009, 0.5611891552725454, 0.5132755860060628, 0.4509595737932007, 0.37384801846274107, 0.2816052335639581, 0.1740241921420135, 0.05109908016532269, -0.08690444254780134, -0.23938444985474966, -0.4053461635853401, -0.5833559164484559, -0.7715076678701134, -0.9674037890694978, -1.168151570345754, -1.3703766351679219, -1.5702541449611225, -1.7635583248647286, -1.945730422058548, -2.1119647210377868, -2.257311689033648, -2.3767967212286982, -2.465552317033193, 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'6.04651957334448189316370596550183', '6.80491798489944905710564185999393', '7.54007372699774709849394215875581', '8.324018514517283215030725231429921', '9.465468168476728427348750021679977'], 'prelabel': '2-1856-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.849705782933242, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.54978540677904334919663387981', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.12752472267340193791689713496', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.52689088308962823922966992057', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 14.820234615149646, 'bad_primes': [2, 29], 'central_character': '1.1', 'conductor': 1856, 'conductor_radical': 58, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1856/2/a/y/1/1'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, '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': '2-1856-1.1-c1-0-5', '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': '2-1856-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.849705782933242, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.54978540677904334919663387981', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '696935800900175563375925032482', 'Lhash_array': ['696935800900175563375925032482'], 'label': '2-1856-1.1-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1856/2/a/y/1/1'}