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lfunc_lfunctions • Show schema
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{'Lhash': '2273947970061664901896454710243', 'a10': [-10.653919501415007, 0.0], 'a2': [-2.6133040376486147, 0.0], 'a3': [1.195991714237707, 0.0], 'a4': [4.829357993190551, 0.0], 'a5': [4.0768006125307705, 0.0], 'a6': [-3.125489975811688, 0.0], 'a7': [3.618293182755668, 0.0], 'a8': [-7.393972667558249, 0.0], 'a9': [-1.569603819474751, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.6688734022447609, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[11, [[1.0, 0], [1.0, 0]]], [19, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [11, 19], 'central_character': '209.1', 'coefficient_field': 'CDF', 'conductor': 209, 'conductor_radical': 209, 'conjugate': '2273947970061664901896454710243', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.6133040376486147, 0], [2.0, 0]], [[1.0, 0], [-1.195991714237707, 0], [3.0, 0]], [[1.0, 0], [-4.0768006125307705, 0], [5.0, 0]], [[1.0, 0], [-3.618293182755668, 0], [7.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], 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'6.52130790402011248370966936783897', '7.83985106599742827476942966363092', '8.565913160388211801843917993778999', '9.326062409880506864726372491086930', '10.15033492401553141639253930737427', '10.91777465262375145779190572583345', '11.97346819375939427866831060833942'], 'prelabel': '2-209-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2918488310343283, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.79382865408832722659243733553', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.44642084002183667295276153334', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.35883619559174249974714204608', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.6688734022447609, 'bad_primes': [11, 19], 'central_character': '1.1', 'conductor': 209, 'conductor_radical': 209, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/209/2/a/d/1/2'], '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': '2-209-1.1-c1-0-4', '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': '2-209-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2918488310343283, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.79382865408832722659243733553', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2273947970061664901896454710243', 'Lhash_array': ['2273947970061664901896454710243'], 'label': '2-209-1.1-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/209/2/a/d/1/2'}