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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': 1, 'A8': 0, 'A9': 1, 'Lhash': '777704054593547796', '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': [0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 1140.2637408638845, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [5, [1]], [7, [1, -1]], [17, [1, 1]]], 'bad_primes': [2, 3, 5, 7, 17], 'central_character': '142800.1', 'coefficient_field': '1.1.1.1', 'conductor': 142800, 'conductor_radical': 3570, 'degree': 2, 'euler_factors': [[1], [1, 1], [1], [1, -1], [1, 1, 11], [1, 4, 13], [1, 1], [1, 6, 19], [1, 7, 23], [1, 2, 29], [1, 5, 31], [1, -4, 37], [1, -4, 41], [1, 0, 43], [1, -3, 47], [1, -10, 53], [1, 5, 59], [1, -13, 61], [1, -3, 67], [1, 5, 71], [1, -1, 73], [1, -4, 79], [1, -9, 83], [1, -6, 89], [1, 2, 97]], 'gamma_factors': [[], [0]], 'index': 88, 'label': '2-142800-1.1-c1-0-88', 'leading_term': '4.40232604522', '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/142800/dl', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 0.9037977773053075, 0.7506838392304745, -0.8056021428877753, -2.766377156845682, -3.28388688194959, -1.555579652667149, 0.8567615411606349, 1.503622801408722, 0.230104165415058, -0.1277821412278672, 2.623048035843389, 6.404764479717492, 6.847573391401269, 3.119786769587281, -0.5606113247820163, -0.5932629791486913, 1.14838941656028, 0.7324110239941269, -1.456242452233552, -1.742231401593811, 0.1965858902495909, 0.665075066128526, -1.329882728907984, -2.063299950952286, 0.03929864523368953, 1.052252843734757, -1.410279553604266, -3.377219813935885, -1.553212825170225, 0.4149460396806556, -1.212208698875839, -2.791623729666627, -0.1612276125518263, 2.594594528073444, 0.147092276009762, -3.620329994307393, -2.199187132659305, 1.594026334052592, 1.108398820728889, -1.808406243507384, -1.360517571833125, 0.6943793523240529, -0.3190754257175958, -1.83951191038357, 0.1090972947255359, 1.965367323573892, 0.1076347221285435, -1.315640879289925, 0.5440634536191092, 1.022971652307776, -1.328963634847731, -0.907663060646151, 2.097879954785278, 0.545401666514484, -4.287413715037621, -3.716777060931505, 1.077343569820814, 1.599818338649716, -0.7900682398694948, 0.4800710187210832, 2.006162024719768, -1.45803291415319, -4.189525982037784, -1.277013604633786, 1.013103669338086, -0.8544716618939814, -0.9476502581007334, 1.686281486534832, 1.360781393180887, -0.4912095022941892, 0.674669868898163, 1.005276402117639, -2.112058714662759, -2.433827645797169, 0.5456275041430296, -0.897227866641028, -4.803777678102781, -2.902830988575965, 0.6892249604327982, -1.114039732510952, -1.915865578860302, 2.952800738291798, 4.629496067774683, 0.3080076062215477, -0.8231900426956748, 1.860973468851573, 1.241447580564653, -0.2300704142332938, 1.340982330416122, 0.4457596957717066, -3.308462048922718, -2.271071875699161, 1.467031831114699, 0.7820627280046695, -0.598168728652438, 0.7634307036257426, -0.5846439208643825, -3.250426828474986, -0.9298102460838475, 0.5259432343645827, -3.994955518373015, -4.782638144259404, 1.048729381303931, 2.320357498423791, -0.6998662717728867, 1.487515519297637, 4.29452044015548, 1.069174262931224, -0.8197120810684129, 1.532474812164732, 1.119910198346728, -0.1719376265519935, 1.997015764606228, 1.40988832334749, -2.669652023906393, -2.193238915536721, 0.2034721433460513, -1.474851930896375, -1.857445212952025, 0.05940827538968646], 'positive_zeros': ['0.6432133920667516', '1.651566854618190', '2.294196082939457', '2.524411246162323', '3.693944206314431', '4.081322442510936', '4.585850520777699', '5.224432158564944', '5.601232721679995', '6.245954631657235', '6.636212712129899', '7.401441934687562', '7.623244385393262', '8.260134860311193', '8.758128557194084', '9.380111051830488', '9.837605388266919', '10.39061637154581', '10.71389417495744', '11.24087693455789', '11.75994606487494', '12.19103559447936', '12.61525646893073', '13.07229824377238', '13.52847559168416', '14.18666751547142', '14.64715372292956', '14.95590651970522', '15.42174844373354', '16.08538832575833', '16.40921596148997', '16.84094956530402', '17.40074183357906', '17.66202830664830', '18.09444695251682', '18.69209406801195', '18.94056429736234', '19.66865052870797', '19.90990365588425'], 'prelabel': '2-142800-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 33.76779147151742, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 777704054593547796, 'z1': {'__RealLiteral__': 0, 'data': '0.6432133920667516', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.651566854618190', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.294196082939457', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1140.2637408638845, 'bad_primes': [2, 3, 5, 7, 17], 'central_character': '1.1', 'conductor': 142800, 'conductor_radical': 3570, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, 0, 0, 1, 0, 1, 0, -1, 0, -4, 0, 0, 0, -1, 0, -6, 0, -1, 0, -7, 0, 0, 0, -1, 0, -2, 0, -5, 0, 1, 0, 0, 0, 4, 0, 4, 0, 4, 0, 0, 0, 0, 0, 3, 0, 1, 0, 1, 0, 10, 0, 0, 0, 6, 0, -5, 0, 13, 0, 1, 0, 0, 0, 3, 0, 7, 0, -5, 0, 1, 0, 0, 0, -1, 0, 4, 0, 1, 0, 9, 0, 0, 0, 2, 0, 6, 0, -4, 0, 5, 0, 0, 0, -2, 0, -1, 0], 'euler11': [1, 1, 11], 'euler13': [1, 4, 13], 'euler17': [1, 1, 0], 'euler19': [1, 6, 19], 'euler2': [1, 0, 0], 'euler23': [1, 7, 23], 'euler29': [1, 2, 29], 'euler3': [1, 1, 0], 'euler31': [1, 5, 31], 'euler37': [1, -4, 37], 'euler41': [1, -4, 41], 'euler43': [1, 0, 43], 'euler47': [1, -3, 47], 'euler5': [1, 0, 0], 'euler53': [1, -10, 53], 'euler59': [1, 5, 59], 'euler61': [1, -13, 61], 'euler67': [1, -3, 67], 'euler7': [1, -1, 0], 'euler71': [1, 5, 71], 'euler73': [1, -1, 73], 'euler79': [1, -4, 79], 'euler83': [1, -9, 83], 'euler89': [1, -6, 89], 'euler97': [1, 2, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 0, 0], [1, -1, 0], [1, 1, 11], [1, 4, 13], [1, 1, 0], [1, 6, 19], [1, 7, 23], [1, 2, 29], [1, 5, 31], [1, -4, 37], [1, -4, 41], [1, 0, 43], [1, -3, 47], [1, -10, 53], [1, 5, 59], [1, -13, 61], [1, -3, 67], [1, 5, 71], [1, -1, 73], [1, -4, 79], [1, -9, 83], [1, -6, 89], [1, 2, 97]], 'index': 88, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/142800/dl'], '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': '2-142800-1.1-c1-0-88', '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': '2-142800-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 33.76779147151742, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 777704054593547796, 'z1': {'__RealLiteral__': 0, 'data': '0.6432133920667516', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '777704054593547796', 'Lhash_array': ['777704054593547796'], 'label': '2-142800-1.1-c1-0-88', 'type': 'ECQ', 'url': 'EllipticCurve/Q/142800/dl'}