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lfunc_lfunctions • Show schema
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{'Lhash': '3313072476735717417994232762160', 'a10': [-1.5381566471856447, -0.8880551543084442], 'a2': [0.5, -0.8660254037844386], 'a3': [-0.34047888522107217, -0.1965755760357697], 'a4': [-0.5, -0.8660254037844386], 'a5': [0.0, -1.7761103086168883], 'a6': [-0.34047888522107217, 0.1965755760357697], 'a7': [-2.1827417887148437, 1.2602065592859604], 'a8': [-1.0, 0.0], 'a9': [-1.4227160858124106, -2.464216545372618], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.5293877693405946, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.5, 0.8660254037844386]]], [13, [[1.0, 0], [-2.9926315232307226, -2.011008842886019]]], [17, [[1.0, 0], [2.520681309155004, -3.2628462632610526]]]], 'bad_primes': [2, 13, 17], 'central_character': '442.373', 'coefficient_field': 'CDF', 'conductor': 442, 'conductor_radical': 442, 'conjugate': '583525839023058926418539577533', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.5, 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'10.00970033102044973411923513490412', '10.59673435627475298778336231180547', '11.38810644098398156068042936950059'], 'prelabel': '2-442-221.152-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8786664869903318, 'root_angle': 0.9830860811015774, 'root_number': '-0.9985885807089212 + 0.053111641640437496*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.491543040551', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.61355335306055761772646173358', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.69376169257994322988373393043', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.99916121078982036100515291464', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.5293877693405946, 'bad_primes': [2, 13, 17], 'central_character': '221.152', 'conductor': 442, 'conductor_radical': 442, 'degree': 2, 'index': 20, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/442/2/m/b/373/6'], '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': '2-442-221.152-c1-0-20', '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': '2-442-221.152-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8786664869903318, 'root_angle': 0.4915430405507887, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.61355335306055761772646173358', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3313072476735717417994232762160', 'Lhash_array': ['3313072476735717417994232762160'], 'label': '2-442-221.152-c1-0-20', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/442/2/m/b/373/6'}