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lfunc_lfunctions • Show schema
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{'Lhash': '285761744335381910266102228681', 'a10': [0.0, 0.0], 'a2': [-0.8464731271145173, -1.4661344634040525], 'a3': [-1.5346553333851023, 0.8030149486234117], 'a4': [-0.43303350985405953, 0.7500360404471091], 'a5': [0.0, 0.0], 'a6': [2.476372389898878, 1.5702804990417718], 'a7': [2.0168833783644544, 1.7123613631699313], 'a8': [-1.9196875915319056, 0.0], 'a9': [1.710333984574679, -2.4647023473857654], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.192146106117222, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.5346553333851023, -0.8030149486234117]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-2.0168833783644544, -1.7123613631699313]]]], 'bad_primes': [3, 5, 7], 'central_character': '525.374', 'coefficient_field': 'CDF', 'conductor': 525, 'conductor_radical': 105, 'conjugate': '2034378821881455036316400834787', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.8464731271145173, 1.4661344634040525], [-1.0, 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[113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-525-105.59-c1-0-1', '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/525/2/q/g/374/5', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.29129192127387377, 0.13720213838873305, -0.03565425847376138, -0.23109388785669405, -0.45165773475562415, -0.6972951977802408, -0.96431414287455, -1.244656342711576, -1.5255230852144746, -1.789384020611533, -2.014420095469072, -2.175454823817538, -2.245408250975371, -2.197265405199304, -2.0064909076001465, -1.6537510080794144, -1.1277324624683305, -0.4277844519606943, 0.43393404501147653, 1.4311329259798733, 2.5232024802848394, 3.6563958626660966, 4.766507508102512, 5.783020541809131, 6.634517843947197, 7.2549652507484845, 7.590305048576485, 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'8.481546955184556596412731125956081', '9.723289641815233044472560801918712', '10.71712985492619850031485990323783'], 'prelabel': '2-525-105.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0474731026602577, 'root_angle': -0.4506478370477339, 'root_number': '0.1544239595096615 - 0.9880046764714013*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.225323918524', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.22542626831394471628631374930', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.18979156653017079658117105181', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.35175149603051981703930991924', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.192146106117222, 'bad_primes': [3, 5, 7], 'central_character': '105.59', 'conductor': 525, 'conductor_radical': 105, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/525/2/q/g/374/5'], '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': '2-525-105.59-c1-0-1', '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': '2-525-105.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0474731026602577, 'root_angle': -0.22532391852386696, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.22542626831394471628631374930', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '285761744335381910266102228681', 'Lhash_array': ['285761744335381910266102228681'], 'label': '2-525-105.59-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/525/2/q/g/374/5'}