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lfunc_lfunctions • Show schema
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{'Lhash': '964265583397762768472164376704', 'a10': [1.9771238753639973, -4.594297578754748e-61], 'a2': [-1.7122395024939598, 0.9885619376819986], 'a3': [-1.1320814188033481, 1.3108743880327354], 'a4': [0.9545094092671755, -1.6532587931533034], 'a5': [-0.8660254037844386, -0.5], 'a6': [0.6425140002231562, -3.363663510983269], 'a7': [-3.189186589529091, 1.8412777359605652], 'a8': [0.0, -0.17988106608455898], 'a9': [-0.4367833224003964, -2.9680330741541394], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.671248518244905, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.1320814188033481, -1.3108743880327354]]], [5, [[1.0, 0], [0.8660254037844386, 0.5]]], [13, [[1.0, 0], [3.5845778225825082, 0.388332117973319]]]], 'bad_primes': [3, 5, 13], 'central_character': '585.571', 'coefficient_field': 'CDF', 'conductor': 585, 'conductor_radical': 195, 'conjugate': '626404234349111622752325613178', 'degree': 2, 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17.079461075182998], [-109.0, 0]], [[1.0, 0], [-2.242138087688835, 3.8834970854623854], [-56.5, -97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 19, 'label': '2-585-117.103-c1-0-19', '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/585/2/bt/b/571/9', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.3389008673046244, 0.3470339196852175, 0.3307797372096815, 0.29001670491313375, 0.22361913434381023, 0.13061183156539924, 0.011335000063981982, -0.13154462831563513, -0.2922818883781332, -0.46163649908170595, -0.6268594277604065, -0.7721439934234764, -0.8795847398472064, -0.9306496468166496, -0.9081153508840476, -0.7983456597800865, -0.59371901274598, -0.2949413561550349, 0.08707063077027256, 0.53007251611085, 1.0004584272380255, 1.4545600893319717, 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'5.10796358458104325722313619453309', '6.42460869023461930667134308749455', '7.29017435328097942736432825961724', '7.76980818742203950784460218822606', '9.167337746340582452760572475696048', '9.745316518999899053833173401603136', '10.64261885342177826444294016114750'], 'prelabel': '2-585-117.103-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.161307131863703, 'root_angle': -0.23438182330048588, 'root_number': '0.7409367296263661 - 0.6715748377437806*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.11719091165', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.76067142099262618999539032514', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.22348014350513760672150747047', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.52882518285558458926860821186', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.671248518244905, 'bad_primes': [3, 5, 13], 'central_character': '117.103', 'conductor': 585, 'conductor_radical': 195, 'degree': 2, 'index': 19, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/585/2/bt/b/571/9'], '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': '2-585-117.103-c1-0-19', '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': '2-585-117.103-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.161307131863703, 'root_angle': -0.11719091165024294, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.76067142099262618999539032514', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '964265583397762768472164376704', 'Lhash_array': ['964265583397762768472164376704'], 'label': '2-585-117.103-c1-0-19', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/585/2/bt/b/571/9'}