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lfunc_lfunctions • Show schema
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{'Lhash': '647528560915930207581223322128', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.5226742942949125, 0.825507718615332], 'a4': [0.0, 0.0], 'a5': [1.3387038286077486, 1.3387038286077486], 'a6': [0.0, 0.0], 'a7': [-0.566234292761839, 2.113215149575013], 'a8': [0.0, 0.0], 'a9': [1.6370740130130197, -2.513958765755208], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.9826650861278985, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [1.5226742942949125, -0.825507718615332]]], [13, [[1.0, 0], [3.2703585893353697, -1.5181418567315677]]]], 'bad_primes': [2, 3, 13], 'central_character': '624.305', 'coefficient_field': 'CDF', 'conductor': 624, 'conductor_radical': 78, 'conjugate': '2456155623701547265203553869428', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.5226742942949125, -0.825507718615332]], [[1.0, 0], [-1.3387038286077486, -1.3387038286077486], [0, 5.0]], [[1.0, 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'8.466894632072980747476472755093884', '9.688158817270199700116800444340182', '10.18739836836752623759991431465216'], 'prelabel': '2-624-39.32-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.232188407399317, 'root_angle': -0.7841831126232516, 'root_number': '-0.778823261780471 - 0.627243435126768*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.392091556312', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.51080996672059978877304988470', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.90658963007191724068549680488', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.62999511103849693711168916535', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.9826650861278985, 'bad_primes': [2, 3, 13], 'central_character': '39.32', 'conductor': 624, 'conductor_radical': 78, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/624/2/cn/f/305/3'], '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': '2-624-39.32-c1-0-3', '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': '2-624-39.32-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.232188407399317, 'root_angle': -0.3920915563116258, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.51080996672059978877304988470', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '647528560915930207581223322128', 'Lhash_array': ['647528560915930207581223322128'], 'label': '2-624-39.32-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/624/2/cn/f/305/3'}