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'primitive': False, 'rational': True, 'root_analytic_conductor': 0.8823499417507115, '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': 1921184322872617398, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.14443759536289464974120539366', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.36274078236633075997521077275', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.36611514249903159304354701171', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 0.36738962761016053, 'bad_primes': [2, 3, 5, 13], 'central_character': '1.1', 'conductor': 5922408960000, 'conductor_radical': 390, 'degree': 8, 'dirichlet_coefficients': [1, 0, 2, 1, 0, 0, 0, 0, 1, 0, 0, 2, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 6, 0, 8, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, -4, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2], 'euler11': [1, 0, 1, 0, 0, 0, 1, 0, 1], 'euler13': [1, -4, 6, -4, 1, 0, 0, 0, 0], 'euler17': [1, 0, -2, 0, 3, 0, -2, 0, 1], 'euler19': [1, 0, -2, 0, 3, 0, -2, 0, 1], 'euler2': [1, 0, -1, 0, 1, 0, 0, 0, 0], 'euler23': [1, 0, 1, 0, 0, 0, 1, 0, 1], 'euler29': [1, 0, 1, 0, 0, 0, 1, 0, 1], 'euler3': [1, -2, 3, -2, 1, 0, 0, 0, 0], 'euler31': [1, 0, 2, 0, 3, 0, 2, 0, 1], 'euler37': [1, -6, 17, -30, 36, -30, 17, -6, 1], 'euler41': [1, 0, -2, 0, 3, 0, -2, 0, 1], 'euler43': [1, 2, 1, 2, 4, 2, 1, 2, 1], 'euler47': [1, 0, -2, 0, 3, 0, -2, 0, 1], 'euler5': [1, 0, 2, 0, 1, 0, 0, 0, 0], 'euler53': [1, 0, -4, 0, 6, 0, -4, 0, 1], 'euler59': [1, 0, 1, 0, 0, 0, 1, 0, 1], 'euler61': [1, 0, 2, 0, 3, 0, 2, 0, 1], 'euler67': [1, 0, 2, 0, 3, 0, 2, 0, 1], 'euler7': [1, 0, -2, 0, 3, 0, -2, 0, 1], 'euler71': [1, 0, -2, 0, 3, 0, -2, 0, 1], 'euler73': [1, 0, 4, 0, 6, 0, 4, 0, 1], 'euler79': [1, 4, 10, 16, 19, 16, 10, 4, 1], 'euler83': [1, 0, 4, 0, 6, 0, 4, 0, 1], 'euler89': [1, 0, -2, 0, 3, 0, -2, 0, 1], 'euler97': [1, 0, -2, 0, 3, 0, -2, 0, 1], 'euler_factors': [[1, 0, -1, 0, 1, 0, 0, 0, 0], [1, -2, 3, -2, 1, 0, 0, 0, 0], [1, 0, 2, 0, 1, 0, 0, 0, 0], [1, 0, -2, 0, 3, 0, -2, 0, 1], [1, 0, 1, 0, 0, 0, 1, 0, 1], [1, -4, 6, -4, 1, 0, 0, 0, 0], [1, 0, -2, 0, 3, 0, -2, 0, 1], [1, 0, -2, 0, 3, 0, -2, 0, 1], [1, 0, 1, 0, 0, 0, 1, 0, 1], [1, 0, 1, 0, 0, 0, 1, 0, 1], [1, 0, 2, 0, 3, 0, 2, 0, 1], [1, -6, 17, -30, 36, -30, 17, -6, 1], [1, 0, -2, 0, 3, 0, -2, 0, 1], [1, 2, 1, 2, 4, 2, 1, 2, 1], [1, 0, -2, 0, 3, 0, -2, 0, 1], [1, 0, -4, 0, 6, 0, -4, 0, 1], [1, 0, 1, 0, 0, 0, 1, 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, 4, 0, 6, 0, 4, 0, 1], [1, 4, 10, 16, 19, 16, 10, 4, 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]], 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1560/1/dk/b'], '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': '8-1560e4-1.1-c0e4-0-2', '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': '8-1560e4-1.1-c0e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.8823499417507115, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0e4-0', 'trace_hash': 1921184322872617398, 'z1': {'__RealLiteral__': 0, 'data': '1.14443759536289464974120539366', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1450747004685524927921228507502,1727479170722166120835648667822,1731756680369770539688745589275,2620109864203985957120094537489', 'Lhash_array': ['1450747004685524927921228507502', '1727479170722166120835648667822', '1731756680369770539688745589275', '2620109864203985957120094537489'], 'label': '8-1560e4-1.1-c0e4-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1560/1/dk/b'}