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lfunc_lfunctions • Show schema
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{'Lhash': '981910334358454869751289047740', 'a10': [-1.6340372631311795, -8.13510902833028e-62], 'a2': [-0.8170186315655897, 1.4151177806019988], 'a3': [1.4035898660436017, 1.0148573732006405], 'a4': [-0.3350388886506178, -0.5803043776542818], 'a5': [0.5, 0.8660254037844386], 'a6': [-2.5829017852255376, 1.1570875938244423], 'a7': [-1.065058145152966, 1.8447348204200051], 'a8': [-2.173142468956024, 0.0], 'a9': [0.9401290241205918, 2.848887049008097], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.671248518244905, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.4035898660436017, -1.0148573732006405]]], [5, [[1.0, 0], [-0.5, -0.8660254037844386]]], [13, [[1.0, 0], [-0.5, -0.8660254037844386]]]], 'bad_primes': [3, 5, 13], 'central_character': '585.196', 'coefficient_field': 'CDF', 'conductor': 585, 'conductor_radical': 195, 'conjugate': '3058658045588934736276250134427', 'degree': 2, 'euler_factors': [[[1.0, 0], 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[-3.117645602675561, -5.399920583827765], [-56.5, 97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 13, 'label': '2-585-9.7-c1-0-13', '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/585/2/i/e/196/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.262889842132404, 1.0415096865127391, 0.8315900513316693, 0.6279762516901913, 0.42736576019282274, 0.22933551938489882, 0.03676771800289087, -0.14428172733936326, -0.305173680226303, -0.4356417893180309, -0.5250348293602106, -0.5637631881662876, -0.5448438688511567, -0.4654035738628713, -0.3279655302611815, -0.1413242614438721, 0.07918697406825999, 0.3122020923803903, 0.5317061786767993, 0.7093101124860041, 0.8173114397678803, 0.8323068968323367, 0.7389947441464392, 0.5337004333553587, 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'6.78852097814854108497509489666683', '7.82833509529398232957365175245992', '8.696447049286355753560512019979946', '9.560247308180284459206293117470473', '9.996795322975517636340017169636047'], 'prelabel': '2-585-9.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.161307131863703, 'root_angle': 0.9540954288907619, 'root_number': '-0.9896192483765249 + 0.1437141024488615*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.477047714445', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.77459067520787707870265516409', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.95659681196968179459465901619', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.07655464688617898193993376958', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.671248518244905, 'bad_primes': [3, 5, 13], 'central_character': '9.7', 'conductor': 585, 'conductor_radical': 195, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/585/2/i/e/196/3'], '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': '2-585-9.7-c1-0-13', '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': '2-585-9.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.161307131863703, 'root_angle': 0.47704771444538097, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.77459067520787707870265516409', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '981910334358454869751289047740', 'Lhash_array': ['981910334358454869751289047740'], 'label': '2-585-9.7-c1-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/585/2/i/e/196/3'}