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lfunc_lfunctions • Show schema
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{'Lhash': '1882647287976310053152452664725', 'a10': [-10000000000.0, 0], 'a2': [1024.0, 0], 'a3': [145819.97715101, 0], 'a4': [1048576.0, 0], 'a5': [-9765625.0, 0], 'a6': [149319656.60263425, 0], 'a7': [-236010757.18957424, 0], 'a8': [1073741824.0, 0], 'a9': [10803112533.321081, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 27.947734428706212, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '10.5', 'prec': 14}, 'bad_lfactors': [[2, [[1.0, 0], [-1024.0, 0]]], [5, [[1.0, 0], [9765625.0, 0]]]], 'bad_primes': [2, 5], 'central_character': '10.1', 'coefficient_field': 'CDF', 'conductor': 10, 'conductor_radical': 10, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1024.0, 0]], [[1.0, 0], [-145819.97715101, 0], [10460353203.0, 0]], [[1.0, 0], [9765625.0, 0]], [[1.0, 0], [236010757.18957424, 0], [558545864083284030, 0]], [[1.0, 0], [-149202299803.82596, 0], [7400249944258161000000, 0]], [[1.0, 0], [-489349823883.4888, 0], [247064529073450400000000, 0]], [[1.0, 0], 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 3, 'label': '2-10-1.1-c21-0-3', 'leading_term': '5.0441188149873502658972947887713206444949573028266362961', 'load_key': 'CMFs-workshop', 'motivic_weight': 21, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [21], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/10/22/a/d/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.09375', 'prec': 24}, 'plot_values': [5.044118814987351, 5.013186054545358, 4.921013011805163, 4.769461349339384, 4.561587306571755, 4.30157298943904, 3.994632326527812, 3.646893788351996, 3.2652624895349183, 2.8572647617273828, 2.4308786880150337, 1.9943544184490207, 1.5560283336790481, 1.1241352835417622, 0.7066231956185023, 0.31097432278549036, -0.05596272192089673, -0.38812620883880267, -0.6803761833886375, -0.9286077645642947, -1.129840075325103, -1.282278565297039, -1.3853490797361507, -1.4397026684931735, -1.4471908014550074, 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'9.426914530971558626016586784040245', '11.53921826035046864923926285741631', '13.11501084736210432123292800820489', '14.30191180182851090555111216749871', '15.13882234462509989118536923004375'], 'prelabel': '2-10-1.1-c21-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.286561683051302, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c21-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.48514684380487484315958066096', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.20267462228395308125262242873', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.05255449788773471739179722733', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 27.947734428706212, 'bad_primes': [2, 5], 'central_character': '1.1', 'conductor': 10, 'conductor_radical': 10, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/10/22/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': '2-10-1.1-c21-0-3', 'motivic_weight': 21, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [21], 'order_of_vanishing': 0, 'prelabel': '2-10-1.1-c21-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.286561683051302, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c21-0', 'z1': {'__RealLiteral__': 0, 'data': '1.48514684380487484315958066096', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1882647287976310053152452664725', 'Lhash_array': ['1882647287976310053152452664725'], 'factors': ['2-10-1.1-c21-0-3'], 'label': '2-10-1.1-c21-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/10/22/a/d/1/2'}