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lfunc_lfunctions • Show schema
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{'Lhash': '2825174324856286058249867780369', 'a10': [0, 0], 'a2': [-1.0, 0], 'a3': [0, -3.0], 'a4': [1.0, 0], 'a5': [0, 0], 'a6': [0, 3.0], 'a7': [0, 0], 'a8': [-1.0, 0], 'a9': [-6.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 13.303076976745318, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 0]]], [7, [[1.0, 0], [0, 0]]], [17, [[1.0, 0], [1.0, -4.0]]]], 'bad_primes': [2, 7, 17], 'central_character': '1666.883', 'coefficient_field': 'CDF', 'conductor': 1666, 'conductor_radical': 238, 'conjugate': '1540836999489996937219954073711', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 0]], [[1.0, 0], [0, 3.0], [-3.0, 0]], [[1.0, 0], [0, 0], [-5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 3.0], [-11.0, 0]], [[1.0, 0], [5.0, 0], [13.0, 0]], [[1.0, 0], [1.0, -4.0]], [[1.0, 0], [4.0, 0], [19.0, 0]], [[1.0, 0], [0, 4.0], [-23.0, 0]], [[1.0, 0], [0, -4.0], [-29.0, 0]], [[1.0, 0], [0, 4.0], [-31.0, 0]], [[1.0, 0], 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-0.42202086962263075, 'root_number': '0.2425356250363329735189064621161221779498352485513894374 - 0.9701425001453318940756258484644887117993409942055577493*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.21101043481131537', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.22866957531329069298922253213', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.12902590028434432809768617726', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.36438747058234289352755295452', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 13.303076976745318, 'bad_primes': [2, 7, 17], 'central_character': '17.16', 'conductor': 1666, 'conductor_radical': 238, 'degree': 2, 'index': 60, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1666/2/b/a/883/1'], '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': '2-1666-17.16-c1-0-60', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-1666-17.16-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.6473383414135463, 'root_angle': -0.21101043481131537, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.22866957531329069298922253213', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2825174324856286058249867780369', 'Lhash_array': ['2825174324856286058249867780369'], 'label': '2-1666-17.16-c1-0-60', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1666/2/b/a/883/1'}