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lfunc_lfunctions • Show schema
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{'Lhash': '1593786907623931045009386597640', 'a10': [367.4163032138755, 1609.7560037393632], 'a2': [3.5337111409616617, 7.337826793512935], 'a3': [-9.428839681646096, 19.579187343788416], 'a4': [-1.4532403048808027, 1.822305703413382], 'a5': [197.65253188728323, 45.112900599963424], 'a6': [-176.9874813158342, -1.0295441329591586e-59], 'a7': [0.0, 222.32175121964312], 'a8': [489.66422391455217, 111.76266375081373], 'a9': [160.08250625403628, 200.73711359620322], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.892325595653594, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.0', 'prec': 10}, 'bad_lfactors': [[43, [[1.0, 0], [70848.47718866676, 36081.246223584974]]]], 'bad_primes': [43], 'central_character': '43.2', 'coefficient_field': 'CDF', 'conductor': 43, 'conductor_radical': 43, 'conjugate': '2894856754269080781381723188544', 'degree': 2, 'euler_factors': [[[1.0, 0], [-3.5337111409616617, -7.337826793512935], [-39.90334731895894, 50.03721487795391]], [[1.0, 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[-309862766628.7715, -388555619470.9139]], [[1.0, 0], [51505.25347481592, 64585.545038683325], [-185353708496.2648, 812087657671.3376]], [[1.0, 0], [-571296.2159853369, 716382.7959023981], [-236210455325.18204, -1034905624164.3679]], [[1.0, 0], [239715.73879255276, 1050263.2744837762], [-1075803945820.0168, 518079875119.9098]], [[1.0, 0], [-464194.15545452817, -223544.1234656971], [935690069717.7205, 1173318235770.8716]], [[1.0, 0], [258699.72104514635, 324399.189555019], [-373189883002.5777, 1635051709582.121]], [[1.0, 0], [-474625.97501636617, 108330.28157354792], [1875773713575.5881, -903325011084.3463]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 8, 'label': '2-43-43.2-c6-0-8', 'load_key': 'CMFs-workshop', 'motivic_weight': 6, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [6], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/43/7/f/a/2/16', 'plot_delta': {'__RealLiteral__': 0, 'data': 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'data': '-0.341026864898', 'prec': 50}, 'spectral_label': 'c6-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.25727618267761136571924130320', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.44060610083032857560999578003', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.69799168766071468053147265359', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.892325595653594, 'bad_primes': [43], 'central_character': '43.2', 'conductor': 43, 'conductor_radical': 43, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/43/7/f/a/2/16'], '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': '2-43-43.2-c6-0-8', 'motivic_weight': 6, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [6], 'order_of_vanishing': 0, 'prelabel': '2-43-43.2-c6-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.1452067651672113, 'root_angle': -0.3410268648981974, 'self_dual': False, 'spectral_label': 'c6-0', 'z1': {'__RealLiteral__': 0, 'data': '1.25727618267761136571924130320', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1593786907623931045009386597640', 'Lhash_array': ['1593786907623931045009386597640'], 'label': '2-43-43.2-c6-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/43/7/f/a/2/16'}