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lfunc_lfunctions • Show schema
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{'Lhash': '1720271863372800332476712964986', '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': [2.8284271247461903, 0.0], 'a8': [0.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 49.826650861278985, '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]]], [13, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '6240.1', 'coefficient_field': 'CDF', 'conductor': 6240, 'conductor_radical': 390, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-2.8284271247461903, 0], [7.0, 0]], [[1.0, 0], [-2.8284271247461903, 0], [11.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [3.65685424949238, 0], [17.0, 0]], [[1.0, 0], [1.17157287525381, 0], [19.0, 0]], [[1.0, 0], [-4.0, 0], [23.0, 0]], [[1.0, 0], 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'2-6240-1.1-c1-0-77', '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': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/6240/2/a/bh/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [-6.873271757090773e-61, 0.16995029103417067, 0.3388450390037729, 0.5055954995155028, 0.6690492309956477, 0.8279648157370371, 0.9809939455466528, 1.126672529768522, 1.2634219208552364, 1.3895607710015851, 1.5033274779430843, 1.602912680800777, 1.686500845113236, 1.7523196344212277, 1.798695499329367, 1.8241137143262802, 1.8272809470651805, 1.8071883450055217, 1.7631730639236203, 1.6949761387958793, 1.6027946099672943, 1.4873258686656898, 1.3498022795032494, 1.1920142777415264, 1.0163203294788659, 0.825642386111663, 0.6234457613030313, 0.4137027080695295, 0.20083937194980808, -0.010333762413222519, -0.21470733796765631, 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'rational': False, 'root_analytic_conductor': 7.058799534005693, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.35705521936650401298490173657', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.03406364065911879725986757058', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.46121125390384002069196025271', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 49.826650861278985, 'bad_primes': [2, 3, 5, 13], 'central_character': '1.1', 'conductor': 6240, 'conductor_radical': 390, 'degree': 2, 'index': 77, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6240/2/a/bh/1/2'], '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': '2-6240-1.1-c1-0-77', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-6240-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.058799534005693, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.35705521936650401298490173657', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1720271863372800332476712964986', 'Lhash_array': ['1720271863372800332476712964986'], 'label': '2-6240-1.1-c1-0-77', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6240/2/a/bh/1/2'}