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lfunc_lfunctions • Show schema
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{'Lhash': '566887230339177840563717189363', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.0, 0.0], 'a4': [0.0, 0.0], 'a5': [-1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-4.465693822431187, 0.0], 'a8': [0.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 44.0774219157468, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-1.0, 0]]], [5, [[1.0, 0], [1.0, 0]]], [23, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 3, 5, 23], 'central_character': '5520.1', 'coefficient_field': 'CDF', 'conductor': 5520, 'conductor_radical': 690, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [4.465693822431187, 0], [7.0, 0]], [[1.0, 0], [3.394125634627469, 0], [11.0, 0]], [[1.0, 0], [4.705649410613527, 0], [13.0, 0]], [[1.0, 0], [6.548295681072598, 0], [17.0, 0]], [[1.0, 0], [-6.225738234248847, 0], [19.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-5520-1.1-c1-0-1', 'leading_term': '0.86544615349992053200722503189811', '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/5520/2/a/cb/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [0.8654461534999205, 0.8543645157249717, 0.8210875481923673, 0.7655278902653768, 0.6875686504838577, 0.5871043326493348, 0.46409408646508377, 0.31862372910064973, 0.15097256736792156, -0.0383190673667245, -0.24838552541997794, -0.47797842023412723, -0.7254192803338705, -0.9885649653769972, -1.2647880141456307, -1.550973564231639, -1.8435339603414669, -2.1384416491589757, -2.4312804380980397, -2.7173146676435245, -2.9915753097851137, -3.248961460195406, -3.484355146173447, -3.6927468376273724, -3.8693685402525593, 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'6.17676926113442828921726172438846', '6.84640733730721831575239808708909', '7.46799117326591776416891949987292', '8.005510937914596088162700017536280'], 'prelabel': '2-5520-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.639082912251269, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.44719517368359605850515577495', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.21802730382417712860980062184', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.89194634994068628803332016180', '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, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5520/2/a/cb/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': '2-5520-1.1-c1-0-1', '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': False, 'root_analytic_conductor': 6.639082912251269, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.44719517368359605850515577495', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '566887230339177840563717189363', 'Lhash_array': ['566887230339177840563717189363'], 'label': '2-5520-1.1-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5520/2/a/cb/1/1'}