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lfunc_lfunctions • Show schema
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{'Lhash': '2296893375678231082317407061650', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.7736590696265117, -0.2513770698908791], 'a4': [0.0, 0.0], 'a5': [0.5, -0.8660254037844386], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [-0.2736590696265117, 0.19882495225804087], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.5489715138963027, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-0.5, 0.8660254037844386]]], [11, [[1.0, 0], [-0.8090169943749475, -0.5877852522924731]]]], 'bad_primes': [2, 5, 11], 'central_character': '1100.109', 'coefficient_field': 'CDF', 'conductor': 1100, 'conductor_radical': 110, 'conjugate': '1931484652821820310548503153098', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.7736590696265117, 0.2513770698908791], [0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 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'2-1100-275.109-c0-0-1', 'leading_term': '1.41820937769601412616830371856', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1100/1/cd/a/109/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.418209377696014, 1.4436100741967794, 1.4847392730502527, 1.5406179887687281, 1.6093780202244365, 1.688521077633803, 1.775174957904087, 1.8662969410804462, 1.9588108724929112, 2.0496880991781903, 2.135990879416462, 2.2148957371459495, 2.283709477918883, 2.3398856827026346, 2.381045715424837, 2.4050057381312695, 2.409809646761637, 2.3937669022614765, 2.355493690803084, 2.2939555431627308, 2.208509382296692, 2.0989428986706993, 1.96550914989835, 1.8089543345097148, 1.6305367967150175, 1.4320354808367846, 1.2157462725603951, 0.9844649405671667, 0.7414557261481486, 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'8.581422061184649703102835586510412', '9.370690975787689761422817702743906', '9.906444828155468277796572918844252'], 'prelabel': '2-1100-275.109-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7409261190539194, 'root_angle': 0.08666666666666667, 'root_number': '0.85536426016050662785189753316966 + 0.51802700937313020962556029870075*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.08666666666666667', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.81192938753367491219292479679', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.12654506143941500733655977629', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.52152131629379639358703178144', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.5489715138963027, 'bad_primes': [2, 5, 11], 'central_character': '275.109', 'conductor': 1100, 'conductor_radical': 110, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1100/1/cd/a/109/2'], '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': '2-1100-275.109-c0-0-1', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-1100-275.109-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7409261190539194, 'root_angle': 0.08666666666666667, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.81192938753367491219292479679', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2296893375678231082317407061650', 'Lhash_array': ['2296893375678231082317407061650'], 'factors': ['2-1100-275.109-c0-0-1'], 'label': '2-1100-275.109-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1100/1/cd/a/109/2'}