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              lfunc_lfunctions •   Show schema
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        {'A10': 0, 'A2': 0, 'A3': 1, 'A4': 0, 'A5': -1, 'A6': 0, 'A7': 2, 'A8': 0, 'A9': 1, 'Lhash': '1514600996521707520', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [-0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [0.7559289460184544, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 1295.4929223932536, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [5, [1, 1]], [13, [1]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '162240.1', 'coefficient_field': '1.1.1.1', 'conductor': 162240, 'conductor_radical': 390, 'degree': 2, 'euler_factors': [[1], [1, -1], [1, 1], [1, -2, 7], [1, 0, 11], [1], [1, 0, 17], [1, 2, 19], [1, -6, 23], [1, 0, 29], [1, 4, 31], [1, -2, 37], [1, -6, 41], [1, 4, 43], [1, 0, 47], [1, -6, 53], [1, 0, 59], [1, -10, 61], [1, 8, 67], [1, 0, 71], [1, 8, 73], [1, 8, 79], [1, -12, 83], [1, 6, 89], [1, 8, 97]], 'gamma_factors': [[], [0]], 'index': 175, 'label': '2-162240-1.1-c1-0-175', 'leading_term': '9.59816906535', '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/162240/fu', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 2.157409650448176, 2.979875517982518, 1.871220301822094, -0.2366002153939769, -1.291315974559112, -0.1722809892250125, 1.736908017875314, 1.92836818856247, 0.01485562384824672, -1.475831730524768, -0.4893154460126995, 1.405218813623585, 1.103018413554288, -1.256754712470205, -2.272950872813911, -0.6681043013870865, 0.4575176859455951, -1.195123426802862, -2.867484880386129, -1.355338275843286, 0.7600521525937425, -1.147290025686883, -5.20933309905046, -4.944799950726481, 0.1138416544454099, 3.073550987704652, 0.7526410362055417, -1.672635331627287, -0.2760421404322438, 1.381199037230901, 0.08166867384156382, -1.000308708595743, 0.5930572452767147, 1.438459949669852, -0.2881334145155956, -0.625963154767943, 1.460626345843473, 0.7350102528414976, -3.589038061408899, -4.645426803819615, -0.6818080870689267, 1.164916104337568, -1.394945077287606, -1.935887434089691, 0.9312963030806359, 1.045538656571898, -1.404845282746726, 0.2499788623262318, 4.497207038588734, 3.830049787415347, 0.01622374862957209, 0.01046765484063055, 1.34802902205199, -1.497881489557347, -4.200230612587478, -1.64173958636246, 1.214945717528975, 0.236032426657641, -0.2490753460048909, 0.9624737375633379, -0.4069161933109723, -2.038305392850308, 0.9387477890924104, 3.434047665682105, 0.4183178280644157, -1.209231689536936, 2.482777866973508, 3.097580783724009, -1.511036622953104, -1.995993094885391, 1.922553847483562, 1.349119826399263, -1.670377108761211, 0.2806093492873133, 2.837457247359464, 0.687339816488267, -0.5283522405760263, 1.35873303742769, 0.3522837215998814, -2.047049417907258, -0.1392352062393481, 1.915392101482428, 0.2768491218335301, 0.3700267050658362, 2.204718378149003, -0.09522285000885584, -1.940693327455244, 2.103293245140835, 3.396099339240127, -2.065850521940676, -3.277012166999262, 1.58542763859994, 1.960967624896991, -0.8602653217072467, 0.7036208111716094, 1.692167888731165, -1.573070250849342, -1.795912608586135, 0.7942476258178559, -0.4295989614509528, -1.155699437248517, 2.300291753409909, 2.33131355224718, -1.124307207323848, 0.2203887193296817, 2.877256488228175, 0.8131245446219453, -0.1272638774199185, 1.621278415788545, 0.156904486839465, -0.717938819111765, 2.259861684222607, 0.6170737314429906, -4.143140385478362, -0.6603895895158185, 4.976049815225226, 1.937924041419501, -0.9698702637817391, 2.466971654759091, 2.412496124718654], 'positive_zeros': ['0.9702981374938472', '1.521782749239839', '2.251657105991709', '2.808561203232312', '3.374188219315211', '4.089252441538601', '4.362617545979461', '5.126447488389406', '5.416633447285365', '6.244627896317679', '6.803705226592192', '7.277664996232322', '7.760068312601398', '8.178775773100913', '8.712899622724399', '9.083529237294824', '9.549655632215293', '10.29318408303371', '10.63407979318350', '11.16925581949428', '11.59864776199220', '11.98489205331024', '12.75160517618853', '12.99866096009113', '13.40623587373347', '14.10694295942673', '14.53706674164361', '14.80215397235697', '15.21058986134524', '15.69505323215892', '16.27667502739881', '16.60354001125719', '17.16939013407526', '17.62389632517396', '18.09156070779641', '18.48167296050475', '19.06240421785617', '19.33065872316576', '19.77897781134545'], 'prelabel': '2-162240-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 35.992956566434685, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1514600996521707520, 'z1': {'__RealLiteral__': 0, 'data': '0.9702981374938472', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.521782749239839', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.251657105991709', 'prec': 57}}
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              lfunc_search •   Show schema
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        {'algebraic': True, 'analytic_conductor': 1295.4929223932536, 'bad_primes': [2, 3, 5, 13], 'central_character': '1.1', 'conductor': 162240, 'conductor_radical': 390, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, -1, 0, 2, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, -2, 0, 2, 0, 6, 0, 1, 0, 1, 0, 0, 0, -4, 0, 0, 0, -2, 0, 2, 0, 0, 0, 6, 0, -4, 0, -1, 0, 0, 0, -3, 0, 0, 0, 6, 0, 0, 0, -2, 0, 0, 0, 10, 0, 2, 0, 0, 0, -8, 0, 6, 0, 0, 0, -8, 0, 1, 0, 0, 0, -8, 0, 1, 0, 12, 0, 0, 0, 0, 0, -6, 0, 0, 0, -4, 0, 2, 0, -8, 0, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, 0, 0], 'euler17': [1, 0, 17], 'euler19': [1, 2, 19], 'euler2': [1, 0, 0], 'euler23': [1, -6, 23], 'euler29': [1, 0, 29], 'euler3': [1, -1, 0], 'euler31': [1, 4, 31], 'euler37': [1, -2, 37], 'euler41': [1, -6, 41], 'euler43': [1, 4, 43], 'euler47': [1, 0, 47], 'euler5': [1, 1, 0], 'euler53': [1, -6, 53], 'euler59': [1, 0, 59], 'euler61': [1, -10, 61], 'euler67': [1, 8, 67], 'euler7': [1, -2, 7], 'euler71': [1, 0, 71], 'euler73': [1, 8, 73], 'euler79': [1, 8, 79], 'euler83': [1, -12, 83], 'euler89': [1, 6, 89], 'euler97': [1, 8, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, 1, 0], [1, -2, 7], [1, 0, 11], [1, 0, 0], [1, 0, 17], [1, 2, 19], [1, -6, 23], [1, 0, 29], [1, 4, 31], [1, -2, 37], [1, -6, 41], [1, 4, 43], [1, 0, 47], [1, -6, 53], [1, 0, 59], [1, -10, 61], [1, 8, 67], [1, 0, 71], [1, 8, 73], [1, 8, 79], [1, -12, 83], [1, 6, 89], [1, 8, 97]], 'index': 175, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/162240/fu'], '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': '2-162240-1.1-c1-0-175', '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': '2-162240-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 35.992956566434685, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1514600996521707520, 'z1': {'__RealLiteral__': 0, 'data': '0.9702981374938472', 'prec': 60}}
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              lfunc_instances •   Show schema
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        {'Lhash': '1514600996521707520', 'Lhash_array': ['1514600996521707520'], 'factors': ['2-162240-1.1-c1-0-175'], 'label': '2-162240-1.1-c1-0-175', 'type': 'ECQ', 'url': 'EllipticCurve/Q/162240/fu'}