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lfunc_lfunctions • Show schema
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{'Lhash': '3204049887242304887946480145768,3809158365960652287870385123431', 'a10': 0, 'a2': 2, 'a3': 2, 'a4': 3, 'a5': 0, 'a6': 4, 'a7': -8, 'a8': 4, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.8286362279166953, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -2, 1]], [3, [1, -2, 3]], [19, [1, -2, 19]]], 'bad_primes': [2, 3, 19], 'central_character': '114.1', 'coefficient_field': '1.1.1.1', 'conductor': 12996, 'conductor_radical': 114, 'degree': 4, 'euler_factors': [[1, -2, 1], [1, -2, 3], [1, 0, -8, 0, 25], [1, 8, 30, 56, 49], [1, 0, 10, 0, 121], [1, 0, -8, 0, 169], [1, 0, -26, 0, 289], [1, -2, 19], [1, 0, -44, 0, 529], [1, 12, 94, 348, 841], [1, 0, -44, 0, 961], [1, 0, -56, 0, 1369], [1, 0, 82, 0, 1681], [1, -4, 90, -172, 1849], [1, 0, -92, 0, 2209], [1, -12, 142, -636, 2809], [1, -24, 262, -1416, 3481], [1, -4, 126, -244, 3721], [1, 0, -134, 0, 4489], [1, 24, 286, 1704, 5041], [1, 8, 162, 584, 5329], [1, 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'3.00489611670191032575990616123983', '3.64773973712878028607102946934520', '4.04605938820785517167919607874000', '5.51443916036930876837155240243655', '5.77270130908789855328915338266306', '6.73832795362808146064718524366850', '6.94909488668822592649725569770949', '7.56995308509356553363623823210516', '8.587510014585810766821465324871628', '9.275813778740862873684277615043487', '9.433711982995668883810367783194116', '10.28203756050024740552854529558501', '10.54303899595967610980929629664505', '11.60928323620627003007230293400392', '11.93527617100321057580621015372438', '12.78992616265785395876288403105994', '13.02674724024610970578432370356339', '13.25092394538342122552329217173691', '13.53467691744317623608872832408193'], 'prelabel': '4-114e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.9540935923915415, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 217437838231551927, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.52754969442324543840005105817', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.00489611670191032575990616124', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.64773973712878028607102946935', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.8286362279166953, 'bad_primes': [2, 3, 19], 'central_character': '1.1', 'conductor': 12996, 'conductor_radical': 114, 'degree': 4, 'dirichlet_coefficients': [1, 2, 2, 3, 0, 4, -8, 4, 1, 0, 0, 6, 0, -16, 0, 5, 0, 2, 2, 0, -16, 0, 0, 8, 8, 0, -4, -24, -12, 0, 0, 6, 0, 0, 0, 3, 0, 4, 0, 0, 0, -32, 4, 0, 0, 0, 0, 10, 34, 16, 0, 0, 12, -8, 0, -32, 4, -24, 24, 0, 4, 0, -8, 7, 0, 0, 0, 0, 0, 0, -24, 4, -8, 0, 16, 6, 0, 0, 0, 0, -11, 0, 0, -48, 0, 8, -24, 0, 12, 0, 0, 0, 0, 0, 0, 12, 0, 68, 0, 24], 'euler11': [1, 0, 10, 0, 121], 'euler13': [1, 0, -8, 0, 169], 'euler17': [1, 0, -26, 0, 289], 'euler19': [1, -2, 19, 0, 0], 'euler2': [1, -2, 1, 0, 0], 'euler23': [1, 0, -44, 0, 529], 'euler29': [1, 12, 94, 348, 841], 'euler3': [1, -2, 3, 0, 0], 'euler31': [1, 0, -44, 0, 961], 'euler37': [1, 0, -56, 0, 1369], 'euler41': [1, 0, 82, 0, 1681], 'euler43': [1, -4, 90, -172, 1849], 'euler47': [1, 0, -92, 0, 2209], 'euler5': [1, 0, -8, 0, 25], 'euler53': [1, -12, 142, -636, 2809], 'euler59': [1, -24, 262, -1416, 3481], 'euler61': [1, -4, 126, -244, 3721], 'euler67': [1, 0, -134, 0, 4489], 'euler7': [1, 8, 30, 56, 49], 'euler71': [1, 24, 286, 1704, 5041], 'euler73': [1, 8, 162, 584, 5329], 'euler79': [1, 0, -140, 0, 6241], 'euler83': [1, 0, -158, 0, 6889], 'euler89': [1, -12, 214, -1068, 7921], 'euler97': [1, 0, -122, 0, 9409], 'euler_factors': [[1, -2, 1, 0, 0], [1, -2, 3, 0, 0], [1, 0, -8, 0, 25], [1, 8, 30, 56, 49], [1, 0, 10, 0, 121], [1, 0, -8, 0, 169], [1, 0, -26, 0, 289], [1, -2, 19, 0, 0], [1, 0, -44, 0, 529], [1, 12, 94, 348, 841], [1, 0, -44, 0, 961], [1, 0, -56, 0, 1369], [1, 0, 82, 0, 1681], [1, -4, 90, -172, 1849], [1, 0, -92, 0, 2209], [1, -12, 142, -636, 2809], [1, -24, 262, -1416, 3481], [1, -4, 126, -244, 3721], [1, 0, -134, 0, 4489], [1, 24, 286, 1704, 5041], [1, 8, 162, 584, 5329], [1, 0, -140, 0, 6241], [1, 0, -158, 0, 6889], [1, -12, 214, -1068, 7921], [1, 0, -122, 0, 9409]], 'index': 11, 'instance_types': ['ECNF', 'HMF', 'CMF'], 'instance_urls': ['EllipticCurve/2.2.57.1/4.1/b', 'ModularForm/GL2/TotallyReal/2.2.57.1/holomorphic/2.2.57.1-4.1-b', 'ModularForm/GL2/Q/holomorphic/114/2/b/d'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': True, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': True, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-114e2-1.1-c1e2-0-11', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-114e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.9540935923915415, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 217437838231551927, 'z1': {'__RealLiteral__': 0, 'data': '2.52754969442324543840005105817', 'prec': 103}}
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lfunc_instances • Show schema
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id: 9969089
{'Lhash': '3204049887242304887946480145768,3809158365960652287870385123431', 'Lhash_array': ['3204049887242304887946480145768', '3809158365960652287870385123431'], 'factors': ['2-114-57.56-c1-0-4', '2-114-57.56-c1-0-7'], 'label': '4-114e2-1.1-c1e2-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/114/2/b/d'}
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id: 9489183
{'Lhash': '_3204049887242304887946480145768', 'Lhash_array': ['_3204049887242304887946480145768'], 'factors': ['4-114e2-1.1-c1e2-0-11'], 'label': '4-114e2-1.1-c1e2-0-11', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.57.1/holomorphic/2.2.57.1-4.1-b'}
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id: 9489071
{'Lhash': '_3204049887242304887946480145768', 'Lhash_array': ['_3204049887242304887946480145768'], 'factors': ['4-114e2-1.1-c1e2-0-11'], 'label': '4-114e2-1.1-c1e2-0-11', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.57.1/4.1/b'}