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lfunc_lfunctions • Show schema
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{'Lhash': '3072602195612097095504244909454', 'a10': [2.414213562373095, 0.0], 'a2': [2.414213562373095, 0.0], 'a3': [-0.41421356237309503, 0.0], 'a4': [3.8284271247461903, 0.0], 'a5': [1.0, 0.0], 'a6': [-1.0, 0.0], 'a7': [0.0, 0.0], 'a8': [4.414213562373095, 0.0], 'a9': [-2.8284271247461903, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.9563348495213704, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [-1.0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [5, 7], 'central_character': '245.1', 'coefficient_field': 'CDF', 'conductor': 245, 'conductor_radical': 35, 'conjugate': '3072602195612097095504244909454', 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.414213562373095, 0], [2.0, 0]], [[1.0, 0], [0.41421356237309503, 0], [3.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.8284271247461901, 0], [11.0, 0]], [[1.0, 0], [4.82842712474619, 0], [13.0, 0]], [[1.0, 0], [-4.82842712474619, 0], [17.0, 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[[1.0, 0], [4.48528137423857, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 7, 'label': '2-245-1.1-c1-0-7', '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/245/2/a/h/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [2.7746933204546607, 2.7881449671137646, 2.8265914630513307, 2.884585413672589, 2.9538646025662274, 3.0242769221601478, 3.0846868708587345, 3.123763984736778, 3.1306594663783467, 3.095621323123555, 3.0105913875121253, 2.8697980018029337, 2.6703263628305773, 2.4126236672545693, 2.1008807577582274, 1.74322602532728, 1.351670515471227, 0.9417551914958848, 0.5318716517956815, 0.14225532692288576, -0.20631641356633593, -0.49405234319508023, -0.7037966999409695, -0.8226633576257297, -0.8434961598226987, -0.7659879615852868, 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'9.381054512580261451282804578374932', '10.51927318717257616782224371613174', '11.59140178287151689150463252319776', '12.21738619107954657487750275838265'], 'prelabel': '2-245-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3986904051724136, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.42385574941462730227162082321', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.52003517756079828896625081031', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.14890638880266816814320518669', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.9563348495213704, 'bad_primes': [5, 7], 'central_character': '1.1', 'conductor': 245, 'conductor_radical': 35, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/245/2/a/h/1/2'], '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': '2-245-1.1-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': '2-245-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3986904051724136, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.42385574941462730227162082321', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3072602195612097095504244909454', 'Lhash_array': ['3072602195612097095504244909454'], 'label': '2-245-1.1-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/245/2/a/h/1/2'}