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lfunc_lfunctions • Show schema
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{'Lhash': '2498980926552501739717863797', 'a10': [-0.3230419109976908, 0.5595250028221438], 'a2': [-0.8660254037844386, 0.5], 'a3': [-2.6808453463817865, -1.54778678238928], 'a4': [0.5, -0.8660254037844386], 'a5': [0.5595250028221438, -0.3230419109976908], 'a6': [3.09557356477856, 0], 'a7': [0, 0], 'a8': [0, 1.0], 'a9': [3.29128784747792, 5.700677774165763], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.607873337894029, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.8660254037844386, -0.5]]], [7, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [2.946944705145184, -1.5216822614517023]]]], 'bad_primes': [2, 7, 11], 'central_character': '1078.1011', 'coefficient_field': 'CDF', 'conductor': 1078, 'conductor_radical': 154, 'conjugate': '1562030278538197561900954770623', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.8660254037844386, -0.5]], [[1.0, 0], [2.6808453463817865, 1.54778678238928], [1.5, 2.598076211353316]], [[1.0, 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'8.887296403465231406290121315803614', '10.01310003330930281846956552093046'], 'prelabel': '2-1078-77.10-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.9339177455910432, 'root_angle': -0.7982158728589902, 'root_number': '-0.805709766844207303208718086710099021189606084028942866 - 0.592310536468711744830458943466039479926899671429665873*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.3991079364294952', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.00197134835585024933867475115', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.59829082047027980874913969758', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.41630936376045601823862884327', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.607873337894029, 'bad_primes': [2, 7, 11], 'central_character': '77.10', 'conductor': 1078, 'conductor_radical': 154, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1078/2/i/b/1011/1'], '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': '2-1078-77.10-c1-0-0', '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': '2-1078-77.10-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.9339177455910432, 'root_angle': -0.3991079364294951, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.00197134835585024933867475115', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2498980926552501739717863797', 'Lhash_array': ['2498980926552501739717863797'], 'label': '2-1078-77.10-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1078/2/i/b/1011/1'}