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lfunc_lfunctions • Show schema
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{'Lhash': '2633472545719627322318212624453', 'a10': [-0.02362942324263922, -0.02362942324263922], 'a2': [-0.02362942324263922, -0.02362942324263922], 'a3': [1.0302775417347816, -1.3923103773932506], 'a4': [0.0, -1.9988833007144404], 'a5': [1.0, 0.0], 'a6': [-0.057244355283580906, 0.008554627101506814], 'a7': [3.4266599435264626, 0.0], 'a8': [-0.09449130601050365, 0.09449130601050365], 'a9': [-0.8770563739938712, -2.868932225905088], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.4734924879256983, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.0302775417347816, 1.3923103773932506]]], [5, [[1.0, 0], [-1.0, 0]]], [29, [[1.0, 0], [4.9142667512202465, 2.2022675354850065]]]], 'bad_primes': [3, 5, 29], 'central_character': '435.191', 'coefficient_field': 'CDF', 'conductor': 435, 'conductor_radical': 435, 'conjugate': '2008791388591709521318275423703', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.02362942324263922, 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0.39744574971259006, 'root_number': '0.31663863470153075 + 0.9485462429498894*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.198722874856', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.07744353629106760757838764030', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.44792478840971265213192353727', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.26910324930048497313111029370', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.4734924879256983, 'bad_primes': [3, 5, 29], 'central_character': '87.17', 'conductor': 435, 'conductor_radical': 435, 'degree': 2, 'index': 30, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/435/2/q/d/191/8'], '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': '2-435-87.17-c1-0-30', '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': '2-435-87.17-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8637307981373539, 'root_angle': 0.19872287485629503, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.07744353629106760757838764030', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2633472545719627322318212624453', 'Lhash_array': ['2633472545719627322318212624453'], 'label': '2-435-87.17-c1-0-30', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/435/2/q/d/191/8'}