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lfunc_lfunctions • Show schema
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{'Lhash': '444035122886897360100787575374', 'a10': [2.1485720922835623, 0.6193851501773645], 'a2': [-0.5, -0.8660254037844386], 'a3': [-0.7588190451025207, -2.831951230073507], 'a4': [-0.5, 0.8660254037844386], 'a5': [-1.6106893209222184, 1.5510254386911657], 'a6': [-2.0731321849709863, 2.0731321849709863], 'a7': [0.455090881300836, 1.6984222910760172], 'a8': [1.0, 0.0], 'a9': [-4.846065214951231, 2.797877056362575], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.9544648747873756, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.5, 0.8660254037844386]]], [5, [[1.0, 0], [1.6106893209222184, -1.5510254386911657]]], [37, [[1.0, 0], [-2.518840096904193, -5.536735912631889]]]], 'bad_primes': [2, 5, 37], 'central_character': '370.103', 'coefficient_field': 'CDF', 'conductor': 370, 'conductor_radical': 370, 'conjugate': '2183975032875375855454637465902', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5, 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[-94.39676901250381, -54.5]], [[1.0, 0], [14.547499026080272, -8.399002478743263], [56.5, -97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-370-185.103-c1-0-0', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/370/2/q/e/103/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.43830561108965077, 0.30561345783934174, 0.1486700753734095, -0.04030865855624551, -0.2696572104849727, -0.5471697791425166, -0.8790719161055353, -1.2690966120059486, -1.7176692226561667, -2.221211581433358, -2.7716023605279947, -3.3558568097932815, -3.9561032679613612, -4.549932701139132, -5.11118086118365, -5.611171751877737, -6.020408142921052, -6.310643179855211, -6.457211332715241, -6.441442981967199, -6.2529418810467625, -5.891476028098126, 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'5.40321827890047302197063494803925', '6.21507407166420386614709285147223', '7.944034274210518567549897978775491', '8.480486517548494220648529488908959', '9.467294671685231420836222058067097', '10.37007662897974730322557570390254', '11.04006297792805229820413319052933'], 'prelabel': '2-370-185.103-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7188556875978203, 'root_angle': -0.21391260835648077, 'root_number': '0.782561766815513 - 0.6225729524470065*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.106956304178', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.35028194899048106830667011841', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.67736805921886314042450089189', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.29068644236957626114046029823', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.9544648747873756, 'bad_primes': [2, 5, 37], 'central_character': '185.103', 'conductor': 370, 'conductor_radical': 370, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/370/2/q/e/103/1'], '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': '2-370-185.103-c1-0-0', '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': '2-370-185.103-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7188556875978203, 'root_angle': -0.10695630417824038, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.35028194899048106830667011841', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '444035122886897360100787575374', 'Lhash_array': ['444035122886897360100787575374'], 'label': '2-370-185.103-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/370/2/q/e/103/1'}