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lfunc_lfunctions • Show schema
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{'Lhash': '2691010808615648858839935139164', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0.3254536855295427, -1.7011995469595087], 'a4': [0, 0], 'a5': [-1.3449174563115533, -1.7863921841825388], 'a6': [0, 0], 'a7': [-1.5398359072972438, -2.151489107245973], 'a8': [0, 0], 'a9': [-2.7881597971504752, -1.1073233247583207], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 13.414867539575111, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-0.3254536855295427, 1.7011995469595087]]], [5, [[1.0, 0], [1.3449174563115533, 1.7863921841825388]]], [7, [[1.0, 0], [1.5398359072972438, 2.151489107245973]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '1680.209', 'coefficient_field': 'CDF', 'conductor': 1680, 'conductor_radical': 210, 'conjugate': '607843865155014319339347915303', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.3254536855295427, 1.7011995469595087]], [[1.0, 0], 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'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.12283322244406771314130860895', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.11982008529284111295141497718', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.85237273672218386426464687427', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 13.414867539575111, 'bad_primes': [2, 3, 5, 7], 'central_character': '105.104', 'conductor': 1680, 'conductor_radical': 210, 'degree': 2, 'index': 89, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1680/2/k/h/209/13'], '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': '2-1680-105.104-c1-0-89', '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': '2-1680-105.104-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.6626312317205936, 'root_angle': -0.4214893996556209, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.12283322244406771314130860895', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2691010808615648858839935139164', 'Lhash_array': ['2691010808615648858839935139164'], 'factors': ['2-1680-105.104-c1-0-89'], 'label': '2-1680-105.104-c1-0-89', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1680/2/k/h/209/13'}