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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -1, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 3, 'A8': 0, 'A9': 1, 'Lhash': '988293412322588271', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [1.1338934190276817, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 124.56662715319746, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [5, [1]], [13, [1, 1]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '15600.1', 'coefficient_field': '1.1.1.1', 'conductor': 15600, 'conductor_radical': 390, 'degree': 2, 'euler_factors': [[1], [1, 1], [1], [1, -3, 7], [1, 3, 11], [1, 1], [1, 3, 17], [1, 0, 19], [1, -3, 23], [1, -8, 29], [1, 4, 31], [1, 1, 37], [1, 3, 41], [1, 4, 43], [1, 10, 47], [1, -9, 53], [1, 4, 59], [1, -9, 61], [1, -4, 67], [1, 7, 71], [1, -6, 73], [1, -5, 79], [1, -10, 83], [1, -11, 89], [1, -1, 97]], 'gamma_factors': [[], [0]], 'index': 48, 'label': '2-15600-1.1-c1-0-48', 'leading_term': '4.34617758458', 'load_key': 'Cremona', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'EllipticCurve/Q/15600/ba', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.026199799779549, 1.675629889694609, 1.579472701154975, 0.6163991294576368, -0.7951580576113235, -1.754164836822449, -1.459363206159668, 0.02350390222193449, 1.526955481060984, 1.550989357193469, -0.3806199334187152, -2.988636517384382, -4.080505853978246, -2.494914156936029, 0.647112572558521, 2.828337498089357, 2.518394129412604, 0.6368808208682757, -0.5907889974307275, -0.2207184044318704, 0.3816260064936001, -0.5775509667848082, -2.759608846027294, -3.807860000865012, -2.299082084310812, 0.1517644444395597, 0.6456015222352807, -1.30976600440529, -3.01838480797448, -2.082258519642659, 0.3190004983465841, 0.9794089629391802, -0.7875837948948308, -1.948828978923128, 0.02703047034367832, 3.216026525152623, 3.422916320403119, -0.0988657256091596, -3.382536230971693, -2.967490298980959, -0.3427721216202883, 0.6358895381741154, -0.6440846255248431, -1.262271457618931, 0.1498207594443069, 1.211874259530004, 0.001440443102027985, -1.33981823814673, 0.1034963941651036, 2.907337191863484, 3.067824060854017, 0.4083744232155084, -0.7795723273096318, 1.47791788999259, 3.361664627984724, 1.164717964956611, -2.600601761257342, -2.967240386746779, -0.317471714000567, 0.4828753373129902, -1.804040347522838, -2.934505059692533, -0.6190410306072995, 1.462110858111761, -0.037770464545628, -2.345806488386588, -1.292443930843607, 1.6491908819756, 2.124883341499865, 0.3084323465198137, -0.1388321504691337, 0.8676561563108758, 0.08694118948405057, -1.973638061949261, -1.014645589520951, 2.852269574606641, 3.790080385318775, -0.224034044094849, -3.27244297749339, -0.9261346536215781, 2.515774202403895, 1.531795289912943, -1.554289345210291, -1.532646457255174, 0.4389399649877772, 0.03077568642854525, -1.512440415133298, 0.01523381630503699, 2.99268672371509, 2.27366718070472, -1.310476975513566, -2.253492954634844, -0.1889112137128673, 0.2089004028444961, -1.477882564365151, -1.151390504494447, 0.9742860727003975, 0.6160495046085697, -1.33918183822887, 0.3059277312091351, 4.325864184903345, 3.690353085532498, -1.706251330754785, -3.831170258155779, -0.1725632415900977, 2.458782785880135, 0.5309993458369412, -1.007372800281289, 0.56403180485732, 0.9745589469761075, -1.37371092948836, -1.810529884013321, 0.8792178988230699, 1.688213906266427, -0.5717798241107004, -1.119549022357792, 0.5813091248565655, -0.3461383462148657, -3.409061999695729, -2.595068831124708], 'positive_zeros': ['1.110721879550951', '1.996656211672393', '2.712686293253548', '3.698988262564904', '4.593258399334252', '5.064137884764465', '5.407524097492107', '6.480493549032704', '6.857043788749007', '7.712616216061724', '8.158289171580181', '8.747935040678532', '9.494194336272716', '10.28994595963119', '10.64669540540418', '11.22934032196111', '11.75018810275777', '12.24058884816358', '13.03998019603514', '13.36952070961480', '14.07139196375910', '14.78411427458426', '15.07365327527106', '15.80094035897652', '16.24661725823891', '16.85541340435991', '17.55434116829474', '17.78933505262838', '18.26048466987144', '18.82140296705491', '19.48848083755137'], 'prelabel': '2-15600-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 11.160942036996584, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 988293412322588271, 'z1': {'__RealLiteral__': 0, 'data': '1.110721879550951', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '1.996656211672393', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.712686293253548', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 124.56662715319746, 'bad_primes': [2, 3, 5, 13], 'central_character': '1.1', 'conductor': 15600, 'conductor_radical': 390, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, 0, 0, 3, 0, 1, 0, -3, 0, -1, 0, 0, 0, -3, 0, 0, 0, -3, 0, 3, 0, 0, 0, -1, 0, 8, 0, -4, 0, 3, 0, 0, 0, -1, 0, 1, 0, -3, 0, -4, 0, 0, 0, -10, 0, 2, 0, 3, 0, 9, 0, 0, 0, 0, 0, -4, 0, 9, 0, 3, 0, 0, 0, 4, 0, -3, 0, -7, 0, 6, 0, 0, 0, -9, 0, 5, 0, 1, 0, 10, 0, 0, 0, -8, 0, 11, 0, -3, 0, 4, 0, 0, 0, 1, 0, -3, 0], 'euler11': [1, 3, 11], 'euler13': [1, 1, 0], 'euler17': [1, 3, 17], 'euler19': [1, 0, 19], 'euler2': [1, 0, 0], 'euler23': [1, -3, 23], 'euler29': [1, -8, 29], 'euler3': [1, 1, 0], 'euler31': [1, 4, 31], 'euler37': [1, 1, 37], 'euler41': [1, 3, 41], 'euler43': [1, 4, 43], 'euler47': [1, 10, 47], 'euler5': [1, 0, 0], 'euler53': [1, -9, 53], 'euler59': [1, 4, 59], 'euler61': [1, -9, 61], 'euler67': [1, -4, 67], 'euler7': [1, -3, 7], 'euler71': [1, 7, 71], 'euler73': [1, -6, 73], 'euler79': [1, -5, 79], 'euler83': [1, -10, 83], 'euler89': [1, -11, 89], 'euler97': [1, -1, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 0, 0], [1, -3, 7], [1, 3, 11], [1, 1, 0], [1, 3, 17], [1, 0, 19], [1, -3, 23], [1, -8, 29], [1, 4, 31], [1, 1, 37], [1, 3, 41], [1, 4, 43], [1, 10, 47], [1, -9, 53], [1, 4, 59], [1, -9, 61], [1, -4, 67], [1, 7, 71], [1, -6, 73], [1, -5, 79], [1, -10, 83], [1, -11, 89], [1, -1, 97]], 'index': 48, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/15600/ba'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-15600-1.1-c1-0-48', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-15600-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 11.160942036996584, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 988293412322588271, 'z1': {'__RealLiteral__': 0, 'data': '1.110721879550951', 'prec': 57}}
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lfunc_instances • Show schema
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{'Lhash': '988293412322588271', 'Lhash_array': ['988293412322588271'], 'factors': ['2-15600-1.1-c1-0-48'], 'label': '2-15600-1.1-c1-0-48', 'type': 'ECQ', 'url': 'EllipticCurve/Q/15600/ba'}