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lfunc_lfunctions • Show schema
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{'Lhash': '3292952799273094725218034902168', 'a10': [-0.8107020111739807, 0.23804358835909653], 'a2': [-0.5533098507729293, -0.6385536077088994], 'a3': [2.8098669243476317, 1.805791823314222], 'a4': [0.18303075759088064, -1.2730068809780122], 'a5': [0.41541501300188644, -0.9096319953545183], 'a6': [-0.40163216505404997, -2.793413066009057], 'a7': [-3.0423141656086594, -0.8933040388643841], 'a8': [-2.3357523669131477, 1.5010968985436457], 'a9': [3.3882229843886575, 7.419173447112515], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.9182796232447249, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [-0.41541501300188644, 0.9096319953545183]]], [23, [[1.0, 0], [-3.6996892130028756, -3.0516060897812753]]]], 'bad_primes': [5, 23], 'central_character': '115.36', 'coefficient_field': 'CDF', 'conductor': 115, 'conductor_radical': 115, 'conjugate': '3001967085272282940174680847433', 'degree': 2, 'euler_factors': [[[1.0, 0], 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[[1.0, 0], [-4.047379869122936, -8.86252569377238], [-54.35344091745866, 62.72721467140344]], [[1.0, 0], [5.817579921433651, 3.738731597063413], [36.97193615716789, 80.95724758655213]], [[1.0, 0], [-6.51624287175811, 14.268581587409], [-63.52149119269265, -73.30770871236305]], [[1.0, 0], [3.271187191166317, 7.16290080701837], [-66.14093412847379, 76.33070700978008]], [[1.0, 0], [8.202060150151667, -9.465682008387237], [-14.658428342148369, -101.95160851373608]], [[1.0, 0], [6.130671569496193, -3.9399433815505294], [44.44940639120185, -97.33062350293346]], [[1.0, 0], [-1.2946694738039086, -9.004623979257758], [-104.58473412398021, 30.708848695715837]], [[1.0, 0], [-1.2822686858089443, -1.479816949276534], [-16.08157672488122, 111.8498229325454]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 4, 'label': '2-115-23.13-c1-0-4', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 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'root_analytic_conductor': 0.9582690766401287, 'root_angle': 0.07942534196237262, 'root_number': '0.9690305526203568 + 0.24694085949531733*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0397126709812', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.59768172608463829038917741999', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.43688316545227890334031045307', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.49037011994246021573420231430', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.9182796232447249, 'bad_primes': [5, 23], 'central_character': '23.13', 'conductor': 115, 'conductor_radical': 115, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/115/2/g/c/36/3'], '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': '2-115-23.13-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': '2-115-23.13-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9582690766401287, 'root_angle': 0.03971267098118631, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.59768172608463829038917741999', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3292952799273094725218034902168', 'Lhash_array': ['3292952799273094725218034902168'], 'label': '2-115-23.13-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/115/2/g/c/36/3'}