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lfunc_lfunctions • Show schema
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{'Lhash': '745573691530178084279014498159', 'a10': [0.0, 0.0], 'a2': [0.38196601125010515, 0.0], 'a3': [2.23606797749979, 0.0], 'a4': [-1.8541019662496845, 0.0], 'a5': [0.0, 0.0], 'a6': [0.8541019662496846, 0.0], 'a7': [-0.2360679774997897, 0.0], 'a8': [-1.4721359549995794, 0.0], 'a9': [2.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 72.06498782420559, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [0, 0]]]], 'bad_primes': [5, 19], 'central_character': '9025.1', 'coefficient_field': 'CDF', 'conductor': 9025, 'conductor_radical': 95, 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.38196601125010515, 0], [2.0, 0]], [[1.0, 0], [-2.23606797749979, 0], [3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.2360679774997897, 0], [7.0, 0]], [[1.0, 0], [3.4721359549995796, 0], [11.0, 0]], [[1.0, 0], [2.0, 0], [13.0, 0]], [[1.0, 0], [1.8541019662496845, 0], [17.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], 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0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 116, 'label': '2-95e2-1.1-c1-0-116', 'leading_term': '2.00773854252445247357104280835', '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/9025/2/a/u/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [2.0077385425244523, 1.9947997934015997, 1.9559628196726575, 1.8911735512141892, 1.8003683533941695, 1.6835118852038944, 1.5406465465444281, 1.3719503421226484, 1.1777995589453478, 0.9588324789210408, 0.7160104018980877, 0.45067249382992264, 0.1645813491054993, -0.14004338246716225, -0.46050544405920685, -0.7936281058851836, -1.1357670620708074, -1.482840639229776, -1.8303773451689003, -2.1735802737805745, -2.5074073783488124, -2.826666132321932, -3.1261206189030406, -3.4006086363704875, 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'4.03933060691991415349575302132128', '4.86032696566018611235211145460708', '5.56275845217199680373185068813607', '6.23808047807277525242572979982974', '7.53199758408307633699694527820092', '7.70946533386677580161801671704541'], 'prelabel': '2-95e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.489109954771795, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.58815393720946770600808150623', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.18123886133608093418840986860', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.58267636702775333577416494771', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 72.06498782420559, 'bad_primes': [5, 19], 'central_character': '1.1', 'conductor': 9025, 'conductor_radical': 95, 'degree': 2, 'index': 116, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9025/2/a/u/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': '2-95e2-1.1-c1-0-116', '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': '2-95e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.489109954771795, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.58815393720946770600808150623', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '745573691530178084279014498159', 'Lhash_array': ['745573691530178084279014498159'], 'label': '2-95e2-1.1-c1-0-116', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9025/2/a/u/1/1'}