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lfunc_lfunctions • Show schema
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{'Lhash': '705528909791182852632786715442', 'a10': [0, 0], 'a2': [0, 0], 'a3': [1.0, 1.4142135623730951], 'a4': [0, 0], 'a5': [1.7320508075688772, 1.4142135623730951], 'a6': [0, 0], 'a7': [-1.0, 2.449489742783178], 'a8': [0, 0], 'a9': [-1.0, 2.8284271247461903], '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], [-1.0, -1.4142135623730951]]], [5, [[1.0, 0], [-1.7320508075688772, -1.4142135623730951]]], [7, [[1.0, 0], [1.0, -2.449489742783178]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '1680.209', 'coefficient_field': 'CDF', 'conductor': 1680, 'conductor_radical': 210, 'conjugate': '2604469905229130271605012278562', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.0, -1.4142135623730951]], [[1.0, 0], [-1.7320508075688772, -1.4142135623730951]], [[1.0, 0], [1.0, -2.449489742783178]], [[1.0, 0], [0, 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'2.64901101061555593697206518937', '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': 21, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1680/2/k/c/209/4'], '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-c1-0-21', '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': -0.42729226361268313, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.55656417443746608427149966215', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '705528909791182852632786715442', 'Lhash_array': ['705528909791182852632786715442'], 'label': '2-1680-105.104-c1-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1680/2/k/c/209/4'}