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lfunc_lfunctions • Show schema
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{'Lhash': '1159089589472480379442607140567', 'a10': [1.1584011040905782, 2.006409567828765], 'a2': [1.1055369250363998, -0.6382820412688365], 'a3': [-0.5839625916042501, -1.011452878378156], 'a4': [-0.1851920715873747, 0.32076207714826566], 'a5': [0.0, 1.8148734089209226], 'a6': [-1.291184415716899, -0.7454656699876013], 'a7': [0.0, 0.0], 'a8': [0.0, 3.025947258993722], 'a9': [0.8179753832136956, -1.4167749230667432], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.086470608755563, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [-3.583053402592878, -0.4021545898875171]]]], 'bad_primes': [7, 13], 'central_character': '637.491', 'coefficient_field': 'CDF', 'conductor': 637, 'conductor_radical': 91, 'conjugate': '2108151286049200725751994877880', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.1055369250363998, 0.6382820412688365], [1.0, -1.7320508075688772]], [[1.0, 0], [0.5839625916042501, 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'8.886825970077863287996359615603341', '9.649543757418732552698777289819846', '10.62044762590518839279276918450929'], 'prelabel': '2-637-13.10-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2553205113144257, 'root_angle': -0.12700720873794732, 'root_number': '0.9214480426935172 - 0.38850161468941946*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.063503604369', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.914360462783511827525090644663', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '3.07508503180677753166180146724', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.49250123848475734483028323202', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.086470608755563, 'bad_primes': [7, 13], 'central_character': '13.10', 'conductor': 637, 'conductor_radical': 91, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/637/2/q/h/491/5'], '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': '2-637-13.10-c1-0-12', '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': '2-637-13.10-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2553205113144257, 'root_angle': -0.06350360436897366, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.914360462783511827525090644663', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1159089589472480379442607140567', 'Lhash_array': ['1159089589472480379442607140567'], 'label': '2-637-13.10-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/637/2/q/h/491/5'}