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lfunc_lfunctions • Show schema
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{'Lhash': '1125283311657120160405301541171', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-2.605551275463989, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 27.308837491277906, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-1.0, 0]]], [19, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 3, 5, 19], 'central_character': '3420.1', 'coefficient_field': 'CDF', 'conductor': 3420, 'conductor_radical': 570, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [2.605551275463989, 0], [7.0, 0]], [[1.0, 0], [-4.60555127546399, 0], [11.0, 0]], [[1.0, 0], [-4.60555127546399, 0], [13.0, 0]], [[1.0, 0], [2.0, 0], [17.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-2.0, 0], [23.0, 0]], [[1.0, 0], [2.605551275463989, 0], [29.0, 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'2.08051078862002508739682957026', '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/3420/2/a/i/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [2.080510788620025, 2.073971941498394, 2.0542937768513685, 2.021298300612686, 1.9747113189440078, 1.9141945875185207, 1.8393879064605585, 1.7499586208440479, 1.6456557112299792, 1.5263656013409583, 1.3921669289419132, 1.2433817664062072, 1.080621084938122, 0.9048225869739506, 0.7172793558108372, 0.5196580759285806, 0.3140058597832411, 0.10274498299836492, -0.11134491040599422, -0.3251573076387116, -0.5353019309562944, -0.7381600522151961, -0.929951313212155, -1.1068110189720903, -1.2648765325097877, -1.400381058770512, -1.5097527732774862, -1.589716939961737, -1.6373983862137438, -1.650421475244716, -1.6270045499971058, 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'8.822585385534432734032987068423628'], 'prelabel': '2-3420-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.225785825239866, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.887692011863933755740100291764', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.95759953865122517374385118595', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.17811019529864423021984349203', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 27.308837491277906, 'bad_primes': [2, 3, 5, 19], 'central_character': '1.1', 'conductor': 3420, 'conductor_radical': 570, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3420/2/a/i/1/1'], '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': '2-3420-1.1-c1-0-8', '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': '2-3420-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.225785825239866, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.887692011863933755740100291764', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1125283311657120160405301541171', 'Lhash_array': ['1125283311657120160405301541171'], 'label': '2-3420-1.1-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3420/2/a/i/1/1'}