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'primitive': False, 'rational': True, 'root_analytic_conductor': 1.3899210998838576, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c0e4-0', 'trace_hash': 344482276159511207, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.62531970869581775371546194955', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.851464515418252297395622892466', 'prec': 107}, 'z3': {'__RealLiteral__': 0, 'data': '1.35545480193398473659176646527', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 13.929039908850575, 'bad_primes': [7, 79], 'central_character': '1.1', 'conductor': 224539465898881, 'conductor_radical': 553, 'degree': 8, 'dirichlet_coefficients': [1, 1, 0, 1, 1, 0, 0, 0, -2, 1, 1, 0, -2, 0, 0, 0, 0, -2, 1, 1, 0, 1, 1, 0, 1, -2, 0, 0, 0, 0, 1, -1, 0, 0, 0, -2, 0, 1, 0, 0, 0, 0, 0, 1, -2, 1, 0, 0, 0, 1, 0, -2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, -1, -2, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, -2, 0, 1, 0, 8, 0, 0, 0, 0, 0, 1, -2, 0, 1, 0, 0, 1, 0, -2, 0, -2, 1], 'euler11': [1, -1, 0, 1, -1, 1, 0, -1, 1], 'euler13': [1, 2, 3, 4, 5, 4, 3, 2, 1], 'euler17': [1, 0, 2, 0, 3, 0, 2, 0, 1], 'euler19': [1, -1, 0, 1, -1, 1, 0, -1, 1], 'euler2': [1, -1, 0, 1, -1, 1, 0, -1, 1], 'euler23': [1, -1, 0, 1, -1, 1, 0, -1, 1], 'euler29': [1, 0, -4, 0, 6, 0, -4, 0, 1], 'euler3': [1, 0, 2, 0, 3, 0, 2, 0, 1], 'euler31': [1, -1, 0, 1, -1, 1, 0, -1, 1], 'euler37': [1, 0, 2, 0, 3, 0, 2, 0, 1], 'euler41': [1, 0, -4, 0, 6, 0, -4, 0, 1], 'euler43': [1, 0, -4, 0, 6, 0, -4, 0, 1], 'euler47': [1, 0, 2, 0, 3, 0, 2, 0, 1], 'euler5': [1, -1, 0, 1, -1, 1, 0, -1, 1], 'euler53': [1, 0, 2, 0, 3, 0, 2, 0, 1], 'euler59': [1, 0, 2, 0, 3, 0, 2, 0, 1], 'euler61': [1, 0, 2, 0, 3, 0, 2, 0, 1], 'euler67': [1, -1, 0, 1, -1, 1, 0, -1, 1], 'euler7': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler71': [1, 0, -4, 0, 6, 0, -4, 0, 1], 'euler73': [1, -1, 0, 1, -1, 1, 0, -1, 1], 'euler79': [1, 2, 3, 2, 1, 0, 0, 0, 0], 'euler83': [1, -8, 28, -56, 70, -56, 28, -8, 1], 'euler89': [1, -1, 0, 1, -1, 1, 0, -1, 1], 'euler97': [1, 2, 3, 4, 5, 4, 3, 2, 1], 'euler_factors': [[1, -1, 0, 1, -1, 1, 0, -1, 1], [1, 0, 2, 0, 3, 0, 2, 0, 1], [1, -1, 0, 1, -1, 1, 0, -1, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, -1, 0, 1, -1, 1, 0, -1, 1], [1, 2, 3, 4, 5, 4, 3, 2, 1], [1, 0, 2, 0, 3, 0, 2, 0, 1], [1, -1, 0, 1, -1, 1, 0, -1, 1], [1, -1, 0, 1, -1, 1, 0, -1, 1], [1, 0, -4, 0, 6, 0, -4, 0, 1], [1, -1, 0, 1, -1, 1, 0, -1, 1], [1, 0, 2, 0, 3, 0, 2, 0, 1], [1, 0, -4, 0, 6, 0, -4, 0, 1], [1, 0, -4, 0, 6, 0, -4, 0, 1], [1, 0, 2, 0, 3, 0, 2, 0, 1], [1, 0, 2, 0, 3, 0, 2, 0, 1], [1, 0, 2, 0, 3, 0, 2, 0, 1], [1, 0, 2, 0, 3, 0, 2, 0, 1], [1, -1, 0, 1, -1, 1, 0, -1, 1], [1, 0, -4, 0, 6, 0, -4, 0, 1], [1, -1, 0, 1, -1, 1, 0, -1, 1], [1, 2, 3, 2, 1, 0, 0, 0, 0], [1, -8, 28, -56, 70, -56, 28, -8, 1], [1, -1, 0, 1, -1, 1, 0, -1, 1], [1, 2, 3, 4, 5, 4, 3, 2, 1]], 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3871/1/m/c'], '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': '8-3871e4-1.1-c0e4-0-4', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0, 0, 0, 0], 'order_of_vanishing': 0, 'prelabel': '8-3871e4-1.1-c0e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.3899210998838576, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0e4-0', 'trace_hash': 344482276159511207, 'z1': {'__RealLiteral__': 0, 'data': '0.62531970869581775371546194955', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '792686904062794935847796850457,1079359504042986012494527937382,1718243093253851549932620437593,2058499141074921649263686557937', 'Lhash_array': ['792686904062794935847796850457', '1079359504042986012494527937382', '1718243093253851549932620437593', '2058499141074921649263686557937'], 'factors': ['2-3871-553.394-c0-0-5', '2-3871-553.473-c0-0-4', '2-3871-553.394-c0-0-15', '2-3871-553.473-c0-0-12'], 'label': '8-3871e4-1.1-c0e4-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3871/1/m/c'}