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lfunc_lfunctions • Show schema
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{'Lhash': '389158800097256246754877299157', 'a10': [0.0, 0.0], 'a2': [0.0, -1.4142135623730951], 'a3': [-2.9154759474226504, -0.7071067811865476], 'a4': [-2.0, 0.0], 'a5': [0.0, 0.0], 'a6': [-1.0, 4.123105625617661], 'a7': [-5.830951894845301, 0.0], 'a8': [0.0, 2.8284271247461903], 'a9': [8.0, 4.123105625617661], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.087203965404454, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 1.4142135623730951]]], [3, [[1.0, 0], [2.9154759474226504, 0.7071067811865476]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '150.101', 'coefficient_field': 'CDF', 'conductor': 150, 'conductor_radical': 30, 'conjugate': '2352232342013420210584783330660', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 1.4142135623730951]], [[1.0, 0], [2.9154759474226504, 0.7071067811865476]], [[1.0, 0], [0, 0]], [[1.0, 0], [5.830951894845301, 0], [49.0, 0]], [[1.0, 0], [0, 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'5.03090508308574517731895224206398', '6.13713334750910270506618633620617', '6.82982408786385634283016123182337', '8.369491442889014870418804495324853', '9.483267814542858491651289402307837', '10.54031178378514465236774573839925', '11.51145452764345310536263030176211', '12.69267043965630418369567781393852'], 'prelabel': '2-150-3.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0216834483678334, 'root_angle': -0.4242609876368533, 'root_number': '0.23570226039551576 - 0.97182531580755*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.212130493818', 'prec': 50}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.30699216331944433983331239245', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.52902477250223485020805119097', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.03090508308574517731895224206', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.087203965404454, 'bad_primes': [2, 3, 5], 'central_character': '3.2', 'conductor': 150, 'conductor_radical': 30, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/150/3/d/d/101/1'], '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': '2-150-3.2-c2-0-1', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-150-3.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0216834483678334, 'root_angle': -0.21213049381842666, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.30699216331944433983331239245', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '389158800097256246754877299157', 'Lhash_array': ['389158800097256246754877299157'], 'label': '2-150-3.2-c2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/150/3/d/d/101/1'}