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lfunc_lfunctions • Show schema
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{'Lhash': '2944766115215889023361930640144', 'a10': [-2.1164985921139428, 0.7214109159000142], 'a2': [0.9238795325112867, -0.3826834323650898], 'a3': [2.1298341341498306, 1.423109670750263], 'a4': [0.7071067811865476, -0.7071067811865476], 'a5': [-2.231461735285287, -0.14345216609579958], 'a6': [2.5123106576195897, 0.4997296605002581], 'a7': [0.0411526348044926, 0.008185768012872132], 'a8': [0.3826834323650898, -0.9238795325112867], 'a9': [1.3629020069115663, 3.290336509271413], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.3574568343617672, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.9238795325112867, 0.3826834323650898]]], [5, [[1.0, 0], [2.231461735285287, 0.14345216609579958]]], [17, [[1.0, 0], [2.378923880724684, -3.3675987245688592]]]], 'bad_primes': [2, 5, 17], 'central_character': '170.23', 'coefficient_field': 'CDF', 'conductor': 170, 'conductor_radical': 170, 'conjugate': 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[58.68986283848344, -58.68986283848344]], [[1.0, 0], [-11.54747059254919, 11.54747059254919], [0, -89.0]], [[1.0, 0], [4.024847651105429, -0.8005919746238367], [89.61631465359481, -37.12029293941371]], [[1.0, 0], [0, 1.246299617641108], [-101.0, 0]], [[1.0, 0], [-6.843276820268003, -6.843276820268003], [0, 103.0]], [[1.0, 0], [0.14917410960606803, 0.7499488924252956], [-98.85510997870769, 40.94712726306461]], [[1.0, 0], [8.799250246091555, -5.879471044144511], [41.712494127794784, -100.70286904373026]], [[1.0, 0], [-5.0637800861742015, 3.383509680702748], [43.24322785725514, -104.3983871737754]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 5, 'label': '2-170-85.23-c1-0-5', '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/170/2/r/b/23/5', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 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'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.32301086331336856098800467278', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.58841560708817857154007292671', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.88670167326713772468236268647', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.3574568343617672, 'bad_primes': [2, 5, 17], 'central_character': '85.23', 'conductor': 170, 'conductor_radical': 170, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/170/2/r/b/23/5'], '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': '2-170-85.23-c1-0-5', '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': '2-170-85.23-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1650994954774323, 'root_angle': -0.024154652284329097, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.32301086331336856098800467278', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2944766115215889023361930640144', 'Lhash_array': ['2944766115215889023361930640144'], 'label': '2-170-85.23-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/170/2/r/b/23/5'}