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lfunc_lfunctions • Show schema
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{'Lhash': '2090156232255824760804788850631', 'a10': [-2.448286313027633, -5.695797506081522e-63], 'a2': [-1.2241431565138166, -2.1202781428196706], 'a3': [-1.7169278982943272, 0.2283825563799127], 'a4': [-1.9970529352792212, 3.458997149308172], 'a5': [0.5, -0.8660254037844386], 'a6': [2.586000079418261, 3.360791752091176], 'a7': [1.9672605808795678, 3.407395277810874], 'a8': [4.882142109616288, 0.0], 'a9': [2.895682815882752, -0.7842327650648985], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.671248518244905, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.7169278982943272, -0.2283825563799127]]], [5, [[1.0, 0], [-0.5, 0.8660254037844386]]], [13, [[1.0, 0], [-0.5, 0.8660254037844386]]]], 'bad_primes': [3, 5, 13], 'central_character': '585.391', 'coefficient_field': 'CDF', 'conductor': 585, 'conductor_radical': 195, 'conjugate': '141130888756202519622681440173', 'degree': 2, 'euler_factors': [[[1.0, 0], 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-6.126089559040117], [-56.5, -97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 27, 'label': '2-585-9.4-c1-0-27', '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/i/e/391/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.1298089591533009, 0.2836973351202825, 0.44724659839328845, 0.6200089845684356, 0.7986438442732251, 0.9758914251989289, 1.1399681452505566, 1.2744084855268665, 1.3583648212659405, 1.3673902617822808, 1.2747353519662183, 1.0531702385791928, 0.6772984680329242, 0.12626363385592337, -0.6133247413031708, -1.544493538653193, -2.6573452439598584, -3.927179445856433, -5.313643527263512, -6.7612171384273685, -8.201244644404394, -9.555592692766409, -10.741834690522346, -11.679665922507203, -12.298054477862882, 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'7.36914608131409111749147972065473', '8.386486086512732800867318986734120', '9.528559935535686918978650739962620', '10.53351157521946458468975790415579', '10.68161576479550778844807752015888'], 'prelabel': '2-585-9.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.161307131863703, 'root_angle': -0.6397433206830173, 'root_number': '-0.4250495170938665 - 0.9051700989417795*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.319871660342', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.64884253743066931481331033992', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.49689393838767806751401622992', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.94919985313441949329677127178', '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': '9.4', 'conductor': 585, 'conductor_radical': 195, 'degree': 2, 'index': 27, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/585/2/i/e/391/1'], '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': '2-585-9.4-c1-0-27', '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': '2-585-9.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.161307131863703, 'root_angle': -0.31987166034150866, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.64884253743066931481331033992', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2090156232255824760804788850631', 'Lhash_array': ['2090156232255824760804788850631'], 'label': '2-585-9.4-c1-0-27', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/585/2/i/e/391/1'}