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lfunc_lfunctions • Show schema
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{'Lhash': '1519947097367375333589795518740', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-1.7242497784694655, -2.986488221248495], 'a4': [0, 0], 'a5': [-0.5, -0.8660254037844386], 'a6': [0, 0], 'a7': [4.4484995569389305, 0], 'a8': [0, 0], 'a9': [-4.446074597104001, 7.7008270964254555], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12.137261107234623, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0.5, 0.8660254037844386]]], [19, [[1.0, 0], [-4.224249778469465, 1.0750413057648867]]]], 'bad_primes': [2, 5, 19], 'central_character': '1520.881', 'coefficient_field': 'CDF', 'conductor': 1520, 'conductor_radical': 190, 'conjugate': '1136960486863364535466079298178', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.7242497784694655, 2.986488221248495], [-1.5, 2.598076211353316]], [[1.0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [-4.4484995569389305, 0], [7.0, 0]], [[1.0, 0], 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'8.273918201093456107811261505403379', '9.274031333468896978621901208125451', '9.666879525238190338816108542011954'], 'prelabel': '2-1520-19.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.483857216826577, 'root_angle': 0.6550962640099576, 'root_number': '-0.4681970632984904444917401873038456516725567972524062772 + 0.8836240772628761568663124000574626944238721247242617911*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.32754813200497884', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.19902684311727707524980299997', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.12226543625697350024152140476', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.02341980433619974835293590638', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 12.137261107234623, 'bad_primes': [2, 5, 19], 'central_character': '19.7', 'conductor': 1520, 'conductor_radical': 190, 'degree': 2, 'index': 21, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1520/2/q/n/881/1'], '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': '2-1520-19.7-c1-0-21', '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': '2-1520-19.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.483857216826577, 'root_angle': 0.3275481320049788, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.19902684311727707524980299997', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1519947097367375333589795518740', 'Lhash_array': ['1519947097367375333589795518740'], 'label': '2-1520-19.7-c1-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1520/2/q/n/881/1'}