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lfunc_lfunctions • Show schema
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{'Lhash': '3554158845614448311368685668942', 'a10': [0.0, 0.0], 'a2': [1.3228756555322954, -2.29128784747792], 'a3': [0.0, 0.0], 'a4': [-2.5, -4.330127018922194], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [-7.937253933193772, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.5214027291384666, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 7], 'central_character': '441.226', 'coefficient_field': 'CDF', 'conductor': 441, 'conductor_radical': 21, 'conjugate': '1141680419774527038939636866570', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.3228756555322954, 2.29128784747792], [-1.0, -1.7320508075688772]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-2.5, -4.330127018922194]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.6457513110645907, 4.58257569495584], [-5.5, 9.526279441628825]], [[1.0, 0], [0, 0], [13.0, 0]], [[1.0, 0], [0, 0], [-8.5, 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['2.80373696425068003917133744312887', '4.27677854760552821654329783542543', '4.95051116933132258606418965210622', '5.93893370170133916050379149531643', '6.97721602225914234708857564190112', '7.56938523000811734448321691772094', '8.483123569785459371681618382767408', '9.500792784477455581086768287217578', '10.65132982982854575039121332586856', '12.20822043061974288554212606168459'], 'prelabel': '2-21e2-7.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8765400952653442, 'root_angle': -0.9596540938921078, 'root_number': '-0.9919779164085226 - 0.12641128651274008*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.479827046946', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.80373696425068003917133744313', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.27677854760552821654329783543', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.95051116933132258606418965211', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.5214027291384666, 'bad_primes': [3, 7], 'central_character': '7.2', 'conductor': 441, 'conductor_radical': 21, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/441/2/e/h/226/2'], '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': '2-21e2-7.2-c1-0-14', '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': '2-21e2-7.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8765400952653442, 'root_angle': -0.4798270469460539, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.80373696425068003917133744313', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3554158845614448311368685668942', 'Lhash_array': ['3554158845614448311368685668942'], 'label': '2-21e2-7.2-c1-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/441/2/e/h/226/2'}