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lfunc_lfunctions • Show schema
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{'Lhash': '715227500061294529658926157294', 'a10': [-1.0, 0.0], 'a2': [1.0, 0.0], 'a3': [-1.0, 0.0], 'a4': [1.0, 0.0], 'a5': [-1.0, 0.0], 'a6': [-1.0, 0.0], 'a7': [-4.246979603717467, 0.0], 'a8': [1.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 40.484153824789175, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [3, [[1.0, 0], [1.0, 0]]], [5, [[1.0, 0], [1.0, 0]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '5070.1', 'coefficient_field': 'CDF', 'conductor': 5070, 'conductor_radical': 390, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [4.246979603717467, 0], [7.0, 0]], [[1.0, 0], [-1.9118539999795807, 0], [11.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [3.3351256037378865, 0], [17.0, 0]], [[1.0, 0], [4.850855075327144, 0], [19.0, 0]], [[1.0, 0], [0.4450418679126288, 0], [23.0, 0]], 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[113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 7, 'label': '2-5070-1.1-c1-0-7', 'leading_term': '1.3759516699200576487287211686828', '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/5070/2/a/bs/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [1.3759516699200576, 1.364959755718954, 1.331936537162618, 1.2767488886138236, 1.1992052948991845, 1.099099200423242, 0.9762655530874611, 0.8306469085071566, 0.6623650403852969, 0.47179388958616086, 0.25962982584528854, 0.026955521964901384, -0.22470582005338563, -0.4933486567844812, -0.7764579612364001, -1.070998503663818, -1.3734218174612567, -1.679691630340175, -1.9853280596676246, -2.285470381683896, -2.5749576817191193, -2.848426175407433, -3.1004214633182143, -3.325523452481381, 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'4.20476325549140907382893883142977', '5.47776371182813631858949389246028', '6.05078219949585402475111603758637', '6.80508162310228320338766050707684', '7.01230856759499802141473967764328', '8.159281116490300651386164560887381'], 'prelabel': '2-5070-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.3627159157697095, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.56421501313731407920695373686', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.10062196279612625538874037092', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.02073169202631455601933722771', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 40.484153824789175, 'bad_primes': [2, 3, 5, 13], 'central_character': '1.1', 'conductor': 5070, 'conductor_radical': 390, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5070/2/a/bs/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': '2-5070-1.1-c1-0-7', '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': '2-5070-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.3627159157697095, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.56421501313731407920695373686', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '715227500061294529658926157294', 'Lhash_array': ['715227500061294529658926157294'], 'label': '2-5070-1.1-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5070/2/a/bs/1/1'}