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lfunc_lfunctions • Show schema
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{'Lhash': '530351481590996361460443653807', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [-2.672823701000948, 0.0], 'a6': [0.0, 0.0], 'a7': [-4.100830432684745, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 18.97245552025623, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 3, 11], 'central_character': '2376.1', 'coefficient_field': 'CDF', 'conductor': 2376, 'conductor_radical': 66, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.672823701000948, 0], [5.0, 0]], [[1.0, 0], [4.100830432684745, 0], [7.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [3.816810237633354, 0], [13.0, 0]], [[1.0, 0], [5.917640670318099, 0], [17.0, 0]], [[1.0, 0], [5.816810237633354, 0], [19.0, 0]], [[1.0, 0], [-3.672823701000948, 0], [23.0, 0]], [[1.0, 0], 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[[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-2376-1.1-c1-0-1', 'leading_term': '0.49283882248952331871313525499873', '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/2376/2/a/p/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [0.4928388224895233, 0.48580620689759463, 0.46465726358180226, 0.4292437714719899, 0.37933528831711627, 0.31464301574179243, 0.23485127630733077, 0.13965491138425357, 0.028800717522216916, -0.09786901129253439, -0.24037270523408638, -0.3985472341216048, -0.5720086661992009, -0.7601174271208342, -0.9619490307499151, -1.1762713842497055, -1.4015295176887554, -1.635838448181733, -1.8769847527620356, -2.122437284465619, -2.3693673151854107, -2.614678221321308, -2.8550446410257515, -3.086960824276367, -3.306797670740984, 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'6.11818522472653199760600187108679', '6.71415192581902656936847399689646', '7.30990854222680139761277628736768', '8.312033199819185786688168356164961', '8.828519659929503097262161799305104'], 'prelabel': '2-2376-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.355738229078537, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.41837354985317816800260393465', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.49875142805317180810603258817', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.10124369080828968200914530076', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 18.97245552025623, 'bad_primes': [2, 3, 11], 'central_character': '1.1', 'conductor': 2376, 'conductor_radical': 66, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2376/2/a/p/1/1'], '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': '2-2376-1.1-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': '2-2376-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.355738229078537, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.41837354985317816800260393465', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '530351481590996361460443653807', 'Lhash_array': ['530351481590996361460443653807'], 'factors': ['2-2376-1.1-c1-0-1'], 'label': '2-2376-1.1-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2376/2/a/p/1/1'}