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lfunc_lfunctions • Show schema
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{'Lhash': '1751361221612981220238597316936', 'a10': [0.0, 0.0], 'a2': [-0.30901699437494745, -0.9510565162951535], 'a3': [0.0, 0.0], 'a4': [-0.8090169943749475, 0.5877852522924731], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.8090169943749475, 0.5877852522924731], 'a9': [0.30901699437494745, -0.9510565162951535], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.247662531582506, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.30901699437494745, 0.9510565162951535]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 5], 'central_character': '2500.751', 'coefficient_field': 'CDF', 'conductor': 2500, 'conductor_radical': 10, 'conjugate': '855612408573709415986915932688', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.30901699437494745, 0.9510565162951535]], [[1.0, 0], [0, 0], [-0.30901699437494745, 0.9510565162951535]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], 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'2-50e2-100.31-c0-0-2', 'leading_term': '0.84157615285223027875708361732839', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/2500/1/j/b/751/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [0.8415761528522303, 0.9022572232043534, 0.9707757115802755, 1.0474448720645597, 1.1315522535886067, 1.221468694705968, 1.314816157264327, 1.408643403151081, 1.499581459099863, 1.5839720228668903, 1.657974113089729, 1.7176582567111793, 1.7590968488963288, 1.7784568813067718, 1.7720985621675034, 1.736681040097881, 1.6692746117859745, 1.5674773862637763, 1.4295333083179658, 1.2544476404074494, 1.042095423381842, 0.79331806102476, 0.5100029969776027, 0.19514147842719168, -0.1471403642791487, -0.5115814433964677, -0.8918203000152677, -1.2804671271411563, -1.6692149266989398, 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'8.005772522897979600576685363861802', '8.345008201121621420508644503122884', '9.158547463739272614864621414131948'], 'prelabel': '2-50e2-100.31-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1169881519436569, 'root_angle': 0.6799999999999999, 'root_number': '-0.53582679497899661827130876786751 + 0.84432792550201507854855806396698*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.34', 'prec': 14}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.38158039865059343066219962935', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.66874459260068934211052937482', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.09836404837452125144220482350', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.247662531582506, 'bad_primes': [2, 5], 'central_character': '100.31', 'conductor': 2500, 'conductor_radical': 10, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2500/1/j/b/751/1'], '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': '2-50e2-100.31-c0-0-2', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-50e2-100.31-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1169881519436569, 'root_angle': 0.33999999999999997, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.38158039865059343066219962935', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1751361221612981220238597316936', 'Lhash_array': ['1751361221612981220238597316936'], 'label': '2-50e2-100.31-c0-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2500/1/j/b/751/1'}