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lfunc_lfunctions • Show schema
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{'Lhash': '2094450656065154659483333171378', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.9396926207859084, -0.3420201433256687], 'a4': [0.0, 0.0], 'a5': [0.13992334497858866, 0.7935447225171668], 'a6': [0.0, 0.0], 'a7': [-0.5801552286523356, -3.290223800812146], 'a8': [0.0, 0.0], 'a9': [0.766044443118978, 0.6427876096865394], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.090715699489701, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0.9396926207859084, 0.3420201433256687]]], [37, [[1.0, 0], [2.49163878843719, 5.54903019886856]]]], 'bad_primes': [2, 3, 37], 'central_character': '888.673', 'coefficient_field': 'CDF', 'conductor': 888, 'conductor_radical': 222, 'conjugate': '449056800970477137744494206161', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.9396926207859084, 0.3420201433256687]], [[1.0, 0], [-0.13992334497858866, -0.7935447225171668], 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[-0.685157451741445, 1.1867275176006038], [-51.5, -89.20061658979718]], [[1.0, 0], [13.22091587587499, -11.09366563527255], [18.580355010361547, -105.37442957230627]], [[1.0, 0], [-9.801533961018675, 3.5674666119601057], [83.49884429996861, -70.06384945583278]], [[1.0, 0], [11.622271572700882, -4.230160907021364], [86.56302207244451, -72.63499989457894]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 16, 'label': '2-888-37.7-c1-0-16', '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/888/2/bo/c/673/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.7057984502568717, 0.9306029905289095, 1.1452123745921365, 1.346820658857185, 1.5281614357815048, 1.6776442708886525, 1.7803377774265632, 1.8195861251141274, 1.7790580117750618, 1.6450526971912147, 1.408882172422559, 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-2.0089676999319823], 'positive_zeros': ['1.65223024048429996448772823056364', '3.07707396941853316418751787198745', '4.20105568413993608032319986698084', '5.45288040710486383884774812437216', '5.88100370418439239321481971453420', '6.76115736801076191153671127206965', '8.165917821351403326884702883636431', '8.851732090276741381893529921784023', '9.358197084820567942326042538802419', '10.70684321827884742049872676290674'], 'prelabel': '2-888-37.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6628397810401023, 'root_angle': 0.7173748845206986, 'root_number': '-0.6310479288784988 + 0.7757438439705191*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.35868744226', 'prec': 44}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.65223024048429996448772823056', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.07707396941853316418751787199', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.20105568413993608032319986698', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.090715699489701, 'bad_primes': [2, 3, 37], 'central_character': '37.7', 'conductor': 888, 'conductor_radical': 222, 'degree': 2, 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/888/2/bo/c/673/3'], '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': '2-888-37.7-c1-0-16', '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': '2-888-37.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6628397810401023, 'root_angle': 0.3586874422603493, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.65223024048429996448772823056', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2094450656065154659483333171378', 'Lhash_array': ['2094450656065154659483333171378'], 'label': '2-888-37.7-c1-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/888/2/bo/c/673/3'}