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lfunc_lfunctions • Show schema
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{'Lhash': '2043226813047070016823048719950', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-2.5635850511066076, -0.8329592760727785], 'a4': [0.0, 0.0], 'a5': [1.186821431437445, -0.8622762430875025], 'a6': [0.0, 0.0], 'a7': [0.8456531353964281, 2.6026527329702223], 'a8': [0.0, 0.0], 'a9': [3.4510961755367378, 2.507368139764094], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.810734151149071, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [-0.12263977269888102, 3.3143565719687382]]]], 'bad_primes': [2, 11], 'central_character': '352.95', 'coefficient_field': 'CDF', 'conductor': 352, 'conductor_radical': 22, 'conjugate': '916097975753260252524901628838', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [2.5635850511066076, 0.8329592760727785], [2.4270509831248424, 1.7633557568774194]], [[1.0, 0], [-1.186821431437445, 0.8622762430875025], [1.545084971874737, 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[[1.0, 0], [2.115218430913785, -0.6872761300387519], [83.32875042061958, -60.54188098612473]], [[1.0, 0], [0.25716995105173046, -0.7914877246080766], [-86.56481839811937, -62.893021995294625]], [[1.0, 0], [0, 13.37424773119315], [-109.0, 0]], [[1.0, 0], [-1.2838846991070179, 3.9513908020728725], [-91.41892036436906, -66.41973350904946]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 5, 'label': '2-352-44.7-c1-0-5', '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/352/2/u/a/95/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.822516328427158, 0.9238834090864052, 1.0209080952586544, 1.1120668180723787, 1.1929132186464797, 1.2563339195221184, 1.2930791289847985, 1.2924659612693077, 1.243202056947712, 1.134312903295839, 0.956162854353299, 0.7015437020660584, 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8.015595655264336, 8.962276234044133, 8.726915240423518], 'positive_zeros': ['1.61182175331215470788658077674148', '3.95137733424658695940010867389038', '4.74180280516005593911758352120671', '5.95181059510808475910608319676018', '6.65127578632235603636701077910832', '7.67327903275739811939027274197163', '9.266147766768505149457525921492336', '10.27703530740919759485088712372878', '10.65153255250700739083255625891525', '11.52475421082400836842439139354068'], 'prelabel': '2-352-44.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6765244260520247, 'root_angle': 0.48390613266367194, 'root_number': '0.05053883646247955 + 0.9987220964858136*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.241953066332', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.61182175331215470788658077674', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.95137733424658695940010867389', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.74180280516005593911758352121', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.810734151149071, 'bad_primes': [2, 11], 'central_character': '44.7', 'conductor': 352, 'conductor_radical': 22, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/352/2/u/a/95/2'], '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': '2-352-44.7-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': '2-352-44.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6765244260520247, 'root_angle': 0.24195306633183597, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.61182175331215470788658077674', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2043226813047070016823048719950', 'Lhash_array': ['2043226813047070016823048719950'], 'label': '2-352-44.7-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/352/2/u/a/95/2'}