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'0.0', 'prec': 10}, 'spectral_label': 'c0e4-0', 'trace_hash': 572629008493397873, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.857268764279335774323015240523', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.37810325116112342368004411780', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.63469389138249823907523463923', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.01810413809885428, 'bad_primes': [3, 5, 7], 'central_character': '1.1', 'conductor': 291843050625, 'conductor_radical': 105, 'degree': 8, 'dirichlet_coefficients': [1, 0, -2, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, -4, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 2, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler11': [1, 0, 2, 0, 3, 0, 2, 0, 1], 'euler13': [1, 0, -4, 0, 6, 0, -4, 0, 1], 'euler17': [1, 0, -2, 0, 3, 0, -2, 0, 1], 'euler19': [1, 0, 0, 0, -1, 0, 0, 0, 1], 'euler2': [1, 0, 0, 0, -1, 0, 0, 0, 1], 'euler23': [1, 0, 0, 0, -1, 0, 0, 0, 1], 'euler29': [1, 0, -4, 0, 6, 0, -4, 0, 1], 'euler3': [1, 2, 3, 2, 1, 0, 0, 0, 0], 'euler31': [1, 0, 0, 0, -1, 0, 0, 0, 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, -2, 3, -2, 1, 0, 0, 0, 0], 'euler53': [1, 0, 0, 0, -1, 0, 0, 0, 1], 'euler59': [1, 0, 2, 0, 3, 0, 2, 0, 1], 'euler61': [1, 0, 0, 0, -1, 0, 0, 0, 1], 'euler67': [1, 0, 2, 0, 3, 0, 2, 0, 1], 'euler7': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler71': [1, 0, -4, 0, 6, 0, -4, 0, 1], 'euler73': [1, 0, 2, 0, 3, 0, 2, 0, 1], 'euler79': [1, 0, -2, 0, 3, 0, -2, 0, 1], 'euler83': [1, 0, 4, 0, 6, 0, 4, 0, 1], 'euler89': [1, 0, 2, 0, 3, 0, 2, 0, 1], 'euler97': [1, 0, -4, 0, 6, 0, -4, 0, 1], 'euler_factors': [[1, 0, 0, 0, -1, 0, 0, 0, 1], [1, 2, 3, 2, 1, 0, 0, 0, 0], [1, -2, 3, -2, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 2, 0, 3, 0, 2, 0, 1], [1, 0, -4, 0, 6, 0, -4, 0, 1], [1, 0, -2, 0, 3, 0, -2, 0, 1], [1, 0, 0, 0, -1, 0, 0, 0, 1], [1, 0, 0, 0, -1, 0, 0, 0, 1], [1, 0, -4, 0, 6, 0, -4, 0, 1], [1, 0, 0, 0, -1, 0, 0, 0, 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, 0, 0, -1, 0, 0, 0, 1], [1, 0, 2, 0, 3, 0, 2, 0, 1], [1, 0, 0, 0, -1, 0, 0, 0, 1], [1, 0, 2, 0, 3, 0, 2, 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, 4, 0, 6, 0, 4, 0, 1], [1, 0, 2, 0, 3, 0, 2, 0, 1], [1, 0, -4, 0, 6, 0, -4, 0, 1]], 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/735/1/o/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': '8-735e4-1.1-c0e4-0-1', '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': '8-735e4-1.1-c0e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.6056507114544296, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0e4-0', 'trace_hash': 572629008493397873, 'z1': {'__RealLiteral__': 0, 'data': '0.857268764279335774323015240523', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1086717263595612498915326006996,1746953413510872484915226189615,2072220692600443930723208966202,3340104900360253606410876264349', 'Lhash_array': ['1086717263595612498915326006996', '1746953413510872484915226189615', '2072220692600443930723208966202', '3340104900360253606410876264349'], 'factors': ['2-735-105.74-c0-0-0', '2-735-105.74-c0-0-1', '2-735-105.44-c0-0-3', '2-735-105.44-c0-0-5'], 'label': '8-735e4-1.1-c0e4-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/735/1/o/c'}