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lfunc_lfunctions • Show schema
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{'Lhash': '3409733288489376047976757250025', 'a10': [131.3283681681308, 0.0], 'a2': [6.5955468252652745, 0.0], 'a3': [-15.285465776733858, 0.0], 'a4': [11.501237924266839, 0.0], 'a5': [19.911672473472088, 0.0], 'a6': [-100.81600527643799, 0.0], 'a7': [48.332595383583104, 0.0], 'a8': [-135.20054513047006, 0.0], 'a9': [-9.354535988298002, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11.387251206721627, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[71, [[1.0, 0], [5041.0, 0]]]], 'bad_primes': [71], 'central_character': '71.1', 'coefficient_field': 'CDF', 'conductor': 71, 'conductor_radical': 71, 'conjugate': '3409733288489376047976757250025', 'degree': 2, 'euler_factors': [[[1.0, 0], [-6.5955468252652745, 0], [32.0, 0]], [[1.0, 0], [15.285465776733858, 0], [243.0, 0]], [[1.0, 0], [-19.911672473472088, 0], [3125.0, 0]], [[1.0, 0], [-48.332595383583104, 0], [16807.0, 0]], [[1.0, 0], [616.1815008606184, 0], [161051.0, 0]], 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-0.9708445108441851, -1.5340319500840012, -1.9357037330216376], 'positive_zeros': ['2.68980528851994658215377546177383', '4.71364094370194921761416360465036', '5.40920811333008798834677325045750', '6.54332654297571256555067438882157', '8.340788683405881635758801590122152', '10.08239671601505218521792756191007', '11.21163024853652632777059633979077', '12.20296877983124413501254690373427', '13.11723759805464309555189536575227'], 'prelabel': '2-71-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.3745001417575353, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.68980528851994658215377546177', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.71364094370194921761416360465', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.40920811333008798834677325046', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 11.387251206721627, 'bad_primes': [71], 'central_character': '1.1', 'conductor': 71, 'conductor_radical': 71, 'degree': 2, 'index': 25, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/71/6/a/a/1/9'], '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': '2-71-1.1-c5-0-25', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 1, 'prelabel': '2-71-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.3745001417575353, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '2.68980528851994658215377546177', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3409733288489376047976757250025', 'Lhash_array': ['3409733288489376047976757250025'], 'label': '2-71-1.1-c5-0-25', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/71/6/a/a/1/9'}