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lfunc_lfunctions • Show schema
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{'Lhash': '517201211128459226393602673194', 'a10': [1.0018742614651608, 0.5784323745510681], 'a2': [-0.5, -0.8660254037844386], 'a3': [0.6589430466228435, 1.601809620806232], 'a4': [-0.5, 0.8660254037844386], 'a5': [-1.0018742614651608, 0.5784323745510681], 'a6': [1.057736300333094, -1.3715662284256123], 'a7': [-0.2962978493257129, -2.6291077544454047], 'a8': [1.0, 0.0], 'a9': [-2.13158812261481, 2.1110026232876806], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.359831950361911, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.5, 0.8660254037844386]]], [3, [[1.0, 0], [-0.6589430466228435, -1.601809620806232]]], [7, [[1.0, 0], [0.2962978493257129, 2.6291077544454047]]], [13, [[1.0, 0], [0.3618027404235154, -3.58735261397901]]]], 'bad_primes': [2, 3, 7, 13], 'central_character': '546.311', 'coefficient_field': 'CDF', 'conductor': 546, 'conductor_radical': 546, 'conjugate': '2586806065180012119596288788861', 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'3.51839446926176403394508944541411', '5.34137253327175335991337181149587', '5.92608288889356975587539516524312', '7.00786736434479192521982797622509', '8.117423015917802754244216515794181', '8.347122024078379223201116335500198', '9.251346140786536519754101391505149', '10.43000769811414531324579696011291'], 'prelabel': '2-546-273.38-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0880210608042034, 'root_angle': -0.668301175951428, 'root_number': '-0.5044403963642027 - 0.8634465163030807*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.334150587976', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.40799981559219999002109066410', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.28150512618890324366855710033', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.51839446926176403394508944541', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.359831950361911, 'bad_primes': [2, 3, 7, 13], 'central_character': '273.38', 'conductor': 546, 'conductor_radical': 546, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/546/2/bg/a/311/11'], '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': '2-546-273.38-c1-0-7', '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': '2-546-273.38-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0880210608042034, 'root_angle': -0.334150587975714, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.40799981559219999002109066410', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '517201211128459226393602673194', 'Lhash_array': ['517201211128459226393602673194'], 'label': '2-546-273.38-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/546/2/bg/a/311/11'}