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lfunc_lfunctions • Show schema
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{'Lhash': '1248304885207857577833279658647', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [-9.741966531952249, 16.873580998976866], 'a6': [0, 0], 'a7': [-18.444633562473733, -1.67197271092191], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 29.736962642893282, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [18.444633562473733, 1.67197271092191]]]], 'bad_primes': [2, 3, 7], 'central_character': '504.89', 'coefficient_field': 'CDF', 'conductor': 504, 'conductor_radical': 42, 'conjugate': '50385361283543041933251097988', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [9.741966531952249, -16.873580998976866], [-62.5, -108.25317547305482]], [[1.0, 0], [18.444633562473733, 1.67197271092191]], [[1.0, 0], [15.108716683515842, -8.723021644337662], [665.5, -1152.6798124370878]], [[1.0, 0], 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-2070.4539055209257], [-1442897.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 12, 'label': '2-504-21.5-c3-0-12', 'leading_term': '0.105253566259602453485716289777584505644320879036567493', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/504/4/bl/a/89/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [0.10525356625960246, 0.25778572236717817, 0.39307566750561057, 0.509663673714237, 0.6062198753905575, 0.6815525531949665, 0.7346194208839589, 0.7645419739020787, 0.770622763436603, 0.7523652650315887, 0.7094958236490292, 0.641986983604998, 0.550081357761131, 0.4343150606155938, 0.29553962863787603, 0.1349412817152389, -0.04594365536957373, -0.24521835085350482, -0.46062122298607205, -0.6895289170834207, -0.928967445723371, -1.1756322785277817, 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'5.10131213435572787511298735227908', '5.89903356430026822608571626403093', '7.41478198686199793206210039277593', '7.972725560621998801225338585700594', '9.116239403727587123262004274711117', '9.564523389002662931452422763502312', '10.75894610876715449195774195719920'], 'prelabel': '2-504-21.5-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.453160793786782, 'root_angle': 0.5398748676599809, 'root_number': '-0.1249432088776976939608587538204084358710036206009466597 + 0.9921638950069408790340303322263190767937293540610007512*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.26993743382999047', 'prec': 64}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.984738921736881758344738113520', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.93946659423737329553369789290', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.01738752081339880088602892242', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 29.736962642893282, 'bad_primes': [2, 3, 7], 'central_character': '21.5', 'conductor': 504, 'conductor_radical': 42, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/504/4/bl/a/89/2'], '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': '2-504-21.5-c3-0-12', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-504-21.5-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.453160793786782, 'root_angle': 0.26993743382999047, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.984738921736881758344738113520', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1248304885207857577833279658647', 'Lhash_array': ['1248304885207857577833279658647'], 'label': '2-504-21.5-c3-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/504/4/bl/a/89/2'}