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lfunc_lfunctions • Show schema
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{'Lhash': '40251309835922271935412848678', 'a10': [1.2688736753270393, -3.8761574120379803], 'a2': [-1.3440324161804897, -0.4399737085963599], 'a3': [0.0, 0.0], 'a4': [1.6128462714879308, 1.1826778532413127], 'a5': [0.0, 2.8839761343356263], 'a6': [0.0, 0.0], 'a7': [-2.247768494494367, 1.395541756866675], 'a8': [-1.647370510030256, -2.2991673281174325], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.0366903928088, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.3440324161804897, 0.4399737085963599]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [2.247768494494367, -1.395541756866675]]]], 'bad_primes': [2, 3, 7], 'central_character': '756.19', 'coefficient_field': 'CDF', 'conductor': 756, 'conductor_radical': 42, 'conjugate': '2992642442688018271446258718630', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.3440324161804897, 0.4399737085963599]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 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[3.9052224966141513, 6.764043778996688], [-56.5, 97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-756-252.187-c1-0-0', '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/756/2/n/b/19/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.04745531217981061, -0.1350527383624582, -0.3063653270915765, -0.46530178152792107, -0.6074438740270481, -0.7248735017938344, -0.8066105180708377, -0.8396428018252717, -0.8104229162568279, -0.7067121132972976, -0.5196426523961293, -0.24583495658246546, 0.11064156462828835, 0.5367186340763548, 1.0094673910026197, 1.496190720331418, 1.9556815993679928, 2.340759939627384, 2.602058995347314, 2.6928602464749094, 2.5745913650067447, 2.222430366654044, 1.6303290772022714, 0.8147094127826418, 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'6.59009524733102352602475334713603', '7.40597699729693654970063298649684', '8.128662108393939133106089025053145', '9.228164946964904903460745861783427', '9.638254215495177776111958282676044'], 'prelabel': '2-756-252.187-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4569677231923093, 'root_angle': 0.8665647950660258, 'root_number': '-0.9134152392420004 + 0.40702899248146834*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.433282397533', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.03175268471349705960564993057', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.46397204738246835002388946190', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.97831123744526555155116539165', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.0366903928088, 'bad_primes': [2, 3, 7], 'central_character': '252.187', 'conductor': 756, 'conductor_radical': 42, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/756/2/n/b/19/4'], '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': '2-756-252.187-c1-0-0', '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': '2-756-252.187-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4569677231923093, 'root_angle': 0.4332823975330129, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.03175268471349705960564993057', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '40251309835922271935412848678', 'Lhash_array': ['40251309835922271935412848678'], 'label': '2-756-252.187-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/756/2/n/b/19/4'}