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lfunc_lfunctions • Show schema
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{'Lhash': '352319301424067121880498525658', 'a10': [0, 0], 'a2': [0, 0], 'a3': [4.768338104359908, 0], 'a4': [0, 0], 'a5': [0, -16.8949730542738], 'a6': [0, 0], 'a7': [0, 0], 'a8': [0, 0], 'a9': [-4.262951722509357, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 46.257497444500665, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 7], 'central_character': '784.783', 'coefficient_field': 'CDF', 'conductor': 784, 'conductor_radical': 14, 'conjugate': '1934668085822001647715342712992', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-4.768338104359908, 0], [27.0, 0]], [[1.0, 0], [0, 16.8949730542738], [-125.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -40.74243418681173], [-1331.0, 0]], [[1.0, 0], [0, -56.73214162835798], [-2197.0, 0]], [[1.0, 0], [0, -122.8340832656112], [-4913.0, 0]], [[1.0, 0], [75.49461361814944, 0], [6859.0, 0]], [[1.0, 0], [0, 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'2.30682785699420011841301618709430', '3.09098661291527423159254289493065', '3.59568286404829101741115058798633', '5.35482013679874747891587133742049', '6.19026675032044126529929080630216', '7.29731338078941002560777938586537', '7.83102414560140434541637814779621', '8.819130524435925428886690117091314', '9.598913253126976840112047326794953'], 'prelabel': '2-28e2-28.27-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.801286455112788, 'root_angle': -0.5605188591618384, 'root_number': '-0.188982236504613613607258268117090030407875655934460728 - 0.981980506061965715697438684370287533353812123593136837*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.2802594295809192', 'prec': 64}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.27793092304822410343652743435', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.30682785699420011841301618709', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.09098661291527423159254289493', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 46.257497444500665, 'bad_primes': [2, 7], 'central_character': '28.27', 'conductor': 784, 'conductor_radical': 14, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/784/4/f/h/783/3'], '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': '2-28e2-28.27-c3-0-8', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-28e2-28.27-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.801286455112788, 'root_angle': -0.2802594295809192, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.27793092304822410343652743435', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '352319301424067121880498525658', 'Lhash_array': ['352319301424067121880498525658'], 'label': '2-28e2-28.27-c3-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/784/4/f/h/783/3'}