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lfunc_lfunctions • Show schema
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{'Lhash': '181054068833273220669590961092', 'a10': [1.5601329370640387, 0.0], 'a2': [-0.35319350787257553, 0.0], 'a3': [-2.8899619510967867, 0.0], 'a4': [-1.8752543459966649, 0.0], 'a5': [-4.417218613278985, 0.0], 'a6': [1.0207157991261466, 0.0], 'a7': [-3.5273637054702816, 0.0], 'a8': [1.3687146763610056, 0.0], 'a9': [5.351880078787146, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 64.20770826531158, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[11, [[1.0, 0], [-1.0, 0]]], [17, [[1.0, 0], [-1.0, 0]]], [43, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [11, 17, 43], 'central_character': '8041.1', 'coefficient_field': 'CDF', 'conductor': 8041, 'conductor_radical': 8041, 'degree': 2, 'euler_factors': [[[1.0, 0], [0.35319350787257553, 0], [2.0, 0]], [[1.0, 0], [2.8899619510967867, 0], [3.0, 0]], [[1.0, 0], [4.417218613278985, 0], [5.0, 0]], [[1.0, 0], [3.5273637054702816, 0], [7.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], 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'2.94401349101978415871139837172033', '3.94951140448758341696021456629105', '4.27096686213420833697947655979197', '4.83702411355448616354357992332678', '5.86324321788653508914122972386909', '6.43028297001072236839797397021719', '7.10657489471365619033647791761995', '7.71100476640874658687749210926285'], 'prelabel': '2-8041-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.012971250747851, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.14282647663376329359965932210', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.02967028054419721926604611992', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.94401349101978415871139837172', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 64.20770826531158, 'bad_primes': [11, 17, 43], 'central_character': '1.1', 'conductor': 8041, 'conductor_radical': 8041, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8041/2/a/j/1/37'], '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': '2-8041-1.1-c1-0-11', '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': '2-8041-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.012971250747851, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.14282647663376329359965932210', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '181054068833273220669590961092', 'Lhash_array': ['181054068833273220669590961092'], 'label': '2-8041-1.1-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8041/2/a/j/1/37'}