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lfunc_lfunctions • Show schema
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{'Lhash': '2556929835295474560559616737021', 'a10': [1.1708508846339634, -1.9050218387073323], 'a2': [0.25881904510252074, -0.9659258262890683], 'a3': [-0.9659258262890683, 0.25881904510252074], 'a4': [-0.8660254037844386, -0.5], 'a5': [2.143148301570504, 0.6378991750076676], 'a6': [4.400336302403101e-61, 1.0], 'a7': [0.15321279442892183, -2.6413113863426405], 'a8': [-0.7071067811865476, 0.7071067811865476], 'a9': [0.8660254037844386, -0.5], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.6768584424468889, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.25881904510252074, 0.9659258262890683]]], [3, [[1.0, 0], [0.9659258262890683, -0.25881904510252074]]], [5, [[1.0, 0], [-2.143148301570504, -0.6378991750076676]]], [7, [[1.0, 0], [-0.15321279442892183, 2.6413113863426405]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '210.157', 'coefficient_field': 'CDF', 'conductor': 210, 'conductor_radical': 210, 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'4.26495674560421212646514405992102', '5.59137904283572491786727749427617', '6.08396863049308863697829727986133', '7.30197388710283977123716378038849', '8.654961941552564583871764429001718', '9.471995945025126883541663939374016', '10.49090301574992147502720874761608', '11.96679936971645756803391702568676', '12.54013383755049740465024312629935'], 'prelabel': '2-210-35.17-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2949356904676343, 'root_angle': 0.3939748806163762, 'root_number': '0.32696260816772516 + 0.9450372759104049*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.196987440308', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.01706198445780068345730315920', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.26495674560421212646514405992', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.59137904283572491786727749428', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.6768584424468889, 'bad_primes': [2, 3, 5, 7], 'central_character': '35.17', 'conductor': 210, 'conductor_radical': 210, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/210/2/u/b/157/4'], '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': '2-210-35.17-c1-0-3', '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': '2-210-35.17-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2949356904676343, 'root_angle': 0.1969874403081881, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.01706198445780068345730315920', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2556929835295474560559616737021', 'Lhash_array': ['2556929835295474560559616737021'], 'label': '2-210-35.17-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/210/2/u/b/157/4'}