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lfunc_lfunctions • Show schema
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{'Lhash': '2298474162320153775427284807327', 'a10': [2.232578559325961, 0.12487184005218016], 'a2': [-0.5, 0.8660254037844386], 'a3': [0, 0], 'a4': [-0.5, -0.8660254037844386], 'a5': [-1.0081470939604853, -1.9959056683468357], 'a6': [0, 0], 'a7': [-2.458433087583291, -0.9778071148624797], 'a8': [1.0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 15.091725982022, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.5, -0.8660254037844386]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [1.0081470939604853, 1.9959056683468357]]], [7, [[1.0, 0], [2.458433087583291, 0.9778071148624797]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '1890.629', 'coefficient_field': 'CDF', 'conductor': 1890, 'conductor_radical': 210, 'conjugate': '19455412355180124905503857523', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.0081470939604853, 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'2-1890-315.209-c1-0-43', 'leading_term': '0.0334120896572100084410360619187644345471010813841766609', '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/1890/2/bf/e/629/7', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [0.03341208965721001, 0.16373775644190808, 0.2981007399606251, 0.4360223735359172, 0.5769414115757399, 0.7201510608826167, 0.8647462053630505, 1.0095840016706916, 1.1532598844398823, 1.2940999415566026, 1.4301697152727064, 1.5592987974896728, 1.679120103395249, 1.7871223787262582, 1.8807142633777527, 1.9572980454960598, 2.0143510588377316, 2.0495124833026184, 2.0606731014721547, 2.0460653521937924, 2.0043508231888336, 1.934702159981117, 1.8368762610666194, 1.7112756011359422, 1.5589945947145314, 1.3818480974135061, 1.182379452010276, 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'8.160416371817224918927736271175547', '9.030679989860738849327796522449290', '9.635118612544263080211039506484931'], 'prelabel': '2-1890-315.209-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.884807071402903, 'root_angle': -0.9339603978421746, 'root_number': '-0.97855528459257127560183027986562466559301190998521552826 - 0.2059843561922891217969523280271946531499017908014825104*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.4669801989210873', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.81317640831498333132932229778', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.87423743100927294102292986542', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.62889375678115607349769421969', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 15.091725982022, 'bad_primes': [2, 3, 5, 7], 'central_character': '315.209', 'conductor': 1890, 'conductor_radical': 210, 'degree': 2, 'index': 43, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1890/2/bf/e/629/7'], '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': '2-1890-315.209-c1-0-43', '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': '2-1890-315.209-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.884807071402903, 'root_angle': -0.4669801989210873, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.81317640831498333132932229778', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2298474162320153775427284807327', 'Lhash_array': ['2298474162320153775427284807327'], 'label': '2-1890-315.209-c1-0-43', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1890/2/bf/e/629/7'}