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lfunc_lfunctions • Show schema
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{'Lhash': '342837896897270124982347531859', 'a10': [-2.052768266237017, 0.0], 'a2': [-2.052768266237017, 0.0], 'a3': [-3.4146603603518195, 0.0], 'a4': [2.213857554869728, 0.0], 'a5': [1.0, 0.0], 'a6': [7.009506427707672, 0.0], 'a7': [-1.0, 0.0], 'a8': [-0.4390000021316187, 0.0], 'a9': [8.659905376558019, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 33.81664525601226, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [-1.0, 0]]], [7, [[1.0, 0], [1.0, 0]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [5, 7, 11], 'central_character': '4235.1', 'coefficient_field': 'CDF', 'conductor': 4235, 'conductor_radical': 385, 'degree': 2, 'euler_factors': [[[1.0, 0], [2.052768266237017, 0], [2.0, 0]], [[1.0, 0], [3.4146603603518195, 0], [3.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [3.6206138430385417, 0], [13.0, 0]], [[1.0, 0], [2.887120803944052, 0], [17.0, 0]], [[1.0, 0], 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[[1.0, 0], [-0.5100018382024156, 0], [109.0, 0]], [[1.0, 0], [6.53128196621064, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 3, 'label': '2-4235-1.1-c1-0-3', 'leading_term': '0.11388084619482454228527081359583', '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/4235/2/a/bo/1/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [0.11388084619482454, 0.10980511515526029, 0.09760173985517358, 0.07734577614141987, 0.04917402020292209, 0.013301526482242799, -0.02995723763924854, -0.0801643496191377, -0.13673347923000032, -0.19890609063702613, -0.2657308288583598, -0.33604798824284154, -0.40848075836094033, -0.4814346933218284, -0.5531065703979459, -0.6215035025634387, -0.6844728512959207, -0.7397431515507338, -0.7849759097674441, 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'1.50386007438978487747290928993139', '2.32621778350012736715354287094699', '4.20253767345730163312104069057816', '4.75859554413424204006475749593269', '5.66328085851031692643097493376399', '6.51277175301171895913795508070079', '6.77249735524242498148318978949188', '7.55068030613286905969457750003813', '8.488765147709747570391083426421233'], 'prelabel': '2-4235-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.8152081008345915, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.27045141369044842537986350832', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.50386007438978487747290928993', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.32621778350012736715354287095', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 33.81664525601226, 'bad_primes': [5, 7, 11], 'central_character': '1.1', 'conductor': 4235, 'conductor_radical': 385, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4235/2/a/bo/1/4'], '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': '2-4235-1.1-c1-0-3', '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': '2-4235-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.8152081008345915, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.27045141369044842537986350832', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '342837896897270124982347531859', 'Lhash_array': ['342837896897270124982347531859'], 'label': '2-4235-1.1-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4235/2/a/bo/1/4'}