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lfunc_lfunctions • Show schema
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{'Lhash': '1067502587155209078269801449140', 'a10': [-1.7320508075688772, 3.3112589136954796e-79], 'a2': [-1.4012585384440734, 1.0180739209102543], 'a3': [0.30901699437494745, 0.9510565162951535], 'a4': [0.6180339887498949, -1.902113032590307], 'a5': [0.8090169943749475, 0.5877852522924731], 'a6': [-1.4012585384440734, -1.0180739209102543], 'a7': [0.0, 0.0], 'a8': [0.5352331346596348, 1.647278207092664], 'a9': [-0.8090169943749475, 0.5877852522924731], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.9058029979288994, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-0.30901699437494745, -0.9510565162951535]]], [5, [[1.0, 0], [-0.8090169943749475, -0.5877852522924731]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5, 11], 'central_character': '1815.1334', 'coefficient_field': 'CDF', 'conductor': 1815, 'conductor_radical': 165, 'conjugate': '2045826418851832927593918051276', 'degree': 2, 'euler_factors': [[[1.0, 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-1815-165.14-c0-0-2', 'leading_term': '0.69484405256465222275113505856731', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1815/1/o/g/1334/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [0.6948440525646522, 0.6492766559280622, 0.6095832441636942, 0.5736135119718331, 0.5391599656534255, 0.5041845005125946, 0.4669791960713085, 0.4262554486888982, 0.3811756690766159, 0.33134771626426207, 0.2767990797299164, 0.21794172552543883, 0.15553308887807962, 0.0906350563195372, 0.024570801757952593, -0.0411214744746316, -0.10473896635896875, -0.16446963301892556, -0.2184528475573425, -0.26484510985755066, -0.3018900493745209, -0.3279914018949611, -0.34178714368267565, -0.3422225257138935, 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'5.09953563008953531685464562589433', '6.08844883332088387479254727283314', '7.06536505448535718743914150711976', '7.910950233041219689386774952785304', '8.388271877850161720679968004987768', '9.182618328409140022838760918961547'], 'prelabel': '2-1815-165.14-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9517368322855323, 'root_angle': -0.9291728723660172, 'root_number': '-0.97534662299168284945167233204879 - 0.22067841992075274146479450842877*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.46458643618300854', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.842111057229030283016995287525', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.74095648868573354325946318003', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.60061573755272976887573038500', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.9058029979288994, 'bad_primes': [3, 5, 11], 'central_character': '165.14', 'conductor': 1815, 'conductor_radical': 165, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1815/1/o/g/1334/1'], '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': '2-1815-165.14-c0-0-2', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-1815-165.14-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9517368322855323, 'root_angle': -0.4645864361830086, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.842111057229030283016995287525', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1067502587155209078269801449140', 'Lhash_array': ['1067502587155209078269801449140'], 'label': '2-1815-165.14-c0-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1815/1/o/g/1334/1'}